Re: Equivalence Principle and Einstein Field Equations

2017-12-23 Thread Lawrence Crowell
On Thursday, December 21, 2017 at 6:54:50 PM UTC-6, Bruce wrote:
>
> On 22/12/2017 11:22 am, agrays...@gmail.com  wrote:
>
> On Thursday, December 21, 2017 at 11:03:53 PM UTC, Brent wrote: 
>>
>>
>> On 12/21/2017 2:04 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> *If Newton's Law of Gravitation is covariant -- that is, coordinate frame 
>> independent -- I'd expect it to to be invariant between inertial frames, 
>> but I don't believe it is. That is, I don't think a LT between inertial 
>> frames will leave the form of the law unchanged. How do you resolve this 
>> problem? TIA, AG * 
>>
>>
>> Don't use a Lorentz transform between frames in a Galilean invariant 
>> theory.
>>
>
> *OK, So why didn't Einstein do what he did for classical mechanics which 
> is not Lorentz invariant, and directly modify Newton's Law of Gravitation? 
> AG*
>
>
> Special relativity is kinematics, gravitation is a dynamical theory -- one 
> doesn't go into the other. You need a new dynamical theory.
>
> Bruce
>

Special relativity as the kinematical theory is global. In isolation it 
assumes spacetime is flat everywhere. However, this may not be the case. 
Suppose we have two regions with bundle sections s and s'. This means there 
are Lorentz vectors X and X' in two local regions that transform according 
to special relativity separately. If these two regions intersect we have a 
transition between them. Let g be the group such that gs → s' and gX → X'. 
There is then a difference between these given by

X's' – Xs = d(Xs) = gXs' - Xs.

Which by g^{-1}g = 1 gives

d(Xs) = (gXg^{-1} - X)s.

The LHS gives us (X' + gdg^{-1})s and so we get 

X' = gXg^{-1} - gdg^{-1}.

This is the transformation principle for vectors and what defines the 
connection coefficients in general relativity. 

LC

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Re: Equivalence Principle and Einstein Field Equations

2017-12-22 Thread Brent Meeker



On 12/22/2017 3:43 AM, agrayson2...@gmail.com wrote:



On Friday, December 22, 2017 at 7:45:42 AM UTC, Brent wrote:



On 12/21/2017 11:06 PM, agrays...@gmail.com  wrote:



On Friday, December 22, 2017 at 4:46:10 AM UTC, Brent wrote:



On 12/21/2017 4:22 PM, agrays...@gmail.com wrote:



On Thursday, December 21, 2017 at 11:03:53 PM UTC, Brent wrote:



On 12/21/2017 2:04 PM, agrays...@gmail.com wrote:



On Tuesday, December 19, 2017 at 8:51:51 PM UTC, Brent
wrote:



On 12/18/2017 11:44 PM, agrays...@gmail.com wrote:


Invariants are always the important things in
physics because they are what we can have
intersubjective agreement on.

Brent


*IIUC, the field equations are covariant, which
means coordinate system independent. *


Right.  Covariant means that something that changes
in such a way that invariant things remain the
same.  So vectors components transform covariantly
so that they keep the vector physically the same.


*Isn't Newton's Law of Gravitation also coordinate
independent? That is, if we use Newton to
calculate the planetary orbits, won't we get the
same results in different coordinate systems? *

Right.

*
If Newton's Law of Gravitation is covariant -- that is,
coordinate frame independent -- I'd expect it to to be
invariant between inertial frames, but I don't believe
it is. That is, I don't think a LT between inertial
frames will leave the form of the law unchanged. How do
you resolve this problem? TIA, AG
*


Don't use a Lorentz transform between frames in a
Galilean invariant theory.


*OK, So why didn't Einstein do what he did for classical
mechanics which is not Lorentz invariant, and directly
modify Newton's Law of Gravitation? AG*


(a) I don't read minds, and especially not Einstein's  and
(b) I don't know what "directly modify" means.

Brent


*He changed (= directly modified) the laws of mechanics to make
them Lorentz invariant. So why can't that be done for Newton's
Law of Gravitation? Does that law work for any inertial frame? AG*


Newton's gravity is a field theory.  It implies an infinite speed
of changes in the gravitational field.  That wasn't consistent
with relativity.  What you're calling "directly modified" was just
local mechanics, not fields.

Brent


*When you think about it, it's apriori highly improbable that 
Newtonian gravity would work as well as it does, say for planetary 
orbits, given the substantial light times between the Sun and the 
planets, and between the planets. AG

*


It's an interesting point that if you just take Newton's theory and 
allow for the finite travel time of gravitational fields, so each body 
is attracted toward the point another body was in past, the theory 
doesn't work at all.


Brent


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Re: Equivalence Principle and Einstein Field Equations

2017-12-22 Thread agrayson2000


On Friday, December 22, 2017 at 7:45:42 AM UTC, Brent wrote:
>
>
>
> On 12/21/2017 11:06 PM, agrays...@gmail.com  wrote:
>
>
>
> On Friday, December 22, 2017 at 4:46:10 AM UTC, Brent wrote: 
>>
>>
>>
>> On 12/21/2017 4:22 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, December 21, 2017 at 11:03:53 PM UTC, Brent wrote: 
>>>
>>>
>>>
>>> On 12/21/2017 2:04 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Tuesday, December 19, 2017 at 8:51:51 PM UTC, Brent wrote: 



 On 12/18/2017 11:44 PM, agrays...@gmail.com wrote:

 Invariants are always the important things in physics because they are 
> what we can have intersubjective agreement on.
>
> Brent
>

 *IIUC, the field equations are covariant, which means coordinate system 
 independent. *


 Right.  Covariant means that something that changes in such a way that 
 invariant things remain the same.  So vectors components transform 
 covariantly so that they keep the vector physically the same.

 *Isn't Newton's Law of Gravitation also coordinate independent? That 
 is, if we use Newton to calculate the planetary orbits, won't we get the 
 same results in different coordinate systems? *

 Right.

>>>
>>>
>>> * If Newton's Law of Gravitation is covariant -- that is, coordinate 
>>> frame independent -- I'd expect it to to be invariant between inertial 
>>> frames, but I don't believe it is. That is, I don't think a LT between 
>>> inertial frames will leave the form of the law unchanged. How do you 
>>> resolve this problem? TIA, AG *
>>>
>>>
>>> Don't use a Lorentz transform between frames in a Galilean invariant 
>>> theory.
>>>
>>
>> *OK, So why didn't Einstein do what he did for classical mechanics which 
>> is not Lorentz invariant, and directly modify Newton's Law of Gravitation? 
>> AG*
>>
>>
>> (a) I don't read minds, and especially not Einstein's  and (b) I don't 
>> know what "directly modify" means.
>>
>> Brent
>>
>
> *He changed (= directly modified) the laws of mechanics to make them 
> Lorentz invariant. So why can't that be done for Newton's Law of 
> Gravitation?  Does that law work for any inertial frame? AG*
>
>
> Newton's gravity is a field theory.  It implies an infinite speed of 
> changes in the gravitational field.  That wasn't consistent with 
> relativity.  What you're calling "directly modified" was just local 
> mechanics, not fields.
>
> Brent
>

*When you think about it, it's apriori highly improbable that Newtonian 
gravity would work as well as it does, say for planetary orbits, given the 
substantial light times between the Sun and the planets, and between the 
planets. AG *

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Re: Equivalence Principle and Einstein Field Equations

2017-12-21 Thread Brent Meeker



On 12/21/2017 11:06 PM, agrayson2...@gmail.com wrote:



On Friday, December 22, 2017 at 4:46:10 AM UTC, Brent wrote:



On 12/21/2017 4:22 PM, agrays...@gmail.com  wrote:



On Thursday, December 21, 2017 at 11:03:53 PM UTC, Brent wrote:



On 12/21/2017 2:04 PM, agrays...@gmail.com wrote:



On Tuesday, December 19, 2017 at 8:51:51 PM UTC, Brent wrote:



On 12/18/2017 11:44 PM, agrays...@gmail.com wrote:


Invariants are always the important things in
physics because they are what we can have
intersubjective agreement on.

Brent


*IIUC, the field equations are covariant, which means
coordinate system independent. *


Right.  Covariant means that something that changes in
such a way that invariant things remain the same.  So
vectors components transform covariantly so that they
keep the vector physically the same.


*Isn't Newton's Law of Gravitation also coordinate
independent? That is, if we use Newton to calculate the
planetary orbits, won't we get the same results in
different coordinate systems? *

Right.

*
If Newton's Law of Gravitation is covariant -- that is,
coordinate frame independent -- I'd expect it to to be
invariant between inertial frames, but I don't believe it
is. That is, I don't think a LT between inertial frames will
leave the form of the law unchanged. How do you resolve this
problem? TIA, AG
*


Don't use a Lorentz transform between frames in a Galilean
invariant theory.


*OK, So why didn't Einstein do what he did for classical
mechanics which is not Lorentz invariant, and directly modify
Newton's Law of Gravitation? AG*


(a) I don't read minds, and especially not Einstein's  and (b) I
don't know what "directly modify" means.

Brent


*He changed (= directly modified) the laws of mechanics to make them 
Lorentz invariant. So why can't that be done for Newton's Law of 
Gravitation?  Does that law work for any inertial frame? AG*


Newton's gravity is a field theory.  It implies an infinite speed of 
changes in the gravitational field.  That wasn't consistent with 
relativity.  What you're calling "directly modified" was just local 
mechanics, not fields.


Brent


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Re: Equivalence Principle and Einstein Field Equations

2017-12-21 Thread agrayson2000


On Friday, December 22, 2017 at 4:46:10 AM UTC, Brent wrote:
>
>
>
> On 12/21/2017 4:22 PM, agrays...@gmail.com  wrote:
>
>
>
> On Thursday, December 21, 2017 at 11:03:53 PM UTC, Brent wrote: 
>>
>>
>>
>> On 12/21/2017 2:04 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Tuesday, December 19, 2017 at 8:51:51 PM UTC, Brent wrote: 
>>>
>>>
>>>
>>> On 12/18/2017 11:44 PM, agrays...@gmail.com wrote:
>>>
>>> Invariants are always the important things in physics because they are 
 what we can have intersubjective agreement on.

 Brent

>>>
>>> *IIUC, the field equations are covariant, which means coordinate system 
>>> independent. *
>>>
>>>
>>> Right.  Covariant means that something that changes in such a way that 
>>> invariant things remain the same.  So vectors components transform 
>>> covariantly so that they keep the vector physically the same.
>>>
>>> *Isn't Newton's Law of Gravitation also coordinate independent? That is, 
>>> if we use Newton to calculate the planetary orbits, won't we get the same 
>>> results in different coordinate systems? *
>>>
>>> Right.
>>>
>>
>>
>> * If Newton's Law of Gravitation is covariant -- that is, coordinate 
>> frame independent -- I'd expect it to to be invariant between inertial 
>> frames, but I don't believe it is. That is, I don't think a LT between 
>> inertial frames will leave the form of the law unchanged. How do you 
>> resolve this problem? TIA, AG *
>>
>>
>> Don't use a Lorentz transform between frames in a Galilean invariant 
>> theory.
>>
>
> *OK, So why didn't Einstein do what he did for classical mechanics which 
> is not Lorentz invariant, and directly modify Newton's Law of Gravitation? 
> AG*
>
>
> (a) I don't read minds, and especially not Einstein's  and (b) I don't 
> know what "directly modify" means.
>
> Brent
>

*He changed (= directly modified) the laws of mechanics to make them 
Lorentz invariant. So why can't that be done for Newton's Law of 
Gravitation?  Does that law work for any inertial frame? AG*

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Re: Equivalence Principle and Einstein Field Equations

2017-12-21 Thread Brent Meeker



On 12/21/2017 4:22 PM, agrayson2...@gmail.com wrote:



On Thursday, December 21, 2017 at 11:03:53 PM UTC, Brent wrote:



On 12/21/2017 2:04 PM, agrays...@gmail.com  wrote:



On Tuesday, December 19, 2017 at 8:51:51 PM UTC, Brent wrote:



On 12/18/2017 11:44 PM, agrays...@gmail.com wrote:


Invariants are always the important things in physics
because they are what we can have intersubjective
agreement on.

Brent


*IIUC, the field equations are covariant, which means
coordinate system independent. *


Right.  Covariant means that something that changes in such a
way that invariant things remain the same.  So vectors
components transform covariantly so that they keep the vector
physically the same.


*Isn't Newton's Law of Gravitation also coordinate
independent? That is, if we use Newton to calculate the
planetary orbits, won't we get the same results in different
coordinate systems? *

Right.

*
If Newton's Law of Gravitation is covariant -- that is,
coordinate frame independent -- I'd expect it to to be invariant
between inertial frames, but I don't believe it is. That is, I
don't think a LT between inertial frames will leave the form of
the law unchanged. How do you resolve this problem? TIA, AG
*


Don't use a Lorentz transform between frames in a Galilean
invariant theory.


*OK, So why didn't Einstein do what he did for classical mechanics 
which is not Lorentz invariant, and directly modify Newton's Law of 
Gravitation? AG*


(a) I don't read minds, and especially not Einstein's  and (b) I don't 
know what "directly modify" means.


Brent

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Re: Equivalence Principle and Einstein Field Equations

2017-12-21 Thread agrayson2000


On Friday, December 22, 2017 at 12:54:50 AM UTC, Bruce wrote:
>
> On 22/12/2017 11:22 am, agrays...@gmail.com  wrote:
>
> On Thursday, December 21, 2017 at 11:03:53 PM UTC, Brent wrote: 
>>
>>
>> On 12/21/2017 2:04 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> *If Newton's Law of Gravitation is covariant -- that is, coordinate frame 
>> independent -- I'd expect it to to be invariant between inertial frames, 
>> but I don't believe it is. That is, I don't think a LT between inertial 
>> frames will leave the form of the law unchanged. How do you resolve this 
>> problem? TIA, AG * 
>>
>>
>> Don't use a Lorentz transform between frames in a Galilean invariant 
>> theory.
>>
>
> *OK, So why didn't Einstein do what he did for classical mechanics which 
> is not Lorentz invariant, and directly modify Newton's Law of Gravitation? 
> AG*
>
>
> Special relativity is kinematics, gravitation is a dynamical theory -- one 
> doesn't go into the other. You need a new dynamical theory.
>

*I don't understand the distinction. I'll have to consult Wiki. AG *

>
> Bruce
>

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Re: Equivalence Principle and Einstein Field Equations

2017-12-21 Thread Bruce Kellett

On 22/12/2017 11:22 am, agrayson2...@gmail.com wrote:

On Thursday, December 21, 2017 at 11:03:53 PM UTC, Brent wrote:


On 12/21/2017 2:04 PM, agrays...@gmail.com  wrote:


*If Newton's Law of Gravitation is covariant -- that is,
coordinate frame independent -- I'd expect it to to be invariant
between inertial frames, but I don't believe it is. That is, I
don't think a LT between inertial frames will leave the form of
the law unchanged. How do you resolve this problem? TIA, AG
*


Don't use a Lorentz transform between frames in a Galilean
invariant theory.


*OK, So why didn't Einstein do what he did for classical mechanics 
which is not Lorentz invariant, and directly modify Newton's Law of 
Gravitation? AG*


Special relativity is kinematics, gravitation is a dynamical theory -- 
one doesn't go into the other. You need a new dynamical theory.


