Strong Equivalence Principle Question

[latentcorpse]

My notes say that a photon traveling from a high altitude to an observer at low altitude appears to have a higher frequency i.e. gravitational blue shift.

now I am having trouble getting this:

the strong equivalence principle says we can substitute this "laboratory" with a laboratory that is undergoing uniform acceleration -g in deep space.

i then drew a box with the photon being emitted from the roof and traveling towards the floor. the box is moving downward with an acceleration g. so as we are moving away from the source we should use the following formula for gravitational doppler effect:

[itex]\nu^{obs}=\nu^{source} \sqrt{\frac{1-\beta}{1+\beta}}[/itex] where [itex]\beta=\frac{v}{c}[/itex] which predicts a gravitational redshift as [itex]\beta[/itex] is positive as we are moving away from the source with velocity v. I'm messing up somewhere but i can't see it.

help!

 

[turin]

... a photon traveling from a high altitude to an observer at low altitude ...
... substitute ... with a laboratory that is undergoing uniform acceleration -g in deep space.
... photon ... emitted from the roof and traveling towards the floor. the box is moving downward with an acceleration g.
... we are moving away from the source ...

In order to emulate Earth's gravity, so that things fall to the floor, the floor should accelerate upwards, not downwards. We are "moving" toward the source (if we are on the floor).

[itex]\nu^{obs}=\nu^{source} \sqrt{\frac{1-\beta}{1+\beta}}[/itex] where [itex]\beta=\frac{v}{c}[/itex]

How are you going to determine β?

 

[latentcorpse]

ok. i think what was confusing me was that whilst gravitation on Earth is [itex]-\vec{g}[/itex] downward. the strong equivalence principle equivalent of this will be a laboratory in deep space which is accelerating "up" with magnitude g, correct?

this would certainly explain why we observe a gravitational blue shift...

its just an introguction course to GR so we were just examining whether [itex]
\beta[/itex] was positive or negative and noting if we see blue shift or red shift as a result...