subject:"Re\: \?"



On Saturday, September 21, 2024 at 3:17:07 AM UTC-6 Alan Grayson wrote:

On Saturday, September 21, 2024 at 3:06:40 AM UTC-6 Alan Grayson wrote:

On Saturday, September 21, 2024 at 3:00:16 AM UTC-6 Quentin Anciaux wrote:

Inflation lasted 10^-32 seconds... inflation is not the cause of 
recessional velocity > c, it's space expansion, not inflation, as long as 
it is *uniform* (the point you seem unable to grasp), object will sooner or 
later recess from each other > c.


Inflation causes space to expand hugely, perhaps as many as 100 doublings 
in an incredibly short time duration. I never claimed otherwise. And as 
long as space is expanding, objects will recede sooner or later from each 
other at velocities > c. I don't see any difference in our respective 
pov's. AG


*Maybe, after Inflation, some law of inertia applies, and space will 
continue to expand at the last rate defining its expansion. I don't think 
the cause of this rate of expansion is known.  AG*


*I think you make a good point, distinguishing between Inflation, which 
hugely increases the size of the universe, and the continuing expansion of 
space. But why is space continuing to expand? AG *


Le sam. 21 sept. 2024, 10:53, Alan Grayson  a écrit :



On Friday, September 20, 2024 at 10:17:34 PM UTC-6 Alan Grayson wrote:

On Thursday, September 19, 2024 at 3:14:33 AM UTC-6 Jesse Mazer wrote:

On Thu, Sep 19, 2024 at 2:57 AM Alan Grayson  wrote:



On Wednesday, September 18, 2024 at 7:10:57 PM UTC-6 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 5:30:06 PM UTC-6 Jesse Mazer wrote:

On Wed, Sep 18, 2024 at 2:01 AM Alan Grayson  wrote:



On Tuesday, September 17, 2024 at 4:20:31 PM UTC-6 Jesse Mazer wrote:

On Tue, Sep 17, 2024 at 2:40 PM Alan Grayson  wrote:



On Tuesday, September 17, 2024 at 10:12:53 AM UTC-6 Jesse Mazer wrote:

On Mon, Sep 16, 2024 at 7:41 PM Alan Grayson  wrote:



On Monday, September 16, 2024 at 12:17:45 PM UTC-6 Jesse Mazer wrote:

The Scientific American article "Misconceptions About The Big Bang" by 
Charles Lineweaver and Tamara Davis at 
https://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf 
(distilled from their more technical review 'Expanding Confusion' at 
https://arxiv.org/abs/astro-ph/0310808 ) covers this question on p. 42-43, 
along with other common misconceptions:

"Running to Stay Still
the idea of seeing faster-than-light galaxies may sound mystical, but it is 
made possible by changes in the expansion rate. Imagine a light beam that 
is farther than the Hubble distance of 14 billion light-years and trying to 
travel in our direction. It is moving toward us at the speed of light with 
respect to its local space, but its local space is receding from us faster 
than the speed of light. Although the light beam is traveling toward us at 
the maximum speed possible, it cannot keep up with the stretching of space. 
It is a bit like a child trying to run the wrong way on a moving sidewalk. 
Photons at the Hubble distance are like the Red Queen and Alice, running as 
fast as they can just to stay in the same place.

One might conclude that the light beyond the Hubble distance would never 
reach us and that its source would be forever undetectable. But the Hubble 
distance is not fixed, because the Hubble constant, on which it depends, 
changes with time. In particular, the constant is proportional to the rate 
of increase in the distance between two galaxies, divided by that distance. 
(Any two galaxies can be used for this calculation.) In models of the 
universe that fit the observational data, the
denominator increases faster than the numerator, so the Hubble constant 
decreases. In this way, the Hubble distance gets larger. As it does, light 
that was initially just outside the Hubble distance and receding from us 
can come within the Hubble distance. The photons then find themselves in a 
region of space that is receding slower than the speed of light. Thereafter 
they can approach us.

The galaxy they came from, though, may continue to recede superluminally. 
Thus, we can observe light from galaxies that have always been and will 
always be receding faster than the speed of light. Another way to put it is 
that the Hubble distance is not fixed and does not mark the edge of the 
observable universe.


*I don't think this is the consensus view, which is that the Hubble 
constant IS constant, and galaxies beyond our event horizon will never be 
seen, if the universe in their region is expanding faster than c. AG *


Davis and Lineweaver are just reviewing the current consensus view in that 
article and paper, not suggesting any new physics. In general relativity's 
cosmological solutions there is a time-dependent "Hubble parameter" whose 
value at any given cosmological time is called the "Hubble constant" at 
that time, but which can change over the long term (see the first paragraph 
of https://lambda.gsfc.nasa.gov/education/graphic_history/hubb_const.html 
for example). Astr

Re: Radius of the Observable universe



On Saturday, September 21, 2024 at 3:06:40 AM UTC-6 Alan Grayson wrote:

On Saturday, September 21, 2024 at 3:00:16 AM UTC-6 Quentin Anciaux wrote:

Inflation lasted 10^-32 seconds... inflation is not the cause of 
recessional velocity > c, it's space expansion, not inflation, as long as 
it is *uniform* (the point you seem unable to grasp), object will sooner or 
later recess from each other > c.


Inflation causes space to expand hugely, perhaps as many as 100 doublings 
in an incredibly short time duration. I never claimed otherwise. And as 
long as space is expanding, objects will recede sooner or later from each 
other at velocities > c. I don't see any difference in our respective 
pov's. AG


*Maybe, after Inflation, some law of inertia applies, and space will 
continue to expand at the last rate defining its expansion. I don't think 
the cause of this rate of expansion is known.  AG*


Le sam. 21 sept. 2024, 10:53, Alan Grayson  a écrit :



On Friday, September 20, 2024 at 10:17:34 PM UTC-6 Alan Grayson wrote:

On Thursday, September 19, 2024 at 3:14:33 AM UTC-6 Jesse Mazer wrote:

On Thu, Sep 19, 2024 at 2:57 AM Alan Grayson  wrote:



On Wednesday, September 18, 2024 at 7:10:57 PM UTC-6 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 5:30:06 PM UTC-6 Jesse Mazer wrote:

On Wed, Sep 18, 2024 at 2:01 AM Alan Grayson  wrote:



On Tuesday, September 17, 2024 at 4:20:31 PM UTC-6 Jesse Mazer wrote:

On Tue, Sep 17, 2024 at 2:40 PM Alan Grayson  wrote:



On Tuesday, September 17, 2024 at 10:12:53 AM UTC-6 Jesse Mazer wrote:

On Mon, Sep 16, 2024 at 7:41 PM Alan Grayson  wrote:



On Monday, September 16, 2024 at 12:17:45 PM UTC-6 Jesse Mazer wrote:

The Scientific American article "Misconceptions About The Big Bang" by 
Charles Lineweaver and Tamara Davis at 
https://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf 
(distilled from their more technical review 'Expanding Confusion' at 
https://arxiv.org/abs/astro-ph/0310808 ) covers this question on p. 42-43, 
along with other common misconceptions:

"Running to Stay Still
the idea of seeing faster-than-light galaxies may sound mystical, but it is 
made possible by changes in the expansion rate. Imagine a light beam that 
is farther than the Hubble distance of 14 billion light-years and trying to 
travel in our direction. It is moving toward us at the speed of light with 
respect to its local space, but its local space is receding from us faster 
than the speed of light. Although the light beam is traveling toward us at 
the maximum speed possible, it cannot keep up with the stretching of space. 
It is a bit like a child trying to run the wrong way on a moving sidewalk. 
Photons at the Hubble distance are like the Red Queen and Alice, running as 
fast as they can just to stay in the same place.

One might conclude that the light beyond the Hubble distance would never 
reach us and that its source would be forever undetectable. But the Hubble 
distance is not fixed, because the Hubble constant, on which it depends, 
changes with time. In particular, the constant is proportional to the rate 
of increase in the distance between two galaxies, divided by that distance. 
(Any two galaxies can be used for this calculation.) In models of the 
universe that fit the observational data, the
denominator increases faster than the numerator, so the Hubble constant 
decreases. In this way, the Hubble distance gets larger. As it does, light 
that was initially just outside the Hubble distance and receding from us 
can come within the Hubble distance. The photons then find themselves in a 
region of space that is receding slower than the speed of light. Thereafter 
they can approach us.

The galaxy they came from, though, may continue to recede superluminally. 
Thus, we can observe light from galaxies that have always been and will 
always be receding faster than the speed of light. Another way to put it is 
that the Hubble distance is not fixed and does not mark the edge of the 
observable universe.


*I don't think this is the consensus view, which is that the Hubble 
constant IS constant, and galaxies beyond our event horizon will never be 
seen, if the universe in their region is expanding faster than c. AG *


Davis and Lineweaver are just reviewing the current consensus view in that 
article and paper, not suggesting any new physics. In general relativity's 
cosmological solutions there is a time-dependent "Hubble parameter" whose 
value at any given cosmological time is called the "Hubble constant" at 
that time, but which can change over the long term (see the first paragraph 
of https://lambda.gsfc.nasa.gov/education/graphic_history/hubb_const.html 
for example). Astrophysicist Ethan Siegel mentions in an article at 
https://bigthink.com/starts-with-a-bang/hubble-constant-changes-time/ that 
even in models that don't have accelerating expansion due to the 
cosmological constant, the Hubble constant still need not be constant in 
time. He

Re: Radius of the Observable universe



On Saturday, September 21, 2024 at 3:00:16 AM UTC-6 Quentin Anciaux wrote:

Inflation lasted 10^-32 seconds... inflation is not the cause of 
recessional velocity > c, it's space expansion, not inflation, as long as 
it is *uniform* (the point you seem unable to grasp), object will sooner or 
later recess from each other > c.


Inflation causes space to expand hugely, perhaps as many as 100 doublings 
in an incredibly short time duration. I never claimed otherwise. And as 
long as space is expanding, objects will recede sooner or later from each 
other at velocities > c. I don't see any difference in our respective 
pov's. AG


Le sam. 21 sept. 2024, 10:53, Alan Grayson  a écrit :



On Friday, September 20, 2024 at 10:17:34 PM UTC-6 Alan Grayson wrote:

On Thursday, September 19, 2024 at 3:14:33 AM UTC-6 Jesse Mazer wrote:

On Thu, Sep 19, 2024 at 2:57 AM Alan Grayson  wrote:



On Wednesday, September 18, 2024 at 7:10:57 PM UTC-6 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 5:30:06 PM UTC-6 Jesse Mazer wrote:

On Wed, Sep 18, 2024 at 2:01 AM Alan Grayson  wrote:



On Tuesday, September 17, 2024 at 4:20:31 PM UTC-6 Jesse Mazer wrote:

On Tue, Sep 17, 2024 at 2:40 PM Alan Grayson  wrote:



On Tuesday, September 17, 2024 at 10:12:53 AM UTC-6 Jesse Mazer wrote:

On Mon, Sep 16, 2024 at 7:41 PM Alan Grayson  wrote:



On Monday, September 16, 2024 at 12:17:45 PM UTC-6 Jesse Mazer wrote:

The Scientific American article "Misconceptions About The Big Bang" by 
Charles Lineweaver and Tamara Davis at 
https://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf 
(distilled from their more technical review 'Expanding Confusion' at 
https://arxiv.org/abs/astro-ph/0310808 ) covers this question on p. 42-43, 
along with other common misconceptions:

"Running to Stay Still
the idea of seeing faster-than-light galaxies may sound mystical, but it is 
made possible by changes in the expansion rate. Imagine a light beam that 
is farther than the Hubble distance of 14 billion light-years and trying to 
travel in our direction. It is moving toward us at the speed of light with 
respect to its local space, but its local space is receding from us faster 
than the speed of light. Although the light beam is traveling toward us at 
the maximum speed possible, it cannot keep up with the stretching of space. 
It is a bit like a child trying to run the wrong way on a moving sidewalk. 
Photons at the Hubble distance are like the Red Queen and Alice, running as 
fast as they can just to stay in the same place.

One might conclude that the light beyond the Hubble distance would never 
reach us and that its source would be forever undetectable. But the Hubble 
distance is not fixed, because the Hubble constant, on which it depends, 
changes with time. In particular, the constant is proportional to the rate 
of increase in the distance between two galaxies, divided by that distance. 
(Any two galaxies can be used for this calculation.) In models of the 
universe that fit the observational data, the
denominator increases faster than the numerator, so the Hubble constant 
decreases. In this way, the Hubble distance gets larger. As it does, light 
that was initially just outside the Hubble distance and receding from us 
can come within the Hubble distance. The photons then find themselves in a 
region of space that is receding slower than the speed of light. Thereafter 
they can approach us.

The galaxy they came from, though, may continue to recede superluminally. 
Thus, we can observe light from galaxies that have always been and will 
always be receding faster than the speed of light. Another way to put it is 
that the Hubble distance is not fixed and does not mark the edge of the 
observable universe.


*I don't think this is the consensus view, which is that the Hubble 
constant IS constant, and galaxies beyond our event horizon will never be 
seen, if the universe in their region is expanding faster than c. AG *


Davis and Lineweaver are just reviewing the current consensus view in that 
article and paper, not suggesting any new physics. In general relativity's 
cosmological solutions there is a time-dependent "Hubble parameter" whose 
value at any given cosmological time is called the "Hubble constant" at 
that time, but which can change over the long term (see the first paragraph 
of https://lambda.gsfc.nasa.gov/education/graphic_history/hubb_const.html 
for example). Astrophysicist Ethan Siegel mentions in an article at 
https://bigthink.com/starts-with-a-bang/hubble-constant-changes-time/ that 
even in models that don't have accelerating expansion due to the 
cosmological constant, the Hubble constant still need not be constant in 
time. He explains this by looking at the first Friedmann equation governing 
an expanding universe, where a term equivalent to the definition of the 
Hubble constant is on the left side of the equality and the right side has 
terms for energy density, global curvature of space,

Re: Radius of the Observable universe

2024-09-21 Thread Quentin Anciaux

Also inflation happened *before* the hot big bang.

Le sam. 21 sept. 2024, 11:00, Quentin Anciaux  a écrit :

> Inflation lasted 10^-32 seconds... inflation is not the cause of
> recessional velocity > c, it's space expansion, not inflation, as long as
> it is *uniform* (the point you seem unable to grasp), object will sooner or
> later recess from each other > c.
>
> Le sam. 21 sept. 2024, 10:53, Alan Grayson  a
> écrit :
>
>>
>>
>> On Friday, September 20, 2024 at 10:17:34 PM UTC-6 Alan Grayson wrote:
>>
>> On Thursday, September 19, 2024 at 3:14:33 AM UTC-6 Jesse Mazer wrote:
>>
>> On Thu, Sep 19, 2024 at 2:57 AM Alan Grayson  wrote:
>>
>>
>>
>> On Wednesday, September 18, 2024 at 7:10:57 PM UTC-6 Alan Grayson wrote:
>>
>> On Wednesday, September 18, 2024 at 5:30:06 PM UTC-6 Jesse Mazer wrote:
>>
>> On Wed, Sep 18, 2024 at 2:01 AM Alan Grayson  wrote:
>>
>>
>>
>> On Tuesday, September 17, 2024 at 4:20:31 PM UTC-6 Jesse Mazer wrote:
>>
>> On Tue, Sep 17, 2024 at 2:40 PM Alan Grayson  wrote:
>>
>>
>>
>> On Tuesday, September 17, 2024 at 10:12:53 AM UTC-6 Jesse Mazer wrote:
>>
>> On Mon, Sep 16, 2024 at 7:41 PM Alan Grayson  wrote:
>>
>>
>>
>> On Monday, September 16, 2024 at 12:17:45 PM UTC-6 Jesse Mazer wrote:
>>
>> The Scientific American article "Misconceptions About The Big Bang" by
>> Charles Lineweaver and Tamara Davis at
>> https://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf
>> (distilled from their more technical review 'Expanding Confusion' at
>> https://arxiv.org/abs/astro-ph/0310808 ) covers this question on p.
>> 42-43, along with other common misconceptions:
>>
>> "Running to Stay Still
>> the idea of seeing faster-than-light galaxies may sound mystical, but it
>> is made possible by changes in the expansion rate. Imagine a light beam
>> that is farther than the Hubble distance of 14 billion light-years and
>> trying to travel in our direction. It is moving toward us at the speed of
>> light with respect to its local space, but its local space is receding from
>> us faster than the speed of light. Although the light beam is traveling
>> toward us at the maximum speed possible, it cannot keep up with the
>> stretching of space. It is a bit like a child trying to run the wrong way
>> on a moving sidewalk. Photons at the Hubble distance are like the Red Queen
>> and Alice, running as fast as they can just to stay in the same place.
>>
>> One might conclude that the light beyond the Hubble distance would never
>> reach us and that its source would be forever undetectable. But the Hubble
>> distance is not fixed, because the Hubble constant, on which it depends,
>> changes with time. In particular, the constant is proportional to the rate
>> of increase in the distance between two galaxies, divided by that distance.
>> (Any two galaxies can be used for this calculation.) In models of the
>> universe that fit the observational data, the
>> denominator increases faster than the numerator, so the Hubble constant
>> decreases. In this way, the Hubble distance gets larger. As it does, light
>> that was initially just outside the Hubble distance and receding from us
>> can come within the Hubble distance. The photons then find themselves in a
>> region of space that is receding slower than the speed of light. Thereafter
>> they can approach us.
>>
>> The galaxy they came from, though, may continue to recede superluminally.
>> Thus, we can observe light from galaxies that have always been and will
>> always be receding faster than the speed of light. Another way to put it is
>> that the Hubble distance is not fixed and does not mark the edge of the
>> observable universe.
>>
>>
>> *I don't think this is the consensus view, which is that the Hubble
>> constant IS constant, and galaxies beyond our event horizon will never be
>> seen, if the universe in their region is expanding faster than c. AG *
>>
>>
>> Davis and Lineweaver are just reviewing the current consensus view in
>> that article and paper, not suggesting any new physics. In general
>> relativity's cosmological solutions there is a time-dependent "Hubble
>> parameter" whose value at any given cosmological time is called the "Hubble
>> constant" at that time, but which can change over the long term (see the
>> first paragraph of
>> https://lambda.gsfc.nasa.gov/education/graphic_history/hubb_const.html
>> for example). Astrophysicist Ethan Siegel mentions in an article at
>> https://bigthink.com/starts-with-a-bang/hubble-constant-changes-time/
>> that even in models that don't have accelerating expansion due to the
>> cosmological constant, the Hubble constant still need not be constant in
>> time. He explains this by looking at the first Friedmann equation governing
>> an expanding universe, where a term equivalent to the definition of the
>> Hubble constant is on the left side of the equality and the right side has
>> terms for energy density, global curvature of space, and the cosmological
>> constant. So, in an expanding univer

Re: Radius of the Observable universe

2024-09-21 Thread Quentin Anciaux

Inflation lasted 10^-32 seconds... inflation is not the cause of
recessional velocity > c, it's space expansion, not inflation, as long as
it is *uniform* (the point you seem unable to grasp), object will sooner or
later recess from each other > c.

Le sam. 21 sept. 2024, 10:53, Alan Grayson  a
écrit :

>
>
> On Friday, September 20, 2024 at 10:17:34 PM UTC-6 Alan Grayson wrote:
>
> On Thursday, September 19, 2024 at 3:14:33 AM UTC-6 Jesse Mazer wrote:
>
> On Thu, Sep 19, 2024 at 2:57 AM Alan Grayson  wrote:
>
>
>
> On Wednesday, September 18, 2024 at 7:10:57 PM UTC-6 Alan Grayson wrote:
>
> On Wednesday, September 18, 2024 at 5:30:06 PM UTC-6 Jesse Mazer wrote:
>
> On Wed, Sep 18, 2024 at 2:01 AM Alan Grayson  wrote:
>
>
>
> On Tuesday, September 17, 2024 at 4:20:31 PM UTC-6 Jesse Mazer wrote:
>
> On Tue, Sep 17, 2024 at 2:40 PM Alan Grayson  wrote:
>
>
>
> On Tuesday, September 17, 2024 at 10:12:53 AM UTC-6 Jesse Mazer wrote:
>
> On Mon, Sep 16, 2024 at 7:41 PM Alan Grayson  wrote:
>
>
>
> On Monday, September 16, 2024 at 12:17:45 PM UTC-6 Jesse Mazer wrote:
>
> The Scientific American article "Misconceptions About The Big Bang" by
> Charles Lineweaver and Tamara Davis at
> https://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf
> (distilled from their more technical review 'Expanding Confusion' at
> https://arxiv.org/abs/astro-ph/0310808 ) covers this question on p.
> 42-43, along with other common misconceptions:
>
> "Running to Stay Still
> the idea of seeing faster-than-light galaxies may sound mystical, but it
> is made possible by changes in the expansion rate. Imagine a light beam
> that is farther than the Hubble distance of 14 billion light-years and
> trying to travel in our direction. It is moving toward us at the speed of
> light with respect to its local space, but its local space is receding from
> us faster than the speed of light. Although the light beam is traveling
> toward us at the maximum speed possible, it cannot keep up with the
> stretching of space. It is a bit like a child trying to run the wrong way
> on a moving sidewalk. Photons at the Hubble distance are like the Red Queen
> and Alice, running as fast as they can just to stay in the same place.
>
> One might conclude that the light beyond the Hubble distance would never
> reach us and that its source would be forever undetectable. But the Hubble
> distance is not fixed, because the Hubble constant, on which it depends,
> changes with time. In particular, the constant is proportional to the rate
> of increase in the distance between two galaxies, divided by that distance.
> (Any two galaxies can be used for this calculation.) In models of the
> universe that fit the observational data, the
> denominator increases faster than the numerator, so the Hubble constant
> decreases. In this way, the Hubble distance gets larger. As it does, light
> that was initially just outside the Hubble distance and receding from us
> can come within the Hubble distance. The photons then find themselves in a
> region of space that is receding slower than the speed of light. Thereafter
> they can approach us.
>
> The galaxy they came from, though, may continue to recede superluminally.
> Thus, we can observe light from galaxies that have always been and will
> always be receding faster than the speed of light. Another way to put it is
> that the Hubble distance is not fixed and does not mark the edge of the
> observable universe.
>
>
> *I don't think this is the consensus view, which is that the Hubble
> constant IS constant, and galaxies beyond our event horizon will never be
> seen, if the universe in their region is expanding faster than c. AG *
>
>
> Davis and Lineweaver are just reviewing the current consensus view in that
> article and paper, not suggesting any new physics. In general relativity's
> cosmological solutions there is a time-dependent "Hubble parameter" whose
> value at any given cosmological time is called the "Hubble constant" at
> that time, but which can change over the long term (see the first paragraph
> of https://lambda.gsfc.nasa.gov/education/graphic_history/hubb_const.html
> for example). Astrophysicist Ethan Siegel mentions in an article at
> https://bigthink.com/starts-with-a-bang/hubble-constant-changes-time/
> that even in models that don't have accelerating expansion due to the
> cosmological constant, the Hubble constant still need not be constant in
> time. He explains this by looking at the first Friedmann equation governing
> an expanding universe, where a term equivalent to the definition of the
> Hubble constant is on the left side of the equality and the right side has
> terms for energy density, global curvature of space, and the cosmological
> constant. So, in an expanding universe that's spatially flat and has zero
> cosmological constant, if the energy density is changing as matter/energy
> becomes more spread out, the term equivalent to the Hubble constant must be
> changing as well. From th

Re: Radius of the Observable universe



On Friday, September 20, 2024 at 10:17:34 PM UTC-6 Alan Grayson wrote:

On Thursday, September 19, 2024 at 3:14:33 AM UTC-6 Jesse Mazer wrote:

On Thu, Sep 19, 2024 at 2:57 AM Alan Grayson  wrote:



On Wednesday, September 18, 2024 at 7:10:57 PM UTC-6 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 5:30:06 PM UTC-6 Jesse Mazer wrote:

On Wed, Sep 18, 2024 at 2:01 AM Alan Grayson  wrote:



On Tuesday, September 17, 2024 at 4:20:31 PM UTC-6 Jesse Mazer wrote:

On Tue, Sep 17, 2024 at 2:40 PM Alan Grayson  wrote:



On Tuesday, September 17, 2024 at 10:12:53 AM UTC-6 Jesse Mazer wrote:

On Mon, Sep 16, 2024 at 7:41 PM Alan Grayson  wrote:



On Monday, September 16, 2024 at 12:17:45 PM UTC-6 Jesse Mazer wrote:

The Scientific American article "Misconceptions About The Big Bang" by 
Charles Lineweaver and Tamara Davis at 
https://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf 
(distilled from their more technical review 'Expanding Confusion' at 
https://arxiv.org/abs/astro-ph/0310808 ) covers this question on p. 42-43, 
along with other common misconceptions:

"Running to Stay Still
the idea of seeing faster-than-light galaxies may sound mystical, but it is 
made possible by changes in the expansion rate. Imagine a light beam that 
is farther than the Hubble distance of 14 billion light-years and trying to 
travel in our direction. It is moving toward us at the speed of light with 
respect to its local space, but its local space is receding from us faster 
than the speed of light. Although the light beam is traveling toward us at 
the maximum speed possible, it cannot keep up with the stretching of space. 
It is a bit like a child trying to run the wrong way on a moving sidewalk. 
Photons at the Hubble distance are like the Red Queen and Alice, running as 
fast as they can just to stay in the same place.