Bruce

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Re: Equivalence Principle and Einstein Field Equations

2017-12-21 Thread agrayson2000


On Thursday, December 21, 2017 at 11:03:53 PM UTC, Brent wrote:
>
>
>
> On 12/21/2017 2:04 PM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, December 19, 2017 at 8:51:51 PM UTC, Brent wrote: 
>>
>>
>>
>> On 12/18/2017 11:44 PM, agrays...@gmail.com wrote:
>>
>> Invariants are always the important things in physics because they are 
>>> what we can have intersubjective agreement on.
>>>
>>> Brent
>>>
>>
>> *IIUC, the field equations are covariant, which means coordinate system 
>> independent. *
>>
>>
>> Right.  Covariant means that something that changes in such a way that 
>> invariant things remain the same.  So vectors components transform 
>> covariantly so that they keep the vector physically the same.
>>
>> *Isn't Newton's Law of Gravitation also coordinate independent? That is, 
>> if we use Newton to calculate the planetary orbits, won't we get the same 
>> results in different coordinate systems? *
>>
>> Right.
>>
>
>
> * If Newton's Law of Gravitation is covariant -- that is, coordinate frame 
> independent -- I'd expect it to to be invariant between inertial frames, 
> but I don't believe it is. That is, I don't think a LT between inertial 
> frames will leave the form of the law unchanged. How do you resolve this 
> problem? TIA, AG *
>
>
> Don't use a Lorentz transform between frames in a Galilean invariant 
> theory.
>

*OK, So why didn't Einstein do what he did for classical mechanics which is 
not Lorentz invariant, and directly modify Newton's Law of Gravitation? AG*

>
> Brent
>

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Re: Equivalence Principle and Einstein Field Equations

2017-12-21 Thread Brent Meeker



On 12/21/2017 2:04 PM, agrayson2...@gmail.com wrote:



On Tuesday, December 19, 2017 at 8:51:51 PM UTC, Brent wrote:



On 12/18/2017 11:44 PM, agrays...@gmail.com  wrote:


Invariants are always the important things in physics because
they are what we can have intersubjective agreement on.

Brent


*IIUC, the field equations are covariant, which means coordinate
system independent. *


Right.  Covariant means that something that changes in such a way
that invariant things remain the same.  So vectors components
transform covariantly so that they keep the vector physically the
same.


*Isn't Newton's Law of Gravitation also coordinate independent?
That is, if we use Newton to calculate the planetary orbits,
won't we get the same results in different coordinate systems? *

Right.

*
If Newton's Law of Gravitation is covariant -- that is, coordinate 
frame independent -- I'd expect it to to be invariant between inertial 
frames, but I don't believe it is. That is, I don't think a LT between 
inertial frames will leave the form of the law unchanged. How do you 
resolve this problem? TIA, AG

*


Don't use a Lorentz transform between frames in a Galilean invariant theory.

Brent

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Re: Equivalence Principle and Einstein Field Equations

2017-12-21 Thread agrayson2000


On Tuesday, December 19, 2017 at 8:51:51 PM UTC, Brent wrote:
>
>
>
> On 12/18/2017 11:44 PM, agrays...@gmail.com  wrote:
>
> Invariants are always the important things in physics because they are 
>> what we can have intersubjective agreement on.
>>
>> Brent
>>
>
> *IIUC, the field equations are covariant, which means coordinate system 
> independent. *
>
>
> Right.  Covariant means that something that changes in such a way that 
> invariant things remain the same.  So vectors components transform 
> covariantly so that they keep the vector physically the same.
>
> *Isn't Newton's Law of Gravitation also coordinate independent? That is, 
> if we use Newton to calculate the planetary orbits, won't we get the same 
> results in different coordinate systems? *
>
> Right.
>


*If Newton's Law of Gravitation is covariant -- that is, coordinate frame 
independent -- I'd expect it to to be invariant between inertial frames, 
but I don't believe it is. That is, I don't think a LT between inertial 
frames will leave the form of the law unchanged. How do you resolve this 
problem? TIA, AG*

>
> *... Is there a distinction in GR between frame independence and 
> coordinate independence? AG*
>
>
> I'd say frame independence is a special case of coordinate independence.  
> It refers only to relative motion of coordinate frames.
>
> Brent
>
>

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Re: Equivalence Principle and Einstein Field Equations

2017-12-20 Thread agrayson2000


On Monday, December 18, 2017 at 8:36:29 PM UTC, Brent wrote:
>
>
>
> On 12/17/2017 2:39 PM, agrays...@gmail.com  wrote:
>
>
>
> On Sunday, December 17, 2017 at 12:21:27 AM UTC, Brent wrote: 
>>
>>
>>
>> On 12/16/2017 2:59 PM, agrays...@gmail.com wrote:
>>
>> There's a problem applying SR in this situation because neither the 
>> ground or orbiting clock is an inertial frame.AG
>>
>>
>> An orbiting clock is in an inertial frame.  An inertial frame is just one 
>> in which no forces are acting (and gravity is not a force) so that it moves 
>> with constant momentum along a geodesic.  Although it's convenient for 
>> engineering calculations, from a fundamental veiwpoint there is no separate 
>> special relativity and general relativity and no separate clock 
>> corrections.  General relativity is just special relativity in curved 
>> spacetime.  So clocks measure the 4-space interval along their path - 
>> whether that path is geodesic (i.e. inertial) or accelerated.
>>
>
> *Interesting way to look at it. So free falling in a gravity field is an 
> extension of SR. But the thing I find puzzling is that in GR the curvature 
> of space-time is caused by the presence of mass, yet I can draw the path of 
> an accelerated body as necessarily a curve in a space-time diagram. I am 
> having trouble resolving these different sources of curvature. AG*
>
>
> An accelerated body, i.e. one a force is acting on (a rocket, you standing 
> on the ground) is following a curved path that is more curved than the 
> "straightest" path.  I put "straightest" in scare quotes because in the 
> curved spacetime the "straight" path is a geodesic which is still 
> curved...it's just the straightest possible path in the given spacetime.  
>
> It is not true that "I can draw the path of an accelerated body as 
> necessarily a curve in a space-time diagram". 
>



*I was referring to flat space-time, for example as a two dimensional 
representation using x and t coordinates. If one models an accelerating 
particle, it necessarily moves on a curved path. So I think this is very 
suggestive; that one can substitute acceleration for space-time curvature 
induced by gravity or mass-energy, insofar as gravity produces an 
acceleration field. AG *

> In general, if you drew a straight line in some coordinate representation 
> of a curved spacetime, it would correspond to an accelerated (non-geodesic) 
> path.  Imagine drawing a straight line past the Earth.  It would take 
> thrust to fly a rocket along that path.  Of course you could construct a 
> coordinate system around the Earth such that straight lines on the diagram 
> corresponded to geodesics, but it would be a very messy and distorted 
> coordinate system.  
>   
> Brent
>

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Re: Equivalence Principle and Einstein Field Equations

2017-12-19 Thread Brent Meeker



On 12/19/2017 7:58 PM, agrayson2...@gmail.com wrote:



On Tuesday, December 19, 2017 at 8:58:18 PM UTC, Brent wrote:



On 12/18/2017 11:54 PM, agrays...@gmail.com  wrote:



On Tuesday, December 19, 2017 at 3:32:22 AM UTC, Brent wrote:



On 12/18/2017 6:36 PM, agrays...@gmail.com wrote:



On Monday, December 18, 2017 at 8:48:08 PM UTC, Brent wrote:



On 12/18/2017 12:19 AM, agrays...@gmail.com wrote:



On Sunday, December 17, 2017 at 10:39:18 PM UTC,
agrays...@gmail.com wrote:



On Sunday, December 17, 2017 at 12:21:27 AM UTC,
Brent wrote:



On 12/16/2017 2:59 PM, agrays...@gmail.com wrote:

There's a problem applying SR in this
situation because neither the ground or
orbiting clock is an inertial frame.AG


An orbiting clock is in an inertial frame.  An
inertial frame is just one in which no forces
are acting (and gravity is not a force) so that
it moves with constant momentum along a
geodesic.  Although it's convenient for
engineering calculations, from a fundamental
veiwpoint there is no separate special
relativity and general relativity and no
separate clock corrections.  General is just
special relativity in curved spacetime.  So
clocks measure the 4-space interval along their
path - whether that path is geodesic (i.e.
inertial) or accelerated.


*Interesting way to look at it. So free falling in
a gravity field is an extension of SR. But the
thing I find puzzling is that in GR the curvature
of space-time is caused by the presence of mass,
yet I can draw the path of an accelerated body as
_necessarily_ a curve in a space-time diagram. I am
having trouble resolving these different sources of
curvature. AG*


*Einstein must have figured that since gravity produces
an acceleration field, and accelerating test particles
move along curved paths in space-time, he could replace
acceleration by inertial paths in a space-time curved
by the presence of mass-energy. But now, when comparing
test particles moving along different paths in
space-time, he couldn't use the Lorentz transformation
because the relative velocities of the frames are not
necessarily constant. So how did he propose to find the
correct transformation equations, and what are they?
And what were the laws of physics, in this case
gravity, that had to be invariant? AG*


What's invariant is the measure along a path in
spacetime - it's what an ideal clock measures.  The
relation between the measure along two different paths
obviously depends on the lumpiness of the spacetime
through which they travel.  It's as if I headed north
thru the Sierras while you sailed up the coast.  There's
no simple relation between our path lengths even if we
travel between the same two points.


*So what's invariant along along two paths with the same
endpoints? *


It's not about two paths.  The length of each path as
measured using Einstein's  theory of the metric (i.e. as
warped by mass-energy) is an invariant. Just as the distance
your car's odometer would measure driving from NY to LA, it's
some number and it depends on (a) the path you took and (b)
the topography along that path.  The interesting point is
that two such paths between a pair of events are different
durations as measured by clocks carried along the trips.

*Why is this surprising? If dS^2 is path invariant between two 
space-time events, and dT^2 is time measured in the co-moving frame, 
one would expect the time duration to be different along different 
paths since the spatial length varies. *


It would surprise Newton.  He assumed that the time interval between two 
events was independent of a how a clock moved between them.



*AG*


That's contrary to Newton, for whom time was an invariant.

*Not clear from what you write. But whatever it is, why is
that deemed to be invariant? *


Because it doesn't depend on what reference system you use in
spacetime.  It's measuring a distance which is a real thing,
not something relative/subjective.


*Shouldn't it be the laws of physics, in this case gravity,
and hence the field equations? AG *


It's the 

Re: Equivalence Principle and Einstein Field Equations

2017-12-19 Thread agrayson2000


On Tuesday, December 19, 2017 at 8:58:18 PM UTC, Brent wrote:
>
>
>
> On 12/18/2017 11:54 PM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, December 19, 2017 at 3:32:22 AM UTC, Brent wrote: 
>>
>>
>>
>> On 12/18/2017 6:36 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, December 18, 2017 at 8:48:08 PM UTC, Brent wrote: 
>>>
>>>
>>>
>>> On 12/18/2017 12:19 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Sunday, December 17, 2017 at 10:39:18 PM UTC, agrays...@gmail.com 
>>> wrote: 



 On Sunday, December 17, 2017 at 12:21:27 AM UTC, Brent wrote: 
>
>
>
> On 12/16/2017 2:59 PM, agrays...@gmail.com wrote:
>
> There's a problem applying SR in this situation because neither the 
> ground or orbiting clock is an inertial frame.AG
>
>
> An orbiting clock is in an inertial frame.  An inertial frame is just 
> one in which no forces are acting (and gravity is not a force) so that it 
> moves with constant momentum along a geodesic.  Although it's convenient 
> for engineering calculations, from a fundamental veiwpoint there is no 
> separate special relativity and general relativity and no separate clock 
> corrections.  General is just special relativity in curved spacetime.  So 
> clocks measure the 4-space interval along their path - whether that path 
> is 
> geodesic (i.e. inertial) or accelerated.
>

 *Interesting way to look at it. So free falling in a gravity field is 
 an extension of SR. But the thing I find puzzling is that in GR the 
 curvature of space-time is caused by the presence of mass, yet I can draw 
 the path of an accelerated body as necessarily a curve in a space-time 
 diagram. I am having trouble resolving these different sources of 
 curvature. AG*

>>>
>>> *Einstein must have figured that since gravity produces an acceleration 
>>> field, and accelerating test particles move along curved paths in 
>>> space-time, he could replace acceleration by inertial paths in a space-time 
>>> curved by the presence of mass-energy. But now, when comparing test 
>>> particles moving along different paths in space-time, he couldn't use the 
>>> Lorentz transformation because the relative velocities of the frames are 
>>> not necessarily constant. So how did he propose to find the correct 
>>> transformation equations, and what are they? And what were the laws of 
>>> physics, in this case gravity, that had to be invariant? AG*
>>>
>>>
>>> What's invariant is the measure along a path in spacetime - it's what an 
>>> ideal clock measures.  The relation between the measure along two different 
>>> paths obviously depends on the lumpiness of the spacetime through which 
>>> they travel.  It's as if I headed north thru the Sierras while you sailed 
>>> up the coast.  There's no simple relation between our path lengths even if 
>>> we travel between the same two points.  
>>>
>>
>> *So what's invariant along along two paths with the same endpoints? *
>>
>>
>> It's not about two paths.  The length of each path as measured using 
>> Einstein's  theory of the metric (i.e. as warped by mass-energy) is an 
>> invariant.  Just as the distance your car's odometer would measure driving 
>> from NY to LA, it's some number and it depends on (a) the path you took and 
>> (b) the topography along that path.  The interesting point is that two such 
>> paths between a pair of events are different durations as measured by 
>> clocks carried along the trips. 
>>
> *Why is this surprising? If dS^2 is path invariant between two space-time 
events, and dT^2 is time measured in the co-moving frame, one would expect 
the time duration to be different along different paths since the spatial 
length varies. AG*

> That's contrary to Newton, for whom time was an invariant. 
>>
>> *Not clear from what you write. But whatever it is, why is that deemed to 
>> be invariant? *
>>
>>
>> Because it doesn't depend on what reference system you use in spacetime.  
>> It's measuring a distance which is a real thing, not something 
>> relative/subjective.
>>
>> *Shouldn't it be the laws of physics, in this case gravity, and hence the 
>> field equations? AG *
>>
>>
>> It's the basis for them.  They can be written in terms of an extremal 
>> principle for the invariant path lengths.
>>
>
> *Is this the method Einstein used to derive the field equations? *
>
>
> No, he worked from analogy with Newton's gravity potential.
>

*But the field equations are not uniquely determined, so there must have 
been additional guidelines. I read that Einstein tried many different 
equations until he found the right set. And the set he settled on in 1915 
had been tried years earlier but mistakenly rejected. AG*  

>
>
> *This is one of my key interests in this subject; to understand the method 
> he used to derive the field equations. If so, why is invariant path lengths 
> such a crucial condition? I agree that physics seeks 

Re: Equivalence Principle and Einstein Field Equations

2017-12-19 Thread Brent Meeker



On 12/18/2017 11:54 PM, agrayson2...@gmail.com wrote:



On Tuesday, December 19, 2017 at 3:32:22 AM UTC, Brent wrote:



On 12/18/2017 6:36 PM, agrays...@gmail.com  wrote:



On Monday, December 18, 2017 at 8:48:08 PM UTC, Brent wrote:



On 12/18/2017 12:19 AM, agrays...@gmail.com wrote:



On Sunday, December 17, 2017 at 10:39:18 PM UTC,
agrays...@gmail.com wrote:



On Sunday, December 17, 2017 at 12:21:27 AM UTC, Brent
wrote:



On 12/16/2017 2:59 PM, agrays...@gmail.com wrote:

There's a problem applying SR in this situation
because neither the ground or orbiting clock is an
inertial frame.AG


An orbiting clock is in an inertial frame.  An
inertial frame is just one in which no forces are
acting (and gravity is not a force) so that it moves
with constant momentum along a geodesic. Although
it's convenient for engineering calculations, from a
fundamental veiwpoint there is no separate special
relativity and general relativity and no separate
clock corrections.  General is just special
relativity in curved spacetime.  So clocks measure
the 4-space interval along their path - whether that
path is geodesic (i.e. inertial) or accelerated.


*Interesting way to look at it. So free falling in a
gravity field is an extension of SR. But the thing I
find puzzling is that in GR the curvature of space-time
is caused by the presence of mass, yet I can draw the
path of an accelerated body as _necessarily_ a curve in
a space-time diagram. I am having trouble resolving
these different sources of curvature. AG*


*Einstein must have figured that since gravity produces an
acceleration field, and accelerating test particles move
along curved paths in space-time, he could replace
acceleration by inertial paths in a space-time curved by the
presence of mass-energy. But now, when comparing test
particles moving along different paths in space-time, he
couldn't use the Lorentz transformation because the relative
velocities of the frames are not necessarily constant. So
how did he propose to find the correct transformation
equations, and what are they? And what were the laws of
physics, in this case gravity, that had to be invariant? AG*


What's invariant is the measure along a path in spacetime -
it's what an ideal clock measures.  The relation between the
measure along two different paths obviously depends on the
lumpiness of the spacetime through which they travel.  It's
as if I headed north thru the Sierras while you sailed up the
coast.  There's no simple relation between our path lengths
even if we travel between the same two points.


