Re: [Vo]:Newtonian Gravity and General Relativity inside a spherical shell.

[H LV]

This is how I understand the "elevator".
It is_infinitely_ small. It encloses a single point in space rather than
region of space so it is impossible to detect tidal variations from inside
the elevator. If the elevator is allowed to have finite dimensions so that
tidal variations are detectable then the equivalence principle ceases to
have any theoretical significance and can be ignored or discarded.

Harry



On Fri, Dec 9, 2016 at 5:02 PM, Stephen A. Lawrence  wrote:

>
>
> On 12/09/2016 01:54 PM, H LV wrote:
>
>
>
> On Wed, Dec 7, 2016 at 4:04 PM, Stephen A. Lawrence 
> wrote:
>
>> Well known result -- gravitational time dilation has to do with the
>> gravitational potential, not the strength of the field.
>>
>>
> ​GR's principle of equivalence depends on the concept of a force and not
> on the concept of a potential.
> A person in an elevator without windows can only detect either the
> presence or an absence of a force.​
>
>
> A person in an elevator also can't detect redshift or blueshift of light
> moving into or out of the elevator, because they are restricted to making
> measurements *inside the elevator*.  Gravitational time dilation is a
> non-local effect, detectable only by comparing the results of measurements
> at highly separated points.  The elevator metaphor doesn't have anything to
> do with it.  In fact there is *no* time dilation of any sort associated
> with either acceleration or a strong local G-field.
>
> On the other hand a person in an elevator *can* tell whether there's a
> gravitational field present, by checking for tidal effects, which are IIRC
> linear in the spatial dimension and hence detectable even at small scales.
> That breaks the "elevator=gravity" correspondence, as real gravitational
> fields *always* exhibit tidal effects.  (Constructed fields which result
> from funniness at a domain boundary don't show tidal effects but they're
> also not real.)
>
> Don't confuse explanations using a metaphor with actual reasoning about
> the results.  The elevator is a metaphor, useful in looking for general
> principles, but imperfect in detail.  The drop-a-rock-down-a-well
> experiment, on the other hand, can in principle be quantified, and in the
> absence of gravitational redshift which depends on the potential, it
> results in a violation of CoE.  In fact it, or a simple variation on it, is
> what led to the concept of gravitational redshift to begin with, or so I've
> read.
>
>
>
>
>
>> Simple gedanken:  Drop a rock through a slender shaft into a spherical
>> hollow cut out of the center of a spherical planet.  The rock has more
>> kinetic energy when it gets to the center of the planet.
>>
>> Turn the rock (along with its kinetic energy) into photons, and beam them
>> back up the shaft.  At the top of the shaft, catch the beam and turn it
>> back into a rock.
>>
>> The rock must have the same mass at the end as it had to start with (or
>> something's very wrong), which is smaller than the mass it had at the
>> bottom of the shaft (due its additional kinetic energy which shows up as a
>> mass excess).  This can only be true if the beam of light was *redder*
>> at the top of the shaft than the bottom.  So, there must have been a
>> gravitational red-shift as the light climbed the shaft.
>>
>> So, the *frequency* of the light at the top of the shaft must be *lower*
>> than the frequency at the bottom of the shaft.
>>
>> But the *total number of wave crests* in the beam of light can't
>> change.  (You can count them, using appropriate equipment; in that sense
>> they behave like marbles.)  A certain number of wave crests in the beam
>> entered the shaft at the bottom; the same number of wave crests must have
>> come out the top.
>>
>> So, if the *frequency* measured by an observer at the top of the shaft
>> is *lower* than the frequency measured at the bottom of the shaft, the
>> wave crests must have taken more time to exit the top of the shaft than
>> they took to enter the bottom of the shaft, and so,
>>
>> *time must be passing faster for the observer at the top of the shaft. *
>>
>
> ​The experiment is different in that it doesn't involve an exchange of
> mass or energy between the surface and the interior.​
>
> Harry
>
>
>
>> On 12/07/2016 12:53 AM, H LV wrote:
>>
>> According to the shell theorem  the gravitational force on a test mass
>> inside a hollow sphere is every where zero. This paper argues that this
>> situation is not equivalent from the standpoint of General Relativity to
>> the situation where gravity falls to zero far outside the sphere. They
>> conclude that General Relativity predicts that a clock located inside a
>> hollow sphere should run slower than a clock located outside the hollow
>> sphere. (By contrast most people are familiar with the fact that General
>> relativity predicts a clock should run faster as the force of gravity
>> approaches zero far from a gravitational body) This could provide a
>> laboratory 

RE: [Vo]:Newtonian Gravity and General Relativity inside a spherical shell.