One might conclude that the light beyond the Hubble distance would never 
reach us and that its source would be forever undetectable. But the Hubble 
distance is not fixed, because the Hubble constant, on which it depends, 
changes with time. In particular, the constant is proportional to the rate 
of increase in the distance between two galaxies, divided by that distance. 
(Any two galaxies can be used for this calculation.) In models of the 
universe that fit the observational data, the
denominator increases faster than the numerator, so the Hubble constant 
decreases. In this way, the Hubble distance gets larger. As it does, light 
that was initially just outside the Hubble distance and receding from us 
can come within the Hubble distance. The photons then find themselves in a 
region of space that is receding slower than the speed of light. Thereafter 
they can approach us.

The galaxy they came from, though, may continue to recede superluminally. 
Thus, we can observe light from galaxies that have always been and will 
always be receding faster than the speed of light. Another way to put it is 
that the Hubble distance is not fixed and does not mark the edge of the 
observable universe.


*I don't think this is the consensus view, which is that the Hubble 
constant IS constant, and galaxies beyond our event horizon will never be 
seen, if the universe in their region is expanding faster than c. AG *


Davis and Lineweaver are just reviewing the current consensus view in that 
article and paper, not suggesting any new physics. In general relativity's 
cosmological solutions there is a time-dependent "Hubble parameter" whose 
value at any given cosmological time is called the "Hubble constant" at 
that time, but which can change over the long term (see the first paragraph 
of https://lambda.gsfc.nasa.gov/education/graphic_history/hubb_const.html 
for example). Astrophysicist Ethan Siegel mentions in an article at 
https://bigthink.com/starts-with-a-bang/hubble-constant-changes-time/ that 
even in models that don't have accelerating expansion due to the 
cosmological constant, the Hubble constant still need not be constant in 
time. He explains this by looking at the first Friedmann equation governing 
an expanding universe, where a term equivalent to the definition of the 
Hubble constant is on the left side of the equality and the right side has 
terms for energy density, global curvature of space, and the cosmological 
constant. So, in an expanding universe that's spatially flat and has zero 
cosmological constant, if the energy density is changing as matter/energy 
becomes more spread out, the term equivalent to the Hubble constant must be 
changing as well. From the article:

"Even if you had a flat Universe (which means you can eliminate the second 
term on the right-hand side) and a Universe without a cosmological constant 
(which would mean eliminating the third term on the right-hand side, too), 
you’d understand immediately that the Hubble “constant” cannot be a 
constant in time.
...
In all cases except for a cosmological constant (i.e., dark energy, to the 
best of our

Re: If the universe is infinite in spatial extent, it is uncreated.



On Friday, September 20, 2024 at 4:46:50 PM UTC-6 Alan Grayson wrote:

On Friday, September 20, 2024 at 4:37:26 PM UTC-6 Alan Grayson wrote:

On Friday, September 20, 2024 at 2:23:10 PM UTC-6 John Clark wrote:

On Fri, Sep 20, 2024 at 11:09 AM Alan Grayson  wrote:


*> Proof by Contradiction: If the universe is infinite in spatial extent, 
and came into being, that would be a type of singularity where it would 
have to instantaneously expand infinitely in spatial extent.*

s

*This entire business started by you asking what would happen at T=0 if the 
universe started running backwards and obviously, regardless of if space is 
finite or infinite, space would have to expand infinitely fast because at 
T=0 it would have a zero amount of time to expand from nothing to 
something.*


*Not exactly. *

*I figured that since the universe is expanding, we could run the clock 
backward and imagine enclosing it in a sphere, say, establishing that it is 
finite, hence **NOT** flat, since flat implies infinite in spatial extent. 
IOW, we can prove the universe is NOT flat using a purely logical argument. 
No need to do any measurements. I sent this analysis to a professor 
emeritus whose main interest is in cosmology who is associated with Case 
Western University. He replied that my analysis dealt only with the 
observable universe and that the universe could be infinite in spatial 
extent, presumably when one considers the unobservable part. I then 
realized that the unobservable part was very likely caused by Inflation, 
and therefore the entire universe would** remain finite** provided we ran 
the clock backward, prior to Inflation. **While considering these issues, I 
realized that a universe infinite in spatial extent must be uncreated, 
since no matter has fast it expands, and for how much time, it cannot 
expand to infinity in spatial extent. IOW, the concept of a created 
universe, one which comes into being, which is infinite in spatial extent, 
assumes a type of singularity which I believe is non-physical and can't be 
realized; namely, a universe which expands infinitely in spatial extent, *
*instantaneously**! So, the professor apparently doesn't realize that his 
critique of my original analysis implies that his claim that the universe 
might **be infinite in spatial extent, contains an implicit denial it had a 
beginning, called the Big Bang. In sum, I believe the universe, our 
expanding bubble, is finite, not flat in its global geometry, and had a 
beginning which we can call the Big Bang. **I haven't written him again to 
relieve him of his apparent misconception, though I might. However, I did 
write Alan Guth about a week ago, asking if he assumed the entire universe, 
or just the observable part existed, when Inflation began, at around 10^-35 
seconds after the Big Bang, when the universe was around the size of a 
proton, or possibly smaller. So far he hasn't replied. *

*AG*


*BTW, I don't agree that the universe would have to expand infinitely fast 
at T=0 to transition from nothing to something. If that were true, we could 
conclude that moving an object at rest to some non-zero velocity would 
require an infinite acceleration. AG* 


*Another point worth considering, is that the global geometry of the 
universe is approximately spherical, for two reasons; firstly, assuming 
that our observation is typical, every observer in the universe sees 
galaxies receding from it (with the exception of local groups), and 
secondly, since the isotropy is not perfectly identical, there must be 
small variations in the rate of recession for all observers, from which, 
together, the characterization of "approximately" originates. AG*

 

*And yes that is a singularity however in physics, unlike pure mathematics, 
when you run into a singularity what that is really telling you is that 
there is some unknown physics going on that you don't understand, or don't 
understand well enough. Everybody knows something is wrong but nobody knows 
what. *

*By the way when people, like me, say that because of AI we're heading 
towards a Singularity they are using poetic license, things in general and 
society in particular won't really be changing infinitely fast, just faster 
than the human meat brain can comprehend. *

John K ClarkSee what's on my new list at  Extropolis 
  
e4b


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Re: If the universe is infinite in spatial extent, it is uncreated.



On Saturday, September 21, 2024 at 1:38:37 AM UTC-6 Russell Standish wrote:

On Fri, Sep 20, 2024 at 09:50:46PM -0700, Alan Grayson wrote: 
> 
> 
> On Friday, September 20, 2024 at 10:39:20 PM UTC-6 Russell Standish 
wrote: 
> The term comes from an expected step change where technology starts to 
> advance hyperbolically rather than exponentially like it has been 
> doing since Ogg smashed rocks together. Hyperbolic growth reaches 
> infinity in a finite amount of time. 
> 
> 
> That's impossible. AG 
>   

It's mathematics! 

https://en.wikipedia.org/wiki/Hyperbolic_growth


You're misinterpreting the mathematics.  E.g., 1/x becomes  arbitrarily 
large as x --> 0,  but the function is undefined at x=0.  So, if you're 
considering something physical, at x=0, you can't get there, and certainly 
not in a finite amount of time. AG

 

Dr Russell Standish Phone 0425 253119 (mobile) 
Principal, High Performance Coders hpc...@hpcoders.com.au 
http://www.hpcoders.com.au 
 


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Re: If the universe is infinite in spatial extent, it is uncreated.

2024-09-21 Thread Russell Standish

On Fri, Sep 20, 2024 at 09:50:46PM -0700, Alan Grayson wrote:
> 
> 
> On Friday, September 20, 2024 at 10:39:20 PM UTC-6 Russell Standish wrote:
> The term comes from an expected step change where technology starts to
> advance hyperbolically rather than exponentially like it has been
> doing since Ogg smashed rocks together. Hyperbolic growth reaches
> infinity in a finite amount of time.
> 
> 
> That's impossible. AG
>  

It's mathematics!

https://en.wikipedia.org/wiki/Hyperbolic_growth


-- 


Dr Russell StandishPhone 0425 253119 (mobile)
Principal, High Performance Coders hpco...@hpcoders.com.au
  http://www.hpcoders.com.au


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Re: If the universe is infinite in spatial extent, it is uncreated.

On Friday, September 20, 2024 at 10:39:20 PM UTC-6 Russell Standish wrote:

On Fri, Sep 20, 2024 at 04:22:28PM -0400, John Clark wrote: 
> By the way when people, like me, say that because of AI we're heading 
towards a 
> Singularity they are using poetic license, things in general and society 
in 
> particular won't really be changing infinitely fast, just faster than the 
human 
> meat brain can comprehend.  

The term comes from an expected step change where technology starts to 
advance hyperbolically rather than exponentially like it has been 
doing since Ogg smashed rocks together. Hyperbolic growth reaches 
infinity in a finite amount of time. 

*That's impossible. AG*

It is a singularity in exactly 
the same sense as the beginning of the universe is a singularity or a 
black hole is a singularity. Of course no actual infinities are 
expected in any of these situations, but our theories break down well 
before. 

-- 

Dr Russell Standish Phone 0425 253119 (mobile) 
Principal, High Performance Coders hpc...@hpcoders.com.au 
http://www.hpcoders.com.au 

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Re: If the universe is infinite in spatial extent, it is uncreated.

2024-09-20 Thread Russell Standish

On Fri, Sep 20, 2024 at 04:22:28PM -0400, John Clark wrote:
> By the way when people, like me, say that because of AI we're heading towards 
> a
> Singularity they are using poetic license, things in general and society in
> particular won't really be changing infinitely fast, just faster than the 
> human
> meat brain can comprehend. 

The term comes from an expected step change where technology starts to
advance hyperbolically rather than exponentially like it has been
doing since Ogg smashed rocks together. Hyperbolic growth reaches
infinity in a finite amount of time. It is a singularity in exactly
the same sense as the beginning of the universe is a singularity or a
black hole is a singularity. Of course no actual infinities are
expected in any of these situations, but our theories break down well
before.

-- 

Dr Russell StandishPhone 0425 253119 (mobile)
Principal, High Performance Coders hpco...@hpcoders.com.au
  http://www.hpcoders.com.au

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Re: Radius of the Observable universe



On Thursday, September 19, 2024 at 3:14:33 AM UTC-6 Jesse Mazer wrote:

On Thu, Sep 19, 2024 at 2:57 AM Alan Grayson  wrote:



On Wednesday, September 18, 2024 at 7:10:57 PM UTC-6 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 5:30:06 PM UTC-6 Jesse Mazer wrote:

On Wed, Sep 18, 2024 at 2:01 AM Alan Grayson  wrote:



On Tuesday, September 17, 2024 at 4:20:31 PM UTC-6 Jesse Mazer wrote:

On Tue, Sep 17, 2024 at 2:40 PM Alan Grayson  wrote:



On Tuesday, September 17, 2024 at 10:12:53 AM UTC-6 Jesse Mazer wrote:

On Mon, Sep 16, 2024 at 7:41 PM Alan Grayson  wrote:



On Monday, September 16, 2024 at 12:17:45 PM UTC-6 Jesse Mazer wrote:

The Scientific American article "Misconceptions About The Big Bang" by 
Charles Lineweaver and Tamara Davis at 
https://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf 
(distilled from their more technical review 'Expanding Confusion' at 
https://arxiv.org/abs/astro-ph/0310808 ) covers this question on p. 42-43, 
along with other common misconceptions:

"Running to Stay Still
the idea of seeing faster-than-light galaxies may sound mystical, but it is 
made possible by changes in the expansion rate. Imagine a light beam that 
is farther than the Hubble distance of 14 billion light-years and trying to 
travel in our direction. It is moving toward us at the speed of light with 
respect to its local space, but its local space is receding from us faster 
than the speed of light. Although the light beam is traveling toward us at 
the maximum speed possible, it cannot keep up with the stretching of space. 
It is a bit like a child trying to run the wrong way on a moving sidewalk. 
Photons at the Hubble distance are like the Red Queen and Alice, running as 
fast as they can just to stay in the same place.

One might conclude that the light beyond the Hubble distance would never 
reach us and that its source would be forever undetectable. But the Hubble 
distance is not fixed, because the Hubble constant, on which it depends, 
changes with time. In particular, the constant is proportional to the rate 
of increase in the distance between two galaxies, divided by that distance. 
(Any two galaxies can be used for this calculation.) In models of the 
universe that fit the observational data, the
denominator increases faster than the numerator, so the Hubble constant 
decreases. In this way, the Hubble distance gets larger. As it does, light 
that was initially just outside the Hubble distance and receding from us 
can come within the Hubble distance. The photons then find themselves in a 
region of space that is receding slower than the speed of light. Thereafter 
they can approach us.

The galaxy they came from, though, may continue to recede superluminally. 
Thus, we can observe light from galaxies that have always been and will 
always be receding faster than the speed of light. Another way to put it is 
that the Hubble distance is not fixed and does not mark the edge of the 
observable universe.


*I don't think this is the consensus view, which is that the Hubble 
constant IS constant, and galaxies beyond our event horizon will never be 
seen, if the universe in their region is expanding faster than c. AG *


Davis and Lineweaver are just reviewing the current consensus view in that 
article and paper, not suggesting any new physics. In general relativity's 
cosmological solutions there is a time-dependent "Hubble parameter" whose 
value at any given cosmological time is called the "Hubble constant" at 
that time, but which can change over the long term (see the first paragraph 
of https://lambda.gsfc.nasa.gov/education/graphic_history/hubb_const.html 
for example). Astrophysicist Ethan Siegel mentions in an article at 
https://bigthink.com/starts-with-a-bang/hubble-constant-changes-time/ that 
even in models that don't have accelerating expansion due to the 
cosmological constant, the Hubble constant still need not be constant in 
time. He explains this by looking at the first Friedmann equation governing 
an expanding universe, where a term equivalent to the definition of the 
Hubble constant is on the left side of the equality and the right side has 
terms for energy density, global curvature of space, and the cosmological 
constant. So, in an expanding universe that's spatially flat and has zero 
cosmological constant, if the energy density is changing as matter/energy 
becomes more spread out, the term equivalent to the Hubble constant must be 
changing as well. From the article:

"Even if you had a flat Universe (which means you can eliminate the second 
term on the right-hand side) and a Universe without a cosmological constant 
(which would mean eliminating the third term on the right-hand side, too), 
you’d understand immediately that the Hubble “constant” cannot be a 
constant in time.
...
In all cases except for a cosmological constant (i.e., dark energy, to the 
best of our understanding), the energy density changes as the Universe 
expands.
If

Re: If the universe is infinite in spatial extent, it is uncreated.



On Friday, September 20, 2024 at 4:46:50 PM UTC-6 Alan Grayson wrote:

On Friday, September 20, 2024 at 4:37:26 PM UTC-6 Alan Grayson wrote:

On Friday, September 20, 2024 at 2:23:10 PM UTC-6 John Clark wrote:

On Fri, Sep 20, 2024 at 11:09 AM Alan Grayson  wrote:


*> Proof by Contradiction: If the universe is infinite in spatial extent, 
and came into being, that would be a type of singularity where it would 
have to instantaneously expand infinitely in spatial extent.*

s

*This entire business started by you asking what would happen at T=0 if the 
universe started running backwards and obviously, regardless of if space is 
finite or infinite, space would have to expand infinitely fast because at 
T=0 it would have a zero amount of time to expand from nothing to 
something.*


*Not exactly. *

*I figured that since the universe is expanding, we could run to clock 
backward and imagine enclosing it in a sphere, say, establishing that it is 
finite, hence **NOT** flat, since flat implies infinite in spatial extent. 
IOW, we can prove the universe is NOT flat using a purely logical argument. 
No need to do any measurements. I sent this analysis to a professor 
emeritus whose main interest is in cosmology who is associated with Case 
Western University. He replied that my analysis dealt only with the 
observable universe and that the universe could be infinite in spatial 
extent, presumably when one considers the unobservable part. I then 
realized that the unobservable part was very likely caused by Inflation, 
and therefore the entire universe would** remain finite** provided we ran 
the clock backward, prior to Inflation. **While considering these issues, I 
realized that a universe infinite in spatial extent must be uncreated, 
since no matter has fast it expands, and for how much time, it cannot 
expand to infinity in spatial extent. IOW, the concept of a created 
universe, one which comes into being, which is infinite in spatial extent, 
assumes a type of singularity which I believe is non-physical and can't be 
realized; namely, a universe which expands infinitely in spatial extent, *
*instantaneously**! So, the professor apparently doesn't realize that his 
critique of my original analysis implies that his claim that the universe 
might **be infinite in spatial extent, contains an implicit denial it had a 
beginning, called the Big Bang. In sum, I believe the universe, our 
expanding bubble, is finite, not flat in its global geometry, and had a 
beginning which we can call the Big Bang. **I haven't written him again to 
relieve him of his apparent misconception, though I might. However, I did 
write Alan Guth about a week ago, asking if he assumed the entire universe, 
or just the observable part existed, when Inflation began, at around 10^-35 
seconds after the Big Bang, when the universe was around the size of a 
proton, or possibly smaller. So far he hasn't replied. *

*AG*


*BTW, I don't agree that the universe would have to expand infinitely fast 
at T=0 to transition from nothing to something. If that were true, we could 
conclude that moving an object at rest to some non-zero velocity would 
require an infinite acceleration. AG* 


*Should read as follows (note all CAPS underlined at beginning):*

*I figured that since the universe is expanding, we could run** THE clock 
backward and imagine enclosing it in a sphere, say, establishing that it is 
finite, hence **NOT** flat, since flat implies infinite in spatial extent. 
IOW, we can prove the universe is NOT flat using a purely logical argument. 
No need to do any measurements. I sent this analysis to a professor 
emeritus whose main interest is in cosmology who is associated with Case 
Western University. He replied that my analysis dealt only with the 
observable universe and that the universe could be infinite in spatial 
extent, presumably when one considers the unobservable part. I then 
realized that the unobservable part was very likely caused by Inflation, 
and therefore the entire universe would** remain finite** provided we ran 
the clock backward, prior to Inflation. **While considering these issues, I 
realized that a universe infinite in spatial extent must be uncreated, 
since no matter has fast it expands, and for how much time, it cannot 
expand to infinity in spatial extent. IOW, the concept of a created 
universe, one which comes into being, which is infinite in spatial extent, 
assumes a type of singularity which I believe is non-physical and can't be 
realized; namely, a universe which expands infinitely in spatial extent, *
*instantaneously**! So, the professor apparently doesn't realize that his 
critique of my original analysis implies that his claim that the 
universe might **be infinite in spatial extent, contains an implicit denial 
it had a beginning, called the Big Bang. In sum, I believe the universe, 
our expanding bubble, is finite, not flat in its global geometry, and had a 
beginning which we can call the B

Re: If the universe is infinite in spatial extent, it is uncreated.

On Friday, September 20, 2024 at 4:37:26 PM UTC-6 Alan Grayson wrote:

On Friday, September 20, 2024 at 2:23:10 PM UTC-6 John Clark wrote:

On Fri, Sep 20, 2024 at 11:09 AM Alan Grayson wrote:

*> Proof by Contradiction: If the universe is infinite in spatial extent,
and came into being, that would be a type of singularity where it would
have to instantaneously expand infinitely in spatial extent.*

*This entire business started by you asking what would happen at T=0 if the
universe started running backwards and obviously, regardless of if space is
finite or infinite, space would have to expand infinitely fast because at
T=0 it would have a zero amount of time to expand from nothing to
something.*

*Not exactly. *

*I figured that since the universe is expanding, we could run to clock
backward and imagine enclosing it in a sphere, say, establishing that it is
finite, hence **NOT** flat, since flat implies infinite in spatial extent.
IOW, we can prove the universe is NOT flat using a purely logical argument.
No need to do any measurements. I sent this analysis to a professor
emeritus whose main interest is in cosmology who is associated with Case
Western University. He replied that my analysis dealt only with the
observable universe and that the universe could be infinite in spatial
extent, presumably when one considers the unobservable part. I then
realized that the unobservable part was very likely caused by Inflation,
and therefore the entire universe would** remain finite** provided we ran
the clock backward, prior to Inflation. **While considering these issues, I
realized that a universe infinite in spatial extent must be uncreated,
since no matter has fast it expands, and for how much time, it cannot
expand to infinity in spatial extent. IOW, the concept of a created
universe, one which comes into being, which is infinite in spatial extent,
assumes a type of singularity which I believe is non-physical and can't be
realized; namely, a universe which expands infinitely in spatial extent, *
*instantaneously**! So, the professor apparently doesn't realize that his
critique of my original analysis implies that his claim that the universe
might **be infinite in spatial extent, contains an implicit denial it had a
beginning, called the Big Bang. In sum, I believe the universe, our
expanding bubble, is finite, not flat in its global geometry, and had a
beginning which we can call the Big Bang. **I haven't written him again to
relieve him of his apparent misconception, though I might. However, I did
write Alan Guth about a week ago, asking if he assumed the entire universe,
or just the observable part existed, when Inflation began, at around 10^-35
seconds after the Big Bang, when the universe was around the size of a
proton, or possibly smaller. So far he hasn't replied. *

*AG*

*BTW, I don't agree that the universe would have to expand infinitely fast
at T=0 to transition from nothing to something. If that were true, we could
conclude that moving an object at rest to some non-zero velocity would
require an infinite acceleration. AG*

*And yes that is a singularity however in physics, unlike pure mathematics,
when you run into a singularity what that is really telling you is that
there is some unknown physics going on that you don't understand, or don't
understand well enough. Everybody knows something is wrong but nobody knows
what. *

*By the way when people, like me, say that because of AI we're heading
towards a Singularity they are using poetic license, things in general and
society in particular won't really be changing infinitely fast, just faster
than the human meat brain can comprehend. *

John K ClarkSee what's on my new list at Extropolis

e4b

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Re: If the universe is infinite in spatial extent, it is uncreated.

On Friday, September 20, 2024 at 2:23:10 PM UTC-6 John Clark wrote:

On Fri, Sep 20, 2024 at 11:09 AM Alan Grayson wrote:

s
*This entire business started by you asking what would happen at T=0 if the
universe started running backwards and obviously, regardless of if space is
finite or infinite, space would have to expand infinitely fast because at
T=0 it would have a zero amount of time to expand from nothing to
something.*

*Not exactly. *

*AG*

John K ClarkSee what's on my new list at Extropolis

e4b

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Re: If the universe is infinite in spatial extent, it is uncreated.

