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Gravitational redshift and length contraction factors


md65536

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  • 2 months later...

Are the length contraction and redshift factors the same in GR?

 

Say there are 2 observers A and B, with A on the surface of a planet and B hovering high above. If A sends a signal to B it loses energy climbing out of the gravitational well, and appears red-shifted to B.

 

Also, B's meter stick appears longer than a meter to A, and A's appears shorter than a meter to B.

 

Suppose A sends a signal with a wavelength of 1 m, and B receives it with a wavelength of 1.1 m, does that mean that A sees B's meter stick measuring 1.1 m long, and B sees A's measuring 0.909 m long?

 

I think I must have this wrong just because the factors aren't the same in SR. I guess time dilation must also affect the redshift, but not the length contraction??? Would the difference in redshift and length contraction factors be fully accounted for with time dilation?

 

Are there any examples online that calculate the two factors in a simple case?

 

Meter sticks and photons are quite different.

 

Photons expand when climbing up from a gravity well.

 

Meter sticks very rarely climb up from a gravity well.

 

Even the rare sticks that climb up from a gravity well don't expand, except maybe in some rare cases, where the climbing energy comes from such a part of the stick that expansion is the result of the energy loss .

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By the way, there is no good reason why meter sticks would change in gravity fields.

 

If relativity is involved and length change is involved, meter sticks can very well be uninvolved, although meter sticks are involved in relativistic length change of meter sticks.

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By the way, there is no good reason why meter sticks would change in gravity fields.

Well, I'm assuming that they don't! I'm talking about ideal meter sticks here, and assuming that they are completely contained in a local frame of reference. If a physical ruler is used, I'm assuming it is small enough (perhaps less than 1m in extreme gravity) that it is completely in local flat spacetime (or at least within any small margin of error you need). So I think that tidal forces can be ignored. And apart from that, 1m is locally 1m for any observer, so a meter stick should not change in a gravitational field.

 

However, distant meter sticks are not necessarily 1m. The problem I think I'm trying to work through is that there's not really a single, obvious way to compare distant meter sticks. You can't bring them side-by-side while still maintaining the difference that occurs at a distance. You can decide to compare how they "look", or measure using timing of light signals, but then you get different answers depending on how you measure, corresponding to the variety of definitions of distance that there are...

 

Anyway when I say "meter stick" I'm referring to "one unit of length as measured by a local observer" (at the stick's location).

Edited by md65536
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Well, I'm assuming that they don't! I'm talking about ideal meter sticks here, and assuming that they are completely contained in a local frame of reference. If a physical ruler is used, I'm assuming it is small enough (perhaps less than 1m in extreme gravity) that it is completely in local flat spacetime (or at least within any small margin of error you need). So I think that tidal forces can be ignored. And apart from that, 1m is locally 1m for any observer, so a meter stick should not change in a gravitational field.

 

However, distant meter sticks are not necessarily 1m. The problem I think I'm trying to work through is that there's not really a single, obvious way to compare distant meter sticks. You can't bring them side-by-side while still maintaining the difference that occurs at a distance. You can decide to compare how they "look", or measure using timing of light signals, but then you get different answers depending on how you measure, corresponding to the variety of definitions of distance that there are...

 

Anyway when I say "meter stick" I'm referring to "one unit of length as measured by a local observer" (at the stick's location).

 

I see. Everybody is confused here.

 

People are trying to make the coordinate velocity of light to be c.

 

Coordinate velocity of a light beam may be anything from zero to infinity.

 

(Distant meter sticks are not necesarily 1 m. Distant light beams are not necessarily 300000 km/s.)

 

 

(Maybe in schwarzschild coorditates light always has coordinate velocity c, but I don't like schwarzschild coordinates, probably the aforementioned confusion is schwarzschild coordinates' fault)

Edited by Toffo
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  • 1 month later...

According to what Feynmann says and according to what is reported here http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html

about the experiment of Pound and Rebka, the gravitational redshift is :

gred.gif

 

it is part of general relativity but can be derived classically. A Photon is attracted like a mass by the gravitational field with g acceleration this way it loses its energy, coming out of a celestial body.

the link to time dilation gtim1.gifdoesn't really come to a redshitf of photons.

here we are talking about frequency shift due to different gravity fields beating different times.

With gravitational redshift described in the first instance, the gravity field is not necessarily variable (is considered constant as g).

Edited by stefano quattrini
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