[bobcook39923]

A related question regarding frequency shifts of photons is associated with the 
apparent changes associated with the expansion of space and the emission of 
photons from distant objects receding at a great velocity from a 
receptor/monitor on earth.  

The explanation I have heard is that it’s  like a Doppler shift associated with 
the classical idea of a source of sound losing frequency because of motion of 
the emitter away from the observer.  This effect should be able to be seen to a 
lesser extent as a result of any galaxies moving away from Earth.   I think it 
is observed in high energy experiments involving particles that decay as they 
move away giving off a reduced energy gamma (red shifted) when compared to a 
low energy particle.  However, I do not think a red shift happens when a 
positron reacts with an electron both of which are receding from the observer 
at the same velocity.   The observer always sees .511…. mev. photons—back to 
back with apparent conservation of momentum and energy.  (It seems the source 
is a non-moving hole to the “other side”.)

Stephen and/or Robin please correct me if I am wrong.

A related question is whether the universal background EM radiation is due to 
the loss of energy from atoms as the space they are in expands, causing a 
longer average distance between their electrons and protons as time proceeds.  
(The expansion of space does not for some reason expand within galaxies, as far 
as I know, and hence there is no  expansion that would effect dimensions of 
stable atoms—no aging of atoms possible.)

If the above  is accepted, it begs the question, where and why does the 
expansion of space cease to happen?  And, iIs the progression of time somehow 
coupled to the universal expansion of space?

Bob Cook


From: mix...@bigpond.com
Sent: Saturday, December 10, 2016 5:18 PM
To: vortex-l@eskimo.com
Subject: Re: [Vo]:Newtonian Gravity and General Relativity inside a 
sphericalshell.

In reply to  David Roberson's message of Sat, 10 Dec 2016 01:54:41 -0500:
Hi,
[snip]
>I agree that a phase shift would occur due to normal path length differences. 
>What I am wondering about is whether or not that basic shift would have an 
>additional component that depends upon the magnitude of the gravitational mass 
>contained within the sphere's shell assuming that the path lengths do not vary.
>
>For example, have a very small mass sphere and use the phase detector to 
>obtain a reference. Then, greatly increase the mass as you maintain the same 
>inner volume and hence total reflection path.  Compare the phase difference in 
>case 2 versus case1 when using the unaffected external photon.
>
>Dave

...now that might be an interesting experiment. You could use two concentric
spheres, and fill the space between with water. Unfortunately, I suspect that
temperature variations would have a larger effect than that which you are trying
to measure, since temperature variations would change the size of the sphere(s),
and hence the path length.
Try doing the math, and see if you can get a figure for the minimum temperature
variation that would be needed to drown out your signal. That should give you an
idea of how hard the experiment would be to do.

Regards,

Robin van Spaandonk

http://rvanspaa.freehostia.com/project.html

Re: [Vo]:Newtonian Gravity and General Relativity inside a spherical shell.

[David Roberson]

I was thinking more of a thought experiment than an actual lab test. As you are 
pointing out, to realize an actual valid experiment would be very difficult. 
But, scientists have actually performed experiments that one might think 
impossible due to noise, temperature, etc. such as detecting gravitational 
waves.

Dave

 

 

 

-Original Message-
From: mixent <mix...@bigpond.com>
To: vortex-l <vortex-l@eskimo.com>
Sent: Sat, Dec 10, 2016 8:18 pm
Subject: Re: [Vo]:Newtonian Gravity and General Relativity inside a spherical 
shell.