2024-09-20 Thread John Clark

On Fri, Sep 20, 2024 at 11:09 AM Alan Grayson 
wrote:

*> Proof by Contradiction: If the universe is infinite in spatial extent,
> and came into being, that would be a type of singularity where it would
> have to instantaneously expand infinitely in spatial extent.*

*This entire business started by you asking what would happen at T=0 if the
universe started running backwards and obviously, regardless of if space is
finite or infinite, space would have to expand infinitely fast because at
T=0 it would have a zero amount of time to expand from nothing to
something. And yes that is a singularity however in physics, unlike pure
mathematics, when you run into a singularity what that is really telling
you is that there is some unknown physics going on that you don't
understand, or don't understand well enough. Everybody knows something is
wrong but nobody knows what. *

*By the way when people, like me, say that because of AI we're heading
towards a Singularity they are using poetic license, things in general and
society in particular won't really be changing infinitely fast, just faster
than the human meat brain can comprehend. *

John K ClarkSee what's on my new list at  Extropolis

e4b

>

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Re: Flat universe implies no Big Bang and Singularity at T = 0



On Friday, September 20, 2024 at 1:19:38 AM UTC-6 Alan Grayson wrote:

On Friday, September 20, 2024 at 12:47:13 AM UTC-6 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 6:50:53 PM UTC-6 Brent Meeker wrote:




On 9/18/2024 5:19 AM, John Clark wrote:



On Wed, Sep 18, 2024 at 8:12 AM Alan Grayson  wrote:



On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson  wrote:

*I'll get back to you on this. I was thinking, as x increases positively or 
negatively, the y values (angles) repeat multiple times, making the 
function many-to-one. In this case, we're mapping all the real numbers, to 
a subset of the y-axis. Am I mistaken? AG *


*Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  
So your plot seems wrong, but it's what is on the Internet. AG *


*That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I 
still think the plot keeps repeating as x increases or decreases. AG*

[image: image.png]


*1) **The range of the Arctangent function is the interval (-π/2,π/2) and 
its range is all the real numbers.*

* 2) By dividing by π,  the range scales to (-1/2, 1/2).*

* 3) Adding 1/2 shifts the range to (0,1) *

*4) Thus for every real number x there is a unique number y between zero 
and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) . 
As I said before, the domain is all the real numbers and the range is (0,1)*
 


*> Yes, but initially you were seeking a 1-1 function, but this one is 
many-to-one. AG *

 FOR DARWIN'S SAKE! I GIVE UP!


Could'a told ya.

Brent 


*I spoke to a friend who is Emeritus Professor in Mathematics at Cal  Poly 
Pomona. He says the inverse tangent function is MULTI VALUED.  AG*

*Is the arctan periodic, or multi-valued? Internet answer:*

No, the arctangent (arctan) function is not periodic; it is considered a 
one-to-one function
* because its domain is restricted to an interval where the tangent 
function (which is periodic) is one-to-one, typically from -π/2 to π/2, 
ensuring that each output value corresponds to a unique input value. *
Explanation: 

   - Tangent periodicity:
   The tangent function (tan(x)) is periodic with a period of π, meaning 
   its values repeat every π radians. 
   - Restricting the domain:
   To create an inverse function (arctan), *we need to restrict the domain *of 
   the tangent function to an interval where it is not repeating, like (-π/2, 
   π/2). 
   

   - *By restricting the domain in this way, the arctangent function is no 
   longer periodic. *
   
*IOW, the arctan is single-valued if its domain is restricted to (**-π/2, 
π/2)*, but Clark defines its domain to all real numbers, making the arctan 
periodic and thus multi-valued. AG


This above is not quite right. Clark is using just the *principle branch *of 
the tangent function, to get its inverse, which is 1-1. But there are many, 
in fact an infinite number of branches and this is where the multi-value 
problem originates. AG 

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Re: Flat universe implies no Big Bang and Singularity at T = 0



On Friday, September 20, 2024 at 12:47:13 AM UTC-6 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 6:50:53 PM UTC-6 Brent Meeker wrote:




On 9/18/2024 5:19 AM, John Clark wrote:



On Wed, Sep 18, 2024 at 8:12 AM Alan Grayson  wrote:



On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson  wrote:

*I'll get back to you on this. I was thinking, as x increases positively or 
negatively, the y values (angles) repeat multiple times, making the 
function many-to-one. In this case, we're mapping all the real numbers, to 
a subset of the y-axis. Am I mistaken? AG *


*Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  
So your plot seems wrong, but it's what is on the Internet. AG *


*That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I 
still think the plot keeps repeating as x increases or decreases. AG*

[image: image.png]


*1) **The range of the Arctangent function is the interval (-π/2,π/2) and 
its range is all the real numbers.*

* 2) By dividing by π,  the range scales to (-1/2, 1/2).*

* 3) Adding 1/2 shifts the range to (0,1) *

*4) Thus for every real number x there is a unique number y between zero 
and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) . 
As I said before, the domain is all the real numbers and the range is (0,1)*
 


*> Yes, but initially you were seeking a 1-1 function, but this one is 
many-to-one. AG *

 FOR DARWIN'S SAKE! I GIVE UP!


Could'a told ya.

Brent 


*I spoke to a friend who is Emeritus Professor in Mathematics at Cal  Poly 
Pomona. He says the inverse tangent function is MULTI VALUED.  AG*

*Is the arctan periodic, or multi-valued? Internet answer:*

No, the arctangent (arctan) function is not periodic; it is considered a 
one-to-one function
* because its domain is restricted to an interval where the tangent 
function (which is periodic) is one-to-one, typically from -π/2 to π/2, 
ensuring that each output value corresponds to a unique input value. *
Explanation: 

   - Tangent periodicity:
   The tangent function (tan(x)) is periodic with a period of π, meaning 
   its values repeat every π radians. 
   - Restricting the domain:
   To create an inverse function (arctan), *we need to restrict the domain *of 
   the tangent function to an interval where it is not repeating, like (-π/2, 
   π/2). 
   

   - *By restricting the domain in this way, the arctangent function is no 
   longer periodic. *
   
*IOW, the arctan is single-valued if its domain is restricted to (**-π/2, 
π/2)*, but Clark defines its domain to all real numbers, making the arctan 
periodic and thus multi-valued. AG

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Re: Flat universe implies no Big Bang and Singularity at T = 0



On Wednesday, September 18, 2024 at 6:50:53 PM UTC-6 Brent Meeker wrote:




On 9/18/2024 5:19 AM, John Clark wrote:



On Wed, Sep 18, 2024 at 8:12 AM Alan Grayson  wrote:



On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson  wrote:

*I'll get back to you on this. I was thinking, as x increases positively or 
negatively, the y values (angles) repeat multiple times, making the 
function many-to-one. In this case, we're mapping all the real numbers, to 
a subset of the y-axis. Am I mistaken? AG *


*Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  
So your plot seems wrong, but it's what is on the Internet. AG *


*That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I 
still think the plot keeps repeating as x increases or decreases. AG*

[image: image.png]


*1) **The range of the Arctangent function is the interval (-π/2,π/2) and 
its range is all the real numbers.*

* 2) By dividing by π,  the range scales to (-1/2, 1/2).*

* 3) Adding 1/2 shifts the range to (0,1) *

*4) Thus for every real number x there is a unique number y between zero 
and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) . 
As I said before, the domain is all the real numbers and the range is (0,1)*
 


*> Yes, but initially you were seeking a 1-1 function, but this one is 
many-to-one. AG *

 FOR DARWIN'S SAKE! I GIVE UP!


Could'a told ya.

Brent 


*I spoke to a friend who is Emeritus Professor in Mathematics at Cal  Poly 
Pomona. He says the inverse tangent function is MULTI VALUED.  AG*


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Re: Flat universe implies no Big Bang and Singularity at T = 0



On Thursday, September 19, 2024 at 6:14:53 AM UTC-6 Cosmin Visan wrote:

Universe doesn't exist. "Universe" is just an idea in consciousness. The 
Big Bang never happened in any past, since past doesn't exist. Only the 
eternal present moment exist. And in the eternal present moment, Big Bang 
happens at all times, since each moment is a moment of creation in which 
the world is being imagined into existence by consciousness inside itself.


*Your ideas are essentially profound, but not accessible to physicists 
primarily because of their subliminal **vanity. On the other hand, your 
ideas are totally useless. They predict nothing and offer us nothing to 
discover and do. AG *


On Thursday 19 September 2024 at 10:14:01 UTC+3 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 7:23:38 PM UTC-6 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 7:02:12 PM UTC-6 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 6:50:53 PM UTC-6 Brent Meeker wrote:




On 9/18/2024 5:19 AM, John Clark wrote:



On Wed, Sep 18, 2024 at 8:12 AM Alan Grayson  wrote:



On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson  wrote:

*I'll get back to you on this. I was thinking, as x increases positively or 
negatively, the y values (angles) repeat multiple times, making the 
function many-to-one. In this case, we're mapping all the real numbers, to 
a subset of the y-axis. Am I mistaken? AG *


*Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  
So your plot seems wrong, but it's what is on the Internet. AG *


*That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I 
still think the plot keeps repeating as x increases or decreases. AG*

[image: image.png]


*1) **The range of the Arctangent function is the interval (-π/2,π/2) and 
its range is all the real numbers.*

* 2) By dividing by π,  the range scales to (-1/2, 1/2).*

* 3) Adding 1/2 shifts the range to (0,1) *

*4) Thus for every real number x there is a unique number y between zero 
and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) . 
As I said before, the domain is all the real numbers and the range is (0,1)*
 


*> Yes, but initially you were seeking a 1-1 function, but this one is 
many-to-one. AG *

 FOR DARWIN'S SAKE! I GIVE UP!


Could'a told ya.

Brent


*Why are you so inclined to join the asshole club? I just made an error. 
Are you immune from that? AG*


 *I conjectured that Inflation caused the unobservable universe to come 
into existence, an original thought you ignore, but your inclination is to 
be petty. Too many physicists are revealed to be a'holes and I see no cure 
for that. AG*


*I admit it's puzzling. Whereas tangent 0 degrees = tangent 360 degrees = 
0, and arctan 0 degrees = 0, I thought arctan 360 degrees is also 0, but it 
apparently isn't. This is how I concluded y = arctan(x) is many-to-one. AG*

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Re: Flat universe implies no Big Bang and Singularity at T = 0



On Thursday, September 19, 2024 at 6:14:53 AM UTC-6 Cosmin Visan wrote:

Universe doesn't exist. "Universe" is just an idea in consciousness. The 
Big Bang never happened in any past, since past doesn't exist. Only the 
eternal present moment exist. And in the eternal present moment, Big Bang 
happens at all times, since each moment is a moment of creation in which 
the world is being imagined into existence by consciousness inside itself.


*Your ideas are essentially profound, not accessible to physicists 
primarily because of their subliminal *
*vanity. On the other hand, your ideas are totally useless. They predict 
nothing and offer us nothing to discover and do. AG *


On Thursday 19 September 2024 at 10:14:01 UTC+3 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 7:23:38 PM UTC-6 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 7:02:12 PM UTC-6 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 6:50:53 PM UTC-6 Brent Meeker wrote:




On 9/18/2024 5:19 AM, John Clark wrote:



On Wed, Sep 18, 2024 at 8:12 AM Alan Grayson  wrote:



On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson  wrote:

*I'll get back to you on this. I was thinking, as x increases positively or 
negatively, the y values (angles) repeat multiple times, making the 
function many-to-one. In this case, we're mapping all the real numbers, to 
a subset of the y-axis. Am I mistaken? AG *


*Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  
So your plot seems wrong, but it's what is on the Internet. AG *


*That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I 
still think the plot keeps repeating as x increases or decreases. AG*

[image: image.png]


*1) **The range of the Arctangent function is the interval (-π/2,π/2) and 
its range is all the real numbers.*

* 2) By dividing by π,  the range scales to (-1/2, 1/2).*

* 3) Adding 1/2 shifts the range to (0,1) *

*4) Thus for every real number x there is a unique number y between zero 
and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) . 
As I said before, the domain is all the real numbers and the range is (0,1)*
 


*> Yes, but initially you were seeking a 1-1 function, but this one is 
many-to-one. AG *

 FOR DARWIN'S SAKE! I GIVE UP!


Could'a told ya.

Brent


*Why are you so inclined to join the asshole club? I just made an error. 
Are you immune from that? AG*


 *I conjectured that Inflation caused the unobservable universe to come 
into existence, an original thought you ignore, but your inclination is to 
be petty. Too many physicists are revealed to be a'holes and I see no cure 
for that. AG*


*I admit it's puzzling. Whereas tangent 0 degrees = tangent 360 degrees = 
0, and arctan 0 degrees = 0, I thought arctan 360 degrees is also 0, but it 
apparently isn't. This is how I concluded y = arctan(x) is many-to-one. AG*

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Re: By far this is the smartest AI yet

2024-09-19 Thread Brent Meeker


So if you find a smart object it must be conscious.


On 9/19/2024 5:18 AM, 'Cosmin Visan' via Everything List wrote:

An object cannot be smart. Only consciousness is smart.


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Re: Trump unfit to serve say 111 former GOP officials and they endorse Harris

2024-09-19 Thread PGC

Brian Fitzpatrick, maybe just a little? This U.S. Representative from 
Pennsylvania has taken moderate positions and has occasionally pushed back 
against Trump's claims regarding the 2020 election. This is already heroic 
given how popular Трамп (Trrramp) is with the base. And Lisa Murkowski, 
Mitt Romney, and Bill Cassidy? There are things like public records. 
Influential politicians that align themselves with authoritarian 
tendencies, should automatically be barred from politics. Gotta move away 
from "this is difficult to prove in free speech contexts"; and just point 
to recordings and alliances. *He said that, they aligned themselves with 
him, and finito.* 

It's so obvious, I feel like I lost some brain cells saying it.  

On Thursday, September 19, 2024 at 1:44:33 PM UTC+2 John Clark wrote:

>
>
> On Wed, Sep 18, 2024 at 8:54 PM Brent Meeker  wrote:
>
> * > But no office-holding Republicans.*
>>
>
> *Yes, I noticed that too.** And that is why, although I have been a 
> Republican for most of my life, I will never vote for a Republican again, 
> not even for dogcatcher. *
>
>  John K ClarkSee what's on my new list at  Extropolis 
> 
> ddg
>
>>
>>

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Re: How Self-Reference Builds the World - my paper

2024-09-19 Thread 'Cosmin Visan' via Everything List

Up.

On Wednesday 4 September 2024 at 13:38:57 UTC+3 Alan Grayson wrote:

> A-OK !
>
> On Wednesday, September 4, 2024 at 4:28:44 AM UTC-6 Cosmin Visan wrote:
>
>> @Alan. Great! If you ever read it, I will like to hear your opinion about 
>> the details of how this is done.
>>
>> On Wednesday 28 August 2024 at 08:37:17 UTC+3 Alan Grayson wrote:
>>
>>> I don't have the energy now to read your paper, but fwiw, I agree that 
>>> the key to consciousness is self-reference. AG
>>>
>>> On Tuesday, June 25, 2024 at 7:09:53 AM UTC-6 Cosmin Visan wrote:
>>>
 I invite you to discover my paper "How Self-Reference Builds the World" 
 which is the theory of everything that people searched for millennia. It 
 can be found on my philpeople profile:
 https://philpeople.org/profiles/cosmin-visan

>>>

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Re: By far this is the smartest AI yet

2024-09-19 Thread 'Cosmin Visan' via Everything List

An object cannot be smart. Only consciousness is smart.

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Re: New AI has an IQ of 120

2024-09-19 Thread 'Cosmin Visan' via Everything List

Intelligence is the ability of consciousness to bring new ideas into 
existence out of nothing. Given this consideration, you just proved that 
your IQ is around 80.

On Wednesday 18 September 2024 at 20:09:26 UTC+3 John Clark wrote:

> *This is why OpenAI o1 preview (alias strawberry, alias Q*)  is so 
> exciting, previous AIs have topped out at about IQ 90, but this one has a 
> 120 IQ. Last November, when this thing was developed, it got everybody so 
> hot and bothered that they fired Sam Altman as head of OpenAI, and then 
> quickly hired him back. I wonder what they've been doing undercover at 
> OpenAI's skunk works for the last 10 months.  *
>
>
> [image: 908B34C4-BB0E-4258-A458-E9F087B90BAA_1_105_c.jpeg]
>
>
> John K ClarkSee what's on my new list at  Extropolis 
> 
> 2oI
>
>

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Re: Flat universe implies no Big Bang and Singularity at T = 0

2024-09-19 Thread 'Cosmin Visan' via Everything List

Universe doesn't exist. "Universe" is just an idea in consciousness. The 
Big Bang never happened in any past, since past doesn't exist. Only the 
eternal present moment exist. And in the eternal present moment, Big Bang 
happens at all times, since each moment is a moment of creation in which 
the world is being imagined into existence by consciousness inside itself.

On Thursday 19 September 2024 at 10:14:01 UTC+3 Alan Grayson wrote:

> On Wednesday, September 18, 2024 at 7:23:38 PM UTC-6 Alan Grayson wrote:
>
> On Wednesday, September 18, 2024 at 7:02:12 PM UTC-6 Alan Grayson wrote:
>
> On Wednesday, September 18, 2024 at 6:50:53 PM UTC-6 Brent Meeker wrote:
>
>
>
>
> On 9/18/2024 5:19 AM, John Clark wrote:
>
>
>
> On Wed, Sep 18, 2024 at 8:12 AM Alan Grayson  wrote:
>
>
>
> On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote:
>
> On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson  wrote:
>
> *I'll get back to you on this. I was thinking, as x increases positively 
> or negatively, the y values (angles) repeat multiple times, making the 
> function many-to-one. In this case, we're mapping all the real numbers, to 
> a subset of the y-axis. Am I mistaken? AG *
>
>
> *Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or 
> pi/2?  So your plot seems wrong, but it's what is on the Internet. AG *
>
>
> *That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I 
> still think the plot keeps repeating as x increases or decreases. AG*
>
> [image: image.png]
>
>
> *1) **The range of the Arctangent function is the interval (-π/2,π/2) and 
> its range is all the real numbers.*
>
> * 2) By dividing by π,  the range scales to (-1/2, 1/2).*
>
> * 3) Adding 1/2 shifts the range to (0,1) *
>
> *4) Thus for every real number x there is a unique number y between zero 
> and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) . 
> As I said before, the domain is all the real numbers and the range is (0,1)*
>  
>
>
> *> Yes, but initially you were seeking a 1-1 function, but this one is 
> many-to-one. AG *
>
>  FOR DARWIN'S SAKE! I GIVE UP!
>
>
> Could'a told ya.
>
> Brent
>
>
> *Why are you so inclined to join the asshole club? I just made an error. 
> Are you immune from that? AG*
>
>
>  *I conjectured that Inflation caused the unobservable universe to come 
> into existence, an original thought you ignore, but your inclination is to 
> be petty. Too many physicists are revealed to be a'holes and I see no cure 
> for that. AG*
>
>
> *I admit it's puzzling. Whereas tangent 0 degrees = tangent 360 degrees = 
> 0, and arctan 0 degrees = 0, I thought arctan 360 degrees is also 0, but it 
> apparently isn't. This is how I concluded y = arctan(x) is many-to-one. AG*
>

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Re: Radius of the Observable universe

2024-09-19 Thread 'Cosmin Visan' via Everything List

Universe doesn't exist. "Universe" is just an idea in consciousness.

On Thursday 19 September 2024 at 12:14:33 UTC+3 Jesse Mazer wrote:

> On Thu, Sep 19, 2024 at 2:57 AM Alan Grayson  wrote:
>
>>
>>
>> On Wednesday, September 18, 2024 at 7:10:57 PM UTC-6 Alan Grayson wrote:
>>
>> On Wednesday, September 18, 2024 at 5:30:06 PM UTC-6 Jesse Mazer wrote:
>>
>> On Wed, Sep 18, 2024 at 2:01 AM Alan Grayson  wrote:
>>
>>
>>
>> On Tuesday, September 17, 2024 at 4:20:31 PM UTC-6 Jesse Mazer wrote:
>>
>> On Tue, Sep 17, 2024 at 2:40 PM Alan Grayson  wrote:
>>
>>
>>
>> On Tuesday, September 17, 2024 at 10:12:53 AM UTC-6 Jesse Mazer wrote:
>>
>> On Mon, Sep 16, 2024 at 7:41 PM Alan Grayson  wrote:
>>
>>
>>
>> On Monday, September 16, 2024 at 12:17:45 PM UTC-6 Jesse Mazer wrote:
>>
>> The Scientific American article "Misconceptions About The Big Bang" by 
>> Charles Lineweaver and Tamara Davis at 
>> https://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf 
>> (distilled from their more technical review 'Expanding Confusion' at 
>> https://arxiv.org/abs/astro-ph/0310808 ) covers this question on p. 
>> 42-43, along with other common misconceptions:
>>
>> "Running to Stay Still
>> the idea of seeing faster-than-light galaxies may sound mystical, but it 
>> is made possible by changes in the expansion rate. Imagine a light beam 
>> that is farther than the Hubble distance of 14 billion light-years and 
>> trying to travel in our direction. It is moving toward us at the speed of 
>> light with respect to its local space, but its local space is receding from 
>> us faster than the speed of light. Although the light beam is traveling 
>> toward us at the maximum speed possible, it cannot keep up with the 
>> stretching of space. It is a bit like a child trying to run the wrong way 
>> on a moving sidewalk. Photons at the Hubble distance are like the Red Queen 
>> and Alice, running as fast as they can just to stay in the same place.
>>
>> One might conclude that the light beyond the Hubble distance would never 
>> reach us and that its source would be forever undetectable. But the Hubble 
>> distance is not fixed, because the Hubble constant, on which it depends, 
>> changes with time. In particular, the constant is proportional to the rate 
>> of increase in the distance between two galaxies, divided by that distance. 
>> (Any two galaxies can be used for this calculation.) In models of the 
>> universe that fit the observational data, the
>> denominator increases faster than the numerator, so the Hubble constant 
>> decreases. In this way, the Hubble distance gets larger. As it does, light 
>> that was initially just outside the Hubble distance and receding from us 
>> can come within the Hubble distance. The photons then find themselves in a 
>> region of space that is receding slower than the speed of light. Thereafter 
>> they can approach us.
>>
>> The galaxy they came from, though, may continue to recede superluminally. 
>> Thus, we can observe light from galaxies that have always been and will 
>> always be receding faster than the speed of light. Another way to put it is 
>> that the Hubble distance is not fixed and does not mark the edge of the 
>> observable universe.
>>
>>
>> *I don't think this is the consensus view, which is that the Hubble 
>> constant IS constant, and galaxies beyond our event horizon will never be 
>> seen, if the universe in their region is expanding faster than c. AG *
>>
>>
>> Davis and Lineweaver are just reviewing the current consensus view in 
>> that article and paper, not suggesting any new physics. In general 
>> relativity's cosmological solutions there is a time-dependent "Hubble 
>> parameter" whose value at any given cosmological time is called the "Hubble 
>> constant" at that time, but which can change over the long term (see the 
>> first paragraph of 
>> https://lambda.gsfc.nasa.gov/education/graphic_history/hubb_const.html 
>> for example). Astrophysicist Ethan Siegel mentions in an article at 
>> https://bigthink.com/starts-with-a-bang/hubble-constant-changes-time/ 
>> that even in models that don't have accelerating expansion due to the 
>> cosmological constant, the Hubble constant still need not be constant in 
>> time. He explains this by looking at the first Friedmann equation governing 
>> an expanding universe, where a term equivalent to the definition of the 
>> Hubble constant is on the left side of the equality and the right side has 
>> terms for energy density, global curvature of space, and the cosmological 
>> constant. So, in an expanding universe that's spatially flat and has zero 
>> cosmological constant, if the energy density is changing as matter/energy 
>> becomes more spread out, the term equivalent to the Hubble constant must be 
>> changing as well. From the article:
>>
>> "Even if you had a flat Universe (which means you can eliminate the 
>> second term on the right-hand side) and a Universe without a cosmological 
>> constant (which

Re: Trump unfit to serve say 111 former GOP officials and they endorse Harris

2024-09-19 Thread John Clark

On Wed, Sep 18, 2024 at 8:54 PM Brent Meeker  wrote:

* > But no office-holding Republicans.*
>

*Yes, I noticed that too.** And that is why, although I have been a
Republican for most of my life, I will never vote for a Republican again,
not even for dogcatcher. *

 John K ClarkSee what's on my new list at  Extropolis

ddg

>
>

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Re: Radius of the Observable universe

2024-09-19 Thread Jesse Mazer

On Thu, Sep 19, 2024 at 2:57 AM Alan Grayson  wrote:

