- #1
johne1618
- 371
- 0
Using a simplified (radial co-ord only, spatially flat) FRW metric with the usual co-ordinates of cosmological time [itex]t[/itex] and co-moving radial distance [itex]r[/itex]:
[itex] ds^2 = -c^2 dt^2 + a(t) dr^2 [/itex]
we find the path a lightbeam takes by setting [itex]ds=0[/itex] to obtain
[itex] \frac{dr}{dt} = \frac{c}{a(t)} [/itex]
Therefore if a co-moving observer measures the speed of light by measuring the time [itex]dt[/itex] light takes to travel a fixed length [itex]dr[/itex] then he will derive a light speed that changes as the Universe grows older.
Is that right?
I think the light speed measured by such an observer should not change with cosmological time.
I think a co-moving observer experiences conformal time [itex]\tau[/itex] such that
[itex] d\tau = \frac{dt}{a(t)} [/itex]
so that when he measures the speed of light over a fixed length he gets
[itex] \frac{dr}{d\tau} = c [/itex]
so that he does not experience the speed of light decaying as the Universe gets older.
[itex] ds^2 = -c^2 dt^2 + a(t) dr^2 [/itex]
we find the path a lightbeam takes by setting [itex]ds=0[/itex] to obtain
[itex] \frac{dr}{dt} = \frac{c}{a(t)} [/itex]
Therefore if a co-moving observer measures the speed of light by measuring the time [itex]dt[/itex] light takes to travel a fixed length [itex]dr[/itex] then he will derive a light speed that changes as the Universe grows older.
Is that right?
I think the light speed measured by such an observer should not change with cosmological time.
I think a co-moving observer experiences conformal time [itex]\tau[/itex] such that
[itex] d\tau = \frac{dt}{a(t)} [/itex]
so that when he measures the speed of light over a fixed length he gets
[itex] \frac{dr}{d\tau} = c [/itex]
so that he does not experience the speed of light decaying as the Universe gets older.
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