A Space & astronomy forum. SpaceBanter.com

Go Back   Home » SpaceBanter.com forum » Astronomy and Astrophysics » Astronomy Misc
Site Map Home Authors List Search Today's Posts Mark Forums Read Web Partners

Odd gravitational effect: unusual Doppler shifts within frame moving in gravity field?



 
 
Thread Tools Display Modes
  #1  
Old January 4th 04, 04:28 AM
Neil
external usenet poster
 
Posts: n/a
Default Odd gravitational effect: unusual Doppler shifts within frame moving in gravity field?

This is a curious problem. It looks basic enough to have been considered before,
but I find nothing related anywhere.

Background: The gravitational Doppler shift formula is straightforward when the
energy change is proportionately small. Tracking energy E, we take
E_received = E0 (1 - g dot h/c^2).
Following the equivalence principle, we expect this to apply in general to
relative gravity fields, whether "real" or caused by relative motion, or even
the *combination of both*.

However, if you directly work out the change in relative energy for a photon
traversing a frame moving at constant velocity in a g-field (ie, elevator), the
result is not as given by the Eq. applied to local values of g and h for the
elevator K'. This problem would not appear in Newtonian physics. (Let us know if
you've heard of anything like this problem, especially with references.) I think
this effect is testable with current equipment. Critique is fine, but it won't
help unless you show your work. I think sci.astro is appropriate given the GR
crowd, and the problem could have cosmological consequences.

The point can be summarized as: First, assume you are in a "rest frame" K which
follows the normal rules given above, and that once light is emitted it follows
consistent rules. Then, consider a moving frame and track the paths and energy
changes of photons emitted from one place to another, combining the effects of
both gravity and local relative velocity. Photons emitted from the trailing end
P1 of the elevator travel farther along the "rest" frame of the gravity field to
catch up, and thus suffer greater gravitational Doppler shift in transit than
would normally apply with that elevator height. Photons emitted from the leading
end P2 of the elevator travel less rest-frame distance than if the elevator were
at rest, and show less GD shift. Since the velocities of the ends are locally
the same, the velocity part of Doppler shift (which acts at the moments of
emission and reception) cancels out, leaving the travel-based discrepancy.
(Putting the math simply: the emission and reception Doppler formulae give
inverse values, leaving the proportional change from gravitational effect to be
solely that determined by the distance the photon travels in K.) Consider also
reflecting a photon from the other end of the elevator: the photon is received
at a different potential (in K) than when emitted, but combined velocity effects
all cancel out. Therefore, it must show a net energy change, which wouldn't
happen in "normal" gravity fields. It perplexes me too, but this is the result
of directly working things out.

I'll work it out in more detail, but using the simple case of light going
parallel to g. If we combine Lorentz contraction (which does locally apply in a
g-field) and "catch-up" calculations, we get the following for the values of h
as actually moved in K, in terms of proper elevator height L0 and its velocity
v, which is locally consistent:

h = gamma*L0 (1 + v/c), with v signed negative when sent from a leading end and
L0 signed negative when light moves down. Things may get more complicated when v
approaches c, but at low v it is clear that the top of the elevator will move
very nearly this extra margin before receiving a photon, etc. Hence, when we
plug this formula into the GD shift we get

E_received = E0 [1 - gamma*g L (1 + v/c)/c^2]


Since the g' felt in K' is multiplied by gamma (check with transformations), the
actual discrepancy versus relative g' is
E_received = E0 [1 - g' L (1 + v/c)/c^2]. This seems like it would violate
energy conservation, since the photon's energy change does not correspond to the
work doing moving the mass-energy in the local g', but remember that when we
move the elevator, the impulse from photon emission and reception must be
accounted for.

This problem raises questions about the equivalence principle also, since we'd
expect things to work out normally for an "elevator" attached to an accelerating
reference frame - after all, the elevator is just "accelerating" at some rate,
albeit refined by hyperbolic motion, and relative signals should follow the
usual (?) rule. OTOH, such an elevator moves through regions of increasing or
decreasing proper acceleration, per Born motion. But the really big problem is
this: if we let a small box free fall within the elevator, the Doppler shifts
from one end to the other won't cancel out, since they are asymmetrical. (That
is, the increments of velocity from falling will not cancel out the asymmetrical
net shifts within the elevator.) Another problem I've thought of about the EP:
if light is sent obliquely from one part of a system in hyperbolic motion
towards a higher region, it should take very long to arrive, and be subject to
great motional Doppler shift - more than the amount appropriate to the
equivalent potential change.

  #2  
Old January 4th 04, 05:02 AM
Neil
external usenet poster
 
Posts: n/a
Default Odd gravitational effect: unusual Doppler shifts within frame moving in gravity field?


"Neil" wrote in message
...
This is a curious problem. It looks basic enough to have been considered

before,
but I find nothing related anywhere.

Background: The gravitational Doppler shift formula is straightforward when

the
energy change is proportionately small. Tracking energy E, we take
E_received = E0 (1 - g dot h/c^2).
Following the equivalence principle, we expect this to apply in general to
relative gravity fields, whether "real" or caused by relative motion, or even
the *combination of both*.

snip
Just so there isn't any confusion about proper versus measured length, here's
the corrected portion referencing proper elevator height L0:

E_received = E0 [1 - gamma*g L0 (1 + v/c)/c^2]


Since the g' felt in K' is multiplied by gamma (check with transformations), the
actual discrepancy versus relative g' is
E_received = E0 [1 - g' L0 (1 + v/c)/c^2]. This seems like it would violate
energy conservation, since the photon's energy change does not correspond to the
work doing moving the mass-energy in the local g', but remember that when we
move the elevator, the impulse from photon emission and reception must be
accounted for.