>
>
> On Wednesday, September 18, 2024 at 7:10:57 PM UTC-6 Alan Grayson wrote:
>
> On Wednesday, September 18, 2024 at 5:30:06 PM UTC-6 Jesse Mazer wrote:
>
> On Wed, Sep 18, 2024 at 2:01 AM Alan Grayson  wrote:
>
>
>
> On Tuesday, September 17, 2024 at 4:20:31 PM UTC-6 Jesse Mazer wrote:
>
> On Tue, Sep 17, 2024 at 2:40 PM Alan Grayson  wrote:
>
>
>
> On Tuesday, September 17, 2024 at 10:12:53 AM UTC-6 Jesse Mazer wrote:
>
> On Mon, Sep 16, 2024 at 7:41 PM Alan Grayson  wrote:
>
>
>
> On Monday, September 16, 2024 at 12:17:45 PM UTC-6 Jesse Mazer wrote:
>
> The Scientific American article "Misconceptions About The Big Bang" by
> Charles Lineweaver and Tamara Davis at
> https://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf
> (distilled from their more technical review 'Expanding Confusion' at
> https://arxiv.org/abs/astro-ph/0310808 ) covers this question on p.
> 42-43, along with other common misconceptions:
>
> "Running to Stay Still
> the idea of seeing faster-than-light galaxies may sound mystical, but it
> is made possible by changes in the expansion rate. Imagine a light beam
> that is farther than the Hubble distance of 14 billion light-years and
> trying to travel in our direction. It is moving toward us at the speed of
> light with respect to its local space, but its local space is receding from
> us faster than the speed of light. Although the light beam is traveling
> toward us at the maximum speed possible, it cannot keep up with the
> stretching of space. It is a bit like a child trying to run the wrong way
> on a moving sidewalk. Photons at the Hubble distance are like the Red Queen
> and Alice, running as fast as they can just to stay in the same place.
>
> One might conclude that the light beyond the Hubble distance would never
> reach us and that its source would be forever undetectable. But the Hubble
> distance is not fixed, because the Hubble constant, on which it depends,
> changes with time. In particular, the constant is proportional to the rate
> of increase in the distance between two galaxies, divided by that distance.
> (Any two galaxies can be used for this calculation.) In models of the
> universe that fit the observational data, the
> denominator increases faster than the numerator, so the Hubble constant
> decreases. In this way, the Hubble distance gets larger. As it does, light
> that was initially just outside the Hubble distance and receding from us
> can come within the Hubble distance. The photons then find themselves in a
> region of space that is receding slower than the speed of light. Thereafter
> they can approach us.
>
> The galaxy they came from, though, may continue to recede superluminally.
> Thus, we can observe light from galaxies that have always been and will
> always be receding faster than the speed of light. Another way to put it is
> that the Hubble distance is not fixed and does not mark the edge of the
> observable universe.
>
>
> *I don't think this is the consensus view, which is that the Hubble
> constant IS constant, and galaxies beyond our event horizon will never be
> seen, if the universe in their region is expanding faster than c. AG *
>
>
> Davis and Lineweaver are just reviewing the current consensus view in that
> article and paper, not suggesting any new physics. In general relativity's
> cosmological solutions there is a time-dependent "Hubble parameter" whose
> value at any given cosmological time is called the "Hubble constant" at
> that time, but which can change over the long term (see the first paragraph
> of https://lambda.gsfc.nasa.gov/education/graphic_history/hubb_const.html
> for example). Astrophysicist Ethan Siegel mentions in an article at
> https://bigthink.com/starts-with-a-bang/hubble-constant-changes-time/
> that even in models that don't have accelerating expansion due to the
> cosmological constant, the Hubble constant still need not be constant in
> time. He explains this by looking at the first Friedmann equation governing
> an expanding universe, where a term equivalent to the definition of the
> Hubble constant is on the left side of the equality and the right side has
> terms for energy density, global curvature of space, and the cosmological
> constant. So, in an expanding universe that's spatially flat and has zero
> cosmological constant, if the energy density is changing as matter/energy
> becomes more spread out, the term equivalent to the Hubble constant must be
> changing as well. From the article:
>
> "Even if you had a flat Universe (which means you can eliminate the second
> term on the right-hand side) and a Universe without a cosmological constant
> (which would mean eliminating the third term on the right-hand side, too),
> you’d understand immediately that the Hubble “constant” cannot be a
> constant in time.
> ...
> In all cases except for a cosmological constant (i.e., dark energy, to the
> best of our understanding), the energy den

Re: Flat universe implies no Big Bang and Singularity at T = 0



On Wednesday, September 18, 2024 at 7:23:38 PM UTC-6 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 7:02:12 PM UTC-6 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 6:50:53 PM UTC-6 Brent Meeker wrote:




On 9/18/2024 5:19 AM, John Clark wrote:



On Wed, Sep 18, 2024 at 8:12 AM Alan Grayson  wrote:



On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson  wrote:

*I'll get back to you on this. I was thinking, as x increases positively or 
negatively, the y values (angles) repeat multiple times, making the 
function many-to-one. In this case, we're mapping all the real numbers, to 
a subset of the y-axis. Am I mistaken? AG *


*Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  
So your plot seems wrong, but it's what is on the Internet. AG *


*That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I 
still think the plot keeps repeating as x increases or decreases. AG*

[image: image.png]


*1) **The range of the Arctangent function is the interval (-π/2,π/2) and 
its range is all the real numbers.*

* 2) By dividing by π,  the range scales to (-1/2, 1/2).*

* 3) Adding 1/2 shifts the range to (0,1) *

*4) Thus for every real number x there is a unique number y between zero 
and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) . 
As I said before, the domain is all the real numbers and the range is (0,1)*
 


*> Yes, but initially you were seeking a 1-1 function, but this one is 
many-to-one. AG *

 FOR DARWIN'S SAKE! I GIVE UP!


Could'a told ya.

Brent


*Why are you so inclined to join the asshole club? I just made an error. 
Are you immune from that? AG*


 *I conjectured that Inflation caused the unobservable universe to come 
into existence, an original thought you ignore, but your inclination is to 
be petty. Too many physicists are revealed to be a'holes and I see no cure 
for that. AG*


*I admit it's puzzling. Whereas tangent 0 degrees = tangent 360 degrees = 
0, and arctan 0 degrees = 0, I thought arctan 360 degrees is also 0, but it 
apparently isn't. This is how I concluded y = arctan(x) is many-to-one. AG*

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Re: Radius of the Observable universe



On Wednesday, September 18, 2024 at 7:10:57 PM UTC-6 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 5:30:06 PM UTC-6 Jesse Mazer wrote:

On Wed, Sep 18, 2024 at 2:01 AM Alan Grayson  wrote:



On Tuesday, September 17, 2024 at 4:20:31 PM UTC-6 Jesse Mazer wrote:

On Tue, Sep 17, 2024 at 2:40 PM Alan Grayson  wrote:



On Tuesday, September 17, 2024 at 10:12:53 AM UTC-6 Jesse Mazer wrote:

On Mon, Sep 16, 2024 at 7:41 PM Alan Grayson  wrote:



On Monday, September 16, 2024 at 12:17:45 PM UTC-6 Jesse Mazer wrote:

The Scientific American article "Misconceptions About The Big Bang" by 
Charles Lineweaver and Tamara Davis at 
https://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf 
(distilled from their more technical review 'Expanding Confusion' at 
https://arxiv.org/abs/astro-ph/0310808 ) covers this question on p. 42-43, 
along with other common misconceptions:

"Running to Stay Still
the idea of seeing faster-than-light galaxies may sound mystical, but it is 
made possible by changes in the expansion rate. Imagine a light beam that 
is farther than the Hubble distance of 14 billion light-years and trying to 
travel in our direction. It is moving toward us at the speed of light with 
respect to its local space, but its local space is receding from us faster 
than the speed of light. Although the light beam is traveling toward us at 
the maximum speed possible, it cannot keep up with the stretching of space. 
It is a bit like a child trying to run the wrong way on a moving sidewalk. 
Photons at the Hubble distance are like the Red Queen and Alice, running as 
fast as they can just to stay in the same place.

One might conclude that the light beyond the Hubble distance would never 
reach us and that its source would be forever undetectable. But the Hubble 
distance is not fixed, because the Hubble constant, on which it depends, 
changes with time. In particular, the constant is proportional to the rate 
of increase in the distance between two galaxies, divided by that distance. 
(Any two galaxies can be used for this calculation.) In models of the 
universe that fit the observational data, the
denominator increases faster than the numerator, so the Hubble constant 
decreases. In this way, the Hubble distance gets larger. As it does, light 
that was initially just outside the Hubble distance and receding from us 
can come within the Hubble distance. The photons then find themselves in a 
region of space that is receding slower than the speed of light. Thereafter 
they can approach us.

The galaxy they came from, though, may continue to recede superluminally. 
Thus, we can observe light from galaxies that have always been and will 
always be receding faster than the speed of light. Another way to put it is 
that the Hubble distance is not fixed and does not mark the edge of the 
observable universe.


*I don't think this is the consensus view, which is that the Hubble 
constant IS constant, and galaxies beyond our event horizon will never be 
seen, if the universe in their region is expanding faster than c. AG *


Davis and Lineweaver are just reviewing the current consensus view in that 
article and paper, not suggesting any new physics. In general relativity's 
cosmological solutions there is a time-dependent "Hubble parameter" whose 
value at any given cosmological time is called the "Hubble constant" at 
that time, but which can change over the long term (see the first paragraph 
of https://lambda.gsfc.nasa.gov/education/graphic_history/hubb_const.html 
for example). Astrophysicist Ethan Siegel mentions in an article at 
https://bigthink.com/starts-with-a-bang/hubble-constant-changes-time/ that 
even in models that don't have accelerating expansion due to the 
cosmological constant, the Hubble constant still need not be constant in 
time. He explains this by looking at the first Friedmann equation governing 
an expanding universe, where a term equivalent to the definition of the 
Hubble constant is on the left side of the equality and the right side has 
terms for energy density, global curvature of space, and the cosmological 
constant. So, in an expanding universe that's spatially flat and has zero 
cosmological constant, if the energy density is changing as matter/energy 
becomes more spread out, the term equivalent to the Hubble constant must be 
changing as well. From the article:

"Even if you had a flat Universe (which means you can eliminate the second 
term on the right-hand side) and a Universe without a cosmological constant 
(which would mean eliminating the third term on the right-hand side, too), 
you’d understand immediately that the Hubble “constant” cannot be a 
constant in time.
...
In all cases except for a cosmological constant (i.e., dark energy, to the 
best of our understanding), the energy density changes as the Universe 
expands.
If the energy density changes, that means the expansion rate changes, too. 
The Hubble constant is only a constant everywhere in s

Re: Flat universe implies no Big Bang and Singularity at T = 0



On Wednesday, September 18, 2024 at 7:34:58 AM UTC-6 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 6:33:35 AM UTC-6 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 6:20:04 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 8:12 AM Alan Grayson  wrote:



On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson  wrote:

*I'll get back to you on this. I was thinking, as x increases positively or 
negatively, the y values (angles) repeat multiple times, making the 
function many-to-one. In this case, we're mapping all the real numbers, to 
a subset of the y-axis. Am I mistaken? AG *


*Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  
So your plot seems wrong, but it's what is on the Internet. AG *


*That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I 
still think the plot keeps repeating as x increases or decreases. AG*

[image: image.png]


*1) **The range of the Arctangent function is the interval (-π/2,π/2) and 
its range is all the real numbers.*

*2) By dividing by π,  the range scales to (-1/2, 1/2).*

*3) Adding 1/2 shifts the range to (0,1) *

*4) Thus for every real number x there is a unique number y between zero 
and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) . 
As I said before, the domain is all the real numbers and the range is (0,1)*
 


*> Yes, but initially you were seeking a 1-1 function, but this one is 
many-to-one. AG *

 FOR DARWIN'S SAKE! I GIVE UP!


*Y**ou ought to cease being a juvenile a'hole. At each x, we get a value of 
y, but this image repeats as x is incremented by 2pi. Same situation at 
every x in the domain. Thus, many-to-one. But what really interests me is 
my claim/proof that an infinite universe must be eternal and hence is not 
subject to a creation. AG*


*I could be mistaken about arctan function. I'll check this again. AG*


*I admit it's puzzling. Whereas tangent 0 degrees = tangent 360 degrees = 
0, and arctan 0 degrees = 0, arctan 360 degrees ne 0. This is how I 
concluded y = arctan(x) is many-to-one. AG*

 

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Re: Flat universe implies no Big Bang and Singularity at T = 0



On Wednesday, September 18, 2024 at 7:02:12 PM UTC-6 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 6:50:53 PM UTC-6 Brent Meeker wrote:




On 9/18/2024 5:19 AM, John Clark wrote:



On Wed, Sep 18, 2024 at 8:12 AM Alan Grayson  wrote:



On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson  wrote:

*I'll get back to you on this. I was thinking, as x increases positively or 
negatively, the y values (angles) repeat multiple times, making the 
function many-to-one. In this case, we're mapping all the real numbers, to 
a subset of the y-axis. Am I mistaken? AG *


*Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  
So your plot seems wrong, but it's what is on the Internet. AG *


*That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I 
still think the plot keeps repeating as x increases or decreases. AG*

[image: image.png]


*1) **The range of the Arctangent function is the interval (-π/2,π/2) and 
its range is all the real numbers.*

* 2) By dividing by π,  the range scales to (-1/2, 1/2).*

* 3) Adding 1/2 shifts the range to (0,1) *

*4) Thus for every real number x there is a unique number y between zero 
and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) . 
As I said before, the domain is all the real numbers and the range is (0,1)*
 


*> Yes, but initially you were seeking a 1-1 function, but this one is 
many-to-one. AG *

 FOR DARWIN'S SAKE! I GIVE UP!


Could'a told ya.

Brent


*Why are you so inclined to join the asshole club? I just made an error. 
Are you immune from that? AG*


 *I conjectured that Inflation caused the unobservable universe to come 
into existence, an original thought you ignore, but your inclination is to 
be petty. Too many physicists are revealed to be a'holes and I see no cure 
for that. AG*

Reply all
Reply to author
Forwar

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Re: Flat universe implies no Big Bang and Singularity at T = 0



On Wednesday, September 18, 2024 at 7:02:12 PM UTC-6 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 6:50:53 PM UTC-6 Brent Meeker wrote:




On 9/18/2024 5:19 AM, John Clark wrote:



On Wed, Sep 18, 2024 at 8:12 AM Alan Grayson  wrote:



On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson  wrote:

*I'll get back to you on this. I was thinking, as x increases positively or 
negatively, the y values (angles) repeat multiple times, making the 
function many-to-one. In this case, we're mapping all the real numbers, to 
a subset of the y-axis. Am I mistaken? AG *


*Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  
So your plot seems wrong, but it's what is on the Internet. AG *


*That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I 
still think the plot keeps repeating as x increases or decreases. AG*

[image: image.png]


*1) **The range of the Arctangent function is the interval (-π/2,π/2) and 
its range is all the real numbers.*

* 2) By dividing by π,  the range scales to (-1/2, 1/2).*

* 3) Adding 1/2 shifts the range to (0,1) *

*4) Thus for every real number x there is a unique number y between zero 
and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) . 
As I said before, the domain is all the real numbers and the range is (0,1)*
 


*> Yes, but initially you were seeking a 1-1 function, but this one is 
many-to-one. AG *

 FOR DARWIN'S SAKE! I GIVE UP!


Could'a told ya.

Brent


*Why are you so inclined to join the asshole club? I just made an error. 
Are you immune from that? AG*


*I conjectured that Inflation caused the unobservable universe to come into 
existence, an original thought you ignore, but your inclination is to be 
petty. Too many physicists are revealed to be a'holes and I see no cure 
that. AG*

-- 
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Re: Radius of the Observable universe



On Wednesday, September 18, 2024 at 5:30:06 PM UTC-6 Jesse Mazer wrote:

On Wed, Sep 18, 2024 at 2:01 AM Alan Grayson  wrote:



On Tuesday, September 17, 2024 at 4:20:31 PM UTC-6 Jesse Mazer wrote:

On Tue, Sep 17, 2024 at 2:40 PM Alan Grayson  wrote:



On Tuesday, September 17, 2024 at 10:12:53 AM UTC-6 Jesse Mazer wrote:

On Mon, Sep 16, 2024 at 7:41 PM Alan Grayson  wrote:



On Monday, September 16, 2024 at 12:17:45 PM UTC-6 Jesse Mazer wrote:

The Scientific American article "Misconceptions About The Big Bang" by 
Charles Lineweaver and Tamara Davis at 
https://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf 
(distilled from their more technical review 'Expanding Confusion' at 
https://arxiv.org/abs/astro-ph/0310808 ) covers this question on p. 42-43, 
along with other common misconceptions:

"Running to Stay Still
the idea of seeing faster-than-light galaxies may sound mystical, but it is 
made possible by changes in the expansion rate. Imagine a light beam that 
is farther than the Hubble distance of 14 billion light-years and trying to 
travel in our direction. It is moving toward us at the speed of light with 
respect to its local space, but its local space is receding from us faster 
than the speed of light. Although the light beam is traveling toward us at 
the maximum speed possible, it cannot keep up with the stretching of space. 
It is a bit like a child trying to run the wrong way on a moving sidewalk. 
Photons at the Hubble distance are like the Red Queen and Alice, running as 
fast as they can just to stay in the same place.

One might conclude that the light beyond the Hubble distance would never 
reach us and that its source would be forever undetectable. But the Hubble 
distance is not fixed, because the Hubble constant, on which it depends, 
changes with time. In particular, the constant is proportional to the rate 
of increase in the distance between two galaxies, divided by that distance. 
(Any two galaxies can be used for this calculation.) In models of the 
universe that fit the observational data, the
denominator increases faster than the numerator, so the Hubble constant 
decreases. In this way, the Hubble distance gets larger. As it does, light 
that was initially just outside the Hubble distance and receding from us 
can come within the Hubble distance. The photons then find themselves in a 
region of space that is receding slower than the speed of light. Thereafter 
they can approach us.

The galaxy they came from, though, may continue to recede superluminally. 
Thus, we can observe light from galaxies that have always been and will 
always be receding faster than the speed of light. Another way to put it is 
that the Hubble distance is not fixed and does not mark the edge of the 
observable universe.


*I don't think this is the consensus view, which is that the Hubble 
constant IS constant, and galaxies beyond our event horizon will never be 
seen, if the universe in their region is expanding faster than c. AG *


Davis and Lineweaver are just reviewing the current consensus view in that 
article and paper, not suggesting any new physics. In general relativity's 
cosmological solutions there is a time-dependent "Hubble parameter" whose 
value at any given cosmological time is called the "Hubble constant" at 
that time, but which can change over the long term (see the first paragraph 
of https://lambda.gsfc.nasa.gov/education/graphic_history/hubb_const.html 
for example). Astrophysicist Ethan Siegel mentions in an article at 
https://bigthink.com/starts-with-a-bang/hubble-constant-changes-time/ that 
even in models that don't have accelerating expansion due to the 
cosmological constant, the Hubble constant still need not be constant in 
time. He explains this by looking at the first Friedmann equation governing 
an expanding universe, where a term equivalent to the definition of the 
Hubble constant is on the left side of the equality and the right side has 
terms for energy density, global curvature of space, and the cosmological 
constant. So, in an expanding universe that's spatially flat and has zero 
cosmological constant, if the energy density is changing as matter/energy 
becomes more spread out, the term equivalent to the Hubble constant must be 
changing as well. From the article:

"Even if you had a flat Universe (which means you can eliminate the second 
term on the right-hand side) and a Universe without a cosmological constant 
(which would mean eliminating the third term on the right-hand side, too), 
you’d understand immediately that the Hubble “constant” cannot be a 
constant in time.
...
In all cases except for a cosmological constant (i.e., dark energy, to the 
best of our understanding), the energy density changes as the Universe 
expands.
If the energy density changes, that means the expansion rate changes, too. 
The Hubble constant is only a constant everywhere in space, as we measure 
it right now. It’s not a constant in the sense that i

Re: Flat universe implies no Big Bang and Singularity at T = 0



On Wednesday, September 18, 2024 at 6:50:53 PM UTC-6 Brent Meeker wrote:




On 9/18/2024 5:19 AM, John Clark wrote:



On Wed, Sep 18, 2024 at 8:12 AM Alan Grayson  wrote:



On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson  wrote:

*I'll get back to you on this. I was thinking, as x increases positively or 
negatively, the y values (angles) repeat multiple times, making the 
function many-to-one. In this case, we're mapping all the real numbers, to 
a subset of the y-axis. Am I mistaken? AG *


*Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  
So your plot seems wrong, but it's what is on the Internet. AG *


*That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I 
still think the plot keeps repeating as x increases or decreases. AG*

[image: image.png]


*1) **The range of the Arctangent function is the interval (-π/2,π/2) and 
its range is all the real numbers.*

* 2) By dividing by π,  the range scales to (-1/2, 1/2).*

* 3) Adding 1/2 shifts the range to (0,1) *

*4) Thus for every real number x there is a unique number y between zero 
and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) . 
As I said before, the domain is all the real numbers and the range is (0,1)*
 


*> Yes, but initially you were seeking a 1-1 function, but this one is 
many-to-one. AG *

 FOR DARWIN'S SAKE! I GIVE UP!


Could'a told ya.

Brent


*Why are you so inclined to join the asshole club? I just made an error. 
Are you immune from that? AG*


 John K ClarkSee what's on my new list at  Extropolis 


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Re: Trump unfit to serve say 111 former GOP officials and they endorse Harris

2024-09-18 Thread Brent Meeker

But no office-holding Republicans.

Brent

On 9/18/2024 6:20 AM, John Clark wrote:
*111 high-ranking Republicans have signed a letter castigating
DonaldTrump and supporting Kamala Harris. In addition to a bunch of
admirals and generals the letter was signed by two former defense
secretaries, a former president of the World Bank, two former C.I.A.
directors, a former director of national intelligence, a former
governor, two members of Trump's presidential administration, and 4
former members of the House of Representatives. Republicans all. *

*
*
*They say Trump had demonstrated “dangerous qualities including an
unusual affinity for dictators like President Vladimir Putin of
Russia and contempt for the norms of decent, ethical and lawful
behavior. As president, he promoted daily chaos in government, praised
our enemies and undermined our allies, politicized the military and
disparaged our veterans, prioritized his personal interest above
American interests and betrayed our values, democracy and this
country’s founding documents. He has violated his oath of office and
brought danger to our country.”*

*
*
*And they say “/_any potential concerns about Ms. Harris pale in
comparison to those over Mr. Trumps'._/*

*Trump "unfit to serve" say 111 Former G.O.P. Officials and back
Harris*

John K Clark See what's on my new list at Extropolis

tus
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Re: Flat universe implies no Big Bang and Singularity at T = 0

2024-09-18 Thread Brent Meeker





On 9/18/2024 5:19 AM, John Clark wrote:



On Wed, Sep 18, 2024 at 8:12 AM Alan Grayson  
wrote:




On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson
 wrote:

*I'll get back to you on this. I was thinking, as
x increases positively or negatively, the y values
(angles) repeat multiple times, making the
function _many-to-one_. In this case, we're
mapping all the real numbers, to a subset of the
y-axis. Am I mistaken? AG *


*Arctan(1) = the angle whose tangent = 1. Isn't this
angle 90 deg or pi/2?  So your plot seems wrong, but
it's what is on the Internet. AG *


*That's wrong. Arctan(1) = pi/4, which is what the plot
indicates. But I still think the plot keeps repeating as x
increases or decreases. AG*

image.png


*1) **The range of the Arctangent function is the interval
(-π/2,π/2) and its range is all the real numbers.*
*
2) By dividing by π,  the rangescales to (-1/2, 1/2).*
*
3) Adding 1/2 shifts the range to (0,1) *

*4) Thus for every real numberx there is a unique number y
between zero and one that corresponds to it, and that number
is Y=1/2 + 1/π Arctan(x) . As I said before, the domain is all
the real numbers and the range is (0,1)*


*> Yes, but initially you were seeking a 1-1 function, but this
one is many-to-one. AG *

 FOR DARWIN'S SAKE! I GIVE UP!


Could'a told ya.