*So what's invariant along along two paths with the same endpoints? *


It's not about two paths.  The length of each path as measured
using Einstein's  theory of the metric (i.e. as warped by
mass-energy) is an invariant.  Just as the distance your car's
odometer would measure driving from NY to LA, it's some number and
it depends on (a) the path you took and (b) the topography along
that path.  The interesting point is that two such paths between a
pair of events are different durations as measured by clocks
carried along the trips.  That's contrary to Newton, for whom time
was an invariant.


*Not clear from what you write. But whatever it is, why is that
deemed to be invariant? *


Because it doesn't depend on what reference system you use in
spacetime.  It's measuring a distance which is a real thing, not
something relative/subjective.


*Shouldn't it be the laws of physics, in this case gravity, and
hence the field equations? AG *


It's the basis for them.  They can be written in terms of an
extremal principle for the invariant path lengths.


*Is this the method Einstein used to derive the field equations? *


No, he worked from analogy with Newton's gravity potential.*

*
*This is one of my key interests in this subject; to understand the 
_method_ he used to derive the field equations. If so, why is 
invariant path lengths such a crucial condition? I agree that physics 
seeks invariants, but why this particular one? AG

*


Having an interval measure is obviously at the heart of a geometric theory.

Brent

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Re: Equivalence Principle and Einstein Field Equations

2017-12-19 Thread Brent Meeker



On 12/18/2017 11:44 PM, agrayson2...@gmail.com wrote:


Invariants are always the important things in physics because they
are what we can have intersubjective agreement on.

Brent


*IIUC, the field equations are covariant, which means coordinate 
system independent. *


Right.  Covariant means that something that changes in such a way that 
invariant things remain the same.  So vectors components transform 
covariantly so that they keep the vector physically the same.


*Isn't Newton's Law of Gravitation also coordinate independent? That 
is, if we use Newton to calculate the planetary orbits, won't we get 
the same results in different coordinate systems? *

Right.

*... Is there a distinction in GR between frame independence and 
coordinate independence? AG*


I'd say frame independence is a special case of coordinate 
independence.  It refers only to relative motion of coordinate frames.


Brent

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Re: Equivalence Principle and Einstein Field Equations

2017-12-18 Thread agrayson2000


On Tuesday, December 19, 2017 at 3:32:22 AM UTC, Brent wrote:
>
>
>
> On 12/18/2017 6:36 PM, agrays...@gmail.com  wrote:
>
>
>
> On Monday, December 18, 2017 at 8:48:08 PM UTC, Brent wrote: 
>>
>>
>>
>> On 12/18/2017 12:19 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Sunday, December 17, 2017 at 10:39:18 PM UTC, agrays...@gmail.com 
>> wrote: 
>>>
>>>
>>>
>>> On Sunday, December 17, 2017 at 12:21:27 AM UTC, Brent wrote: 



 On 12/16/2017 2:59 PM, agrays...@gmail.com wrote:

 There's a problem applying SR in this situation because neither the 
 ground or orbiting clock is an inertial frame.AG


 An orbiting clock is in an inertial frame.  An inertial frame is just 
 one in which no forces are acting (and gravity is not a force) so that it 
 moves with constant momentum along a geodesic.  Although it's convenient 
 for engineering calculations, from a fundamental veiwpoint there is no 
 separate special relativity and general relativity and no separate clock 
 corrections.  General is just special relativity in curved spacetime.  So 
 clocks measure the 4-space interval along their path - whether that path 
 is 
 geodesic (i.e. inertial) or accelerated.

>>>
>>> *Interesting way to look at it. So free falling in a gravity field is an 
>>> extension of SR. But the thing I find puzzling is that in GR the curvature 
>>> of space-time is caused by the presence of mass, yet I can draw the path of 
>>> an accelerated body as necessarily a curve in a space-time diagram. I am 
>>> having trouble resolving these different sources of curvature. AG*
>>>
>>
>> *Einstein must have figured that since gravity produces an acceleration 
>> field, and accelerating test particles move along curved paths in 
>> space-time, he could replace acceleration by inertial paths in a space-time 
>> curved by the presence of mass-energy. But now, when comparing test 
>> particles moving along different paths in space-time, he couldn't use the 
>> Lorentz transformation because the relative velocities of the frames are 
>> not necessarily constant. So how did he propose to find the correct 
>> transformation equations, and what are they? And what were the laws of 
>> physics, in this case gravity, that had to be invariant? AG*
>>
>>
>> What's invariant is the measure along a path in spacetime - it's what an 
>> ideal clock measures.  The relation between the measure along two different 
>> paths obviously depends on the lumpiness of the spacetime through which 
>> they travel.  It's as if I headed north thru the Sierras while you sailed 
>> up the coast.  There's no simple relation between our path lengths even if 
>> we travel between the same two points.  
>>
>
> *So what's invariant along along two paths with the same endpoints? *
>
>
> It's not about two paths.  The length of each path as measured using 
> Einstein's  theory of the metric (i.e. as warped by mass-energy) is an 
> invariant.  Just as the distance your car's odometer would measure driving 
> from NY to LA, it's some number and it depends on (a) the path you took and 
> (b) the topography along that path.  The interesting point is that two such 
> paths between a pair of events are different durations as measured by 
> clocks carried along the trips.  That's contrary to Newton, for whom time 
> was an invariant.
>
> *Not clear from what you write. But whatever it is, why is that deemed to 
> be invariant? *
>
>
> Because it doesn't depend on what reference system you use in spacetime.  
> It's measuring a distance which is a real thing, not something 
> relative/subjective.
>
> *Shouldn't it be the laws of physics, in this case gravity, and hence the 
> field equations? AG *
>
>
> It's the basis for them.  They can be written in terms of an extremal 
> principle for the invariant path lengths.
>



*Is this the method Einstein used to derive the field equations? This is 
one of my key interests in this subject; to understand the method he used 
to derive the field equations. If so, why is invariant path lengths such a 
crucial condition? I agree that physics seeks invariants, but why this 
particular one? AG* 

The Lorentz transformation is just the simple limiting case of flat, smooth 
> spacetime.  It's useful because in a sufficiently small local region 
> spacetime is going to be flat and smooth.
>
> Brent
>
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Re: Equivalence Principle and Einstein Field Equations

2017-12-18 Thread agrayson2000


On Tuesday, December 19, 2017 at 3:34:41 AM UTC, Brent wrote:
>
>
>
> On 12/18/2017 6:54 PM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, December 19, 2017 at 2:36:32 AM UTC, agrays...@gmail.com 
> wrote: 
>>
>>
>>
>> On Monday, December 18, 2017 at 8:48:08 PM UTC, Brent wrote: 
>>>
>>>
>>>
>>> On 12/18/2017 12:19 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Sunday, December 17, 2017 at 10:39:18 PM UTC, agrays...@gmail.com 
>>> wrote: 



 On Sunday, December 17, 2017 at 12:21:27 AM UTC, Brent wrote: 
>
>
>
> On 12/16/2017 2:59 PM, agrays...@gmail.com wrote:
>
> There's a problem applying SR in this situation because neither the 
> ground or orbiting clock is an inertial frame.AG
>
>
> An orbiting clock is in an inertial frame.  An inertial frame is just 
> one in which no forces are acting (and gravity is not a force) so that it 
> moves with constant momentum along a geodesic.  Although it's convenient 
> for engineering calculations, from a fundamental veiwpoint there is no 
> separate special relativity and general relativity and no separate clock 
> corrections.  General is just special relativity in curved spacetime.  So 
> clocks measure the 4-space interval along their path - whether that path 
> is 
> geodesic (i.e. inertial) or accelerated.
>

 *Interesting way to look at it. So free falling in a gravity field is 
 an extension of SR. But the thing I find puzzling is that in GR the 
 curvature of space-time is caused by the presence of mass, yet I can draw 
 the path of an accelerated body as necessarily a curve in a space-time 
 diagram. I am having trouble resolving these different sources of 
 curvature. AG*

>>>
>>> *Einstein must have figured that since gravity produces an acceleration 
>>> field, and accelerating test particles move along curved paths in 
>>> space-time, he could replace acceleration by inertial paths in a space-time 
>>> curved by the presence of mass-energy. But now, when comparing test 
>>> particles moving along different paths in space-time, he couldn't use the 
>>> Lorentz transformation because the relative velocities of the frames are 
>>> not necessarily constant. So how did he propose to find the correct 
>>> transformation equations, and what are they? And what were the laws of 
>>> physics, in this case gravity, that had to be invariant? AG*
>>>
>>>
>>> What's invariant is the measure along a path in spacetime - it's what an 
>>> ideal clock measures.  The relation between the measure along two different 
>>> paths obviously depends on the lumpiness of the spacetime through which 
>>> they travel.  It's as if I headed north thru the Sierras while you sailed 
>>> up the coast.  There's no simple relation between our path lengths even if 
>>> we travel between the same two points.  
>>>
>>
>> *So what's invariant along along two paths with the same endpoints? Not 
>> clear from what you write. But whatever it is, why is that deemed to be 
>> invariant? Shouldn't it be the laws of physics, in this case gravity, and 
>> hence the field equations? AG *
>>
>
> *I think you mean the dS^2 value is invariant along two paths with the 
> same endpoints, but not the path length of the spatial coordinates. 
> Correct? *
>
>
> Right.
>
> *But why is this particular invariant so important, and perhaps used as a 
> guide to Einstein? AG*
>
>
> Invariants are always the important things in physics because they are 
> what we can have intersubjective agreement on.
>
> Brent
>

*IIUC, the field equations are covariant, which means coordinate system 
independent. Isn't Newton's Law of Gravitation also coordinate independent? 
That is, if we use Newton to calculate the planetary orbits, won't we get 
the same results in different coordinate systems? ... Is there a 
distinction in GR between frame independence and coordinate independence? 
AG*

>
>
>> The Lorentz transformation is just the simple limiting case of flat, 
>>> smooth spacetime.  It's useful because in a sufficiently small local region 
>>> spacetime is going to be flat and smooth.
>>>
>>> Brent
>>>
>> -- 
> You received this message because you are subscribed to the Google Groups 
> "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an 
> email to everything-li...@googlegroups.com .
> To post to this group, send email to everyth...@googlegroups.com 
> .
> Visit this group at https://groups.google.com/group/everything-list.
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>
>
>

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Re: Equivalence Principle and Einstein Field Equations

2017-12-18 Thread Brent Meeker



On 12/18/2017 6:54 PM, agrayson2...@gmail.com wrote:



On Tuesday, December 19, 2017 at 2:36:32 AM UTC, agrays...@gmail.com 
wrote:




On Monday, December 18, 2017 at 8:48:08 PM UTC, Brent wrote:



On 12/18/2017 12:19 AM, agrays...@gmail.com wrote:



On Sunday, December 17, 2017 at 10:39:18 PM UTC,
agrays...@gmail.com wrote:



On Sunday, December 17, 2017 at 12:21:27 AM UTC, Brent
wrote:



On 12/16/2017 2:59 PM, agrays...@gmail.com wrote:

There's a problem applying SR in this situation
because neither the ground or orbiting clock is an
inertial frame.AG


An orbiting clock is in an inertial frame. An
inertial frame is just one in which no forces are
acting (and gravity is not a force) so that it moves
with constant momentum along a geodesic.  Although
it's convenient for engineering calculations, from a
fundamental veiwpoint there is no separate special
relativity and general relativity and no separate
clock corrections.  General is just special
relativity in curved spacetime.  So clocks measure
the 4-space interval along their path - whether that
path is geodesic (i.e. inertial) or accelerated.


*Interesting way to look at it. So free falling in a
gravity field is an extension of SR. But the thing I find
puzzling is that in GR the curvature of space-time is
caused by the presence of mass, yet I can draw the path
of an accelerated body as _necessarily_ a curve in a
space-time diagram. I am having trouble resolving these
different sources of curvature. AG*


*Einstein must have figured that since gravity produces an
acceleration field, and accelerating test particles move
along curved paths in space-time, he could replace
acceleration by inertial paths in a space-time curved by the
presence of mass-energy. But now, when comparing test
particles moving along different paths in space-time, he
couldn't use the Lorentz transformation because the relative
velocities of the frames are not necessarily constant. So how
did he propose to find the correct transformation equations,
and what are they? And what were the laws of physics, in this
case gravity, that had to be invariant? AG*


What's invariant is the measure along a path in spacetime -
it's what an ideal clock measures.  The relation between the
measure along two different paths obviously depends on the
lumpiness of the spacetime through which they travel.  It's as
if I headed north thru the Sierras while you sailed up the
coast.  There's no simple relation between our path lengths
even if we travel between the same two points.


*So what's invariant along along two paths with the same
endpoints? Not clear from what you write. But whatever it is, why
is that deemed to be invariant? Shouldn't it be the laws of
physics, in this case gravity, and hence the field equations? AG *


*I think you mean the dS^2 value is invariant along two paths with the 
same endpoints, but not the path length of the spatial coordinates. 
Correct? *


Right.*

*
*But why is this particular invariant so important, and perhaps used 
as a guide to Einstein? AG*


Invariants are always the important things in physics because they are 
what we can have intersubjective agreement on.


Brent



The Lorentz transformation is just the simple limiting case of
flat, smooth spacetime.  It's useful because in a sufficiently
small local region spacetime is going to be flat and smooth.

Brent

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Groups "Everything List" group.
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Re: Equivalence Principle and Einstein Field Equations

2017-12-18 Thread Brent Meeker



On 12/18/2017 6:36 PM, agrayson2...@gmail.com wrote:



On Monday, December 18, 2017 at 8:48:08 PM UTC, Brent wrote:



On 12/18/2017 12:19 AM, agrays...@gmail.com  wrote:



On Sunday, December 17, 2017 at 10:39:18 PM UTC,
agrays...@gmail.com wrote:



On Sunday, December 17, 2017 at 12:21:27 AM UTC, Brent wrote:



On 12/16/2017 2:59 PM, agrays...@gmail.com wrote:

There's a problem applying SR in this situation because
neither the ground or orbiting clock is an inertial frame.AG


An orbiting clock is in an inertial frame.  An inertial
frame is just one in which no forces are acting (and
gravity is not a force) so that it moves with constant
momentum along a geodesic.  Although it's convenient for
engineering calculations, from a fundamental veiwpoint
there is no separate special relativity and general
relativity and no separate clock corrections.  General is
just special relativity in curved spacetime.  So clocks
measure the 4-space interval along their path - whether
that path is geodesic (i.e. inertial) or accelerated.


*Interesting way to look at it. So free falling in a gravity
field is an extension of SR. But the thing I find puzzling is
that in GR the curvature of space-time is caused by the
presence of mass, yet I can draw the path of an accelerated
body as _necessarily_ a curve in a space-time diagram. I am
having trouble resolving these different sources of
curvature. AG*


*Einstein must have figured that since gravity produces an
acceleration field, and accelerating test particles move along
curved paths in space-time, he could replace acceleration by
inertial paths in a space-time curved by the presence of
mass-energy. But now, when comparing test particles moving along
different paths in space-time, he couldn't use the Lorentz
transformation because the relative velocities of the frames are
not necessarily constant. So how did he propose to find the
correct transformation equations, and what are they? And what
were the laws of physics, in this case gravity, that had to be
invariant? AG*


What's invariant is the measure along a path in spacetime - it's
what an ideal clock measures.  The relation between the measure
along two different paths obviously depends on the lumpiness of
the spacetime through which they travel.  It's as if I headed
north thru the Sierras while you sailed up the coast.  There's no
simple relation between our path lengths even if we travel between
the same two points.


*So what's invariant along along two paths with the same endpoints? *


It's not about two paths.  The length of each path as measured using 
Einstein's  theory of the metric (i.e. as warped by mass-energy) is an 
invariant.  Just as the distance your car's odometer would measure 
driving from NY to LA, it's some number and it depends on (a) the path 
you took and (b) the topography along that path.  The interesting point 
is that two such paths between a pair of events are different durations 
as measured by clocks carried along the trips.  That's contrary to 
Newton, for whom time was an invariant.