In reply to  David Roberson's message of Sat, 10 Dec 2016 01:54:41 -0500:
Hi,
[snip]
>I agree that a phase shift would occur due to normal path length differences. 
>What I am wondering about is whether or not that basic shift would have an 
>additional component that depends upon the magnitude of the gravitational mass 
>contained within the sphere's shell assuming that the path lengths do not vary.
>
>For example, have a very small mass sphere and use the phase detector to 
>obtain a reference. Then, greatly increase the mass as you maintain the same 
>inner volume and hence total reflection path.  Compare the phase difference in 
>case 2 versus case1 when using the unaffected external photon.
>
>Dave

...now that might be an interesting experiment. You could use two concentric
spheres, and fill the space between with water. Unfortunately, I suspect that
temperature variations would have a larger effect than that which you are trying
to measure, since temperature variations would change the size of the sphere(s),
and hence the path length.
Try doing the math, and see if you can get a figure for the minimum temperature
variation that would be needed to drown out your signal. That should give you an
idea of how hard the experiment would be to do.

Regards,

Robin van Spaandonk

http://rvanspaa.freehostia.com/project.html

Re: [Vo]:Newtonian Gravity and General Relativity inside a spherical shell.

[mixent]

In reply to  David Roberson's message of Sat, 10 Dec 2016 01:54:41 -0500:
Hi,
[snip]
>I agree that a phase shift would occur due to normal path length differences. 
>What I am wondering about is whether or not that basic shift would have an 
>additional component that depends upon the magnitude of the gravitational mass 
>contained within the sphere's shell assuming that the path lengths do not vary.
>
>For example, have a very small mass sphere and use the phase detector to 
>obtain a reference. Then, greatly increase the mass as you maintain the same 
>inner volume and hence total reflection path.  Compare the phase difference in 
>case 2 versus case1 when using the unaffected external photon.
>
>Dave

...now that might be an interesting experiment. You could use two concentric
spheres, and fill the space between with water. Unfortunately, I suspect that
temperature variations would have a larger effect than that which you are trying
to measure, since temperature variations would change the size of the sphere(s),
and hence the path length.
Try doing the math, and see if you can get a figure for the minimum temperature
variation that would be needed to drown out your signal. That should give you an
idea of how hard the experiment would be to do.

Regards,

Robin van Spaandonk

http://rvanspaa.freehostia.com/project.html

Re: [Vo]:Newtonian Gravity and General Relativity inside a spherical shell.

[David Roberson]

I agree that a phase shift would occur due to normal path length differences. 
What I am wondering about is whether or not that basic shift would have an 
additional component that depends upon the magnitude of the gravitational mass 
contained within the sphere's shell assuming that the path lengths do not vary.

For example, have a very small mass sphere and use the phase detector to obtain 
a reference. Then, greatly increase the mass as you maintain the same inner 
volume and hence total reflection path.  Compare the phase difference in case 2 
versus case1 when using the unaffected external photon.

Dave

 

 

 

-Original Message-
From: mixent <mix...@bigpond.com>
To: vortex-l <vortex-l@eskimo.com>
Sent: Fri, Dec 9, 2016 5:21 pm
Subject: Re: [Vo]:Newtonian Gravity and General Relativity inside a spherical 
shell.

In reply to  David Roberson's message of Fri, 9 Dec 2016 17:10:45 -0500:
Hi,
[snip]
>Interesting question. Since the frequency of a photon increases as it gains 
>energy on the way into the hollow gravitational sphere one might expect time 
>to speed up for it.  If it is allowed to pass through another hole on the 
>other side the time rate would return to the original value once it reaches 
>the same distance away from the sphere in that direction.
>
>This appears to be a paradox of some type. It is common to speak of time 
>slowing down, but a bit strange to think of it as speeding up under some 
>conditions. Wonder where I went wrong with this arguement?
>
>Perhaps the photon could bounce around inside the hollow reflective sphere for 
>a long time before exiting an offset hole. Since its frequency is higher while 
>trapped inside it appears that many more cycles of oscillation would take 
>place for this photon than for a brother photon reflecting between two mirrors 
>outside the sphere for the same elapsed time.  Would a phase detector 
>comparing the two show anything?
>
>Dave

Since the lengths of the respective paths would be different, there should be a
phase difference, even if no time shift had taken place.

Regards,

Robin van Spaandonk

http://rvanspaa.freehostia.com/project.html

Re: [Vo]:Newtonian Gravity and General Relativity inside a spherical shell.