Brent


John K Clark    See what's on my new list at Extropolis 



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Re: Radius of the Observable universe

2024-09-18 Thread Jesse Mazer

On Wed, Sep 18, 2024 at 2:01 AM Alan Grayson  wrote:

>
>
> On Tuesday, September 17, 2024 at 4:20:31 PM UTC-6 Jesse Mazer wrote:
>
> On Tue, Sep 17, 2024 at 2:40 PM Alan Grayson  wrote:
>
>
>
> On Tuesday, September 17, 2024 at 10:12:53 AM UTC-6 Jesse Mazer wrote:
>
> On Mon, Sep 16, 2024 at 7:41 PM Alan Grayson  wrote:
>
>
>
> On Monday, September 16, 2024 at 12:17:45 PM UTC-6 Jesse Mazer wrote:
>
> The Scientific American article "Misconceptions About The Big Bang" by
> Charles Lineweaver and Tamara Davis at
> https://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf
> (distilled from their more technical review 'Expanding Confusion' at
> https://arxiv.org/abs/astro-ph/0310808 ) covers this question on p.
> 42-43, along with other common misconceptions:
>
> "Running to Stay Still
> the idea of seeing faster-than-light galaxies may sound mystical, but it
> is made possible by changes in the expansion rate. Imagine a light beam
> that is farther than the Hubble distance of 14 billion light-years and
> trying to travel in our direction. It is moving toward us at the speed of
> light with respect to its local space, but its local space is receding from
> us faster than the speed of light. Although the light beam is traveling
> toward us at the maximum speed possible, it cannot keep up with the
> stretching of space. It is a bit like a child trying to run the wrong way
> on a moving sidewalk. Photons at the Hubble distance are like the Red Queen
> and Alice, running as fast as they can just to stay in the same place.
>
> One might conclude that the light beyond the Hubble distance would never
> reach us and that its source would be forever undetectable. But the Hubble
> distance is not fixed, because the Hubble constant, on which it depends,
> changes with time. In particular, the constant is proportional to the rate
> of increase in the distance between two galaxies, divided by that distance.
> (Any two galaxies can be used for this calculation.) In models of the
> universe that fit the observational data, the
> denominator increases faster than the numerator, so the Hubble constant
> decreases. In this way, the Hubble distance gets larger. As it does, light
> that was initially just outside the Hubble distance and receding from us
> can come within the Hubble distance. The photons then find themselves in a
> region of space that is receding slower than the speed of light. Thereafter
> they can approach us.
>
> The galaxy they came from, though, may continue to recede superluminally.
> Thus, we can observe light from galaxies that have always been and will
> always be receding faster than the speed of light. Another way to put it is
> that the Hubble distance is not fixed and does not mark the edge of the
> observable universe.
>
>
> *I don't think this is the consensus view, which is that the Hubble
> constant IS constant, and galaxies beyond our event horizon will never be
> seen, if the universe in their region is expanding faster than c. AG *
>
>
> Davis and Lineweaver are just reviewing the current consensus view in that
> article and paper, not suggesting any new physics. In general relativity's
> cosmological solutions there is a time-dependent "Hubble parameter" whose
> value at any given cosmological time is called the "Hubble constant" at
> that time, but which can change over the long term (see the first paragraph
> of https://lambda.gsfc.nasa.gov/education/graphic_history/hubb_const.html
> for example). Astrophysicist Ethan Siegel mentions in an article at
> https://bigthink.com/starts-with-a-bang/hubble-constant-changes-time/
> that even in models that don't have accelerating expansion due to the
> cosmological constant, the Hubble constant still need not be constant in
> time. He explains this by looking at the first Friedmann equation governing
> an expanding universe, where a term equivalent to the definition of the
> Hubble constant is on the left side of the equality and the right side has
> terms for energy density, global curvature of space, and the cosmological
> constant. So, in an expanding universe that's spatially flat and has zero
> cosmological constant, if the energy density is changing as matter/energy
> becomes more spread out, the term equivalent to the Hubble constant must be
> changing as well. From the article:
>
> "Even if you had a flat Universe (which means you can eliminate the second
> term on the right-hand side) and a Universe without a cosmological constant
> (which would mean eliminating the third term on the right-hand side, too),
> you’d understand immediately that the Hubble “constant” cannot be a
> constant in time.
> ...
> In all cases except for a cosmological constant (i.e., dark energy, to the
> best of our understanding), the energy density changes as the Universe
> expands.
> If the energy density changes, that means the expansion rate changes, too.
> The Hubble constant is only a constant everywhere in space, as we measure
> it right now. It’s

Re: Flat universe implies no Big Bang and Singularity at T = 0



On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson  wrote:

*I'll get back to you on this. I was thinking, as x increases positively or 
negatively, the y values (angles) repeat multiple times, making the 
function many-to-one. In this case, we're mapping all the real numbers, to 
a subset of the y-axis. Am I mistaken? AG *


*Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  
So your plot seems wrong, but it's what is on the Internet. AG *


*That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I 
still think the plot keeps repeating as x increases or decreases. AG*

[image: image.png]


*1) **The range of the Arctangent function is the interval (-π/2,π/2) and 
its range is all the real numbers.*


*What's the protocol here; to rant about Darwin because you have a typo 
above? AG *


*2) By dividing by π,  the range scales to (-1/2, 1/2).*

*3) Adding 1/2 shifts the range to (0,1) *

*4) Thus for every real number x there is a unique number y between zero 
and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) . 
As I said before, the domain is all the real numbers and the range is (0,1)*

 John K ClarkSee what's on my new list at  Extropolis 

rdi


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Re: Flat universe implies no Big Bang and Singularity at T = 0



On Wednesday, September 18, 2024 at 6:33:35 AM UTC-6 Alan Grayson wrote:

On Wednesday, September 18, 2024 at 6:20:04 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 8:12 AM Alan Grayson  wrote:



On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson  wrote:

*I'll get back to you on this. I was thinking, as x increases positively or 
negatively, the y values (angles) repeat multiple times, making the 
function many-to-one. In this case, we're mapping all the real numbers, to 
a subset of the y-axis. Am I mistaken? AG *


*Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  
So your plot seems wrong, but it's what is on the Internet. AG *


*That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I 
still think the plot keeps repeating as x increases or decreases. AG*

[image: image.png]


*1) **The range of the Arctangent function is the interval (-π/2,π/2) and 
its range is all the real numbers.*

*2) By dividing by π,  the range scales to (-1/2, 1/2).*

*3) Adding 1/2 shifts the range to (0,1) *

*4) Thus for every real number x there is a unique number y between zero 
and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) . 
As I said before, the domain is all the real numbers and the range is (0,1)*
 


*> Yes, but initially you were seeking a 1-1 function, but this one is 
many-to-one. AG *

 FOR DARWIN'S SAKE! I GIVE UP!


*Y**ou ought to cease being a juvenile a'hole. At each x, we get a value of 
y, but this image repeats as x is incremented by 2pi. Same situation at 
every x in the domain. Thus, many-to-one. But what really interests me is 
my claim/proof that an infinite universe must be eternal and hence is not 
subject to a creation. AG*


*I could be mistaken about arctan function. I'll check this again. AG *

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Re: Radius of the Observable universe

On Wednesday, September 18, 2024 at 6:14:21 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 2:01 AM Alan Grayson wrote:

*> I can't see how anything can recede at velocity > c and remain within
our Observable Universe. *

*It sure the hell was moving away faster than light speed due to Inflation.
In fact, it was Inflation that caused the UNobservable universe to come
into existence. AG*

*Thus even though we can see the galaxy we could NEVER travel to it, not
even if we could move at the speed of light, not even in an infinite number
of years. You can object to the definition of "observable universe" if you
want to but remember we can NOT observe ANYTHING as it is now. It takes a
finite amount of time for light to go from the tip of your nose to your
eye, so even that observation is in the past.*

*Our observational horizon is shrinking, in about 1 trillion years we will
not be able to see any galaxies except those in our local group, and they
would probably all have merged into a single large globular galaxy by
then. So if there are any astronomers around in 1 trillion years they will
incorrectly conclude what astronomers in the early 20th century concluded,
the entire universe consists of just one galaxy surrounded by an infinity
of nothingness. That is to say surrounded by an infinite boundless
homogeneity. *

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Re: Flat universe implies no Big Bang and Singularity at T = 0



On Wednesday, September 18, 2024 at 6:20:04 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 8:12 AM Alan Grayson  wrote:



On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson  wrote:

*I'll get back to you on this. I was thinking, as x increases positively or 
negatively, the y values (angles) repeat multiple times, making the 
function many-to-one. In this case, we're mapping all the real numbers, to 
a subset of the y-axis. Am I mistaken? AG *


*Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  
So your plot seems wrong, but it's what is on the Internet. AG *


*That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I 
still think the plot keeps repeating as x increases or decreases. AG*

[image: image.png]


*1) **The range of the Arctangent function is the interval (-π/2,π/2) and 
its range is all the real numbers.*

*2) By dividing by π,  the range scales to (-1/2, 1/2).*

*3) Adding 1/2 shifts the range to (0,1) *

*4) Thus for every real number x there is a unique number y between zero 
and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) . 
As I said before, the domain is all the real numbers and the range is (0,1)*
 


*> Yes, but initially you were seeking a 1-1 function, but this one is 
many-to-one. AG *

 FOR DARWIN'S SAKE! I GIVE UP!


*Y**ou ought to cease being a juvenile a'hole. At each x, we get a value of 
y, but this image repeats as x is incremented by 2pi. Same situation at 
every x in the domain. Thus, many-to-one. But what really interests me is 
my claim/proof that an infinite universe must be eternal and hence is not 
subject to a creation. AG*

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Re: Flat universe implies no Big Bang and Singularity at T = 0

2024-09-18 Thread John Clark

On Wed, Sep 18, 2024 at 8:12 AM Alan Grayson  wrote:

>
>
> On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote:
>
> On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson  wrote:
>
> *I'll get back to you on this. I was thinking, as x increases positively
> or negatively, the y values (angles) repeat multiple times, making the
> function many-to-one. In this case, we're mapping all the real numbers, to
> a subset of the y-axis. Am I mistaken? AG *
>
>
> *Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or
> pi/2?  So your plot seems wrong, but it's what is on the Internet. AG *
>
>
> *That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I
> still think the plot keeps repeating as x increases or decreases. AG*
>
> [image: image.png]
>
>
> *1) **The range of the Arctangent function is the interval (-π/2,π/2) and
> its range is all the real numbers.*
>
> *2) By dividing by π,  the range scales to (-1/2, 1/2).*
>
> *3) Adding 1/2 shifts the range to (0,1) *
>
> *4) Thus for every real number x there is a unique number y between zero
> and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) .
> As I said before, the domain is all the real numbers and the range is (0,1)*
>
>
>
> *> Yes, but initially you were seeking a 1-1 function, but this one is
> many-to-one. AG *
>
>  FOR DARWIN'S SAKE! I GIVE UP!

 John K ClarkSee what's on my new list at  Extropolis

ugi

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Re: Radius of the Observable universe

2024-09-18 Thread John Clark

On Wed, Sep 18, 2024 at 2:01 AM Alan Grayson wrote:

*> I can't see how anything can recede at velocity > c and remain within
> our Observable Universe. *

*We can observe a very distant galaxy even though it is now moving away
from us faster than the speed of light because we are not observing the
galaxy as it is now, we are observing it as it was 13 billion years ago;
and back then it was NOT moving away from us faster than the speed of
light. Thus even though we can see the galaxy we could NEVER travel to it,
not even if we could move at the speed of light, not even in an infinite
number of years. You can object to the definition of "observable universe"
if you want to but remember we can NOT observe ANYTHING as it is now. It
takes a finite amount of time for light to go from the tip of your nose to
your eye, so even that observation is in the past.*

John K ClarkSee what's on my new list at Extropolis

ius

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Re: Flat universe implies no Big Bang and Singularity at T = 0



On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote:

On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson  wrote:

*I'll get back to you on this. I was thinking, as x increases positively or 
negatively, the y values (angles) repeat multiple times, making the 
function many-to-one. In this case, we're mapping all the real numbers, to 
a subset of the y-axis. Am I mistaken? AG *


*Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  
So your plot seems wrong, but it's what is on the Internet. AG *


*That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I 
still think the plot keeps repeating as x increases or decreases. AG*

[image: image.png]


*1) **The range of the Arctangent function is the interval (-π/2,π/2) and 
its range is all the real numbers.*

*2) By dividing by π,  the range scales to (-1/2, 1/2).*

*3) Adding 1/2 shifts the range to (0,1) *

*4) Thus for every real number x there is a unique number y between zero 
and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) . 
As I said before, the domain is all the real numbers and the range is (0,1)*
 


*Yes, but initially you were seeking a 1-1 function, but this one is 
many-to-one. AG *

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Re: Flat universe implies no Big Bang and Singularity at T = 0

2024-09-18 Thread John Clark

On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson  wrote:

*I'll get back to you on this. I was thinking, as x increases positively or
> negatively, the y values (angles) repeat multiple times, making the
> function many-to-one. In this case, we're mapping all the real numbers, to
> a subset of the y-axis. Am I mistaken? AG *
>
>
> *Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or
> pi/2?  So your plot seems wrong, but it's what is on the Internet. AG *
>
>
> *That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I
> still think the plot keeps repeating as x increases or decreases. AG*
>
> [image: image.png]
>

*1) **The range of the Arctangent function is the interval (-π/2,π/2) and
its range is all the real numbers.*

*2) By dividing by π,  the range scales to (-1/2, 1/2).*

*3) Adding 1/2 shifts the range to (0,1) *

*4) Thus for every real number x there is a unique number y between zero
and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) .
As I said before, the domain is all the real numbers and the range is (0,1)*

 John K ClarkSee what's on my new list at  Extropolis

rdi

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Re: Radius of the Observable universe



On Wednesday, September 18, 2024 at 12:01:13 AM UTC-6 Alan Grayson wrote:

On Tuesday, September 17, 2024 at 4:20:31 PM UTC-6 Jesse Mazer wrote:

On Tue, Sep 17, 2024 at 2:40 PM Alan Grayson  wrote:



On Tuesday, September 17, 2024 at 10:12:53 AM UTC-6 Jesse Mazer wrote:

On Mon, Sep 16, 2024 at 7:41 PM Alan Grayson  wrote:



On Monday, September 16, 2024 at 12:17:45 PM UTC-6 Jesse Mazer wrote:

The Scientific American article "Misconceptions About The Big Bang" by 
Charles Lineweaver and Tamara Davis at 
https://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf 
(distilled from their more technical review 'Expanding Confusion' at 
https://arxiv.org/abs/astro-ph/0310808 ) covers this question on p. 42-43, 
along with other common misconceptions:

"Running to Stay Still
the idea of seeing faster-than-light galaxies may sound mystical, but it is 
made possible by changes in the expansion rate. Imagine a light beam that 
is farther than the Hubble distance of 14 billion light-years and trying to 
travel in our direction. It is moving toward us at the speed of light with 
respect to its local space, but its local space is receding from us faster 
than the speed of light. Although the light beam is traveling toward us at 
the maximum speed possible, it cannot keep up with the stretching of space. 
It is a bit like a child trying to run the wrong way on a moving sidewalk. 
Photons at the Hubble distance are like the Red Queen and Alice, running as 
fast as they can just to stay in the same place.

One might conclude that the light beyond the Hubble distance would never 
reach us and that its source would be forever undetectable. But the Hubble 
distance is not fixed, because the Hubble constant, on which it depends, 
changes with time. In particular, the constant is proportional to the rate 
of increase in the distance between two galaxies, divided by that distance. 
(Any two galaxies can be used for this calculation.) In models of the 
universe that fit the observational data, the
denominator increases faster than the numerator, so the Hubble constant 
decreases. In this way, the Hubble distance gets larger. As it does, light 
that was initially just outside the Hubble distance and receding from us 
can come within the Hubble distance. The photons then find themselves in a 
region of space that is receding slower than the speed of light. Thereafter 
they can approach us.

The galaxy they came from, though, may continue to recede superluminally. 
Thus, we can observe light from galaxies that have always been and will 
always be receding faster than the speed of light. Another way to put it is 
that the Hubble distance is not fixed and does not mark the edge of the 
observable universe.


*I don't think this is the consensus view, which is that the Hubble 
constant IS constant, and galaxies beyond our event horizon will never be 
seen, if the universe in their region is expanding faster than c. AG *


Davis and Lineweaver are just reviewing the current consensus view in that 
article and paper, not suggesting any new physics. In general relativity's 
cosmological solutions there is a time-dependent "Hubble parameter" whose 
value at any given cosmological time is called the "Hubble constant" at 
that time, but which can change over the long term (see the first paragraph 
of https://lambda.gsfc.nasa.gov/education/graphic_history/hubb_const.html 
for example). Astrophysicist Ethan Siegel mentions in an article at 
https://bigthink.com/starts-with-a-bang/hubble-constant-changes-time/ that 
even in models that don't have accelerating expansion due to the 
cosmological constant, the Hubble constant still need not be constant in 
time. He explains this by looking at the first Friedmann equation governing 
an expanding universe, where a term equivalent to the definition of the 
Hubble constant is on the left side of the equality and the right side has 
terms for energy density, global curvature of space, and the cosmological 
constant. So, in an expanding universe that's spatially flat and has zero 
cosmological constant, if the energy density is changing as matter/energy 
becomes more spread out, the term equivalent to the Hubble constant must be 
changing as well. From the article:

"Even if you had a flat Universe (which means you can eliminate the second 
term on the right-hand side) and a Universe without a cosmological constant 
(which would mean eliminating the third term on the right-hand side, too), 
you’d understand immediately that the Hubble “constant” cannot be a 
constant in time.
...
In all cases except for a cosmological constant (i.e., dark energy, to the 
best of our understanding), the energy density changes as the Universe 
expands.
If the energy density changes, that means the expansion rate changes, too. 
The Hubble constant is only a constant everywhere in space, as we measure 
it right now. It’s not a constant in the sense that it changes over time."

Siegel has another article cove

Re: Radius of the Observable universe



On Tuesday, September 17, 2024 at 4:20:31 PM UTC-6 Jesse Mazer wrote:

On Tue, Sep 17, 2024 at 2:40 PM Alan Grayson  wrote:



On Tuesday, September 17, 2024 at 10:12:53 AM UTC-6 Jesse Mazer wrote:

On Mon, Sep 16, 2024 at 7:41 PM Alan Grayson  wrote:



On Monday, September 16, 2024 at 12:17:45 PM UTC-6 Jesse Mazer wrote:

The Scientific American article "Misconceptions About The Big Bang" by 
Charles Lineweaver and Tamara Davis at 
https://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf 
(distilled from their more technical review 'Expanding Confusion' at 
https://arxiv.org/abs/astro-ph/0310808 ) covers this question on p. 42-43, 
along with other common misconceptions:

"Running to Stay Still
the idea of seeing faster-than-light galaxies may sound mystical, but it is 
made possible by changes in the expansion rate. Imagine a light beam that 
is farther than the Hubble distance of 14 billion light-years and trying to 
travel in our direction. It is moving toward us at the speed of light with 
respect to its local space, but its local space is receding from us faster 
than the speed of light. Although the light beam is traveling toward us at 
the maximum speed possible, it cannot keep up with the stretching of space. 
It is a bit like a child trying to run the wrong way on a moving sidewalk. 
Photons at the Hubble distance are like the Red Queen and Alice, running as 
fast as they can just to stay in the same place.

One might conclude that the light beyond the Hubble distance would never 
reach us and that its source would be forever undetectable. But the Hubble 
distance is not fixed, because the Hubble constant, on which it depends, 
changes with time. In particular, the constant is proportional to the rate 
of increase in the distance between two galaxies, divided by that distance. 
(Any two galaxies can be used for this calculation.) In models of the 
universe that fit the observational data, the
denominator increases faster than the numerator, so the Hubble constant 
decreases. In this way, the Hubble distance gets larger. As it does, light 
that was initially just outside the Hubble distance and receding from us 
can come within the Hubble distance. The photons then find themselves in a 
region of space that is receding slower than the speed of light. Thereafter 
they can approach us.

The galaxy they came from, though, may continue to recede superluminally. 
Thus, we can observe light from galaxies that have always been and will 
always be receding faster than the speed of light. Another way to put it is 
that the Hubble distance is not fixed and does not mark the edge of the 
observable universe.


*I don't think this is the consensus view, which is that the Hubble 
constant IS constant, and galaxies beyond our event horizon will never be 
seen, if the universe in their region is expanding faster than c. AG *


Davis and Lineweaver are just reviewing the current consensus view in that 
article and paper, not suggesting any new physics. In general relativity's 
cosmological solutions there is a time-dependent "Hubble parameter" whose 
value at any given cosmological time is called the "Hubble constant" at 
that time, but which can change over the long term (see the first paragraph 
of https://lambda.gsfc.nasa.gov/education/graphic_history/hubb_const.html 
for example). Astrophysicist Ethan Siegel mentions in an article at 
https://bigthink.com/starts-with-a-bang/hubble-constant-changes-time/ that 
even in models that don't have accelerating expansion due to the 
cosmological constant, the Hubble constant still need not be constant in 
time. He explains this by looking at the first Friedmann equation governing 
an expanding universe, where a term equivalent to the definition of the 
Hubble constant is on the left side of the equality and the right side has 
terms for energy density, global curvature of space, and the cosmological 
constant. So, in an expanding universe that's spatially flat and has zero 
cosmological constant, if the energy density is changing as matter/energy 
becomes more spread out, the term equivalent to the Hubble constant must be 
changing as well. From the article:

"Even if you had a flat Universe (which means you can eliminate the second 
term on the right-hand side) and a Universe without a cosmological constant 
(which would mean eliminating the third term on the right-hand side, too), 
you’d understand immediately that the Hubble “constant” cannot be a 
constant in time.
...
In all cases except for a cosmological constant (i.e., dark energy, to the 
best of our understanding), the energy density changes as the Universe 
expands.
If the energy density changes, that means the expansion rate changes, too. 
The Hubble constant is only a constant everywhere in space, as we measure 
it right now. It’s not a constant in the sense that it changes over time."

Siegel has another article covering a lot of the same issues at 
https://www.forbes.com/sites/startswithab

Re: Flat universe implies no Big Bang and Singularity at T = 0



On Tuesday, September 17, 2024 at 11:16:10 PM UTC-6 Alan Grayson wrote:

On Tuesday, September 17, 2024 at 7:49:17 AM UTC-6 Alan Grayson wrote:

On Tuesday, September 17, 2024 at 6:48:19 AM UTC-6 Alan Grayson wrote:

On Tuesday, September 17, 2024 at 4:57:12 AM UTC-6 John Clark wrote:

On Mon, Sep 16, 2024 at 11:46 PM Alan Grayson  wrote:

> How would you map (0,1) 1-1 onto the real numbers?


*F(x)=1/2 + 1/π Arctan(x) . The domain is all the real numbers and the 
range is (0.1)*


*> This map isn't 1-1. Many x's correspond to the same point in (0,1). AG *


*This is a graph of the Arctan function. Show me many X's, or even one 
X, that corresponds to the same point in y.*


*I'll get back to you on this. I was thinking, as x increases positively or 
negatively, the y values (angles) repeat multiple times, making the 
function many-to-one. In this case, we're mapping all the real numbers, to 
a subset of the y-axis. Am I mistaken? AG *


*Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  
So your plot seems wrong, but it's what is on the Internet. AG *


*That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I 
still think the plot keeps repeating as x increases or decreases. AG*


*It repeats as follows: Arctan(x) = Arctan(x + n*2*pi), n=0,1,2,3 ...  AG*


[image: image.png]


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Re: Flat universe implies no Big Bang and Singularity at T = 0



On Tuesday, September 17, 2024 at 7:49:17 AM UTC-6 Alan Grayson wrote:

On Tuesday, September 17, 2024 at 6:48:19 AM UTC-6 Alan Grayson wrote:

On Tuesday, September 17, 2024 at 4:57:12 AM UTC-6 John Clark wrote:

On Mon, Sep 16, 2024 at 11:46 PM Alan Grayson  wrote:

> How would you map (0,1) 1-1 onto the real numbers?