  #3  
Old January 7th 04, 02:10 AM
Jim Greenfield
external usenet poster
 
Posts: n/a
Default Odd gravitational effect: unusual Doppler shifts within frame moving in gravity field?

"Neil" wrote in message ...
This is a curious problem. It looks basic enough to have been considered before,
but I find nothing related anywhere.

Background: The gravitational Doppler shift formula is straightforward when the
energy change is proportionately small. Tracking energy E, we take
E_received = E0 (1 - g dot h/c^2).
Following the equivalence principle, we expect this to apply in general to
relative gravity fields, whether "real" or caused by relative motion, or even
the *combination of both*.

However, if you directly work out the change in relative energy for a photon
traversing a frame moving at constant velocity in a g-field (ie, elevator), the
result is not as given by the Eq. applied to local values of g and h for the
elevator K'. This problem would not appear in Newtonian physics. (Let us know if
you've heard of anything like this problem, especially with references.) I think
this effect is testable with current equipment. Critique is fine, but it won't
help unless you show your work. I think sci.astro is appropriate given the GR
crowd, and the problem could have cosmological consequences.

The point can be summarized as: First, assume you are in a "rest frame" K which
follows the normal rules given above, and that once light is emitted it follows
consistent rules. Then, consider a moving frame and track the paths and energy
changes of photons emitted from one place to another, combining the effects of
both gravity and local relative velocity. Photons emitted from the trailing end
P1 of the elevator travel farther along the "rest" frame of the gravity field to
catch up, and thus suffer greater gravitational Doppler shift in transit than
would normally apply with that elevator height. Photons emitted from the leading
end P2 of the elevator travel less rest-frame distance than if the elevator were
at rest, and show less GD shift. Since the velocities of the ends are locally
the same, the velocity part of Doppler shift (which acts at the moments of
emission and reception) cancels out, leaving the travel-based discrepancy.
(Putting the math simply: the emission and reception Doppler formulae give
inverse values, leaving the proportional change from gravitational effect to be
solely that determined by the distance the photon travels in K.) Consider also
reflecting a photon from the other end of the elevator: the photon is received
at a different potential (in K) than when emitted, but combined velocity effects
all cancel out. Therefore, it must show a net energy change, which wouldn't
happen in "normal" gravity fields. It perplexes me too, but this is the result
of directly working things out.

I'll work it out in more detail, but using the simple case of light going
parallel to g. If we combine Lorentz contraction (which does locally apply in a
g-field) and "catch-up" calculations, we get the following for the values of h
as actually moved in K, in terms of proper elevator height L0 and its velocity
v, which is locally consistent:

h = gamma*L0 (1 + v/c), with v signed negative when sent from a leading end and
L0 signed negative when light moves down. Things may get more complicated when v
approaches c, but at low v it is clear that the top of the elevator will move
very nearly this extra margin before receiving a photon, etc. Hence, when we
plug this formula into the GD shift we get

E_received = E0 [1 - gamma*g L (1 + v/c)/c^2]


Since the g' felt in K' is multiplied by gamma (check with transformations), the
actual discrepancy versus relative g' is
E_received = E0 [1 - g' L (1 + v/c)/c^2]. This seems like it would violate
energy conservation, since the photon's energy change does not correspond to the
work doing moving the mass-energy in the local g', but remember that when we
move the elevator, the impulse from photon emission and reception must be
accounted for.

This problem raises questions about the equivalence principle also, since we'd
expect things to work out normally for an "elevator" attached to an accelerating
reference frame - after all, the elevator is just "accelerating" at some rate,
albeit refined by hyperbolic motion, and relative signals should follow the
usual (?) rule. OTOH, such an elevator moves through regions of increasing or
decreasing proper acceleration, per Born motion. But the really big problem is
this: if we let a small box free fall within the elevator, the Doppler shifts
from one end to the other won't cancel out, since they are asymmetrical. (That
is, the increments of velocity from falling will not cancel out the asymmetrical
net shifts within the elevator.) Another problem I've thought of about the EP:
if light is sent obliquely from one part of a system in hyperbolic motion
towards a higher region, it should take very long to arrive, and be subject to
great motional Doppler shift - more than the amount appropriate to the
equivalent potential change.


In any situation where velocity (direction) is ARBITRARILY given +/-,
you may come across this contradiction, as velocity, force etc are
ALWAYS +. They may be 'less than', but not reliant on direction for
sign, and NOT 0. The Lorentz Transforms, SRelativity therefore
BS......

Jim G
 




Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

vB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Forum Jump

Similar Threads
Thread Thread Starter Forum Replies Last Post
Bullwinkle Unbound Jeff Root Astronomy Misc 74 January 22nd 04 06:09 AM
Sakharov's Emergent Gravity Jack Sarfatti Astronomy Misc 0 November 17th 03 09:07 PM
Nature of Gravity: was Vector Gravitational Equations CC Astronomy Misc 2 September 10th 03 01:31 AM
Electric Gravity&Instantaneous Light ralph sansbury Astronomy Misc 8 August 31st 03 02:53 AM
PLANETS ORBIT THE SUN TO CONSERVE TOTAL ENERGY GRAVITYMECHANIC2 Astronomy Misc 0 July 20th 03 04:59 PM


All times are GMT +1. The time now is 06:05 PM.


Powered by vBulletin® Version 3.6.4
Copyright ©2000 - 2024, Jelsoft Enterprises Ltd.
Copyright ©2004-2024 SpaceBanter.com.
The comments are property of their posters.