[mixent]

In reply to  David Roberson's message of Fri, 9 Dec 2016 17:10:45 -0500:
Hi,
[snip]
>Interesting question. Since the frequency of a photon increases as it gains 
>energy on the way into the hollow gravitational sphere one might expect time 
>to speed up for it.  If it is allowed to pass through another hole on the 
>other side the time rate would return to the original value once it reaches 
>the same distance away from the sphere in that direction.
>
>This appears to be a paradox of some type. It is common to speak of time 
>slowing down, but a bit strange to think of it as speeding up under some 
>conditions. Wonder where I went wrong with this arguement?
>
>Perhaps the photon could bounce around inside the hollow reflective sphere for 
>a long time before exiting an offset hole. Since its frequency is higher while 
>trapped inside it appears that many more cycles of oscillation would take 
>place for this photon than for a brother photon reflecting between two mirrors 
>outside the sphere for the same elapsed time.  Would a phase detector 
>comparing the two show anything?
>
>Dave

Since the lengths of the respective paths would be different, there should be a
phase difference, even if no time shift had taken place.

Regards,

Robin van Spaandonk

http://rvanspaa.freehostia.com/project.html

Re: [Vo]:Newtonian Gravity and General Relativity inside a spherical shell.

[David Roberson]

Interesting question. Since the frequency of a photon increases as it gains 
energy on the way into the hollow gravitational sphere one might expect time to 
speed up for it.  If it is allowed to pass through another hole on the other 
side the time rate would return to the original value once it reaches the same 
distance away from the sphere in that direction.

This appears to be a paradox of some type. It is common to speak of time 
slowing down, but a bit strange to think of it as speeding up under some 
conditions. Wonder where I went wrong with this arguement?

Perhaps the photon could bounce around inside the hollow reflective sphere for 
a long time before exiting an offset hole. Since its frequency is higher while 
trapped inside it appears that many more cycles of oscillation would take place 
for this photon than for a brother photon reflecting between two mirrors 
outside the sphere for the same elapsed time.  Would a phase detector comparing 
the two show anything?

Dave

 

 

 

-Original Message-
From: H LV <hveeder...@gmail.com>
To: vortex-l <vortex-l@eskimo.com>
Sent: Fri, Dec 9, 2016 1:42 pm
Subject: Re: [Vo]:Newtonian Gravity and General Relativity inside a spherical 
shell.







On Wed, Dec 7, 2016 at 4:04 PM, Stephen A. Lawrence <sa...@pobox.com> wrote:

  
Well known result -- gravitational time dilation has to do with the
gravitational potential, not the strength of the field.





 

Simple gedanken:  Drop a rock through a slender shaft into aspherical 
hollow cut out of the center of a spherical planet.  Therock has more 
kinetic energy when it gets to the center of theplanet.

Turn the rock (along with its kinetic energy) into photons, and beam
them back up the shaft.  At the top of the shaft, catch the beam andturn it 
back into a rock.

The rock must have the same mass at the end as it had to start with(or 
something's very wrong), which is smaller than the mass it hadat the bottom 
of the shaft (due its additional kinetic energy whichshows up as a mass 
excess).  This can only be true if the beam oflight was redder at the top 
of the shaft than the bottom. So, there must have been a gravitational 
red-shift as the lightclimbed the shaft.

So, the frequency of the light at the top of the shaft mustbe lower 
than the frequency at the bottom of the shaft.

But the total number of wave crests in the beam of lightcan't change.  
(You can count them, using appropriate equipment; inthat sense they behave 
like marbles.)  A certain number of wavecrests in the beam entered the 
shaft at the bottom; the same numberof wave crests must have come out the 
top.

So, if the frequency measured by an observer at the top ofthe shaft is 
lower than the frequency measured at the bottomof the shaft, the wave 
crests must have taken more time to exit thetop of the shaft than they took 
to enter the bottom of the shaft,and so, time must be passing faster for 
the observer at the top  of the shaft.
  