*Not clear from what you write. But whatever it is, why is that deemed 
to be invariant? *


Because it doesn't depend on what reference system you use in 
spacetime.  It's measuring a distance which is a real thing, not 
something relative/subjective.


*Shouldn't it be the laws of physics, in this case gravity, and hence 
the field equations? AG *


It's the basis for them.  They can be written in terms of an extremal 
principle for the invariant path lengths.


Brent


The Lorentz transformation is just the simple limiting case of
flat, smooth spacetime.  It's useful because in a sufficiently
small local region spacetime is going to be flat and smooth.

Brent

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Re: Equivalence Principle and Einstein Field Equations

2017-12-18 Thread agrayson2000


On Tuesday, December 19, 2017 at 2:36:32 AM UTC, agrays...@gmail.com wrote:
>
>
>
> On Monday, December 18, 2017 at 8:48:08 PM UTC, Brent wrote:
>>
>>
>>
>> On 12/18/2017 12:19 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Sunday, December 17, 2017 at 10:39:18 PM UTC, agrays...@gmail.com 
>> wrote: 
>>>
>>>
>>>
>>> On Sunday, December 17, 2017 at 12:21:27 AM UTC, Brent wrote: 



 On 12/16/2017 2:59 PM, agrays...@gmail.com wrote:

 There's a problem applying SR in this situation because neither the 
 ground or orbiting clock is an inertial frame.AG


 An orbiting clock is in an inertial frame.  An inertial frame is just 
 one in which no forces are acting (and gravity is not a force) so that it 
 moves with constant momentum along a geodesic.  Although it's convenient 
 for engineering calculations, from a fundamental veiwpoint there is no 
 separate special relativity and general relativity and no separate clock 
 corrections.  General is just special relativity in curved spacetime.  So 
 clocks measure the 4-space interval along their path - whether that path 
 is 
 geodesic (i.e. inertial) or accelerated.

>>>
>>> *Interesting way to look at it. So free falling in a gravity field is an 
>>> extension of SR. But the thing I find puzzling is that in GR the curvature 
>>> of space-time is caused by the presence of mass, yet I can draw the path of 
>>> an accelerated body as necessarily a curve in a space-time diagram. I am 
>>> having trouble resolving these different sources of curvature. AG*
>>>
>>
>> *Einstein must have figured that since gravity produces an acceleration 
>> field, and accelerating test particles move along curved paths in 
>> space-time, he could replace acceleration by inertial paths in a space-time 
>> curved by the presence of mass-energy. But now, when comparing test 
>> particles moving along different paths in space-time, he couldn't use the 
>> Lorentz transformation because the relative velocities of the frames are 
>> not necessarily constant. So how did he propose to find the correct 
>> transformation equations, and what are they? And what were the laws of 
>> physics, in this case gravity, that had to be invariant? AG*
>>
>>
>> What's invariant is the measure along a path in spacetime - it's what an 
>> ideal clock measures.  The relation between the measure along two different 
>> paths obviously depends on the lumpiness of the spacetime through which 
>> they travel.  It's as if I headed north thru the Sierras while you sailed 
>> up the coast.  There's no simple relation between our path lengths even if 
>> we travel between the same two points.  
>>
>
> *So what's invariant along along two paths with the same endpoints? Not 
> clear from what you write. But whatever it is, why is that deemed to be 
> invariant? Shouldn't it be the laws of physics, in this case gravity, and 
> hence the field equations? AG *
>

*I think you mean the dS^2 value is invariant along two paths with the same 
endpoints, but not the path length of the spatial coordinates. Correct? But 
why is this particular invariant so important, and perhaps used as a guide 
to Einstein? AG*

>
> The Lorentz transformation is just the simple limiting case of flat, 
>> smooth spacetime.  It's useful because in a sufficiently small local region 
>> spacetime is going to be flat and smooth.
>>
>> Brent
>>
>

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Re: Equivalence Principle and Einstein Field Equations

2017-12-18 Thread agrayson2000


On Monday, December 18, 2017 at 8:48:08 PM UTC, Brent wrote:
>
>
>
> On 12/18/2017 12:19 AM, agrays...@gmail.com  wrote:
>
>
>
> On Sunday, December 17, 2017 at 10:39:18 PM UTC, agrays...@gmail.com 
> wrote: 
>>
>>
>>
>> On Sunday, December 17, 2017 at 12:21:27 AM UTC, Brent wrote: 
>>>
>>>
>>>
>>> On 12/16/2017 2:59 PM, agrays...@gmail.com wrote:
>>>
>>> There's a problem applying SR in this situation because neither the 
>>> ground or orbiting clock is an inertial frame.AG
>>>
>>>
>>> An orbiting clock is in an inertial frame.  An inertial frame is just 
>>> one in which no forces are acting (and gravity is not a force) so that it 
>>> moves with constant momentum along a geodesic.  Although it's convenient 
>>> for engineering calculations, from a fundamental veiwpoint there is no 
>>> separate special relativity and general relativity and no separate clock 
>>> corrections.  General is just special relativity in curved spacetime.  So 
>>> clocks measure the 4-space interval along their path - whether that path is 
>>> geodesic (i.e. inertial) or accelerated.
>>>
>>
>> *Interesting way to look at it. So free falling in a gravity field is an 
>> extension of SR. But the thing I find puzzling is that in GR the curvature 
>> of space-time is caused by the presence of mass, yet I can draw the path of 
>> an accelerated body as necessarily a curve in a space-time diagram. I am 
>> having trouble resolving these different sources of curvature. AG*
>>
>
> *Einstein must have figured that since gravity produces an acceleration 
> field, and accelerating test particles move along curved paths in 
> space-time, he could replace acceleration by inertial paths in a space-time 
> curved by the presence of mass-energy. But now, when comparing test 
> particles moving along different paths in space-time, he couldn't use the 
> Lorentz transformation because the relative velocities of the frames are 
> not necessarily constant. So how did he propose to find the correct 
> transformation equations, and what are they? And what were the laws of 
> physics, in this case gravity, that had to be invariant? AG*
>
>
> What's invariant is the measure along a path in spacetime - it's what an 
> ideal clock measures.  The relation between the measure along two different 
> paths obviously depends on the lumpiness of the spacetime through which 
> they travel.  It's as if I headed north thru the Sierras while you sailed 
> up the coast.  There's no simple relation between our path lengths even if 
> we travel between the same two points.  
>

*So what's invariant along along two paths with the same endpoints? Not 
clear from what you write. But whatever it is, why is that deemed to be 
invariant? Shouldn't it be the laws of physics, in this case gravity, and 
hence the field equations? AG *

> The Lorentz transformation is just the simple limiting case of flat, 
> smooth spacetime.  It's useful because in a sufficiently small local region 
> spacetime is going to be flat and smooth.
>
> Brent
>

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Re: Equivalence Principle and Einstein Field Equations

2017-12-18 Thread Brent Meeker



On 12/18/2017 12:19 AM, agrayson2...@gmail.com wrote:



On Sunday, December 17, 2017 at 10:39:18 PM UTC, agrays...@gmail.com 
wrote:




On Sunday, December 17, 2017 at 12:21:27 AM UTC, Brent wrote:



On 12/16/2017 2:59 PM, agrays...@gmail.com wrote:

There's a problem applying SR in this situation because
neither the ground or orbiting clock is an inertial frame.AG


An orbiting clock is in an inertial frame.  An inertial frame
is just one in which no forces are acting (and gravity is not
a force) so that it moves with constant momentum along a
geodesic.  Although it's convenient for engineering
calculations, from a fundamental veiwpoint there is no
separate special relativity and general relativity and no
separate clock corrections.  General is just special
relativity in curved spacetime.  So clocks measure the 4-space
interval along their path - whether that path is geodesic
(i.e. inertial) or accelerated.


*Interesting way to look at it. So free falling in a gravity field
is an extension of SR. But the thing I find puzzling is that in GR
the curvature of space-time is caused by the presence of mass, yet
I can draw the path of an accelerated body as _necessarily_ a
curve in a space-time diagram. I am having trouble resolving these
different sources of curvature. AG*


*Einstein must have figured that since gravity produces an 
acceleration field, and accelerating test particles move along curved 
paths in space-time, he could replace acceleration by inertial paths 
in a space-time curved by the presence of mass-energy. But now, when 
comparing test particles moving along different paths in space-time, 
he couldn't use the Lorentz transformation because the relative 
velocities of the frames are not necessarily constant. So how did he 
propose to find the correct transformation equations, and what are 
they? And what were the laws of physics, in this case gravity, that 
had to be invariant? AG*


What's invariant is the measure along a path in spacetime - it's what an 
ideal clock measures.  The relation between the measure along two 
different paths obviously depends on the lumpiness of the spacetime 
through which they travel.  It's as if I headed north thru the Sierras 
while you sailed up the coast.  There's no simple relation between our 
path lengths even if we travel between the same two points.   The 
Lorentz transformation is just the simple limiting case of flat, smooth 
spacetime.  It's useful because in a sufficiently small local region 
spacetime is going to be flat and smooth.


Brent

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Re: Equivalence Principle and Einstein Field Equations

2017-12-18 Thread Brent Meeker



On 12/17/2017 2:39 PM, agrayson2...@gmail.com wrote:



On Sunday, December 17, 2017 at 12:21:27 AM UTC, Brent wrote:



On 12/16/2017 2:59 PM, agrays...@gmail.com  wrote:

There's a problem applying SR in this situation because neither
the ground or orbiting clock is an inertial frame.AG


An orbiting clock is in an inertial frame.  An inertial frame is
just one in which no forces are acting (and gravity is not a
force) so that it moves with constant momentum along a geodesic. 
Although it's convenient for engineering calculations, from a
fundamental veiwpoint there is no separate special relativity and
general relativity and no separate clock corrections.  General
relativity is just special relativity in curved spacetime.  So
clocks measure the 4-space interval along their path - whether
that path is geodesic (i.e. inertial) or accelerated.


*Interesting way to look at it. So free falling in a gravity field is 
an extension of SR. But the thing I find puzzling is that in GR the 
curvature of space-time is caused by the presence of mass, yet I can 
draw the path of an accelerated body as _necessarily_ a curve in a 
space-time diagram. I am having trouble resolving these different 
sources of curvature. AG*


An accelerated body, i.e. one a force is acting on (a rocket, you 
standing on the ground) is following a curved path that is more curved 
than the "straightest" path.  I put "straightest" in scare quotes 
because in the curved spacetime the "straight" path is a geodesic which 
is still curved...it's just the straightest possible path in the given 
spacetime.


It is not true that "I can draw the path of an accelerated body as 
necessarily a curve in a space-time diagram".  In general, if you drew a 
straight line in some coordinate representation of a curved spacetime, 
it would correspond to an accelerated (non-geodesic) path.  Imagine 
drawing a straight line past the Earth.  It would take thrust to fly a 
rocket along that path.  Of course you could construct a coordinate 
system around the Earth such that straight lines on the diagram 
corresponded to geodesics, but it would be a very messy and distorted 
coordinate system.


Brent

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Re: Equivalence Principle and Einstein Field Equations

2017-12-18 Thread agrayson2000


On Sunday, December 17, 2017 at 10:39:18 PM UTC, agrays...@gmail.com wrote:
>
>
>
> On Sunday, December 17, 2017 at 12:21:27 AM UTC, Brent wrote:
>>
>>
>>
>> On 12/16/2017 2:59 PM, agrays...@gmail.com wrote:
>>
>> There's a problem applying SR in this situation because neither the 
>> ground or orbiting clock is an inertial frame.AG
>>
>>
>> An orbiting clock is in an inertial frame.  An inertial frame is just one 
>> in which no forces are acting (and gravity is not a force) so that it moves 
>> with constant momentum along a geodesic.  Although it's convenient for 
>> engineering calculations, from a fundamental veiwpoint there is no separate 
>> special relativity and general relativity and no separate clock 
>> corrections.  General is just special relativity in curved spacetime.  So 
>> clocks measure the 4-space interval along their path - whether that path is 
>> geodesic (i.e. inertial) or accelerated.
>>
>
> *Interesting way to look at it. So free falling in a gravity field is an 
> extension of SR. But the thing I find puzzling is that in GR the curvature 
> of space-time is caused by the presence of mass, yet I can draw the path of 
> an accelerated body as necessarily a curve in a space-time diagram. I am 
> having trouble resolving these different sources of curvature. AG*
>

*Einstein must have figured that since gravity produces an acceleration 
field, and accelerating test particles move along curved paths in 
space-time, he could replace acceleration by inertial paths in a space-time 
curved by the presence of mass-energy. But now, when comparing test 
particles moving along different paths in space-time, he couldn't use the 
Lorentz transformation because the relative velocities of the frames are 
not necessarily constant. So how did he propose to find the correct 
transformation equations, and what are they? And what were the laws of 
physics, in this case gravity, that had to be invariant? AG*

>
>
>> Brent
>>
>

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Re: Equivalence Principle and Einstein Field Equations

2017-12-17 Thread agrayson2000


On Sunday, December 17, 2017 at 12:21:27 AM UTC, Brent wrote:
>
>
>
> On 12/16/2017 2:59 PM, agrays...@gmail.com  wrote:
>
> There's a problem applying SR in this situation because neither the ground 
> or orbiting clock is an inertial frame.AG
>
>
> An orbiting clock is in an inertial frame.  An inertial frame is just one 
> in which no forces are acting (and gravity is not a force) so that it moves 
> with constant momentum along a geodesic.  Although it's convenient for 
> engineering calculations, from a fundamental veiwpoint there is no separate 
> special relativity and general relativity and no separate clock 
> corrections.  General relativity is just special relativity in curved 
> spacetime.  So clocks measure the 4-space interval along their path - 
> whether that path is geodesic (i.e. inertial) or accelerated.
>

*Interesting way to look at it. So free falling in a gravity field is an 
extension of SR. But the thing I find puzzling is that in GR the curvature 
of space-time is caused by the presence of mass, yet I can draw the path of 
an accelerated body as necessarily a curve in a space-time diagram. I am 
having trouble resolving these different sources of curvature. AG*

>
> Brent
>

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Re: Equivalence Principle and Einstein Field Equations

2017-12-16 Thread John Clark
On Sat, Dec 16, 2017 at 8:18 PM,  wrote:


​> ​
> The actual clock readings depends on the number of ticks. So if you claim
> the number of ticks is the same for both clocks, there will no difference
> in their readings.