*F(x)=1/2 + 1/π Arctan(x) . The domain is all the real numbers and the 
range is (0.1)*


*> This map isn't 1-1. Many x's correspond to the same point in (0,1). AG *


*This is a graph of the Arctan function. Show me many X's, or even one 
X, that corresponds to the same point in y.*


*I'll get back to you on this. I was thinking, as x increases positively or 
negatively, the y values (angles) repeat multiple times, making the 
function many-to-one. In this case, we're mapping all the real numbers, to 
a subset of the y-axis. Am I mistaken? AG *


*Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  
So your plot seems wrong, but it's what is on the Internet. AG *


*That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I 
still think the plot keeps repeating as x increases or decreases. AG*


[image: image.png]


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Re: Radius of the Observable universe

2024-09-17 Thread Jesse Mazer

On Tue, Sep 17, 2024 at 2:40 PM Alan Grayson  wrote:

>
>
> On Tuesday, September 17, 2024 at 10:12:53 AM UTC-6 Jesse Mazer wrote:
>
> On Mon, Sep 16, 2024 at 7:41 PM Alan Grayson  wrote:
>
>
>
> On Monday, September 16, 2024 at 12:17:45 PM UTC-6 Jesse Mazer wrote:
>
> The Scientific American article "Misconceptions About The Big Bang" by
> Charles Lineweaver and Tamara Davis at
> https://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf
> (distilled from their more technical review 'Expanding Confusion' at
> https://arxiv.org/abs/astro-ph/0310808 ) covers this question on p.
> 42-43, along with other common misconceptions:
>
> "Running to Stay Still
> the idea of seeing faster-than-light galaxies may sound mystical, but it
> is made possible by changes in the expansion rate. Imagine a light beam
> that is farther than the Hubble distance of 14 billion light-years and
> trying to travel in our direction. It is moving toward us at the speed of
> light with respect to its local space, but its local space is receding from
> us faster than the speed of light. Although the light beam is traveling
> toward us at the maximum speed possible, it cannot keep up with the
> stretching of space. It is a bit like a child trying to run the wrong way
> on a moving sidewalk. Photons at the Hubble distance are like the Red Queen
> and Alice, running as fast as they can just to stay in the same place.
>
> One might conclude that the light beyond the Hubble distance would never
> reach us and that its source would be forever undetectable. But the Hubble
> distance is not fixed, because the Hubble constant, on which it depends,
> changes with time. In particular, the constant is proportional to the rate
> of increase in the distance between two galaxies, divided by that distance.
> (Any two galaxies can be used for this calculation.) In models of the
> universe that fit the observational data, the
> denominator increases faster than the numerator, so the Hubble constant
> decreases. In this way, the Hubble distance gets larger. As it does, light
> that was initially just outside the Hubble distance and receding from us
> can come within the Hubble distance. The photons then find themselves in a
> region of space that is receding slower than the speed of light. Thereafter
> they can approach us.
>
> The galaxy they came from, though, may continue to recede superluminally.
> Thus, we can observe light from galaxies that have always been and will
> always be receding faster than the speed of light. Another way to put it is
> that the Hubble distance is not fixed and does not mark the edge of the
> observable universe.
>
>
> *I don't think this is the consensus view, which is that the Hubble
> constant IS constant, and galaxies beyond our event horizon will never be
> seen, if the universe in their region is expanding faster than c. AG *
>
>
> Davis and Lineweaver are just reviewing the current consensus view in that
> article and paper, not suggesting any new physics. In general relativity's
> cosmological solutions there is a time-dependent "Hubble parameter" whose
> value at any given cosmological time is called the "Hubble constant" at
> that time, but which can change over the long term (see the first paragraph
> of https://lambda.gsfc.nasa.gov/education/graphic_history/hubb_const.html
> for example). Astrophysicist Ethan Siegel mentions in an article at
> https://bigthink.com/starts-with-a-bang/hubble-constant-changes-time/
> that even in models that don't have accelerating expansion due to the
> cosmological constant, the Hubble constant still need not be constant in
> time. He explains this by looking at the first Friedmann equation governing
> an expanding universe, where a term equivalent to the definition of the
> Hubble constant is on the left side of the equality and the right side has
> terms for energy density, global curvature of space, and the cosmological
> constant. So, in an expanding universe that's spatially flat and has zero
> cosmological constant, if the energy density is changing as matter/energy
> becomes more spread out, the term equivalent to the Hubble constant must be
> changing as well. From the article:
>
> "Even if you had a flat Universe (which means you can eliminate the second
> term on the right-hand side) and a Universe without a cosmological constant
> (which would mean eliminating the third term on the right-hand side, too),
> you’d understand immediately that the Hubble “constant” cannot be a
> constant in time.
> ...
> In all cases except for a cosmological constant (i.e., dark energy, to the
> best of our understanding), the energy density changes as the Universe
> expands.
> If the energy density changes, that means the expansion rate changes, too.
> The Hubble constant is only a constant everywhere in space, as we measure
> it right now. It’s not a constant in the sense that it changes over time."
>
> Siegel has another article covering a lot of the same issues at
> https://w

Re: Radius of the Observable universe

On Tuesday, September 17, 2024 at 10:12:53 AM UTC-6 Jesse Mazer wrote:

On Mon, Sep 16, 2024 at 7:41 PM Alan Grayson wrote:

On Monday, September 16, 2024 at 12:17:45 PM UTC-6 Jesse Mazer wrote:

The Scientific American article "Misconceptions About The Big Bang" by
Charles Lineweaver and Tamara Davis at
https://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf
(distilled from their more technical review 'Expanding Confusion' at
https://arxiv.org/abs/astro-ph/0310808 ) covers this question on p. 42-43,
along with other common misconceptions:

"Running to Stay Still
the idea of seeing faster-than-light galaxies may sound mystical, but it is
made possible by changes in the expansion rate. Imagine a light beam that
is farther than the Hubble distance of 14 billion light-years and trying to
travel in our direction. It is moving toward us at the speed of light with
respect to its local space, but its local space is receding from us faster
than the speed of light. Although the light beam is traveling toward us at
the maximum speed possible, it cannot keep up with the stretching of space.
It is a bit like a child trying to run the wrong way on a moving sidewalk.
Photons at the Hubble distance are like the Red Queen and Alice, running as
fast as they can just to stay in the same place.

One might conclude that the light beyond the Hubble distance would never
reach us and that its source would be forever undetectable. But the Hubble
distance is not fixed, because the Hubble constant, on which it depends,
changes with time. In particular, the constant is proportional to the rate
of increase in the distance between two galaxies, divided by that distance.
(Any two galaxies can be used for this calculation.) In models of the
universe that fit the observational data, the
denominator increases faster than the numerator, so the Hubble constant
decreases. In this way, the Hubble distance gets larger. As it does, light
that was initially just outside the Hubble distance and receding from us
can come within the Hubble distance. The photons then find themselves in a
region of space that is receding slower than the speed of light. Thereafter
they can approach us.

The galaxy they came from, though, may continue to recede superluminally.
Thus, we can observe light from galaxies that have always been and will
always be receding faster than the speed of light. Another way to put it is
that the Hubble distance is not fixed and does not mark the edge of the
observable universe.

*I don't think this is the consensus view, which is that the Hubble
constant IS constant, and galaxies beyond our event horizon will never be
seen, if the universe in their region is expanding faster than c. AG *

Davis and Lineweaver are just reviewing the current consensus view in that
article and paper, not suggesting any new physics. In general relativity's
cosmological solutions there is a time-dependent "Hubble parameter" whose
value at any given cosmological time is called the "Hubble constant" at
that time, but which can change over the long term (see the first paragraph
of https://lambda.gsfc.nasa.gov/education/graphic_history/hubb_const.html
for example). Astrophysicist Ethan Siegel mentions in an article at
https://bigthink.com/starts-with-a-bang/hubble-constant-changes-time/ that
even in models that don't have accelerating expansion due to the
cosmological constant, the Hubble constant still need not be constant in
time. He explains this by looking at the first Friedmann equation governing
an expanding universe, where a term equivalent to the definition of the
Hubble constant is on the left side of the equality and the right side has
terms for energy density, global curvature of space, and the cosmological
constant. So, in an expanding universe that's spatially flat and has zero
cosmological constant, if the energy density is changing as matter/energy
becomes more spread out, the term equivalent to the Hubble constant must be
changing as well. From the article:

"Even if you had a flat Universe (which means you can eliminate the second
term on the right-hand side) and a Universe without a cosmological constant
(which would mean eliminating the third term on the right-hand side, too),
you’d understand immediately that the Hubble “constant” cannot be a
constant in time.
...
In all cases except for a cosmological constant (i.e., dark energy, to the
best of our understanding), the energy density changes as the Universe
expands.
If the energy density changes, that means the expansion rate changes, too.
The Hubble constant is only a constant everywhere in space, as we measure
it right now. It’s not a constant in the sense that it changes over time."

Siegel has another article covering a lot of the same issues at
https://www.forbes.com/sites/startswithabang/2018/06/29/surprise-the-hubble-constant-changes-over-time/

where he also mentions that it got the name "Hubble constant"

Re: Radius of the Observable universe

2024-09-17 Thread Jesse Mazer

On Mon, Sep 16, 2024 at 7:41 PM Alan Grayson  wrote:

>
>
> On Monday, September 16, 2024 at 12:17:45 PM UTC-6 Jesse Mazer wrote:
>
> The Scientific American article "Misconceptions About The Big Bang" by
> Charles Lineweaver and Tamara Davis at
> https://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf
> (distilled from their more technical review 'Expanding Confusion' at
> https://arxiv.org/abs/astro-ph/0310808 ) covers this question on p.
> 42-43, along with other common misconceptions:
>
> "Running to Stay Still
> the idea of seeing faster-than-light galaxies may sound mystical, but it
> is made possible by changes in the expansion rate. Imagine a light beam
> that is farther than the Hubble distance of 14 billion light-years and
> trying to travel in our direction. It is moving toward us at the speed of
> light with respect to its local space, but its local space is receding from
> us faster than the speed of light. Although the light beam is traveling
> toward us at the maximum speed possible, it cannot keep up with the
> stretching of space. It is a bit like a child trying to run the wrong way
> on a moving sidewalk. Photons at the Hubble distance are like the Red Queen
> and Alice, running as fast as they can just to stay in the same place.
>
> One might conclude that the light beyond the Hubble distance would never
> reach us and that its source would be forever undetectable. But the Hubble
> distance is not fixed, because the Hubble constant, on which it depends,
> changes with time. In particular, the constant is proportional to the rate
> of increase in the distance between two galaxies, divided by that distance.
> (Any two galaxies can be used for this calculation.) In models of the
> universe that fit the observational data, the
> denominator increases faster than the numerator, so the Hubble constant
> decreases. In this way, the Hubble distance gets larger. As it does, light
> that was initially just outside the Hubble distance and receding from us
> can come within the Hubble distance. The photons then find themselves in a
> region of space that is receding slower than the speed of light. Thereafter
> they can approach us.
>
> The galaxy they came from, though, may continue to recede superluminally.
> Thus, we can observe light from galaxies that have always been and will
> always be receding faster than the speed of light. Another way to put it is
> that the Hubble distance is not fixed and does not mark the edge of the
> observable universe.
>
>
> *I don't think this is the consensus view, which is that the Hubble
> constant IS constant, and galaxies beyond our event horizon will never be
> seen, if the universe in their region is expanding faster than c. AG *
>

Davis and Lineweaver are just reviewing the current consensus view in that
article and paper, not suggesting any new physics. In general relativity's
cosmological solutions there is a time-dependent "Hubble parameter" whose
value at any given cosmological time is called the "Hubble constant" at
that time, but which can change over the long term (see the first paragraph
of https://lambda.gsfc.nasa.gov/education/graphic_history/hubb_const.html
for example). Astrophysicist Ethan Siegel mentions in an article at
https://bigthink.com/starts-with-a-bang/hubble-constant-changes-time/ that
even in models that don't have accelerating expansion due to the
cosmological constant, the Hubble constant still need not be constant in
time. He explains this by looking at the first Friedmann equation governing
an expanding universe, where a term equivalent to the definition of the
Hubble constant is on the left side of the equality and the right side has
terms for energy density, global curvature of space, and the cosmological
constant. So, in an expanding universe that's spatially flat and has zero
cosmological constant, if the energy density is changing as matter/energy
becomes more spread out, the term equivalent to the Hubble constant must be
changing as well. From the article:

"Even if you had a flat Universe (which means you can eliminate the second
term on the right-hand side) and a Universe without a cosmological constant
(which would mean eliminating the third term on the right-hand side, too),
you’d understand immediately that the Hubble “constant” cannot be a
constant in time.
...
In all cases except for a cosmological constant (i.e., dark energy, to the
best of our understanding), the energy density changes as the Universe
expands.
If the energy density changes, that means the expansion rate changes, too.
The Hubble constant is only a constant everywhere in space, as we measure
it right now. It’s not a constant in the sense that it changes over time."

Siegel has another article covering a lot of the same issues at
https://www.forbes.com/sites/startswithabang/2018/06/29/surprise-the-hubble-constant-changes-over-time/
where he also mentions that it got the name "Hubble constant" because "for
generations, the only distances w

Re: Flat universe implies no Big Bang and Singularity at T = 0



On Tuesday, September 17, 2024 at 6:48:19 AM UTC-6 Alan Grayson wrote:

On Tuesday, September 17, 2024 at 4:57:12 AM UTC-6 John Clark wrote:

On Mon, Sep 16, 2024 at 11:46 PM Alan Grayson  wrote:

> How would you map (0,1) 1-1 onto the real numbers?


*F(x)=1/2 + 1/π Arctan(x) . The domain is all the real numbers and the 
range is (0.1)*


*> This map isn't 1-1. Many x's correspond to the same point in (0,1). AG *


*This is a graph of the Arctan function. Show me many X's, or even one 
X, that corresponds to the same point in y.*


*I'll get back to you on this. I was thinking, as x increases positively or 
negatively, the y values (angles) repeat multiple times, making the 
function many-to-one. In this case, we're mapping all the real numbers, to 
a subset of the y-axis. Am I mistaken? AG *


*Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or pi/2?  
So your plot seems wrong, but it's what is on the Internet. AG *


[image: image.png]


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Re: Radius of the Observable universe

On Tuesday, September 17, 2024 at 5:36:05 AM UTC-6 John Clark wrote:

On Mon, Sep 16, 2024 at 7:31 PM Alan Grayson wrote:

> *when we approach the observable event horizon, the spatial expansion is
still increasing less than c,*

*Yes. Obviously you will not be able to see any stars receding from you
faster than c. *

> *so I don't see how the observational event horizon is 46 BLY. AG *

*If you are 5 billion light years away from me then in one direction you
will be able to see stars that I cannot see, but in the opposite direction
I will be able to see stars that you cannot see. And If you see the light
from a star that has travel for 13.8 billion years before entering your
telescope and then you get into a spaceship that travels at 99.999% the
speed of light for 13.8 billion years, you will still be nowhere near that
star, and if you travel for 46 billion years you will STILL be nowhere near
that star, although you will be able to see many stars that I cannot see,
but you will not be able to see any of the stars that I, who has remained
on the Earth, can currently see. *

*> the observable universe, space is expanding at a rate less than c.
Correct? So the 46 BLY distance doesn't seem right. *

*Even if you forget about General Relativity, and even if you forget that
the universe is accelerating, we've known for a century that the universe
is expanding, so if you're looking at a star as it was 13.8 billion years
ago then even Newton would say that by now that star is much further away
than 13.8 billion light years. *

*I agree. But my problem is that 46 BLY seems too large. It seems to imply
the expansion rate is greater than c in the observable universe. AG*

*fa*

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Re: Flat universe implies no Big Bang and Singularity at T = 0

On Tuesday, September 17, 2024 at 4:57:12 AM UTC-6 John Clark wrote:

On Mon, Sep 16, 2024 at 11:46 PM Alan Grayson wrote:

> How would you map (0,1) 1-1 onto the real numbers?

*F(x)=1/2 + 1/π Arctan(x) . The domain is all the real numbers and the
range is (0.1)*

*> This map isn't 1-1. Many x's correspond to the same point in (0,1). AG *

*This is a graph of the Arctan function. Show me many X's, or even one
X, that corresponds to the same point in y.*

*I'll get back to you on this. I was thinking, as x increases positively or
negatively, the y values (angles) repeat multiple times, making the
function many-to-one. In this case, we're mapping all the real numbers, to
a subset of the y-axis. Am I mistaken? AG *

[image: image.png]

*>> If a set is infinitely large then there is a proper subset of that set
that can be put into a one to one correspondence with the entire set, in
fact that is the mathematical definition of "infinity".*

*> That's circular. AG *

*>I deleted the post with the circular comment. Why are you responding to
it? AG*

*I responded to your email. Apparently you thought you knew a way to delete
an email that was already on my computer or delete my memory of reading
that email. Neither worked. *

*I deleted it from the List, wherever it's located. AG *

*> an infinite universe cannot be created. If one exists, it is
eternal. The reason is because the creation would require something
non-physical; infinite spatial expansion instantaneously. So no BB for a
spatially infinite universe.*

*I will now quote somebody named Alan Grayson "You keep doing the same
thing; asserting a result without proving it " *

*Actually, I did prove it, above. When a universe is created, or shall we
say "comes into being" it can either be finite or infinite. If it's alleged
to be infinite but doesn't include some spatial points, that would be a
contradiction to the assumption that it's infinite, and thus it must be
finite (since, as we agree, a universe cannot transform from finite to
infinite, or vis-versa). OTOH, if it's really infinite and includes all of
space, it couldn't have reached that state through any progressive
evolution, as that would make it finite. So, if the universe is really
infinite, it must be eternally infinite since it can't evolve to that
state. Not every proof is mathematical. This one's based solely on logic.
AG*

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Re: Radius of the Observable universe

2024-09-17 Thread John Clark

On Mon, Sep 16, 2024 at 7:31 PM Alan Grayson  wrote:

> *when we approach the observable event horizon, the spatial expansion is
> still increasing less than c,*
>

*Yes. Obviously you will not be able to see any stars receding from you
faster than c. *

> *so I don't see how the observational event horizon is 46 BLY. AG *
>

*If you are 5 billion light years away from me then in one direction you
will be able to see stars that I cannot see, but in the opposite direction
I will be able to see stars that you cannot see. And If you see the light
from a star that has travel for 13.8 billion years before entering your
telescope and then you get into a spaceship that travels at 99.999% the
speed of light for 13.8 billion years, you will still be nowhere near that
star, and if you travel for 46 billion years you will STILL be nowhere near
that star, although you will be able to see many stars that I cannot see,
but you will not be able to see any of the stars that I, who has remained
on the Earth, can currently see.  *

*> the observable universe, space is expanding at a rate less than c.
> Correct? So the 46 BLY distance doesn't seem right. *

*Even if you forget about General Relativity, and even if you forget that
the universe is accelerating, we've known for a century that the universe
is expanding, so if you're looking at a star as it was 13.8 billion years
ago then even Newton would say that by now that star is much further away
than 13.8 billion light years.  *

 John K ClarkSee what's on my new list at  Extropolis

mfa

>

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Re: Brain aged more slowly in monkeys given a cheap diabetes drug

2024-09-17 Thread John Clark

On Tue, Sep 17, 2024 at 1:20 AM Brent Meeker  wrote:

> The link goes to a Nature article: "Dimensional crossover in a quantum
> gas of light."
> at  https://www.nature.com/articles/s41567-024-02641-7
>

*Yeah I was reading both articles and sent the wrong link. Sorry. This is
the correct link. *

*The brain aged more slowly in monkeys given a cheap diabetes drug*


John K Clark



>
>

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Re: Flat universe implies no Big Bang and Singularity at T = 0

2024-09-17 Thread John Clark

On Mon, Sep 16, 2024 at 11:46 PM Alan Grayson 
wrote:

> How would you map (0,1) 1-1 onto the real numbers?
>
>
> *F(x)=1/2 + 1/π Arctan(x) . The domain is all the real numbers and the
> range is (0.1)*
>
>
> *> This map isn't 1-1. Many x's correspond to the same point in (0,1). AG *
>

*This is a graph of the Arctan function. Show me many X's, or even one
X, that corresponds to the same point in y.*

[image: image.png]


*>> If a set is infinitely large then there is a proper subset of that set
> that can be put into a one to one correspondence with the entire set, in
> fact that is the mathematical definition of "infinity".*
>
>
> *> That's circular. AG *
>
>
> *>I deleted the post with the circular comment. Why are you responding to
> it? AG*
>

*I responded to your email. Apparently you thought you knew a way to delete
an email that was already on my computer or delete my memory of reading
that email. Neither worked.   *

*>  an infinite universe cannot be created. If one exists, it is
> eternal. The reason is because the creation would require something
> non-physical; infinite spatial expansion instantaneously. So no BB for a
> spatially infinite universe.*
>


*I will now quote somebody named Alan Grayson "You keep doing the same
thing; asserting a result without proving it " *

John K ClarkSee what's on my new list at  Extropolis

agd

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Re: Brain aged more slowly in monkeys given a cheap diabetes drug

2024-09-16 Thread Brent Meeker

The link goes to a Nature article: "Dimensional crossover in a quantum 
gas of light."

at https://www.nature.com/articles/s41567-024-02641-7

Brent

On 9/16/2024 1:34 PM, John Clark wrote:
*Brain aged more slowly in monkeys given a cheap diabetes drug* 



John K Clark    See what's on my new list at Extropolis 


qez


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Re: Flat universe implies no Big Bang and Singularity at T = 0

On Monday, September 16, 2024 at 9:12:58 PM UTC-6 John Clark wrote:

On Mon, Sep 16, 2024 at 9:36 PM Alan Grayson wrote:

> How would you map (0,1) 1-1 onto the real numbers?

*F(x)=1/2 + 1/π Arctan(x) . The domain is all the real numbers and the
range is (0.1)*

*This map isn't 1-1. Many x's correspond to the same point in (0,1). AG *

*> **Both sets have the same cardinality.*

* And a short line in a long line have the same cardinality, and there is a
very simple geometric proof showing that they can be put into a one to one
correspondence. Just draw a triangle with a line from the apex running
through the short line to the long line at the base of the triangle *

*> If a set is infinitely large then there is a proper subset of that set
that can be put into a one to one correspondence with the entire set, in
fact that is the mathematical definition of "infinity".*

*> That's circular. AG *

*I deleted the post with the circular comment. Why are you responding to
it? AG *

*Alan, if you open any book on set theory you will find that the formal
mathematical definition of infinity is that something is infinite if and
only if a proper subset of it can be put into a one to one correspondence
with the entire thing. *

*Returning to the focus of this thread is my claim that an infinite
universe cannot be created. If one exists, it is eternal. The reason is
because the creation would require something non-physical; infinite spatial
expansion instantaneously. So no BB for a spatially infinite universe. The
situation for a finite universe is different. It can start small and
expand, notwithstanding the fact that we don't know how any universe can be
created. AG *

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Re: Flat universe implies no Big Bang and Singularity at T = 0

On Mon, Sep 16, 2024 at 9:36 PM Alan Grayson  wrote:

> How would you map (0,1) 1-1 onto the real numbers?
>

*F(x)=1/2 + 1/π Arctan(x) . The domain is all the real numbers and the
range is (0.1)*

*> **Both sets have the same cardinality.*
>

* And a short line in a long line have the same cardinality, and there is a
very simple geometric proof showing that they can be put into a one to one
correspondence.  Just draw a triangle with a line from the apex running
through the short line to the long line at the base of the triangle *

*> If a set is infinitely large then there is a proper subset of that set
> that can be put into a one to one correspondence with the entire set, in
> fact that is the mathematical definition of "infinity".*

> *> That's circular. AG *

*Alan, if you open any book on set theory you will find that the formal
mathematical definition of infinity is that something is infinite if and
only if a proper subset of it can be put into a one to one correspondence
with the entire thing. *

John K ClarkSee what's on my new list at  Extropolis

ioi

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Re: Flat universe implies no Big Bang and Singularity at T = 0



On Monday, September 16, 2024 at 3:05:27 PM UTC-6 John Clark wrote:



On Mon, Sep 16, 2024 at 4:51 PM Alan Grayson  wrote:

>  *an infinite universe cannot expand*


*NO! In an infinite universe the distance between every particle in it and 
every other particle in it can still increase indefinitely. If a set is 
infinitely large then there is a proper subset of that set that can be put 
into a one to one correspondence with the entire set, in fact that is the 
mathematical definition of "infinity".*


How would you map (0,1) 1-1 onto the real numbers? Both sets have the same 
cardinality. AG 

d

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Re: Flat universe implies no Big Bang and Singularity at T = 0



On Monday, September 16, 2024 at 3:05:27 PM UTC-6 John Clark wrote:



On Mon, Sep 16, 2024 at 4:51 PM Alan Grayson  wrote:

>  *an infinite universe cannot expand*


*NO! In an infinite universe the distance between every particle in it and 
every other particle in it can still increase indefinitely. *


And your proof is what? AG
 

*If a set is infinitely large then there is a proper subset of that set 
that can be put into a one to one correspondence with the entire set, in 
fact that is the mathematical definition of "infinity". *

 John K ClarkSee what's on my new list at  Extropolis 
 
imd

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Re: Flat universe implies no Big Bang and Singularity at T = 0



On Monday, September 16, 2024 at 3:05:27 PM UTC-6 John Clark wrote:



On Mon, Sep 16, 2024 at 4:51 PM Alan Grayson  wrote:

>  *an infinite universe cannot expand*


*NO! In an infinite universe the distance between every particle in it and 
every other particle in it can still increase indefinitely. *


And your proof is what? AG
 

*If a set is infinitely large then there is a proper subset of that set 
that can be put into a one to one correspondence with the entire set, in 
fact that is the mathematical definition of "infinity".*


That's circular. AG 

md

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Re: Radius of the Observable universe

On Monday, September 16, 2024 at 12:17:45 PM UTC-6 Jesse Mazer wrote:

What does mark the edge of observable space? Here again there has been
confusion. If space were not expanding, the most distant object we could
see would now be about 14 billion light-years away from us, the distance
light could have traveled in the 14 billion years since the big bang. But
because the universe is expanding, the space traversed by a photon expands
behind it during the voyage. Consequently, the current distance to the most
distant object we can see is about three times farther, or 46 billion
light-years."