On 12/07/2016 12:53 AM, H LV wrote:


  

According to the shell theorem  the  gravitational force on a test mass 
inside a hollow sphere is  every where zero. This paper argues that 
this situation is not  equivalent from the standpoint of General 
Relativity to the  situation where gravity falls to zero far outside 
the sphere.  They conclude that General Relativity predicts that a 
clock  located inside a hollow sphere should run slower than a clock
  located outside the hollow sphere. (By contrast most people  are 
familiar with the fact that General relativity predicts a  clock should 
run faster as the force of gravity approaches  zero far from a 
gravitational body) This could provide a  laboratory test of Newtonian 
gravity which predicts that both  clocks should run at the same rate. 
  
  
  https://arxiv.org/pdf/1203.4428.pdf








Harry
  


  

Re: [Vo]:Newtonian Gravity and General Relativity inside a spherical shell.

[Stephen A. Lawrence]

On 12/09/2016 01:54 PM, H LV wrote:



On Wed, Dec 7, 2016 at 4:04 PM, Stephen A. Lawrence > wrote:


Well known result -- gravitational time dilation has to do with
the gravitational potential, not the strength of the field.


​GR's principle of equivalence depends on the concept of a force and 
not on the concept of a potential.
A person in an elevator without windows can only detect either the 
presence or an absence of a force.​


A person in an elevator also can't detect redshift or blueshift of light 
moving into or out of the elevator, because they are restricted to 
making measurements /inside the elevator/. Gravitational time dilation 
is a non-local effect, detectable only by comparing the results of 
measurements at highly separated points.  The elevator metaphor doesn't 
have anything to do with it. In fact there is *no* time dilation of any 
sort associated with either acceleration or a strong local G-field.


On the other hand a person in an elevator */can/* tell whether there's a 
gravitational field present, by checking for tidal effects, which are 
IIRC linear in the spatial dimension and hence detectable even at small 
scales.  That breaks the "elevator=gravity" correspondence, as real 
gravitational fields /always/ exhibit tidal effects.  (Constructed 
fields which result from funniness at a domain boundary don't show tidal 
effects but they're also not real.)


Don't confuse explanations using a metaphor with actual reasoning about 
the results.  The elevator is a metaphor, useful in looking for general 
principles, but imperfect in detail.  The drop-a-rock-down-a-well 
experiment, on the other hand, can in principle be quantified, and in 
the absence of gravitational redshift which depends on the potential, it 
results in a violation of CoE.  In fact it, or a simple variation on it, 
is what led to the concept of gravitational redshift to begin with, or 
so I've read.





Simple gedanken:  Drop a rock through a slender shaft into a
spherical hollow cut out of the center of a spherical planet.  The
rock has more kinetic energy when it gets to the center of the planet.

Turn the rock (along with its kinetic energy) into photons, and
beam them back up the shaft.  At the top of the shaft, catch the
beam and turn it back into a rock.

The rock must have the same mass at the end as it had to start
with (or something's very wrong), which is smaller than the mass
it had at the bottom of the shaft (due its additional kinetic
energy which shows up as a mass excess).  This can only be true if
the beam of light was *redder* at the top of the shaft than the
bottom. So, there must have been a gravitational red-shift as the
light climbed the shaft.

So, the /frequency/ of the light at the top of the shaft must be
*lower* than the frequency at the bottom of the shaft.

But the *total number of wave crests* in the beam of light can't
change.  (You can count them, using appropriate equipment; in that
sense they behave like marbles.)  A certain number of wave crests
in the beam entered the shaft at the bottom; the same number of
wave crests must have come out the top.

So, if the /frequency/ measured by an observer at the top of the
shaft is /lower/ than the frequency measured at the bottom of the
shaft, the wave crests must have taken more time to exit the top
of the shaft than they took to enter the bottom of the shaft, and
so, /time must be passing faster for the observer at the top of
the shaft.

/


​The experiment is different in that it doesn't involve an exchange of 
mass or energy between the surface and the interior.​


Harry

On 12/07/2016 12:53 AM, H LV wrote:

According to the shell theorem  the gravitational force on a test
mass inside a hollow sphere is every where zero. This paper
argues that this situation is not equivalent from the standpoint
of General Relativity to the situation where gravity falls to
zero far outside the sphere. They conclude that General
Relativity predicts that a clock located inside a hollow sphere
should run slower than a clock located outside the hollow sphere.
(By contrast most people are familiar with the fact that General
relativity predicts a clock should run faster as the force of
gravity approaches zero far from a gravitational body) This could
provide a laboratory test of Newtonian gravity which predicts
that both clocks should run at the same rate.


https://arxiv.org/pdf/1203.4428.pdf



Harry

Re: [Vo]:Newtonian Gravity and General Relativity inside a spherical shell.