*​Both clocks produced the same number of ticks in the time it takes the
laser to go from one wall to the other, ​ ​but in one case (the curved
case) light ​went a longer distance than the other case, you know that
light can't change its speed so you have to conclude that the 2 clocks
can't be running at the same rate.*


​>​
>  I still question why SR is relevant


*​If the 2 clocks were stationary relative to ​each other then it wouldn't
be, but they aren't so it is. *

*​John K Clark​ *







>

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Re: Equivalence Principle and Einstein Field Equations

2017-12-16 Thread agrayson2000


On Sunday, December 17, 2017 at 12:13:49 AM UTC, John Clark wrote:
>
> On Sat, Dec 16, 2017 at 5:59 PM,  
> wrote:
>
> >>​
>>> A curved line from one wall to the other is longer than a straight line
>>> ​,​
>>>  and yet when you measure the time it takes for light to do this with 
>>> your very accurate clock you notice its exactly the same. You already know 
>>> the measured speed of light never changes so 
>>> ​if something is moving at the same speed and moves a greater distance 
>>> in the same number of clock ticks then 
>>> you'd have to conclude that being accelerated makes your clock run slow.
>>>
>>
>> ​> ​
>> Since a clock in the gravity field measures less elapsed time, the number 
>> of ticks in your example cannot be identical in those two cases. 
>
>
> ​
> A clock at 1g produces  ticks at a slower rate
> ​
> but the laser beam  from one side on the 
> ​elevator ​
> cab 
> ​to the other ​
> is curved and thus longer
> ​​
> . 
> ​ ​
> ​A clock at zero g will produce ticks ​at a faster rate but the 
> laser beam  from one side on the 
> ​elevator ​
> cab 
> ​to the other ​
> is 
> ​straight​
>  and thus 
> ​shorter​
> ​ 5. So when observers in both cabs count the number of ticks it takes for 
> the Laser to go from one side of the cab to the other then get the same 
> number,​
>

The actual clock readings depends on the number of ticks. So if you claim 
the number of ticks is the same for both clocks, there will no difference 
in their readings. AG 

>
>
> ​
>>> ​>>​
>>> T​
>>> he 
>>> ​GPS ​
>>> satellite is moving very fast so due to Special Relativity the 
>>> satellite's clock will LOSE 7210 nanoseconds a day, but the satellite's 
>>> clock is in a weaker gravitational field than the clock 
>>> ​on the ground 
>>> because it is further from the Earth's center, so due to GENERAL 
>>> RELATIVITY the clock will GAIN 45850 nanoseconds a day. Taking these 2 
>>> factors into account the satellite's clocks gains 45850 −7210 = 38,640 
>>> nanoseconds a day relative to 
>>> ​a​
>>>  clock 
>>> ​on the ground. If this were not taken into account the GPS system would 
>>> drift off by 6 miles a day.
>>>
>>>
>> ​> ​
>> There's a problem applying SR in this situation because neither the 
>> ground or orbiting clock is an inertial frame.
>>
>
> ​That's why general relativity must also we used. Two different thing 
> must be taken into account for the GPS ​to be accurate, the clock on the 
> earth and the clock in space are in gravitational fields of different 
> strengths AND the clocks are in motion relative to each other. 
>  
>

As Brent points out, the orbiting clock is in an inertial frame, but IMO 
not the ground clock. So I still question why SR is relevant. AG 

> ​
>
> John K Clark​
>
>
>
>
>
>

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Re: Equivalence Principle and Einstein Field Equations

2017-12-16 Thread Brent Meeker



On 12/16/2017 2:59 PM, agrayson2...@gmail.com wrote:
There's a problem applying SR in this situation because neither the 
ground or orbiting clock is an inertial frame.AG


An orbiting clock is in an inertial frame.  An inertial frame is just 
one in which no forces are acting (and gravity is not a force) so that 
it moves with constant momentum along a geodesic.  Although it's 
convenient for engineering calculations, from a fundamental veiwpoint 
there is no separate special relativity and general relativity and no 
separate clock corrections.  General relativity is just special 
relativity in curved spacetime.  So clocks measure the 4-space interval 
along their path - whether that path is geodesic (i.e. inertial) or 
accelerated.


Brent

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Re: Equivalence Principle and Einstein Field Equations

2017-12-16 Thread John Clark
On Sat, Dec 16, 2017 at 5:59 PM,  wrote:

>>​
>> A curved line from one wall to the other is longer than a straight line
>> ​,​
>>  and yet when you measure the time it takes for light to do this with
>> your very accurate clock you notice its exactly the same. You already know
>> the measured speed of light never changes so
>> ​if something is moving at the same speed and moves a greater distance in
>> the same number of clock ticks then
>> you'd have to conclude that being accelerated makes your clock run slow.
>>
>
> ​> ​
> Since a clock in the gravity field measures less elapsed time, the number
> of ticks in your example cannot be identical in those two cases.


​
A clock at 1g produces  ticks at a slower rate
​
but the laser beam  from one side on the
​elevator ​
cab
​to the other ​
is curved and thus longer
​​
.
​ ​
​A clock at zero g will produce ticks ​at a faster rate but the
laser beam  from one side on the
​elevator ​
cab
​to the other ​
is
​straight​
 and thus
​shorter​
​ 5. So when observers in both cabs count the number of ticks it takes for
the Laser to go from one side of the cab to the other then get the same
number,​


​
>> ​>>​
>> T​
>> he
>> ​GPS ​
>> satellite is moving very fast so due to Special Relativity the
>> satellite's clock will LOSE 7210 nanoseconds a day, but the satellite's
>> clock is in a weaker gravitational field than the clock
>> ​on the ground
>> because it is further from the Earth's center, so due to GENERAL
>> RELATIVITY the clock will GAIN 45850 nanoseconds a day. Taking these 2
>> factors into account the satellite's clocks gains 45850 −7210 = 38,640
>> nanoseconds a day relative to
>> ​a​
>>  clock
>> ​on the ground. If this were not taken into account the GPS system would
>> drift off by 6 miles a day.
>>
>>
> ​> ​
> There's a problem applying SR in this situation because neither the ground
> or orbiting clock is an inertial frame.
>

​That's why general relativity must also we used. Two different thing must
be taken into account for the GPS ​to be accurate, the clock on the earth
and the clock in space are in gravitational fields of different strengths
AND the clocks are in motion relative to each other.

​

John K Clark​

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Re: Equivalence Principle and Einstein Field Equations

2017-12-16 Thread agrayson2000


On Wednesday, December 13, 2017 at 12:08:35 AM UTC, John Clark wrote:
>
>
> On Mon, Dec 11, 2017 at 5:11 PM,  
> wrote:
>
>
> ​>> ​
>>> The Equivalence Principle says if 
>>> ​you
>>>  ignore tidal effects and you're in a windowless elevator cab there is 
>>> no way to know if you're sitting on the Earth in a gravitational field or 
>>> in deep intergalactic space being accelerated by a rocket upward at 1G. If 
>>> you feel zero G and fire a Laser pointer from one wall 
>>> ​to the other ​
>>> it will go in a straight line and hit the exact opposite side on the 
>>> other wall. But if you were being accelerated upward the elevator cab will 
>>> move 
>>> ​slightly ​
>>> upward in the time it takes for the light to go from one wall to the 
>>> other so the spot the laser makes on the other wall will be slightly lower 
>>> than it was when you were in zero G, you see the laser beam follow a curve.
>>>
>>
>> ​> ​
>> At rest on Earth is not a situation of zero G; it's 1G. Or, say, if you 
>> want a straight beam, one can assume an inertial frame,
>>
>
> ​The surface of the Earth is in a gravitational field and so it is *NOT* a 
> inertial frame, and so light from a Laser pointer does curve, although not 
> by a lot. The interior of an 
> elevator in which the cable has been cut would be a inertial frame, until 
> it hit the ground. ​
>  
>
> ​>>​
>>> A curved line from one wall to the other is longer than a straight line
>>> ​,​
>>> and yet when you measure the time it takes for light to do this with 
>>> your very accurate clock you notice its exactly the same. You already know 
>>> the measured speed of light never changes so 
>>> ​if something is moving at the same speed and moves a greater distance 
>>> in the same number of clock ticks then 
>>> you'd have to conclude that being accelerated makes your clock run slow.
>>>
>>
Since a clock in the gravity field measures less elapsed time, the number 
of ticks in your example cannot be identical in those two cases.  Moreover, 
I can't convince myself that the measured time in the two scenarios is 
identical. AG

>
>> ​> ​
>> I think most of last paragraph incorrect. In experiments with GPS clocks, 
>> the ground clock, in the stronger gravity field, runs slower than an 
>> orbiting clock. 
>>
>
>
> ​T​
> he 
> ​GPS ​
> satellite is moving very fast so due to Special Relativity the 
> satellite's clock will LOSE 7210 nanoseconds a day, but the satellite's 
> clock is in a weaker gravitational field than the clock 
> ​on the ground 
> because it is further from the Earth's center, so due to GENERAL 
> RELATIVITY the clock will GAIN 45850 nanoseconds a day. Taking these 2 
> factors into account the satellite's clocks gains 45850 −7210 = 38,640 
> nanoseconds a day relative to 
> ​a​
>  clock 
> ​on the ground. If this were not taken into account the GPS system would 
> drift off by 6 miles a day.
>
>
There's a problem applying SR in this situation because neither the ground 
or orbiting clock is an inertial frame.AG

>  
>
>> ​> ​
>> Fewer ticks in ground clock
>>
>
> ​Yes, a clock on the ground in a 1G gravitational field ​
>  
> ​or a clock in deep space being accelerated by a rocket at 1G will record 
> fewer ticks than a non-accelerating clock in no gravitational field.
>
> ​> ​
>> In your elevator example, where zero G can be interpreted as being in an 
>> inertial frame, you claim the elapsed time duration using ticks, is 
>> identical for both beams. 
>
>
> ​I'm not sure which 2 beams you're talking about. The interior of the 
> elevator sitting on the ground 
>  
> ​and the elevator in deep space being accelerated by a rocket are 
> identical.
>

Agreed. IIRC, I was thinking of the orbiting clock being so far removed, 
that it would effectively be in an inertial frame. AG
 

> ​The elevator with the broken cable near the earth and the elevator with 
> no rocket in deep space are identical.
>
> John K Clark
>
>
>
>

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Re: Equivalence Principle and Einstein Field Equations

2017-12-12 Thread John Clark
On Mon, Dec 11, 2017 at 5:11 PM,  wrote:


​>> ​
>> The Equivalence Principle says if
>> ​you
>>  ignore tidal effects and you're in a windowless elevator cab there is no
>> way to know if you're sitting on the Earth in a gravitational field or in
>> deep intergalactic space being accelerated by a rocket upward at 1G. If you
>> feel zero G and fire a Laser pointer from one wall
>> ​to the other ​
>> it will go in a straight line and hit the exact opposite side on the
>> other wall. But if you were being accelerated upward the elevator cab will
>> move
>> ​slightly ​
>> upward in the time it takes for the light to go from one wall to the
>> other so the spot the laser makes on the other wall will be slightly lower
>> than it was when you were in zero G, you see the laser beam follow a curve.
>>
>
> ​> ​
> At rest on Earth is not a situation of zero G; it's 1G. Or, say, if you
> want a straight beam, one can assume an inertial frame,
>

​The surface of the Earth is in a gravitational field and so it is *NOT* a
inertial frame, and so light from a Laser pointer does curve, although not
by a lot. The interior of an
elevator in which the cable has been cut would be a inertial frame, until
it hit the ground. ​


​>>​
>> A curved line from one wall to the other is longer than a straight line
>> ​,​
>> and yet when you measure the time it takes for light to do this with your
>> very accurate clock you notice its exactly the same. You already know the
>> measured speed of light never changes so
>> ​if something is moving at the same speed and moves a greater distance in
>> the same number of clock ticks then
>> you'd have to conclude that being accelerated makes your clock run slow.
>>
>
> ​> ​
> I think most of last paragraph incorrect. In experiments with GPS clocks,
> the ground clock, in the stronger gravity field, runs slower than an
> orbiting clock.
>


​T​
he
​GPS ​
satellite is moving very fast so due to Special Relativity the satellite's
clock will LOSE 7210 nanoseconds a day, but the satellite's clock is in a
weaker gravitational field than the clock
​on the ground
because it is further from the Earth's center, so due to GENERAL RELATIVITY
 the clock will GAIN 45850 nanoseconds a day. Taking these 2 factors into
account the satellite's clocks gains 45850 −7210 = 38,640 nanoseconds a day
relative to
​a​
 clock
​on the ground. If this were not taken into account the GPS system would
drift off by 6 miles a day.



> ​> ​
> Fewer ticks in ground clock
>

​Yes, a clock on the ground in a 1G gravitational field ​

​or a clock in deep space being accelerated by a rocket at 1G will record
fewer ticks than a non-accelerating clock in no gravitational field.

​> ​
> In your elevator example, where zero G can be interpreted as being in an
> inertial frame, you claim the elapsed time duration using ticks, is
> identical for both beams.


​I'm not sure which 2 beams you're talking about. The interior of the
elevator sitting on the ground

​and the elevator in deep space being accelerated by a rocket are
identical. ​The elevator with the broken cable near the earth and
the elevator with no rocket in deep space are identical.

John K Clark

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Re: Equivalence Principle and Einstein Field Equations

2017-12-11 Thread Russell Standish
On Mon, Dec 11, 2017 at 12:15:58PM -0800, agrayson2...@gmail.com wrote:
> 
> *IIUC, you're saying that tensors transform covariantly, that is, 
> independent of coordinate system, but you haven't addressed my question why 
> Einstein would think accelerating frames are equivalent, or why a theory of 
> gravity could be, or must be covariant. BTW, is it correct to say that 
> "covariance" is a synonym for "Lorentz invariant"? TIA, AG*

All physical theories must be covariant. It is nonsense for physical
law to depend on one's chosen coordinate system.

Lorentz invariance is just one form of covariance.

As for the principle of equivalence, that is something else, unrelated
to covariance. Empirically they have been found to be identical, plus
it is required in Newtonian mechanics in order to have stable orbits.

Even now, there are still experiments directly testing the principle of
equivalence. A finding of a departure from it would be very big news!



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Visiting Senior Research Fellowhpco...@hpcoders.com.au
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Re: Equivalence Principle and Einstein Field Equations

2017-12-11 Thread Brent Meeker



On 12/11/2017 2:19 PM, agrayson2...@gmail.com wrote:



What is the connection between the Equivalence Principle and
Einstein's Field Equations?


It led to the idea that force-free paths in space could be
geodesic paths in spacetime, so the apparent acceleration falling
objects could be modelled by geodesic paths in curved spacetime.


*Insofar as acceleration results / causes curved paths in space-time, 
as seen by a simple space-time diagram, one can invoke the EP to link 
acceleration to gravity -- but we already knew that! So what gave 
Einstein the idea that gravity warps space-time? AG *


Gravity causes acceleration in the Newtonian sense.  But if spacetime is 
warped this apparent curvature can be inertial motion. The advantage of 
this view is it automatically entails that everything falls with the 
same "acceleration" per the Etovos results.


Brent

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Re: Equivalence Principle and Einstein Field Equations

2017-12-11 Thread agrayson2000


On Sunday, December 10, 2017 at 10:43:27 PM UTC, Brent wrote:
>
>
>
> On 12/10/2017 8:49 AM, agrays...@gmail.com  wrote:
>
> What is the connection between the Equivalence Principle and Einstein's 
> Field Equations? 
>
>
> It led to the idea that force-free paths in space could be geodesic paths 
> in spacetime, so the apparent acceleration falling objects could be 
> modelled by geodesic paths in curved spacetime. 
>

*Insofar as acceleration results / causes curved paths in space-time, as 
seen by a simple space-time diagram, one can invoke the EP to link 
acceleration to gravity -- but we already knew that! So what gave Einstein 
the idea that gravity warps space-time? AG  *

>
> How did the former lead to the latter? Why was the man falling from the 
> ladder so decisive in leading to the Theory of General Relativity? TIA, AG
>
>
> You have asked for a "connection" and then you imply that one "led to" GR 
> and finally predicated a question on the "connection" being "decisive" in 
> leading to GR.  The "connection" is just one of suggesting an idea.  
>
> Brent
>
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Re: Equivalence Principle and Einstein Field Equations

2017-12-11 Thread agrayson2000


On Sunday, December 10, 2017 at 11:41:21 PM UTC, John Clark wrote:
>
>
>
> On Sun, Dec 10, 2017 at 4:42 PM,  
> wrote:
>
> ​> ​
>> What is the connection between the Equivalence Principle and Einstein's 
>> Field Equations? How did the former lead to the latter? Why was the man 
>> falling from the ladder so decisive in leading to the Theory of General 
>> Relativity? 
>>
>
>
> The Equivalence Principle says if 
> ​you
>  ignore tidal effects and you're in a windowless elevator cab there is no 
> way to know if you're sitting on the Earth in a gravitational field or in 
> deep intergalactic space being accelerated by a rocket upward at 1G. If you 
> feel zero G and fire a Laser pointer from one wall 
> ​to the other ​
> it will go in a straight line and hit the exact opposite side on the other 
> wall. But if you were being accelerated upward the elevator cab will move 
> ​slightly ​
> upward in the time it takes for the light to go from one wall to the other 
> so the spot the laser makes on the other wall will be slightly lower than 
> it was when you were in zero G, you see the laser beam follow a curve.
>

At rest on Earth is not a situation of zero G; it's 1G. Or, say, if you 
want a straight beam, one can assume an inertial frame, and of course, in 
either frame one will observe the beam as straight. AG 

>
> A curved line from one wall to the other is longer than a straight line
> ​,​
> and yet when you measure the time it takes for light to do this with your 
> very accurate clock you notice its exactly the same. You already know the 
> measured speed of light never changes so 
> ​if something is moving at the same speed and moves a greater distance in 
> the same number of clock ticks then 
> you'd have to conclude that being accelerated makes your clock run slow.
>