*But within the observable universe, space is expanding at a rate less than
c. Correct? So the 46 BLY distance doesn't seem right. AG*

On Mon, Sep 16, 2024 at 12:53 AM Alan Grayson wrote:

It's claimed to be 46 billion LY, but its age is only measured as 13.8
billion years. What I find puzzling about these numbers is that it seems
this would imply the rate of expansion must have been greater than c during
its lifetime. But AFAICT, the measured rate of expansion using Hubble's law
never exceeded light speed before it reached its present size. Can anyone
explain this apparent discrepancy? TY, AG

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Re: Radius of the Observable universe



On Monday, September 16, 2024 at 11:47:56 AM UTC-6 John Clark wrote:

On Mon, Sep 16, 2024 at 10:40 AM Alan Grayson  wrote:

*>> It has taken light from a star (or more likely from the CMB) 13.8 
billion years to reach us but during those 13.8 billion years the star has 
not remained stationary relative to us, it has been accelerating away. In 
fact telescopic observation tells us that 9 billion years ago, when Dark 
Energy became more dominant than Dark Matter (plus regular matter), the 
acceleration has been accelerating. This *MIGHT* be because as the universe 
expands Dark Matter (plus regular matter) becomes more dilute but Dark 
Energy does not become diluted because it is an intrinsic part of space 
itself, so the more space you have the more Dark Energy you have.*


*> If an object is receding for 13.8 BY, and the universe is expanding 
during that time, doesn't that imply a recession velocity faster than c, 
for the object to be on our observational horizon of 46 BLY? AG *


*Yes and that is a clear violation of Special Relativity, however that was 
not Einstein's last word on the subject, that came 10 years later with 
General Relativity.  Einstein still says matter, energy and information 
cannot travel through space faster than light, BUT space itself is free to 
expand at any speed, including much faster than light.*


But when we approach the observable event horizon, the spatial expansion is 
still increasing less than c, so I don't see how the observational event 
horizon is 46 BLY. AG 


*l*

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Re: Flat universe implies no Big Bang and Singularity at T = 0



On Monday, September 16, 2024 at 3:05:27 PM UTC-6 John Clark wrote:



On Mon, Sep 16, 2024 at 4:51 PM Alan Grayson  wrote:

>  *an infinite universe cannot expand*


*NO! In an infinite universe the distance between every particle in it and 
every other particle in it can still increase indefinitely.*


And your proof is what? AG

* If a set is infinitely large then there is a proper subset of that set 
that can be put into a one to one correspondence with the entire set, in 
fact that is the mathematical definition of "infinity".*


That's probably wrong. The real numbers cannot be put in a 1-1 
correspondence with a proper subset of itself. For example, how would you 
map the open set (0, 1), 1-1 onto the real numbers even though they have 
the same cardinality?  AG 


d

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Re: Flat universe implies no Big Bang and Singularity at T = 0

2024-09-16 Thread Jesse Mazer

"Expansion of space" in the general relativity sense does not depend on the
total volume of the universe increasing--imagine something like an infinite
chessboard where all the squares are increasing in area while the pieces
stay the same size and centered on their respective squares, so each
piece's distance from its neighbors is continually growing.

Jesse

On Mon, Sep 16, 2024 at 4:51 PM Alan Grayson  wrote:

>
> On Monday, September 16, 2024 at 11:36:13 AM UTC-6 John Clark wrote:
>
>
>
> On Mon, Sep 16, 2024 at 10:54 AM Alan Grayson  wrote:
>
> *> At t = 0, what an infinite universe in spatial extent implies; namely,
> no big bang, since that would require creating infinite spatial extent
> instantaneously*
>
>
> *Neither Quantum Mechanics nor General Relativity can explain how
> something with infinite spatial extent could instantaneously come into
> existence at t=0, but they can't explain how something with finite spatial
> extent could do so either.  If we can ever find a way to stop those two
> theories from fighting each other, maybe we could figure it out.*
>
>
> *> Another way to look at it is this; if the universe was finite in
> spatial extent when the BB occurred, it will always remain finite, but if
> it was infinite in spatial extent when the BB "occurred", it was always
> infinite*
>
>
> *As I said in my previous post, if it's infinite now then it was infinite
> at the time of the Big Bang, and if it was finite then it's finite now.*
>
> *> and the BB didn't occur.*
>
>
> *That does not compute.  *
>
>
> While it's true that our theories cannot explain the *creation* of a
> finite or infinite universe, our measurements indicate an expanding
> universe. But an infinite universe cannot expand, so if one exists, it was
> uncreated. Thus no BB for an infinite universe. AG
>
>
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> 
> .
>

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Re: Brain aged more slowly in monkeys given a cheap diabetes drug

*Sorry I gave a bad link. Let me try that again: *

*The brain aged more slowly in monkeys given a cheap diabetes drug*


John K Clark

On Mon, Sep 16, 2024 at 4:34 PM John Clark  wrote:

> *Brain aged more slowly in monkeys given a cheap diabetes drug*
> 
>
> John K ClarkSee what's on my new list at  Extropolis
> 
> qez
>
>
>

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Re: Flat universe implies no Big Bang and Singularity at T = 0

On Mon, Sep 16, 2024 at 4:51 PM Alan Grayson  wrote:

>  *an infinite universe cannot expand*


*NO! In an infinite universe the distance between every particle in it and
every other particle in it can still increase indefinitely. If a set is
infinitely large then there is a proper subset of that set that can be put
into a one to one correspondence with the entire set, in fact that is the
mathematical definition of "infinity". *

 John K ClarkSee what's on my new list at  Extropolis

imd

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Re: Flat universe implies no Big Bang and Singularity at T = 0


On Monday, September 16, 2024 at 11:36:13 AM UTC-6 John Clark wrote:



On Mon, Sep 16, 2024 at 10:54 AM Alan Grayson  wrote:

*> At t = 0, what an infinite universe in spatial extent implies; namely, 
no big bang, since that would require creating infinite spatial extent 
instantaneously*

 
*Neither Quantum Mechanics nor General Relativity can explain how something 
with infinite spatial extent could instantaneously come into existence at 
t=0, but they can't explain how something with finite spatial extent could 
do so either.  If we can ever find a way to stop those two theories from 
fighting each other, maybe we could figure it out.*


*> Another way to look at it is this; if the universe was finite in spatial 
extent when the BB occurred, it will always remain finite, but if it was 
infinite in spatial extent when the BB "occurred", it was always infinite*


*As I said in my previous post, if it's infinite now then it was infinite 
at the time of the Big Bang, and if it was finite then it's finite now.*

*> and the BB didn't occur.*


*That does not compute.  *


While it's true that our theories cannot explain the *creation* of a finite 
or infinite universe, our measurements indicate an expanding universe. But 
an infinite universe cannot expand, so if one exists, it was uncreated. 
Thus no BB for an infinite universe. AG 


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Re: Radius of the Observable universe

2024-09-16 Thread Jesse Mazer

The Scientific American article "Misconceptions About The Big Bang" by
Charles Lineweaver and Tamara Davis at
https://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf
(distilled from their more technical review 'Expanding Confusion' at
https://arxiv.org/abs/astro-ph/0310808 ) covers this question on p. 42-43,
along with other common misconceptions:

"Running to Stay Still
the idea of seeing faster-than-light galaxies may sound mystical, but it is
made possible by changes in the expansion rate. Imagine a light beam that
is farther than the Hubble distance of 14 billion light-years and trying to
travel in our direction. It is moving toward us at the speed of light with
respect to its local space, but its local space is receding from us faster
than the speed of light. Although the light beam is traveling toward us at
the maximum speed possible, it cannot keep up with the stretching of space.
It is a bit like a child trying to run the wrong way on a moving sidewalk.
Photons at the Hubble distance are like the Red Queen and Alice, running as
fast as they can just to stay in the same place.

One might conclude that the light beyond the Hubble distance would never
reach us and that its source would be forever undetectable. But the Hubble
distance is not fixed, because the Hubble constant, on which it depends,
changes with time. In particular, the constant is proportional to the rate
of increase in the distance between two galaxies, divided by that distance.
(Any two galaxies can be used for this calculation.) In models of the
universe that fit the observational data, the
denominator increases faster than the numerator, so the Hubble constant
decreases. In this way, the Hubble distance gets larger. As it does, light
that was initially just outside the Hubble distance and receding from us
can come within the Hubble distance. The photons then find themselves in a
region of space that is receding slower than the speed of light. Thereafter
they can approach us.

The galaxy they came from, though, may continue to recede superluminally.
Thus, we can observe light from galaxies that have always been and will
always be receding faster than the speed of light. Another way to put it is
that the Hubble distance is not fixed and does not mark the edge of the
observable universe.

What does mark the edge of observable space? Here again there has been
confusion. If space were not expanding, the most distant object we could
see would now be about 14 billion light-years away from us, the distance
light could have traveled in the 14 billion years since the big bang. But
because the universe is expanding, the space traversed by a photon expands
behind it during the voyage. Consequently, the current distance to the most
distant object we can see is about three times farther, or 46 billion
light-years."

On Mon, Sep 16, 2024 at 12:53 AM Alan Grayson 
wrote:

> It's claimed to be 46 billion LY, but its age is only measured as 13.8
> billion years. What I find puzzling about these numbers is that it seems
> this would imply the rate of expansion must have been greater than c during
> its lifetime. But AFAICT, the measured rate of expansion using Hubble's law
> never exceeded light speed before it reached its present size. Can anyone
> explain this apparent discrepancy? TY, AG
>
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Re: Radius of the Observable universe

On Mon, Sep 16, 2024 at 10:40 AM Alan Grayson 
wrote:

*>> It has taken light from a star (or more likely from the CMB) 13.8
> billion years to reach us but during those 13.8 billion years the star has
> not remained stationary relative to us, it has been accelerating away. In
> fact telescopic observation tells us that 9 billion years ago, when Dark
> Energy became more dominant than Dark Matter (plus regular matter), the
> acceleration has been accelerating. This *MIGHT* be because as the universe
> expands Dark Matter (plus regular matter) becomes more dilute but Dark
> Energy does not become diluted because it is an intrinsic part of space
> itself, so the more space you have the more Dark Energy you have.*
>
>
> *> If an object is receding for 13.8 BY, and the universe is expanding
> during that time, doesn't that imply a recession velocity faster than c,
> for the object to be on our observational horizon of 46 BLY? AG *
>

*Yes and that is a clear violation of Special Relativity, however that was
not Einstein's last word on the subject, that came 10 years later with
General Relativity.  Einstein still says matter, energy and information
cannot travel through space faster than light, BUT space itself is free to
expand at any speed, including much faster than light.*

 John K ClarkSee what's on my new list at  Extropolis

*mfl*

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Re: Flat universe implies no Big Bang and Singularity at T = 0

On Mon, Sep 16, 2024 at 10:54 AM Alan Grayson 
wrote:

*> At t = 0, what an infinite universe in spatial extent implies; namely,
> no big bang, since that would require creating infinite spatial extent
> instantaneously*

*Neither Quantum Mechanics nor General Relativity can explain how something
with infinite spatial extent could instantaneously come into existence at
t=0, but they can't explain how something with finite spatial extent could
do so either.  If we can ever find a way to stop those two theories from
fighting each other, maybe we could figure it out.*

*> Another way to look at it is this; if the universe was finite in spatial
> extent when the BB occurred, it will always remain finite, but if it was
> infinite in spatial extent when the BB "occurred", it was always infinite*

*As I said in my previous post, if it's infinite now then it was infinite
at the time of the Big Bang, and if it was finite then it's finite now.*

*> and the BB didn't occur.*

*That does not compute.  *
 John K ClarkSee what's on my new list at  Extropolis

stn

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Re: Flat universe implies no Big Bang and Singularity at T = 0



On Monday, September 16, 2024 at 8:01:30 AM UTC-6 Alan Grayson wrote:

On Monday, September 16, 2024 at 6:11:05 AM UTC-6 John Clark wrote:

On Mon, Sep 16, 2024 at 6:58 AM Alan Grayson  wrote:

*> If Flat implies infinite in spatial extent, it can't be realized 
instantaneously at T = 0 (a type of singularity IMO). AG*

 

*Regardless of if the universe is infinite or finite or flat or curved, we 
know that our current physics cannot tell us what things were like at T=0, 
and we will never know until we resolve the discrepancy between our best 
theory of gravity, General Relativity, and our best theory of the other 
three forces of nature, Quantum Mechanics. Both theories have been tested 
with incredibly precise experiments and both theories have passed with 
flying colors. Physicists have been trying for nearly a century to find a 
way to get those two very successful theories to play nice together, but so 
far no luck.*


This issue has nothing to do with a possible unifying theory at t = 0, but 
what an infinite universe in spatial extent implies; namely, no big bang, 
since that would require creating infinite spatial extent instantaneously 
(a condition I associate with a type of singularity). AG 


Another way to look at it is this; if the universe was finite in spatial 
extent when the BB occurred, it will always remain finite, but if it was 
infinite in spatial extent when the BB "occurred", it was always infinite 
and the BB didn't occur. AG 

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Re: Radius of the Observable universe



On Monday, September 16, 2024 at 6:41:02 AM UTC-6 John Clark wrote:

On Mon, Sep 16, 2024 at 12:53 AM Alan Grayson  wrote:

*> It's claimed to be 46 billion LY, but its age is only measured as 13.8 
billion years. What I find puzzling about these numbers is that it seems 
this would imply the rate of expansion must have been greater than c during 
its lifetime.*


 
*No. It has taken light from a star (or more likely from the CMB) 13.8 
billion years to reach us but during those 13.8 billion years the star has 
not remained stationary relative to us, it has been accelerating away. In 
fact telescopic observation tells us that 9 billion years ago, when Dark 
Energy became more dominant than Dark Matter (plus regular matter), the 
acceleration has been accelerating. This *MIGHT* be because as the universe 
expands Dark Matter (plus regular matter) becomes more dilute but Dark 
Energy does not become diluted because it is an intrinsic part of space 
itself, so the more space you have the more Dark Energy you have.*


If an object is receding for 13.8 BY, and the universe is expanding during 
that time, doesn't that imply a recession velocity faster than c, for the 
object to be on our observational horizon of 46 BLY? AG 


 

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Re: Flat universe implies no Big Bang and Singularity at T = 0



On Monday, September 16, 2024 at 6:11:05 AM UTC-6 John Clark wrote:

On Mon, Sep 16, 2024 at 6:58 AM Alan Grayson  wrote:

*> If Flat implies infinite in spatial extent, it can't be realized 
instantaneously at T = 0 (a type of singularity IMO). AG*

 

*Regardless of if the universe is infinite or finite or flat or curved, we 
know that our current physics cannot tell us what things were like at T=0, 
and we will never know until we resolve the discrepancy between our best 
theory of gravity, General Relativity, and our best theory of the other 
three forces of nature, Quantum Mechanics. Both theories have been tested 
with incredibly precise experiments and both theories have passed with 
flying colors. Physicists have been trying for nearly a century to find a 
way to get those two very successful theories to play nice together, but so 
far no luck.*


This issue has nothing to do with a possible unifying theory at t = 0, but 
what an infinite universe in spatial extent implies; namely, no big bang, 
since that would require creating infinite spatial extent instantaneously 
(a condition I associate with a type of singularity). AG 

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Re: Radius of the Observable universe

On Mon, Sep 16, 2024 at 12:53 AM Alan Grayson 
wrote:

*> It's claimed to be 46 billion LY, but its age is only measured as 13.8
> billion years. What I find puzzling about these numbers is that it seems
> this would imply the rate of expansion must have been greater than c during
> its lifetime.*

*No. It has taken light from a star (or more likely from the CMB) 13.8
billion years to reach us but during those 13.8 billion years the star has
not remained stationary relative to us, it has been accelerating away. In
fact telescopic observation tells us that 9 billion years ago, when Dark
Energy became more dominant than Dark Matter (plus regular matter), the
acceleration has been accelerating. This *MIGHT* be because as the universe
expands Dark Matter (plus regular matter) becomes more dilute but Dark
Energy does not become diluted because it is an intrinsic part of space
itself, so the more space you have the more Dark Energy you have.*

 John K ClarkSee what's on my new list at  Extropolis

mde

>

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Re: Flat universe implies no Big Bang and Singularity at T = 0

On Mon, Sep 16, 2024 at 6:58 AM Alan Grayson  wrote:

*> If Flat implies infinite in spatial extent, it can't be realized
> instantaneously at T = 0 (a type of singularity IMO). AG*



*Regardless of if the universe is infinite or finite or flat or curved, we
know that our current physics cannot tell us what things were like at T=0,
and we will never know until we resolve the discrepancy between our best
theory of gravity, General Relativity, and our best theory of the other
three forces of nature, Quantum Mechanics. Both theories have been tested
with incredibly precise experiments and both theories have passed with
flying colors. Physicists have been trying for nearly a century to find a
way to get those two very successful theories to play nice together, but so
far no luck.*

 John K ClarkSee what's on my new list at  Extropolis

cfl

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Re: Length contraction in Special Relativity

2024-09-15 Thread Jesse Mazer

On Sun, Sep 15, 2024 at 8:24 AM John Clark  wrote:

> On Sun, Sep 15, 2024 at 3:26 AM Alan Grayson 
> wrote:
>
>  > *I prefer approximately spherical compared to flat because as we go
>> backward in time, we can enclose the universe in a sphere, implying it
>> is finite in spatial extent (not infinite).*
>
>
> *There is no such implication. If the universe is a 3-sphere then it could
> be finite or infinite. A  3-sphere is a compact, connected, 3-dimensional
> manifold without boundary embedded in 4-space, any loop on a 3-sphere can
> be continuously shrunk to a point without leaving the 3-sphere.*
>


https://math.stackexchange.com/questions/2990455/do-all-compact-manifolds-have-finite-volume
seems to be saying that compactness implies finite volume.

Jesse



>
> * > It then occurred to me that the Unobservable universe was plausibly
>> created during Inflation, *
>
>
> *NO. The rate of expansion during inflation was mind blowingly gargantuan,
> but it was finite. If the universe was infinite before inflation then it
> was infinite after it, and if it was finite before inflation then it was
> finite after it.  *
>
> *> to Alan Guth. I asked him, when he assumes the universe was around the
>> size of a proton when Inflation began, was he referring only to the
>> Observable universe,*
>
>
> *I know for a fact Guth was referring to the observable universe because
> he's a good enough physicist to know that a proton and the observable
> universe have one thing in common, both of them are finite in size. And no
> physical process can turn a finite thing into an infinite thing. *
>
> * > or both hypothetic parts, Observable and Unobservable. *
>
>
> *If the universe has any curvature at the largest possible scale it is
> unobservable, and if you insist that postulating that something you cannot
> observe and will never be able to observe nevertheless exists is
> unscientific, then you would have to conclude that the pope was right and
> Galileo was wrong because the Earth really is the center of the universe.
> Do you really want to insist on that?  *
>   John K ClarkSee what's on my new list at  Extropolis
> 
>
> uss
>
>
>
>> --
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> 
> .
>

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Re: Length contraction in Special Relativity

2024-09-15 Thread Alan Grayson

On Sunday, September 15, 2024 at 6:24:40 AM UTC-6 John Clark wrote:

On Sun, Sep 15, 2024 at 3:26 AM Alan Grayson wrote:

> *I prefer approximately spherical compared to flat because as we go
backward in time, we can enclose the universe in a sphere, implying it
is finite in spatial extent (not infinite).*

*There is no such implication. If the universe is a 3-sphere then it could
be finite or infinite. *

*The sphere I am referring to is finite in spatial extent. AG *

*A 3-sphere is a compact, connected, 3-dimensional manifold without
boundary embedded in 4-space, any loop on a 3-sphere can be continuously
shrunk to a point without leaving the 3-sphere.*

* > It then occurred to me that the Unobservable universe was plausibly
created during Inflation, *

*NO. The rate of expansion during inflation was mind blowingly gargantuan,
but it was finite. If the universe was infinite before inflation then it
was infinite after it, and if it was finite before inflation then it was
finite after it. *

*Why the "NO"? I completely agree with your comment and never intended
otherwise. I am saying that if the universe was finite when Inflation
began, it might have created an Unobservable but FINITE region as a result
of Inflation. And then, if we run the clock backward, this FINITE,
presently Unobservable region, will come back into view. AG *

*> to Alan Guth. I asked him, when he assumes the universe was around the
size of a proton when Inflation began, was he referring only to the
Observable universe,*

*I know for a fact Guth was referring to the observable universe because
he's a good enough physicist to know that a proton and the observable
universe have one thing in common, both of them are finite in size. And no
physical process can turn a finite thing into an infinite thing.*

*Of course; I never stated otherwise! Note that a physicist holding a
prestigious position at a US university disagreed that the universe might
be finite before Inflation began, implying that Guth might NOT have
considered the very early universe as finite. I asked Guth about this very
issue. Hopefully, we'll get an answer. AG *

* > or both hypothetic parts, Observable and Unobservable. *

*If the universe has any curvature at the largest possible scale it is
unobservable, and if you insist that postulating that something you cannot
observe and will never be able to observe nevertheless exists is
unscientific, then you would have to conclude that the pope was right and
Galileo was wrong because the Earth really is the center of the universe.
Do you really want to insist on that? *

*I tend to believe the universe is positively curved, but beyond our
ability to distinguish curved from flat. I wasn't insisting on anything. I
was just wondering what Guth assumed, finiteness or not, when Inflation
began, given the physicist's critique of my conjecture. You seem to have an
obsession in proving I am mistaken, when you obviously have no clue of my
reasoning in this matter. I am just trying to determine Guth's intention,
not claiming to be able to do the impossible, such as measuring something
in the unobservable universe. AG*

John K ClarkSee what's on my new list at Extropolis

uss

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Re: Length contraction in Special Relativity

2024-09-15 Thread John Clark

On Sun, Sep 15, 2024 at 3:26 AM Alan Grayson  wrote:

 > *I prefer approximately spherical compared to flat because as we go
> backward in time, we can enclose the universe in a sphere, implying it
> is finite in spatial extent (not infinite).*

*There is no such implication. If the universe is a 3-sphere then it could
be finite or infinite. A  3-sphere is a compact, connected, 3-dimensional
manifold without boundary embedded in 4-space, any loop on a 3-sphere can
be continuously shrunk to a point without leaving the 3-sphere.*

* > It then occurred to me that the Unobservable universe was plausibly
> created during Inflation, *

*NO. The rate of expansion during inflation was mind blowingly gargantuan,
but it was finite. If the universe was infinite before inflation then it
was infinite after it, and if it was finite before inflation then it was
finite after it.  *

*> to Alan Guth. I asked him, when he assumes the universe was around the
> size of a proton when Inflation began, was he referring only to the
> Observable universe,*

*I know for a fact Guth was referring to the observable universe because
he's a good enough physicist to know that a proton and the observable
universe have one thing in common, both of them are finite in size. And no
physical process can turn a finite thing into an infinite thing. *

* > or both hypothetic parts, Observable and Unobservable. *

*If the universe has any curvature at the largest possible scale it is
unobservable, and if you insist that postulating that something you cannot
observe and will never be able to observe nevertheless exists is
unscientific, then you would have to conclude that the pope was right and
Galileo was wrong because the Earth really is the center of the universe.
Do you really want to insist on that?  *
  John K ClarkSee what's on my new list at  Extropolis

uss

>

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Re: Length contraction in Special Relativity

2024-09-15 Thread Alan Grayson

On Sunday, September 15, 2024 at 1:26:44 AM UTC-6 Alan Grayson wrote:

On Saturday, September 14, 2024 at 11:40:13 PM UTC-6 Brent Meeker wrote:

On 9/14/2024 8:50 PM, Alan Grayson wrote:

On Saturday, September 14, 2024 at 2:53:08 PM UTC-6 Alan Grayson wrote:

On Saturday, September 14, 2024 at 2:31:39 PM UTC-6 Brent Meeker wrote:

On 9/14/2024 12:30 AM, Alan Grayson wrote:

But it's not a property of an expanding sphere without the condition that
the expansion has a constant proportional rate; so the relative distances
keep the same proportions. The further away something is the faster it is
moving away. That's why your first assumption ds/dt=const gives a result
inconsistent with Hubble's law, it doesn't keep theta constant for every
point.