[H LV]

On Wed, Dec 7, 2016 at 4:04 PM, Stephen A. Lawrence  wrote:

> Well known result -- gravitational time dilation has to do with the
> gravitational potential, not the strength of the field.
>
>
​GR's principle of equivalence depends on the concept of a force and not on
the concept of a potential.
A person in an elevator without windows can only detect either the presence
or an absence of a force.​



> Simple gedanken:  Drop a rock through a slender shaft into a spherical
> hollow cut out of the center of a spherical planet.  The rock has more
> kinetic energy when it gets to the center of the planet.
>
> Turn the rock (along with its kinetic energy) into photons, and beam them
> back up the shaft.  At the top of the shaft, catch the beam and turn it
> back into a rock.
>
> The rock must have the same mass at the end as it had to start with (or
> something's very wrong), which is smaller than the mass it had at the
> bottom of the shaft (due its additional kinetic energy which shows up as a
> mass excess).  This can only be true if the beam of light was *redder* at
> the top of the shaft than the bottom.  So, there must have been a
> gravitational red-shift as the light climbed the shaft.
>
> So, the *frequency* of the light at the top of the shaft must be *lower*
> than the frequency at the bottom of the shaft.
>
> But the *total number of wave crests* in the beam of light can't change.
> (You can count them, using appropriate equipment; in that sense they behave
> like marbles.)  A certain number of wave crests in the beam entered the
> shaft at the bottom; the same number of wave crests must have come out the
> top.
>
> So, if the *frequency* measured by an observer at the top of the shaft is
> *lower* than the frequency measured at the bottom of the shaft, the wave
> crests must have taken more time to exit the top of the shaft than they
> took to enter the bottom of the shaft, and so,
>
> *time must be passing faster for the observer at the top of the shaft. *
>

​The experiment is different in that it doesn't involve an exchange of mass
or energy between the surface and the interior.​

Harry



> On 12/07/2016 12:53 AM, H LV wrote:
>
> According to the shell theorem  the gravitational force on a test mass
> inside a hollow sphere is every where zero. This paper argues that this
> situation is not equivalent from the standpoint of General Relativity to
> the situation where gravity falls to zero far outside the sphere. They
> conclude that General Relativity predicts that a clock located inside a
> hollow sphere should run slower than a clock located outside the hollow
> sphere. (By contrast most people are familiar with the fact that General
> relativity predicts a clock should run faster as the force of gravity
> approaches zero far from a gravitational body) This could provide a
> laboratory test of Newtonian gravity which predicts that both clocks should
> run at the same rate.
>
>
> https://arxiv.org/pdf/1203.4428.pdf
>
>
> Harry
>
>
>

Re: [Vo]:Newtonian Gravity and General Relativity inside a spherical shell.

[H LV]

On Wed, Dec 7, 2016 at 4:04 PM, Stephen A. Lawrence  wrote:

> Well known result -- gravitational time dilation has to do with the
> gravitational potential, not the strength of the field.
>
>