I think most of last paragraph incorrect. In experiments with GPS clocks, 
the ground clock, in the stronger gravity field, runs slower than an 
orbiting clock. Fewer ticks in ground clock, which is objectively behind 
the orbiting clock. In your elevator example, where zero G can be 
interpreted as being in an inertial frame, you claim the elapsed time 
duration using ticks, is identical for both beams. This contradicts GPS 
experiments if we assume for direct comparison that the orbiting clock is 
very far from Earth, effectively in the weaker (zero) gravity field. AG 

> And because of the Equivalence Principle you'd have to 
> ​also ​
> conclude that a gravitational field bends light and makes time run slow 
> ​just as acceleration does.​
>
> ​John K Clark​
>
>
>
>  
>

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Re: Equivalence Principle and Einstein Field Equations

2017-12-11 Thread agrayson2000


On Monday, December 11, 2017 at 9:14:09 AM UTC, Russell Standish wrote:
>
> On Sun, Dec 10, 2017 at 07:06:00PM -0800, agrays...@gmail.com 
>  wrote: 
> > Excellent summary. TY. But why would Einstein think there could be a 
> > covariant theory for accelerating frames when an observer inside such a 
> > frame can do measurements to confirm acceleration and differences with 
> > other such frames, unlike the case for inertial frames which are clearly 
> > equivalent? AG 
>
> If I have a tensor equation like C=\sum_{ij} A_{ij}B_{ij} where C is a 
> scalar quantity, then the coefficients of A and B must "covary" with 
> each other as you select different coordinate systems, since C must 
> remain unchanged regardless of coordinate system. Given the 
> setting is spacetime, that includes rotations in the time dimension 
> too, which is equivalent to changes in inertial reference frame by 
> velocity boost. 
>
> This is really obvious if we use things like the 4 dimensional dot 
> product, but traditional tensor equations are written in component 
> form, so one must ensure the covariance property is preserved to have 
> a valid equation. Indeed, in the above equation, superscripts are used 
> to represent the covariant indices, ie 
>
>   C = A_{ij}B^{ij} 
>
> where the summation sign is dropped, since it is obvious from the way 
> the equation is written. 
>

*IIUC, you're saying that tensors transform covariantly, that is, 
independent of coordinate system, but you haven't addressed my question why 
Einstein would think accelerating frames are equivalent, or why a theory of 
gravity could be, or must be covariant. BTW, is it correct to say that 
"covariance" is a synonym for "Lorentz invariant"? TIA, AG*

>
>
> -- 
>
>  
>
> Dr Russell StandishPhone 0425 253119 (mobile) 
> Principal, High Performance Coders 
> Visiting Senior Research Fellowhpc...@hpcoders.com.au 
>  
> Economics, Kingston University http://www.hpcoders.com.au 
>  
>
>

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Re: Equivalence Principle and Einstein Field Equations

2017-12-11 Thread John Clark
On Sun, Dec 10, 2017 at 10:06 PM,  wrote:

​> ​
> Excellent summary. TY. But why would Einstein think there could be a
> covariant theory for accelerating frames
>

​The speed of light doesn't change even for an accelerating observer ​nor
does the spacetime distance between 2 events.

​
Einstein figured there must be a reason why. ​
​Also, before Einstein there were 2 different kinds of mass, inertial mass
and gravitational mass, Einstein had a hunch there was really only one sort
of mass and tried to find a relation between the two. ​And he found it.


> ​> ​
> when an observer inside such a frame can do measurements to confirm
> acceleration and differences with other such frames
>

​The observer can't tell if he is accelerating or in a gravitational
 field.​



> ​> ​
> unlike the case for inertial frames which are clearly equivalent?
>

Not everything is equivalent. You and I may not be accelerating and both be
in inertial frames but if we
​ are​
moving at different velocities then 2 events that are simultaneous for me
may not be simultaneous for you. The fact that simultaneity is not the same
for everyone turns what would otherwise be a logical paradox into something
that is just very strange
​;​
if we're
​both ​
in inertial frames
​and ​
in motion with respect to each other then I see your clock running slow and
you see my clock running slow.

 John K Clark

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Re: Equivalence Principle and Einstein Field Equations

2017-12-11 Thread Russell Standish
On Sun, Dec 10, 2017 at 07:06:00PM -0800, agrayson2...@gmail.com wrote:
> Excellent summary. TY. But why would Einstein think there could be a 
> covariant theory for accelerating frames when an observer inside such a 
> frame can do measurements to confirm acceleration and differences with 
> other such frames, unlike the case for inertial frames which are clearly 
> equivalent? AG 

If I have a tensor equation like C=\sum_{ij} A_{ij}B_{ij} where C is a
scalar quantity, then the coefficients of A and B must "covary" with
each other as you select different coordinate systems, since C must
remain unchanged regardless of coordinate system. Given the
setting is spacetime, that includes rotations in the time dimension
too, which is equivalent to changes in inertial reference frame by
velocity boost.

This is really obvious if we use things like the 4 dimensional dot
product, but traditional tensor equations are written in component
form, so one must ensure the covariance property is preserved to have
a valid equation. Indeed, in the above equation, superscripts are used
to represent the covariant indices, ie

  C = A_{ij}B^{ij}

where the summation sign is dropped, since it is obvious from the way
the equation is written.


-- 


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Principal, High Performance Coders
Visiting Senior Research Fellowhpco...@hpcoders.com.au
Economics, Kingston University http://www.hpcoders.com.au


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Re: Equivalence Principle and Einstein Field Equations

2017-12-10 Thread agrayson2000


On Sunday, December 10, 2017 at 11:41:21 PM UTC, John Clark wrote:
>
>
>
> On Sun, Dec 10, 2017 at 4:42 PM,  
> wrote:
>
> ​> ​
>> What is the connection between the Equivalence Principle and Einstein's 
>> Field Equations? How did the former lead to the latter? Why was the man 
>> falling from the ladder so decisive in leading to the Theory of General 
>> Relativity? 
>>
>
>
> The Equivalence Principle says if 
> ​you
>  ignore tidal effects and you're in a windowless elevator cab there is no 
> way to know if you're sitting on the Earth in a gravitational field or in 
> deep intergalactic space being accelerated by a rocket upward at 1G. If you 
> feel zero G and fire a Laser pointer from one wall 
> ​to the other ​
> it will go in a straight line and hit the exact opposite side on the other 
> wall. But if you were being accelerated upward the elevator cab will move 
> ​slightly ​
> upward in the time it takes for the light to go from one wall to the other 
> so the spot the laser makes on the other wall will be slightly lower than 
> it was when you were in zero G, you see the laser beam follow a curve.
>
> A curved line from one wall to the other is longer than a straight line
> ​,​
> and yet when you measure the time it takes for light to do this with your 
> very accurate clock you notice its exactly the same. You already know the 
> measured speed of light never changes so 
> ​if something is moving at the same speed and moves a greater distance in 
> the same number of clock ticks then 
> you'd have to conclude that being accelerated makes your clock run slow. 
> And because of the Equivalence Principle you'd have to 
> ​also ​
> conclude that a gravitational field bends light and makes time run slow 
> ​just as acceleration does.​
>
> ​John K Clark​
>
>
Excellent summary. TY. But why would Einstein think there could be a 
covariant theory for accelerating frames when an observer inside such a 
frame can do measurements to confirm acceleration and differences with 
other such frames, unlike the case for inertial frames which are clearly 
equivalent? AG 

>
>
>  
>

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Re: Equivalence Principle and Einstein Field Equations

2017-12-10 Thread John Clark
On Sun, Dec 10, 2017 at 4:42 PM,  wrote:

​> ​
> What is the connection between the Equivalence Principle and Einstein's
> Field Equations? How did the former lead to the latter? Why was the man
> falling from the ladder so decisive in leading to the Theory of General
> Relativity?
>


The Equivalence Principle says if
​you
 ignore tidal effects and you're in a windowless elevator cab there is no
way to know if you're sitting on the Earth in a gravitational field or in
deep intergalactic space being accelerated by a rocket upward at 1G. If you
feel zero G and fire a Laser pointer from one wall
​to the other ​
it will go in a straight line and hit the exact opposite side on the other
wall. But if you were being accelerated upward the elevator cab will move
​slightly ​
upward in the time it takes for the light to go from one wall to the other
so the spot the laser makes on the other wall will be slightly lower than
it was when you were in zero G, you see the laser beam follow a curve.

A curved line from one wall to the other is longer than a straight line
​,​
and yet when you measure the time it takes for light to do this with your
very accurate clock you notice its exactly the same. You already know the
measured speed of light never changes so
​if something is moving at the same speed and moves a greater distance in
the same number of clock ticks then
you'd have to conclude that being accelerated makes your clock run slow.
And because of the Equivalence Principle you'd have to
​also ​
conclude that a gravitational field bends light and makes time run slow
​just as acceleration does.​

​John K Clark​

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Re: Equivalence Principle and Einstein Field Equations

2017-12-10 Thread Brent Meeker



On 12/10/2017 8:49 AM, agrayson2...@gmail.com wrote:
What is the connection between the Equivalence Principle and 
Einstein's Field Equations?


It led to the idea that force-free paths in space could be geodesic 
paths in spacetime, so the apparent acceleration falling objects could 
be modelled by geodesic paths in curved spacetime.


How did the former lead to the latter? Why was the man falling from 
the ladder so decisive in leading to the Theory of General Relativity? 
TIA, AG


You have asked for a "connection" and then you imply that one "led to" 
GR and finally predicated a question on the "connection" being 
"decisive" in leading to GR.  The "connection" is just one of suggesting 
an idea.


Brent


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Re: Equivalence Principle and Einstein Field Equations

2017-12-10 Thread agrayson2000


On Sunday, December 10, 2017 at 4:49:54 PM UTC, agrays...@gmail.com wrote:
>
> What is the connection between the Equivalence Principle and Einstein's 
> Field Equations? How did the former lead to the latter? Why was the man 
> falling from the ladder so decisive in leading to the Theory of General 
> Relativity? TIA, AG
>

More specifically for starters, given that NON accelerating frames are 
indistinguishable for observers within such frames (implying a covariant 
theory for such frames), whereas the same is NOT the case for accelerating 
frames, why did Einstein think there could be a covariant theory for 
accelerating frames? TIA, AG 

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Re: equivalence between math and computations

2012-08-18 Thread Alberto G. Corona
2012/8/16 Bruno Marchal marc...@ulb.ac.be


 On 15 Aug 2012, at 15:14, Alberto G. Corona wrote:

 I ´m seduced and intrigued by the Bruno´s final conclussións of the COMP
 hypothesis. But I had a certain disconfort with the idea of a simulation of
 the reality by means of an algorithm for reasons I will describe later.


 Comp is I am a machine. It is NOT reality is a machine.

 If comp is true, both reality and physical reality are NOT machine, for
 the output of the many self-multiplication is NOT emulable by a Turing
 machine. You might not yet grasp fully the impact of the first person
 indeterminacy.

 In a sense: I am a machine implies that everything else is not.

 Indeed, the apparent computability of nature might in fine be a problem
 for comp. It is behind the whole measure problem.


 It is not emulable, I suppose, for the reason that if  the physical
reality has a underlying mathematical structure, if this is continuous it
can not be emulable but in a discrete approximation. This emulation at the
substitution level is what may be a physical
reality indistinguishableness from the mathematical reality.




  I found that either if the nature of our perception of reality) can be of
 the thesis of a simulation at a certain level of substitution of a phisical
 or mathematical reality, this simulation is, and only is, a discrete
 manifold, with discreteness defined by the substitution level, which is a
 subset of a continuous manifold that is the equation M of superstring
 theory of wathever mathematical structure that describe the universe.  The
 equivalence may be shown as follows:

 A imperative computation  is equivalent to a mathematical structure thanks
 to the work on denotational semantics
 http://en.wikipedia.org/wiki/Denotational_semanticsand the application
 of category theory to it 
 https://www.google.es/search?q=denotational+semantics+imperative+monadssugexp=chrome,mod=11sourceid=chromeie=UTF-8#hl=ensugexp=efrshgs_nf=1tok=VMyaXoMGarRPPBvFsyx1Cgpq=denotational%20semantics%20imperative%20monadscp=49gs_id=1qxhr=tq=denotational+semantics+imperative+category+theorypf=psafe=offsclient=psy-aboq=denotational+semantics+imperative+category+theorygs_l=pbx=1bav=on.2,or.r_gc.r_pw.r_cp.r_qf.fp=4beb944d59246923biw=1092bih=514
  .


 Or just by definition.




 Suppose that we know the M theory equation.


 You are still assuming a physical reality.

I assume a mathematical reality



  If the M theory equation is correct, it has to be derived from addition
 and multiplication


?
, and comp at the metalevel. But it has to admit non computable solution,
because with comp the physical reality is not computable, a priori.
a continuous reality is uncomputable, but this is not a problem for someone
who assume a mathematical reality.





 A particular simulation can be obtained in a straighfordward way by means
 of an algorithm that compute a sequence of positions and the respective
 values in the M equation (which must specify wether there is a particle,
 its nature and state at this point or more precisely the value of the wave
 equation at this N-position or wathever are the relevant parameters at this
 level of substitution), perhaps the sucession of points can be let´s say in
 a progression of concentric n-dimensional circles around the singularity.
 this algoritm is equivalent to the ordered set obtained by the combination
 of two kind of functions (1) for obtaining sucessive N-dimensional
 positions and (2) the function M(pos) itself for that particular point. The
 simulation then is a mathematical structure composed by the ordered set of
 these points, which is a subset of the manifold described by the M
 equation. (When a computation is pure, like this, the arrows between
 categories are functions).

 Suppose that we do not know the equation fo the M theory, and maybe it
 does not exist, but COMP holds and we  start with the dovetailer algoritm
 at a fortunate substitution level.


 The universal dovetailer simulates all the level, and below a level, we
 can see only the result of a statistics beaing on infinities of
 computation. This is NOT simulable by any algorithm, a priori.


 It don´t have to be a single equation. But it is a mathematical structure,
given the above said.


 Then we are sure that a complete mathematical description of reality exist
 (perhaps not the more concrete for  our local universe), since the
 imperative algoritm can be  (tanks to  denotational semantics) described in
 terms of category theory.


 Not really. The reality we see result from our first person indeterminacy.
 You cannot simulate it, and it is not describable by any equation.

 again it may be aproximated exactly, but discretely, by a mathematical
structure. the dovetailer algorithm. At least one of the infinite
superpositions that predict the Everett interpretation. Surely, there is a
mathematical structure that integrate the infinite set of algoritms for all
the superpositions.




 In any case, I 

Re: equivalence between math and computations

2012-08-16 Thread Bruno Marchal


On 15 Aug 2012, at 15:14, Alberto G. Corona wrote:

I ´m seduced and intrigued by the Bruno´s final conclussións of the  
COMP hypothesis. But I had a certain disconfort with the idea of a  
simulation of the reality by means of an algorithm for reasons I  
will describe later.


Comp is I am a machine. It is NOT reality is a machine.

If comp is true, both reality and physical reality are NOT machine,  
for the output of the many self-multiplication is NOT emulable by a  
Turing machine. You might not yet grasp fully the impact of the first  
person indeterminacy.


In a sense: I am a machine implies that everything else is not.

Indeed, the apparent computability of nature might in fine be a  
problem for comp. It is behind the whole measure problem.






I found that either if the nature of our perception of reality) can  
be of the thesis of a simulation at a certain level of substitution  
of a phisical or mathematical reality, this simulation is, and only  
is, a discrete manifold, with discreteness defined by the  
substitution level, which is a subset of a continuous manifold that  
is the equation M of superstring theory of wathever mathematical  
structure that describe the universe.  The equivalence may be shown  
as follows:


A imperative computation  is equivalent to a mathematical structure  
thanks to the work on denotational semantics and the application of  
category theory to it  .


Or just by definition.





Suppose that we know the M theory equation.


You are still assuming a physical reality. If the M theory equation is  
correct, it has to be derived from addition and multiplication, and  
comp at the metalevel. But it has to admit non computable solution,  
because with comp the physical reality is not computable, a priori.