Brent

I never assumed ds/dt = const. Rather I calculated ds/dt and found it not
surprisingly positive, which I concluded was insufficient to show ds/dt
would eventually be > c. AG

Hubble's law or something equivalent is necessary to give more definition
to the problem. The balloon model does the same as Hubble's law; it posits
that the expansion preserves proportions, i.e. if s=>s+ds then n*s=>n*s
+n*ds.

Brent

I recall from years ago the proportion issue we discussed. Obviously, if r,
the radius of sphere, increases by x%, so will any great circle on the
sphere since its circumference also increases by x%, given the formula for
circumference 2*pi*r. So, Hubble's measurements indirectly imply that the
global geometry of the universe is spherical. AG

Let's face it; Hubble's measurements strongly confirm an unexpected result;
namely, that the global geometry of the universe is spherical, not flat, as
I have previously articulated. AG

Actually it appears to be flat, which means distances obey Pythagoras
theorem, and infinite. It's the same in all directions, and so has
rotational symmetry, which isn't exactly the same as spherical.

Brent

I should have written "approximately spherical" since the universe is not
perfectly isotropic. But I prefer approximately spherical compared to flat
because as we go backward in time, we can enclose the universe in a sphere,
implying it is *finite *in spatial extent (not infinite). A physicist I was
in contact with, objected to this model on the grounds that I hadn't taken
into account the *Unobservable* universe, which could be infinite. It then
occurred to me that the Unobservable universe was plausibly created during
Inflation, when in a mind-boggling short time interval, the universe
underwent a *HUGE* expansion in space, much much faster than the speed of
light. I pointed out this possibility to the physicist I was in brief
contact with, but he never replied. Very recently I posed this conjecture
(which I have no possible experiment for testing it) to Alan Guth. I also
asked him, when he assumes the universe was around the size of a proton
when Inflation began, was he referring only to the Observable universe, or
both hypothetic parts, Observable and Unobservable. Did he make any
distinction among the possible choices? I am hoping he will reply. AG

One other thing; if the universe is approximately spherical and expands
forever, it will become *asymptotically* flat, but never actually,
mathematically flat. Moreover, it's likely to be so large now, that our
measurements cannot distinguish between actually, mathematically flat, and
extremely small but positive curvature. AG

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Re: Length contraction in Special Relativity

2024-09-15 Thread Alan Grayson

On Saturday, September 14, 2024 at 11:40:13 PM UTC-6 Brent Meeker wrote:

On 9/14/2024 8:50 PM, Alan Grayson wrote:

On Saturday, September 14, 2024 at 2:53:08 PM UTC-6 Alan Grayson wrote:

On Saturday, September 14, 2024 at 2:31:39 PM UTC-6 Brent Meeker wrote:

On 9/14/2024 12:30 AM, Alan Grayson wrote:

Brent

I never assumed ds/dt = const. Rather I calculated ds/dt and found it not
surprisingly positive, which I concluded was insufficient to show ds/dt
would eventually be > c. AG

Brent

Let's face it; Hubble's measurements strongly confirm an unexpected result;
namely, that the global geometry of the universe is spherical, not flat, as
I have previously articulated. AG

Brent

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Re: Length contraction in Special Relativity

2024-09-14 Thread Brent Meeker

On 9/14/2024 8:50 PM, Alan Grayson wrote:

On Saturday, September 14, 2024 at 2:53:08 PM UTC-6 Alan Grayson wrote:

On Saturday, September 14, 2024 at 2:31:39 PM UTC-6 Brent Meeker
wrote:

On 9/14/2024 12:30 AM, Alan Grayson wrote:

But it's not a property of an expanding sphere without
the condition that the expansion has a constant
proportional rate; so the relative distances keep the
same proportions. The further away something is the
faster it is moving away. That's why your first
assumption ds/dt=const gives a result inconsistent with
Hubble's law, it doesn't keep theta constant for every point.

Brent

I never assumed ds/dt = const. Rather I calculated ds/dt and
found it not surprisingly positive, which I concluded was
insufficient to show ds/dt would eventually be > c. AG

Hubble's law or something equivalent is necessary to give more
definition to the problem. The balloon model does the same as
Hubble's law; it posits that the expansion preserves
proportions, i.e. if s=>s+ds then n*s=>n*s +n*ds.

Brent

I recall from years ago the proportion issue we discussed.
Obviously, if r, the radius of sphere, increases by x%, so will
any great circle on the sphere since its circumference also
increases by x%, given the formula for circumference 2*pi*r. So,
Hubble's measurements indirectly imply that the global geometry of
the universe is spherical. AG

Let's face it; Hubble's measurements strongly confirm an unexpected
result; namely, that the global geometry of the universe is spherical,
not flat, as I have previously articulated. AG

Brent

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Re: Length contraction in Special Relativity

On Saturday, September 14, 2024 at 2:53:08 PM UTC-6 Alan Grayson wrote:

On Saturday, September 14, 2024 at 2:31:39 PM UTC-6 Brent Meeker wrote:

On 9/14/2024 12:30 AM, Alan Grayson wrote:

Brent

I never assumed ds/dt = const. Rather I calculated ds/dt and found it not
surprisingly positive, which I concluded was insufficient to show ds/dt
would eventually be > c. AG

Brent

Let's face it; Hubble's measurements strongly confirm an unexpected result;
namely, that the global geometry of the universe is spherical, not flat, as
I have previously articulated. AG

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Re: Amoeba's Secret openly available under CC-BY license

2024-09-14 Thread Brent Meeker





On 9/14/2024 10:02 AM, John Clark wrote:
Work is force over a "distance", but for the very concept of 
"distance" to be meaningful it must have four properties: 


No. "Distance" is a word.  Work is force acting over distance.

Brent

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Re: That's not me!

2024-09-14 Thread 'Tomasz Rola' via Everything List

On Mon, Jul 29, 2024 at 08:47:21AM -0400, John Clark wrote:
> *It's not easy having a ridiculously boring and common name like "John
> Clark". I was reading an article about Trump giving a speech at a right
> wing evangelical Christian convention that said John Clark, a 26 year old
> graphic designer from Minneapolis attended the convention and said he was
> going to vote for Trump but “I don’t think Trump’s perfect, he’s not Jesus,
> so best not to idolize him. As much as he represents conservative values,
> he also doesn’t, in a lot of ways. Like, being, let’s say, hateful in some
> ways.”*
> 
> *I hope I'm a little more eloquent than that, and I'm not 26, I'm not an
> evangelical Christian, I'm not a graphic designer, I've never been to
> Minneapolis, and I'm not going to vote for Trump; but I do agree with Mr.
> Clark that Trump is hateful and it's a good idea to not idolize him.*

"The lady doth protest too much, methinks" (W.S. "Hamlet")

Huh? :-)

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Tomasz Rola

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** A C programmer asked whether computer had Buddha's nature.  **
** As the answer, master did "rm -rif" on the programmer's home**
** directory. And then the C programmer became enlightened...  **
** **
** Tomasz Rola  mailto:tomasz_r...@bigfoot.com **

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Re: Length contraction in Special Relativity

On Saturday, September 14, 2024 at 2:31:39 PM UTC-6 Brent Meeker wrote:

On 9/14/2024 12:30 AM, Alan Grayson wrote:

Brent

I never assumed ds/dt = const. Rather I calculated ds/dt and found it not
surprisingly positive, which I concluded was insufficient to show ds/dt
would eventually be > c. AG

Brent

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Re: Length contraction in Special Relativity

2024-09-14 Thread Brent Meeker





On 9/14/2024 12:30 AM, Alan Grayson wrote:


But it's not a property of an expanding sphere without the
condition that the expansion has a constant proportional rate; so
the relative distances keep the same proportions.  The further
away something is the faster it is moving away. That's why your
first assumption ds/dt=const gives a result inconsistent with
Hubble's law, it doesn't keep theta constant for every point.

Brent


I never assumed ds/dt = const. Rather I calculated ds/dt and found it 
not surprisingly positive, which I concluded was insufficient to show 
ds/dt would eventually be > c. AG


Hubble's law or something equivalent is necessary to give more 
definition to the problem.  The balloon model does the same as Hubble's 
law; it posits that the expansion preserves proportions, i.e.  if 
s=>s+ds then n*s=>n*s +n*ds.


Brent

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Re: Amoeba's Secret openly available under CC-BY license

2024-09-14 Thread John Clark

On Fri, Sep 13, 2024 at 5:51 PM Brent Meeker  wrote:

* >> physics is the language of mathematics, it's very good at describing
>> things. An equation can describe how system X, that is made of mass/energy,
>> can in an interval of time change into something different, system Y.  But
>> a language by itself can't do anything because neither mathematics nor the
>> English language can change with time unless there is a brain made of atoms
>> to think about them. *
>
>
> *> Language is representation. *
>

* Yes, as I said mathematics is "very good at describing things".*

*> **Its "energy" can't do work either.  Its "distance" isn't far away
> whatever you think about it. *

*Work is force over a "distance", but for the very concept of "distance" to
be meaningful it must have four properties: *

*1) The distance between X and Y must be greater than or equal to zero for
all X and Y.*
*2) The distance between X and Y equals zero if and only if X=Y.*
*3) The distance between X and Y must be the same as the  distance
between Y and X.*
*4) The distance between X and Z must be less than or equal to the distance
between X and Y plus the distance between Y and Z, for all X, Y, and Z.*

*The real numbers and the complex numbers all have the above four
properties so they could be used to measure "distance" BUT it turns out
there is another fundamentally different type of number that also has those
four properties called P-adic numbers.  For any prime number p, is a p-adic
number system and in those systems the size of a number does not depend on
how far it is from zero but by how the visible that number is by powers of
P. It can lead to some unintuitive results, in the 5-adic system, 25 is
smaller than 5.*

*But if both the Real Numbers and the P-adic numbers are equally consistent
why don't we start teaching first graders about P-adic numbers? Because the
real numbers are extremely useful in physics, a.k.a. the physical world,
but the  P-adic numbers are almost useless in physics, although they are
helpful  in pure mathematics, Andrew Wiles used them to prove Fermat's Last
Theorem,*

*> mathematics doesn't change just because you think about it.*

*Yes but that's the problem, the** very fact that mathematics doesn't
change in time is the reason it can't produce intelligence or
consciousness. Physics is needed for that.*

*>> Neither intelligence nor consciousness can exist without something
>> changing with time. *
>
>
> *>I think you're just making a philosophical position out of a tautology
> change=>time.*

*The great thing about tautologies is that all of them are 100% true.  *

*You might as well add motion=>distance and heating=>temperature.*
>

*I can imagine that an intelligent conscious being might not be changing
its position in space, and it might not be changing its temperature, but I
can't imagine an intelligent conscious being not changing its thoughts in
time. The trouble with pure mathematics is that it's timeless. *

*>> The symbols that make up mathematical equations can't change with time,
>> *
>
>
> *> They can't change with distance either, or the ink used, or motion,...
> But their meaning changes in different applications.*

*"Meaning" does not "mean" anything unless there is an intelligent
conscious being around because they are the only ones that are in the
meaning conferring business.   *

*> Modern philosophers define "reality" as a substance that actually exists
> in an external world, and they define "existence" as the state of having
> "reality". And round and round we go.That's why I say in the modern age
> it's mathematicians and physicists who are in the vanguard of the
> investigation into the fundamental nature of reality, while those who write
> "philosopher" on their tax forms when it asks about occupation are really
> in the synonym business not the philosophy business.  **And I would also
> maintain that the semiconductor industry is an existence proof that
> equations alone are not sufficient because they can't DO anything. **And
> I would also maintain that the semiconductor industry is an existence proof
> that equations alone are not sufficient because they can't DO anything.*

*> The existence of something that's not equations alone and does
> something, is not a proof that nothing is done by equations alone. It's a
> proof that at least one thing requires more than equations to be done. *
>

*It's proof that if you want something that can  DO things, anything, then
it's going to need to have Physics up its sleeve because pure mathematics
is not sufficient. *

*>> If you want to actually DO something, that is to say if you want to
>> make a change over a period of time, then you're going to need mass/energy.*
>
>
> > *Actually those are conserved.  What you need is low entropy energy. *

*Conservation is irrelevant. What you need if you want to produce
intelligence or consciousness is an arrangement of atoms that can process
information; those configurations tend to

Re: Length contraction in Special Relativity




See my previous answer, the expansion is uniform hence exponential. 


Your "hence" demands some mathematics! AG


Why uniform expansion implies exponential growth

Uniform expansion does not necessarily mean that the sphere grows linearly. 
In fact, uniform expansion implies that the proportion of growth remains 
constant at every moment, which is the definition of exponential growth. If 
the distance between the points increases proportionally to the current 
distance, then we obtain exponential expansion.


You keep doing the same thing; asserting a result without proving it. 
Please start by *defining *"uniform expansion", mathematically. AG 



Defining "Uniform Expansion"

Mathematically, uniform expansion means:

At each moment, the distance between two points increases by a rate 
proportional to the current distance.


*This is presumably based on the geometry of an expanding sphere. Have you 
proven your above comment anywhere? I surmise that your final result will 
show that Hubble's law can be derived exclusively from the geometry of an 
expanding sphere. Do you agree? AG *


We express this as the following differential equation:

d/dt [d(t)] = k * d(t)

where:

d(t) is the distance between two points at time t,

d/dt [d(t)] is the rate of change of the distance,

k is a constant proportionality factor (the expansion rate).


*Please use standard mathematical notation, so your d(t) should be writen 
as ds. Then your differential equation needs to be rewritten, as ds/dt = 
k*s (I  think), which is what Brent wrote earlier. AG*


This equation states that the rate of change of the distance is 
proportional to the current distance.

Solving the Differential Equation

Rewriting the equation:

d/dt [d(t)] = k * d(t)

We can solve this by separating variables:

1 / d(t) * d(d(t)) = k * dt

Integrating both sides:

ln(d(t)) = k * t + C

Exponentiating both sides:

d(t) = e^(k * t + C)

This simplifies to:

d(t) = e^C * e^(k * t)

Let d_0 = e^C represent the initial distance between the points at t = 0. 
The solution becomes:

d(t) = d_0 * e^(k * t)

Exponential Growth from Uniform Expansion

The solution shows that uniform expansion — where the rate of change is 
proportional to the current distance — leads to exponential growth. The 
distance between the points increases exponentially over time:

d(t) = d_0 * e^(k * t)

Summary:

"Uniform expansion" means distances grow proportionally to their current 
size.

This leads to the exponential formula d(t) = d_0 * e^(k * t), where k is a 
constant.

As a result, distances increase exponentially over time.


*Now what? After some increment of time, the distance increases more than 
light can traverse it, so the light never reaches the galaxy it is receding 
from. AG *

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Re: Length contraction in Special Relativity




See my previous answer, the expansion is uniform hence exponential. 


Your "hence" demands some mathematics! AG


Why uniform expansion implies exponential growth

Uniform expansion does not necessarily mean that the sphere grows linearly. 
In fact, uniform expansion implies that the proportion of growth remains 
constant at every moment, which is the definition of exponential growth. If 
the distance between the points increases proportionally to the current 
distance, then we obtain exponential expansion.


You keep doing the same thing; asserting a result without proving it. 
Please start by *defining *"uniform expansion", mathematically. AG 



Defining "Uniform Expansion"

Mathematically, uniform expansion means:

At each moment, the distance between two points increases by a rate 
proportional to the current distance.


*This is presumably based on the geometry of an expanding sphere. Have you 
proven your above comment anywhere? I surmise that your final result will 
show that Hubble's law can be derived exclusively from the geometry of an 
expanding sphere. Do you agree? AG *


We express this as the following differential equation:

d/dt [d(t)] = k * d(t)

where:

d(t) is the distance between two points at time t,

d/dt [d(t)] is the rate of change of the distance,

k is a constant proportionality factor (the expansion rate).


*Please use standard mathematical notation, so your d(t) should be writen 
as ds. Then your differential equation needs to be rewritten, as ds/dt = 
k*s (I  think), which is what Brent wrote earlier. AG*
Reply all
Reply to author
Forward


This equation states that the rate of change of the distance is 
proportional to the current distance.

Solving the Differential Equation

Rewriting the equation:

d/dt [d(t)] = k * d(t)

We can solve this by separating variables:

1 / d(t) * d(d(t)) = k * dt

Integrating both sides:

ln(d(t)) = k * t + C

Exponentiating both sides:

d(t) = e^(k * t + C)

This simplifies to:

d(t) = e^C * e^(k * t)

Let d_0 = e^C represent the initial distance between the points at t = 0. 
The solution becomes:

d(t) = d_0 * e^(k * t)

Exponential Growth from Uniform Expansion

The solution shows that uniform expansion — where the rate of change is 
proportional to the current distance — leads to exponential growth. The 
distance between the points increases exponentially over time:

d(t) = d_0 * e^(k * t)

Summary:

"Uniform expansion" means distances grow proportionally to their current 
size.

This leads to the exponential formula d(t) = d_0 * e^(k * t), where k is a 
constant.

As a result, distances increase exponentially over time.




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.

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Re: Length contraction in Special Relativity




See my previous answer, the expansion is uniform hence exponential. 


Your "hence" demands some mathematics! AG


Why uniform expansion implies exponential growth

Uniform expansion does not necessarily mean that the sphere grows linearly. 
In fact, uniform expansion implies that the proportion of growth remains 
constant at every moment, which is the definition of exponential growth. If 
the distance between the points increases proportionally to the current 
distance, then we obtain exponential expansion.


You keep doing the same thing; asserting a result without proving it. 
Please start by *defining *"uniform expansion", mathematically. AG 



Defining "Uniform Expansion"

Mathematically, uniform expansion means:

At each moment, the distance between two points increases by a rate 
proportional to the current distance.


We express this as the following differential equation:

d/dt [d(t)] = k * d(t)

where:

d(t) is the distance between two points at time t,


*Please use standard mathematical notation, so your d(t) is normally 
written as ds. Then your differential equation needs to be rewritten. Not 
sure how. AG*


d/dt [d(t)] is the rate of change of the distance,

k is a constant proportionality factor (the expansion rate).


This equation states that the rate of change of the distance is 
proportional to the current distance.

Solving the Differential Equation

Rewriting the equation:

d/dt [d(t)] = k * d(t)

We can solve this by separating variables:

1 / d(t) * d(d(t)) = k * dt

Integrating both sides:

ln(d(t)) = k * t + C

Exponentiating both sides:

d(t) = e^(k * t + C)

This simplifies to:

d(t) = e^C * e^(k * t)

Let d_0 = e^C represent the initial distance between the points at t = 0. 
The solution becomes:

d(t) = d_0 * e^(k * t)

Exponential Growth from Uniform Expansion

The solution shows that uniform expansion — where the rate of change is 
proportional to the current distance — leads to exponential growth. The 
distance between the points increases exponentially over time:

d(t) = d_0 * e^(k * t)

Summary:

"Uniform expansion" means distances grow proportionally to their current 
size.

This leads to the exponential formula d(t) = d_0 * e^(k * t), where k is a 
constant.

As a result, distances increase exponentially over time.

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Re: Length contraction in Special Relativity

2024-09-14 Thread Quentin Anciaux

Le sam. 14 sept. 2024, 11:17, Alan Grayson  a
écrit :

>
>
> On Saturday, September 14, 2024 at 2:57:43 AM UTC-6 Quentin Anciaux wrote:
>
>
>
> Le sam. 14 sept. 2024, 09:32, Alan Grayson  a écrit :
>
>
>
> On Saturday, September 14, 2024 at 12:40:01 AM UTC-6 Quentin Anciaux wrote:
>
>
>
> Le sam. 14 sept. 2024, 07:09, Brent Meeker  a écrit :
>
>
>
>
> On 9/13/2024 7:58 PM, Alan Grayson wrote:
>
>
>
> On Friday, September 13, 2024 at 8:48:25 PM UTC-6 Brent Meeker wrote:
>
>
>
>
> On 9/13/2024 7:10 PM, Alan Grayson wrote:
>
>
>
> On Friday, September 13, 2024 at 4:03:45 PM UTC-6 Brent Meeker wrote:
>
>
>
>
> On 9/13/2024 4:56 AM, Alan Grayson wrote:
>
>
>
> On Friday, September 13, 2024 at 4:06:49 AM UTC-6 Alan Grayson wrote:
>
> On Thursday, September 12, 2024 at 11:07:49 PM UTC-6 Alan Grayson wrote:
>
> On Thursday, September 12, 2024 at 11:00:21 PM UTC-6 Brent Meeker wrote:
>
>
>
>
> On 9/12/2024 9:21 PM, Alan Grayson wrote:
>
>
>
> On Thursday, September 12, 2024 at 3:55:45 AM UTC-6 Quentin Anciaux wrote:
>
>
>
> Le jeu. 12 sept. 2024, 11:53, Alan Grayson  a écrit :
>
>
>
> On Thursday, September 12, 2024 at 2:40:56 AM UTC-6 Quentin Anciaux wrote:
>
> I just gave you a full proof that as long as the expansion is uniform and
> expansion rate > 0, then it follows objects will sooner or later recess
> from each other at speed > c.
>
>
> What was the justification for the geometric progression? I made no such
> assumption in my "proof".
>
>
> As explained multiple times and in the quote you made, expansion is
> uniform and happens at every point in space.
>
>
> What bothers me about your method is that you* assume* a geometric
> increase in the separation distance, when, IMO, that's the variable that
> must be calculated (which I did). So no matter how many times you affirm
> your proof as valid, I can't agree. AG
>
>
> You didn't calculate the expansion parameter, which is the Hubble
> constant.  It's an observed value.
>
> Brent
>
>
> Why must I do that, when I just want to show that eventually the
> recessional velocity exceeds c? Also, I don't see why theta is fixed, when
> the end of the arc defines the position of the receding galaxy. AG
>
>
> Now I am not sure I proved the recessional velocity is greater than c,
> after some time has passed. If the sphere is expanding, then the distance
> between any two fixed points on the sphere will increase as time passes.
> But that was obvious due to the expansion. What's wrong, if anything? AG
>
>
> Now I see the light. We've been struggling to prove that a receding galaxy
> will fall out of view if the universe is expanding, but all the so-called
> "proofs" fail, but for different reasons. What Quentin offers is not a
> proof. He's just repeating a result done by someone else,* using
> mathematics*, which he believes (and might be true). Brent is mistaken in
> his apparent belief that the proof of concept requires appeal to Hubble's
> law. This is also mistaken IMO since the result to be proven depends
> *exclusively* on the *geometry *of an expanding sphere. Finally, my proof
> also fails, since it's obvious that the arclength, s,  between two galaxies
> on an expanding  sphere, will obviously increase as the sphere expands.
> That is, ds/dt will obviously be positive since the arclength is
> increasing. IOW, a constantly increasing arclength s, assuming a uniformly
> expanding sphere, necessarily yields ds/dt > 0, but it does NOT demonstrate
> that the velocity of the receding galaxy eventually increases to be greater
> than c. When I have the energy, I will calculate the *second time
> derivative* of the arclength, s, hopefully to demonstrate, that for a
> uniformly expanding sphere, the *four* terms of the second derivative of
> s, imply a* positive acceleration*. This will establish that eventually
> the receding galaxy will pass out of view for the observer on the assumed
> stationary galaxy. Comments welcome. AG
>
> It's already proven that ds/dt=ks  => s=j*exp(kt) where k with dimensions
> of 1/time and j is an arbitrary constant of integration with the same
> dimensions as s.  Going to second derivatives won't gain any more.
>
> Brent
>
>
> We have different objectives. Your equation represents Hubble's law, but
> what I want to show is that Hubble's law is the inherent result of the
> geometry of an expanding sphere. So I believe going to the second
> derivative will demonstrate this. BTW, what's your argument that theta is a
> constant? AG
>
> Notice I didn't mention Hubble's law and avoided using H.  I deliberately
> used j and k for undetermined constants.
>
>
> But you didn't pull that equation out of the proverbial hat. You assumed
> the recessional velocity ds/dt depends linearly on s,  which is what Hubble
> measured. AG
>
>
> Theta's constant under the assumption that it's the angle between two
> points that at FIXED on the expanding surface.
>
>
> Yes, the two points are fixed but the distance between them, s. increases
> due to the increase

Re: Length contraction in Special Relativity