> Simple gedanken:  Drop a rock through a slender shaft into a spherical
> hollow cut out of the center of a spherical planet.  The rock has more
> kinetic energy when it gets to the center of the planet.
>
> Turn the rock (along with its kinetic energy) into photons, and beam them
> back up the shaft.  At the top of the shaft, catch the beam and turn it
> back into a rock.
>
> The rock must have the same mass at the end as it had to start with (or
> something's very wrong), which is smaller than the mass it had at the
> bottom of the shaft (due its additional kinetic energy which shows up as a
> mass excess).  This can only be true if the beam of light was *redder* at
> the top of the shaft than the bottom.  So, there must have been a
> gravitational red-shift as the light climbed the shaft.
>
> So, the *frequency* of the light at the top of the shaft must be *lower*
> than the frequency at the bottom of the shaft.
>
> But the *total number of wave crests* in the beam of light can't change.
> (You can count them, using appropriate equipment; in that sense they behave
> like marbles.)  A certain number of wave crests in the beam entered the
> shaft at the bottom; the same number of wave crests must have come out the
> top.
>
> So, if the *frequency* measured by an observer at the top of the shaft is
> *lower* than the frequency measured at the bottom of the shaft, the wave
> crests must have taken more time to exit the top of the shaft than they
> took to enter the bottom of the shaft, and so,
>
> *time must be passing faster for the observer at the top of the shaft. *
> On 12/07/2016 12:53 AM, H LV wrote:
>
> According to the shell theorem  the gravitational force on a test mass
> inside a hollow sphere is every where zero. This paper argues that this
> situation is not equivalent from the standpoint of General Relativity to
> the situation where gravity falls to zero far outside the sphere. They
> conclude that General Relativity predicts that a clock located inside a
> hollow sphere should run slower than a clock located outside the hollow
> sphere. (By contrast most people are familiar with the fact that General
> relativity predicts a clock should run faster as the force of gravity
> approaches zero far from a gravitational body) This could provide a
> laboratory test of Newtonian gravity which predicts that both clocks should
> run at the same rate.
>
>
> https://arxiv.org/pdf/1203.4428.pdf
>
>
> Harry
>
>
>

Re: [Vo]:Newtonian Gravity and General Relativity inside a spherical shell.

[Stephen A. Lawrence]

Well known result -- gravitational time dilation has to do with the 
gravitational potential, not the strength of the field.


Simple gedanken:  Drop a rock through a slender shaft into a spherical 
hollow cut out of the center of a spherical planet.  The rock has more 
kinetic energy when it gets to the center of the planet.


Turn the rock (along with its kinetic energy) into photons, and beam 
them back up the shaft.  At the top of the shaft, catch the beam and 
turn it back into a rock.


The rock must have the same mass at the end as it had to start with (or 
something's very wrong), which is smaller than the mass it had at the 
bottom of the shaft (due its additional kinetic energy which shows up as 
a mass excess).  This can only be true if the beam of light was *redder* 
at the top of the shaft than the bottom. So, there must have been a 
gravitational red-shift as the light climbed the shaft.


So, the /frequency/ of the light at the top of the shaft must be *lower* 
than the frequency at the bottom of the shaft.


But the *total number of wave crests* in the beam of light can't 
change.  (You can count them, using appropriate equipment; in that sense 
they behave like marbles.)  A certain number of wave crests in the beam 
entered the shaft at the bottom; the same number of wave crests must 
have come out the top.


So, if the /frequency/ measured by an observer at the top of the shaft 
is /lower/ than the frequency measured at the bottom of the shaft, the 
wave crests must have taken more time to exit the top of the shaft than 
they took to enter the bottom of the shaft, and so, /time must be 
passing faster for the observer at the top of the shaft.


/
On 12/07/2016 12:53 AM, H LV wrote:
According to the shell theorem  the gravitational force on a test mass 
inside a hollow sphere is every where zero. This paper argues that 
this situation is not equivalent from the standpoint of General 
Relativity to the situation where gravity falls to zero far outside 
the sphere. They conclude that General Relativity predicts that a 
clock located inside a hollow sphere should run slower than a clock 
located outside the hollow sphere. (By contrast most people are 
familiar with the fact that General relativity predicts a clock should 
run faster as the force of gravity approaches zero far from a 
gravitational body) This could provide a laboratory test of Newtonian 
gravity which predicts that both clocks should run at the same rate.



https://arxiv.org/pdf/1203.4428.pdf


Harry

[Vo]:Newtonian Gravity and General Relativity inside a spherical shell.

[H LV]

According to the shell theorem  the gravitational force on a test mass
inside a hollow sphere is every where zero. This paper argues that this
situation is not equivalent from the standpoint of General Relativity to
the situation where gravity falls to zero far outside the sphere. They
conclude that General Relativity predicts that a clock located inside a
hollow sphere should run slower than a clock located outside the hollow
sphere. (By contrast most people are familiar with the fact that General
relativity predicts a clock should run faster as the force of gravity
approaches zero far from a gravitational body) This could provide a
laboratory test of Newtonian gravity which predicts that both clocks should
run at the same rate.


https://arxiv.org/pdf/1203.4428.pdf


Harry