A particular simulation can be obtained in a straighfordward way by  
means of an algorithm that compute a sequence of positions and the  
respective values in the M equation (which must specify wether there  
is a particle, its nature and state at this point or more precisely  
the value of the wave equation at this N-position or wathever are  
the relevant parameters at this level of substitution), perhaps the  
sucession of points can be let´s say in a progression of concentric  
n-dimensional circles around the singularity. this algoritm is  
equivalent to the ordered set obtained by the combination of two  
kind of functions (1) for obtaining sucessive N-dimensional  
positions and (2) the function M(pos) itself for that particular  
point. The simulation then is a mathematical structure composed by  
the ordered set of these points, which is a subset of the manifold  
described by the M equation. (When a computation is pure, like this,  
the arrows between categories are functions).


Suppose that we do not know the equation fo the M theory, and maybe  
it does not exist, but COMP holds and we  start with the dovetailer  
algoritm at a fortunate substitution level.


The universal dovetailer simulates all the level, and below a level,  
we can see only the result of a statistics beaing on infinities of  
computation. This is NOT simulable by any algorithm, a priori.




Then we are sure that a complete mathematical description of reality  
exist (perhaps not the more concrete for  our local universe), since  
the imperative algoritm can be  (tanks to  denotational semantics)  
described in terms of category theory.


Not really. The reality we see result from our first person  
indeterminacy. You cannot simulate it, and it is not describable by  
any equation.






In any case, I believe, similar conclussion holds. Although in the  
consequence of machine psychology in the case of COMP, the mind  
imposes a fortunate and robust algoritm as description of our local  
universe,


Not really, for the reason above. We belongs to infinities of  
computations, and the physical reality is a sum on all those  
computations existing below our substitution level. QM confirms this.




and in the case of a mathematical universe this requirement is  
substituted by a fortunate and coherent mathematical structure.  
Anyhow,  both are equivalent since one implies the other. Both of  
them reject phisicalism and the mind stablish requirement for the  
nature of what we call Physics. Perhaps one may be more general, and  
the other may bring more details


A question open is the nature of time and the progression of the  
simulation of the points. Theoretically, for obtaining a subset of  
the points of a mathematical structure, the simulation can proceed  
in any direction, independent on the gradient of entropy. It can  
proceed backwards or laterally, since the value of a ndimensional  
point does not depend on any other point, if we have the M equation.  
Moreover, time is local, there is no meaning of absolute time for  
the universe, so the simulation can not progress with a uniform  
notion of time. A local portion of the universe does make sense to  

RE: Equivalence

2005-06-04 Thread Lee Corbin
Sorry, but I don't have much of an idea of what is being discussed
in this thread.  Could you try to enlighten me?

Rmiller originally wrote

 Equivalence
 If the individual exists simultaneously across a many-world manifold, then 
 how can one even define a copy?

Well, I would say this (i.e., those words mean the following to me):

Are you asking what the *meaning* of copy is in this context?  That is,
are you suggesting that from a physics standpoint, if we have two
identical (or nearly identical) quantum states at different points
of the multiverse, then how can *one* of them be picked out as a
copy of the *other*?  I agree it seems reflexive; that is, if A is
a copy of B, then B is a copy of A.  But I don't see the significance
of where this is leading.

1. An *exact* copy (which I think you are talking about) could in
   principle be obtained from a machine that made an exact molecular
   replicant of one.  Let us further stipulate that one's *exact*
   environment (say out to a few light-seconds) is also duplicated.
   Then the person has two copies both having identical experiences.
   In fact, I would use this to help *define* what is meant by existing
   simultaneously across a many-world manifold.


 If the words match at some points and differ at others, then the
 personality would at a maximum, do likewise---though this is not
 necessary---or, for some perhaps, not even likely.

What?  What do you mean by the words match?  Do you mean that if
each copy happens to be speaking?

 It's been long established that the inner world we navigate is an 
 abstraction of the real thing---even if the real world only consists of 
 one version.  If it consists of several versions, blended into one another, 
 then how can we  differentiate between them?

By the inner world being an abstraction of the real thing, I guess
that you mean our perception of 3 space around us is not an identical
map of the 3 space around us.  Is that right?  But how could the
real world be one version? Or do you mean one instance from a set
of identical versions?

 From a mathematical POV, 200 
 worlds that are absolute copies of themselves, are equivalent to one world. 

Yes, it is a convention of set theory that the set {1, 2, 3, 1, 4, 5}
really has only five elements, not six.  But a good number of us here
suppose that just as in probability and measure theory, a single point
can be associated with either a high or low probability.

But one is free to observe, say, N electrons all in the same state. We
persist in regarding these as separate electrons, and I don't think 
that there is anything wrong with that.  It does depend on how you look
at it (is there only one electron in the universe? Feynman and Wheeler
suppose that there was in one paper).

 If these worlds differ minutely in areas *not encountered or interacted 
 with by the percipient (individual), then again we have one percipient, one 
 world-equivalent...

I just couldn't follow any more of what you are saying.

Thanks for any clarification, 

Lee



Re: Equivalence

2005-06-03 Thread Stephen Paul King

Dear R.,

   You make a very good point, one that I was hoping to communicate but 
failed. The notion of making copies is only coherent if and when we can 
compare the copied produce to each other. Failing to be able to do this, 
what remains? Your suggestion seems to imply that precognition, coincidence 
and synchronicity are some form resonance between decohered QM systems. 
Could it be that decoherence is not an all or nothing process; could it be 
that some 'parts' of a QM system decohere with respect to each other while 
others do not and/or that decoherence might occur at differing rates within 
a QM system?


Stephen

- Original Message - 
From: rmiller [EMAIL PROTECTED]
To: Stathis Papaioannou [EMAIL PROTECTED]; 
[EMAIL PROTECTED]; everything-list@eskimo.com

Sent: Friday, June 03, 2005 1:07 AM
Subject: Equivalence



Equivalence
If the individual exists simultaneously across a many-world manifold, then 
how can one even define a copy?  If the words match at some points and 
differ at others, then the personality would at a maximum, do 
likewise---though this is not necessary---or, for some perhaps, not even 
likely.  It's been long established that the inner world we navigate is an 
abstraction of the real thing---even if the real world only consists of 
one version.  If it consists of several versions, blended into one 
another, then how can we  differentiate between them?  From a mathematical 
POV, 200 worlds that are absolute copies of themselves, are equivalent to 
one world. If these worlds differ minutely in areas *not encountered or 
interacted with by the percipient (individual), then again we have one 
percipient, one world-equivalent.   I suspect it's not as though we're all 
run through a Xerox and distributed to countless (infinite!) places that 
differ broadly from one another.  I rather think the various worlds we 
inhabit are equivalent--and those that differ from one another do by 
small--though perceptible---degrees.  Some parts of the many-world 
spectrum are likely equivalent and others are not.  In essence, there are 
probably zones of equivalence (your room where there are no outside 
interferences) and zones of difference.  Even if we did manage to make the 
copies, then there would still be areas on the various prints that would 
be equivalent, i.e. the same.   Those that are different, we would notice 
and possibly tag these differences with a term: decoherence.  Perhaps that 
is all there is to it.   If this is the case, it would certainly explain a 
few things: i.e. precognition, coincidence and synchronicity.


R. Miller





Re: Equivalence

2005-06-03 Thread rmiller

At 10:23 AM 6/3/2005, Stephen Paul King wrote:

Dear R.,

   You make a very good point, one that I was hoping to communicate but 
failed. The notion of making copies is only coherent if and when we can 
compare the copied produce to each other. Failing to be able to do this, 
what remains? Your suggestion seems to imply that precognition, 
coincidence and synchronicity are some form resonance between 
decohered QM systems. Could it be that decoherence is not an all or 
nothing process; could it be that some 'parts' of a QM system decohere 
with respect to each other while others do not and/or that decoherence 
might occur at differing rates within a QM system?


Stephen


Yes, that's what I am suggesting.  The rates may remain constant---i.e. 
less than a few milliseconds (as Patrick L. earlier noted) however, I 
suspect there is a topology where regions of decoherence coexist and border 
regions of coherence.  An optics experiment might be able to test this (if 
it hasn't been done already), and it might be experimentally testable as a 
psychology experiment.


RM






- Original Message - From: rmiller [EMAIL PROTECTED]
To: Stathis Papaioannou [EMAIL PROTECTED]; 
[EMAIL PROTECTED]; everything-list@eskimo.com

Sent: Friday, June 03, 2005 1:07 AM
Subject: Equivalence



Equivalence
If the individual exists simultaneously across a many-world manifold, 
then how can one even define a copy?  If the words match at some points 
and differ at others, then the personality would at a maximum, do 
likewise---though this is not necessary---or, for some perhaps, not even 
likely.  It's been long established that the inner world we navigate is 
an abstraction of the real thing---even if the real world only consists 
of one version.  If it consists of several versions, blended into one 
another, then how can we  differentiate between them?  From a 
mathematical POV, 200 worlds that are absolute copies of themselves, are 
equivalent to one world. If these worlds differ minutely in areas *not 
encountered or interacted with by the percipient (individual), then again 
we have one percipient, one world-equivalent.   I suspect it's not as 
though we're all run through a Xerox and distributed to countless 
(infinite!) places that differ broadly from one another.  I rather think 
the various worlds we inhabit are equivalent--and those that differ from 
one another do by small--though perceptible---degrees.  Some parts of the 
many-world spectrum are likely equivalent and others are not.  In 
essence, there are probably zones of equivalence (your room where there 
are no outside interferences) and zones of difference.  Even if we did 
manage to make the copies, then there would still be areas on the various 
prints that would be equivalent, i.e. the same.   Those that are 
different, we would notice and possibly tag these differences with a 
term: decoherence.  Perhaps that is all there is to it.   If this is the 
case, it would certainly explain a few things: i.e. precognition, 
coincidence and synchronicity.


R. Miller







Re: Equivalence

2005-06-03 Thread rmiller

At 11:27 AM 6/3/2005, rmiller wrote:

At 10:23 AM 6/3/2005, Stephen Paul King wrote:

Dear R.,

   You make a very good point, one that I was hoping to communicate but 
failed. The notion of making copies is only coherent if and when we can 
compare the copied produce to each other. Failing to be able to do this, 
what remains? Your suggestion seems to imply that precognition, 
coincidence and synchronicity are some form resonance between 
decohered QM systems. Could it be that decoherence is not an all or 
nothing process; could it be that some 'parts' of a QM system decohere 
with respect to each other while others do not and/or that decoherence 
might occur at differing rates within a QM system?


Stephen


Yes, that's what I am suggesting.  The rates may remain constant---i.e. 
less than a few milliseconds (as Patrick L. earlier noted) however, I 
suspect there is a topology where regions of decoherence coexist and 
border regions of coherence.  An optics experiment might be able to test 
this (if it hasn't been done already), and it might be experimentally 
testable as a psychology experiment.\\


More to the point---Optical experiments in QM often return counterintuitive 
results, but they support the QM math (of course).  No one has 
satisfactorily resolved the issue of measurement to everyone's liking, but 
most would agree that in some brands of QM consciousness plays a role.  On 
one side we have Fred Alan Wolf and Sarfatti who seem to take the qualia 
approach, while on the other side we have those like Roger Penrose who (I 
think) take a mechanical view (microtubules in the brain harbor 
Bose-Einstein condensates.)   All this model-building (and discussion) is 
fine, of course, but there are a number of psychological experiments out 
there that consistently return counterintuitive and heretofore 
unexplainable results.  Among them, is Helmut Schmidt's retro pk 
experiment which consistently returns odd results.  The PEAR lab at 
Princeton has some startling remote viewing results, and of course, 
there's Rupert Sheldrake's work.   As far as I know, Sheldrake is the only 
one who has tried to create a model (morphic resonance), and most QM 
folks typically avoid discussing the experiments--except to deride them as 
nonscientific.  I think it may be time to revisit some of these ESP 
experiments to see if the results are telling us something in terms of QM, 
i.e. decoherence.   Changing our assumptions about decoherence, then 
applying the model to those strange experiments may clarify things.


RM



RM






- Original Message - From: rmiller [EMAIL PROTECTED]
To: Stathis Papaioannou [EMAIL PROTECTED]; 
[EMAIL PROTECTED]; everything-list@eskimo.com

Sent: Friday, June 03, 2005 1:07 AM
Subject: Equivalence



Equivalence
If the individual exists simultaneously across a many-world manifold, 
then how can one even define a copy?  If the words match at some 
points and differ at others, then the personality would at a maximum, do 
likewise---though this is not necessary---or, for some perhaps, not even 
likely.  It's been long established that the inner world we navigate is 
an abstraction of the real thing---even if the real world only 
consists of one version.  If it consists of several versions, blended 
into one another, then how can we  differentiate between them?  From a 
mathematical POV, 200 worlds that are absolute copies of themselves, are 
equivalent to one world. If these worlds differ minutely in areas *not 
encountered or interacted with by the percipient (individual), then 
again we have one percipient, one world-equivalent.   I suspect it's not 
as though we're all run through a Xerox and distributed to countless 
(infinite!) places that differ broadly from one another.  I rather think 
the various worlds we inhabit are equivalent--and those that differ from 
one another do by small--though perceptible---degrees.  Some parts of 
the many-world spectrum are likely equivalent and others are not.  In 
essence, there are probably zones of equivalence (your room where there 
are no outside interferences) and zones of difference.  Even if we did 
manage to make the copies, then there would still be areas on the 
various prints that would be equivalent, i.e. the same.   Those that are 
different, we would notice and possibly tag these differences with a 
term: decoherence.  Perhaps that is all there is to it.   If this is the 
case, it would certainly explain a few things: i.e. precognition, 
coincidence and synchronicity.


R. Miller








Re: Equivalence

2005-06-03 Thread Jesse Mazer

rmiller wrote:


At 11:27 AM 6/3/2005, rmiller wrote:

At 10:23 AM 6/3/2005, Stephen Paul King wrote:

Dear R.,

   You make a very good point, one that I was hoping to communicate but 
failed. The notion of making copies is only coherent if and when we can 
compare the copied produce to each other. Failing to be able to do this, 
what remains? Your suggestion seems to imply that precognition, 
coincidence and synchronicity are some form resonance between 
decohered QM systems. Could it be that decoherence is not an all or 
nothing process; could it be that some 'parts' of a QM system decohere 
with respect to each other while others do not and/or that decoherence 
might occur at differing rates within a QM system?


Stephen


Yes, that's what I am suggesting.  The rates may remain constant---i.e. 
less than a few milliseconds (as Patrick L. earlier noted) however, I 
suspect there is a topology where regions of decoherence coexist and 
border regions of coherence.  An optics experiment might be able to test 
this (if it hasn't been done already), and it might be experimentally 
testable as a psychology experiment.\\


More to the point---Optical experiments in QM often return counterintuitive 
results, but they support the QM math (of course).  No one has 
satisfactorily resolved the issue of measurement to everyone's liking, but 
most would agree that in some brands of QM consciousness plays a role.  On 
one side we have Fred Alan Wolf and Sarfatti who seem to take the qualia 
approach


What do you mean by the qualia approach? Do you mean a sort of dualistic 
view of the relationship between mind and matter? From the discussion at 
http://www.fourmilab.ch/rpkp/rhett.html it seems that Sarfatti suggests some 
combination of Bohm's interpretation of QM (where particles are guided by a 
'pilot wave') with the idea of adding a nonlinear term to the Schrodinger 
equation (contradicting the existing 'QM math', which is entirely linear), 
and he identifies the pilot wave with the mind and has some hand-wavey 
notion that life involves some kind of self-organizing feedback loop between 
the pilot wave and the configuration of particles (normally Bohm's 
interpretation says the configuration of particles has no effect on the 
pilot wave, but that's where the nonlinear term comes in I guess). Since 
Bohm's interpretation is wholly deterministic, I'd think Sarfatti's altered 
version would be too, the nonlinear term shouldn't change this.


while on the other
side we have those like Roger Penrose who (I think) take a mechanical view 
(microtubules in the brain harbor Bose-Einstein condensates.)


Penrose's proposal has nothing to do with consciousness collapsing the 
wavefunction, he just proposes that when a system in superposition crosses a 
certain threshold of *mass* (probably the Planck mass), then it collapses 
automatically. The microtubule idea is more speculative, but he's just 
suggesting that the brain somehow takes advantage of not-yet-understood 
quantum gravity effects to go beyond what computers can do, but the collapse 
of superposed states in the brain would still be gravitationally-induced.


  All this model-building (and discussion) is fine, of
course, but there are a number of psychological experiments out there that 
consistently return counterintuitive and heretofore unexplainable results.  
Among them, is Helmut Schmidt's retro pk experiment which consistently 
returns odd results.  The PEAR lab at Princeton has some startling remote 
viewing results, and of course, there's Rupert Sheldrake's work.   As far 
as I know, Sheldrake is the only one who has tried to create a model 
(morphic resonance), and most QM folks typically avoid discussing the 
experiments--except to deride them as nonscientific.  I think it may be 
time to revisit some of these ESP experiments to see if the results are 
telling us something in terms of QM, i.e. decoherence.   Changing our 
assumptions about decoherence, then applying the model to those strange 
experiments may clarify things.


RM


Here's a skeptical evaluation of some of the ESP experiments you mention:

http://web.archive.org/web/20040603153145/www.btinternet.com/~neuronaut/webtwo_features_psi_two.htm

Anyway, if it were possible for the mind to induce even a slight statistical 
bias in the probability of a bit flipping 1 or 0, then simply by picking a 
large enough number of trials it would be possible to very reliably insure 
that the majority would be the number the person was focusing on. So by 
doing multiple sets with some sufficiently large number N of trials in each 
set, it would be possible to actually send something like a 10-digit bit 
string (for example, if the majority of digits in the first N trials came up 
1, you'd have the first digit of your 10-digit string be a 1), something 
which would not require a lot of tricky statistical analysis to see was very 
unlikely to occur by chance. If the retro-PK effect you mentioned was 
real, 

Re: Equivalence

2005-06-03 Thread rmiller


At 01:46 PM 6/3/2005, rmiller wrote:

(snip)


What do you mean by the qualia approach? Do you mean a sort of 
dualistic view of the relationship between mind and matter? From the 
discussion at http://www.fourmilab.ch/rpkp/rhett.html it seems that 
Sarfatti suggests some combination of Bohm's interpretation of QM (where 
particles are guided by a 'pilot wave') with the idea of adding a 
nonlinear term to the Schrodinger equation (contradicting the existing 
'QM math', which is entirely linear), and he identifies the pilot wave 
with the mind and has some hand-wavey notion that life involves some 
kind of self-organizing feedback loop between the pilot wave and the 
configuration of particles (normally Bohm's interpretation says the 
configuration of particles has no effect on the pilot wave, but that's 
where the nonlinear term comes in I guess). Since Bohm's interpretation 
is wholly deterministic, I'd think Sarfatti's altered version would be 
too, the nonlinear term shouldn't change this.



Seems to me you've described the qualia approach pretty well.




while on the other
side we have those like Roger Penrose who (I think) take a mechanical 
view (microtubules in the brain harbor Bose-Einstein condensates.)


Penrose's proposal has nothing to do with consciousness collapsing the 
wavefunction, he just proposes that when a system in superposition 
crosses a certain threshold of *mass* (probably the Planck mass), then it 
collapses automatically. The microtubule idea is more speculative, but 
he's just suggesting that the brain somehow takes advantage of 
not-yet-understood quantum gravity effects to go beyond what computers 
can do, but the collapse of superposed states in the brain would still be 
gravitationally-induced.


Penrose has a *lot* of things to say about QM---and his new book has the 
best description of fibre bundles I've seen in quite a while---but no, I 
didn't mean to suggest his entire argument was based on BECs in the 
microtubules.  I suggested Penrose because his approach seems diametrically 
opposed to the qualia guys.





  All this model-building (and discussion) is fine, of
course, but there are a number of psychological experiments out there 
that consistently return counterintuitive and heretofore unexplainable 
results.
Among them, is Helmut Schmidt's retro pk experiment which consistently 
returns odd results.  The PEAR lab at Princeton has some startling 
remote viewing results, and of course, there's Rupert Sheldrake's 
work.   As far as I know, Sheldrake is the only one who has tried to 
create a model (morphic resonance), and most QM folks typically avoid 
discussing the experiments--except to deride them as nonscientific.  I 
think it may be time to revisit some of these ESP experiments to see 
if the results are telling us something in terms of QM, i.e. 
decoherence.   Changing our assumptions about decoherence, then applying 
the model to those strange experiments may clarify things.


RM


Here's a skeptical evaluation of some of the ESP experiments you mention:

http://web.archive.org/web/20040603153145/www.btinternet.com/~neuronaut/webtwo_features_psi_two.htm

Anyway, if it were possible for the mind to induce even a slight 
statistical bias in the probability of a bit flipping 1 or 0, then simply 
by picking a large enough number of trials it would be possible to very 
reliably insure that the majority would be the number the person was 
focusing on. So by doing multiple sets with some sufficiently large 
number N of trials in each set, it would be possible to actually send 
something like a 10-digit bit string (for example, if the majority of 
digits in the first N trials came up 1, you'd have the first digit of 
your 10-digit string be a 1), something which would not require a lot of 
tricky statistical analysis to see was very unlikely to occur by chance. 
If the retro-PK effect you mentioned was real, this could even be used 
to reliably send information into the past!


I spoke with Schmidt in '96.  He told me that it is very unlikely that 
causation can be reversed, but rather that the retropk results suggest many 
worlds.


When these ESP researchers are able to do a straightforward demonstration 
like this, that's when I'll start taking these claims seriously, until 
then extraordinary claims require extraordinary evidence.


The extraordinary claims---evidence rule is good practical guidance, but 
it's crummy science.  Why should new results require an astronomical Z 
score, when proven results need only a Z of 1.96?  Think about the poor 
fellow who discovered that ulcers were caused by helicobacter 
pylori---took him ten years for science to take him seriously, and then 
only after he drank a vial of h.pylori broth himself.   Then there's the 
fellow at U of I (Ames) who believed that Earth is being pummeled by 
snowballs--as big as houses--from space.  He was thoroughly derided (some 
demanded he be fired) for ten years or so---until a UV 

Re: Equivalence

2005-06-03 Thread Jesse Mazer


rmiller wrote:



At 01:46 PM 6/3/2005, rmiller wrote:

(snip)


What do you mean by the qualia approach? Do you mean a sort of 
dualistic view of the relationship between mind and matter? From the 
discussion at http://www.fourmilab.ch/rpkp/rhett.html it seems that 
Sarfatti suggests some combination of Bohm's interpretation of QM (where 
particles are guided by a 'pilot wave') with the idea of adding a 
nonlinear term to the Schrodinger equation (contradicting the existing 
'QM math', which is entirely linear), and he identifies the pilot wave 
with the mind and has some hand-wavey notion that life involves some 
kind of self-organizing feedback loop between the pilot wave and the 
configuration of particles (normally Bohm's interpretation says the 
configuration of particles has no effect on the pilot wave, but that's 
where the nonlinear term comes in I guess). Since Bohm's interpretation 
is wholly deterministic, I'd think Sarfatti's altered version would be 
too, the nonlinear term shouldn't change this.



Seems to me you've described the qualia approach pretty well.


But why do you call it that? It seems like it's just a philosophical add-on 
to interpret the pilot wave as mind and the particles guided by it as 
matter, even if Sarfatti's nonlinear QM theory were correct, and the idea 
that life depends on a self-organizing feedback loop between the pilot wave 
and particles could get beyond the pure hand-wavey stage (both of which seem 
very unlikely), there'd be no obligation to interpret the pilot wave in 
terms of mind/qualia.







while on the other
side we have those like Roger Penrose who (I think) take a mechanical 
view (microtubules in the brain harbor Bose-Einstein condensates.)


Penrose's proposal has nothing to do with consciousness collapsing the 
wavefunction, he just proposes that when a system in superposition 
crosses a certain threshold of *mass* (probably the Planck mass), then it 
collapses automatically. The microtubule idea is more speculative, but 
he's just suggesting that the brain somehow takes advantage of 
not-yet-understood quantum gravity effects to go beyond what computers 
can do, but the collapse of superposed states in the brain would still be 
gravitationally-induced.


Penrose has a *lot* of things to say about QM---and his new book has the 
best description of fibre bundles I've seen in quite a while---but no, I 
didn't mean to suggest his entire argument was based on BECs in the 
microtubules.  I suggested Penrose because his approach seems diametrically 
opposed to the qualia guys.


But you brought him up in the context of the consciousness plays a critical 
role in understanding QM idea, when Penrose doesn't fall into this camp at 
all.







  All this model-building (and discussion) is fine, of
course, but there are a number of psychological experiments out there 
that consistently return counterintuitive and heretofore unexplainable 
results.
Among them, is Helmut Schmidt's retro pk experiment which consistently 
returns odd results.  The PEAR lab at Princeton has some startling 
remote viewing results, and of course, there's Rupert Sheldrake's 
work.   As far as I know, Sheldrake is the only one who has tried to 
create a model (morphic resonance), and most QM folks typically avoid 
discussing the experiments--except to deride them as nonscientific.  I 
think it may be time to revisit some of these ESP experiments to see 
if the results are telling us something in terms of QM, i.e. 
decoherence.   Changing our assumptions about decoherence, then applying 
the model to those strange experiments may clarify things.


RM


Here's a skeptical evaluation of some of the ESP experiments you mention:

http://web.archive.org/web/20040603153145/www.btinternet.com/~neuronaut/webtwo_features_psi_two.htm

Anyway, if it were possible for the mind to induce even a slight 
statistical bias in the probability of a bit flipping 1 or 0, then simply 
by picking a large enough number of trials it would be possible to very 
reliably insure that the majority would be the number the person was 
focusing on. So by doing multiple sets with some sufficiently large 
number N of trials in each set, it would be possible to actually send 
something like a 10-digit bit string (for example, if the majority of 
digits in the first N trials came up 1, you'd have the first digit of 
your 10-digit string be a 1), something which would not require a lot of 
tricky statistical analysis to see was very unlikely to occur by chance. 
If the retro-PK effect you mentioned was real, this could even be used 
to reliably send information into the past!


I spoke with Schmidt in '96.  He told me that it is very unlikely that 
causation can be reversed, but rather that the retropk results suggest many 
worlds.


But that is presumably just his personal intuition, not something that's 
based on any experimental data (like getting a message from a possible 
future or alternate world, for 

Re: Equivalence

2005-06-03 Thread rmiller

At 04:40 PM 6/3/2005, rmiller wrote:

At 03:25 PM 6/3/2005, you wrote:



(snip)
I spoke with Schmidt in '96.  He told me that it is very unlikely that 
causation can be reversed, but rather that the retropk results suggest 
many worlds.


But that is presumably just his personal intuition, not something that's 
based on any experimental data (like getting a message from a possible 
future or alternate world, for example).


Actually, he couldn't say why the result came out the way it did.  His 
primary detractor back then, was Henry Stapp---whom Schmidt invited to take 
part in the experiment.  After which Stapp modified his views somewhat.





When these ESP researchers are able to do a straightforward 
demonstration like this, that's when I'll start taking these claims 
seriously, until then extraordinary claims require extraordinary evidence.

(snip)


The issue is not the Z score in isolation, it's 1) whether we trust that 
the correct statistical analysis has been done on the data to obtain that 
Z score (whether reporting bias has been eliminated, for example)--that's 
why I suggested the test of trying to transmit a 10-digit number using 
ESP, which would be a lot more transparent--and 2) whether we trust that 
the possibility of cheating has been kept small enough, which as the 
article I linked to suggested, may not have been met in the PEAR results:



Suspicions have hardened as sceptics have looked more closely at the 
fine detail of Jahn's results. Attention has focused on the fact that one 
of the experimental subjects - believed actually to be a member of the 
PEAR lab staff - is almost single-handedly responsible for the 
significant results of the studies. It was noted as long ago as 1985, in 
a report to the US Army by a fellow parapsychologist, John Palmer of 
Durham University, North Carolina, that one subject - known as operator 
10 - was by far the best performer. This trend has continued. On the most 
recently available figures, operator 10 has been involved in 15 percent 
of the 14 million trials yet contributed a full half of the total excess 
hits. If this person's figures are taken out of the data pool, scoring in 
the low intention condition falls to chance while high intention 
scoring drops close to the .05 boundary considered weakly significant in 
scientific results.


First, you're right about that set of the PEAR results, but operator 10 was 
involved in the original anomalies experiments---she was not involved in 
the remote viewing (as I understand).  But p0.05 is weakly 
significant?  Hm. It was good enough for Fisher. . .it's good enough for 
the courts (Daubert).



Sceptics like James Alcock and Ray Hyman say naturally it is a serious 
concern that PEAR lab staff have been acting as guinea pigs in their own 
experiments. But it becomes positively alarming if one of the staff - 
with intimate knowledge of the data recording and processing procedures - 
is getting most of the hits.


I agree, but again, I don't think Operator 10 was involved in all the 
experiments. Have any of these skeptics tried to replicate?  I believe Ray 
Hyman is an Oregon State English Prof, so he probably couldn't replicate 
some of the PEAR lab work, but surely there are others who could.



Alcock says t(snip) . . . distort Jahn's results. 


If Hyman and Alcock believe Jahn et al were cheating, then they shouldn't 
mince words; instead, they should file a complaint with Princeton.




Of course, both these concerns would be present in any statistical test, 
even one involving something like the causes of ulcers like in the quote 
you posted above, but here I would use a Bayesian approach and say that 
we should start out with some set of prior probabilities, then update 
them based on the data. Let's say that in both the tests for ulcer causes 
and the tests for ESP our estimate of the prior probability for either 
flawed statistical analysis or cheating on the part of the experimenters 
is about the same. But based on what we currently know about the way the 
world works, I'd say the prior probability of ESP existing should be far, 
far lower than the prior probability that ulcers are caused by bacteria. 
It would be extremely difficult to integrate ESP into what we currently 
know about the laws of physics and neurobiology. If someone can propose a 
reasonable theory of how it could work without throwing everything else 
we know out the window, then that could cause us to revise these priors 
and see ESP as less of an extraordinary claim, but I don't know of any 
good proposals (Sarfatti's seems totally vague on the precise nature of 
the feedback loop between the pilot wave and particles, for example, and 
on how this would relate to ESP phenomena...if he could provide a 
mathematical model or simulation showing how a simple brain-like system 
could influence the outcome of random quantum events in the context of 
his theory, then it'd be a different story).


A couple of 

RE: Equivalence

2005-06-03 Thread Brent Meeker
-Original Message-
From: rmiller [mailto:[EMAIL PROTECTED]
Sent: Friday, June 03, 2005 4:59 PM
To: Stephen Paul King; everything-list@eskimo.com
Subject: Re: Equivalence


At 11:27 AM 6/3/2005, rmiller wrote:
At 10:23 AM 6/3/2005, Stephen Paul King wrote:
Dear R.,

You make a very good point, one that I was hoping to communicate but
 failed. The notion of making copies is only coherent if and when we can
 compare the copied produce to each other. Failing to be able to do this,
 what remains? Your suggestion seems to imply that precognition,
 coincidence and synchronicity are some form resonance between
 decohered QM systems. Could it be that decoherence is not an all or
 nothing process; could it be that some 'parts' of a QM system decohere
 with respect to each other while others do not and/or that decoherence
 might occur at differing rates within a QM system?

Stephen

Yes, that's what I am suggesting.  The rates may remain constant---i.e.
less than a few milliseconds (as Patrick L. earlier noted) however, I
suspect there is a topology where regions of decoherence coexist and
border regions of coherence.

Coherence is assumed to always remain, since QM evolution is unitary.  It just
gets entangled with the environment so there is no practical way to detect it.
Just google decoherence Zeh.

An optics experiment might be able to test
this (if it hasn't been done already), and it might be experimentally
testable as a psychology experiment.\\

More to the point---Optical experiments in QM often return counterintuitive
results, but they support the QM math (of course).  No one has
satisfactorily resolved the issue of measurement to everyone's liking, but
most would agree that in some brands of QM consciousness plays a role.  On
one side we have Fred Alan Wolf and Sarfatti who seem to take the qualia
approach, while on the other side we have those like Roger Penrose who (I
think) take a mechanical view (microtubules in the brain harbor
Bose-Einstein condensates.)   All this model-building (and discussion) is
fine, of course, but there are a number of psychological experiments out
there that consistently return counterintuitive and heretofore
unexplainable results.

And they consistently fail when someone tries to replicate them or have them
performed so as to eliminate fraud and self-deception.

Brent Meeker