Doppler shift, c, observation, recession, spacetime expansion

[Bojan Keevill]

Hi all,

It is my understanding that a Doppler shift is the result of a change in wave frequency due to a change in distance of a signal source, relative to the observer.
I assume that the change in distance must be continuous, in order to observe a Doppler effect:

frequency increase = decreasing distance / time
frequency decrease = increasing distance / time

Assuming this simple explanation is correct, and that the velocity of light is constant for all inertial frames of reference, then no Doppler shift should be observed. However, a Doppler shift (redshift) is apparent.

It is my understanding that the apparent cosmological redshift has given rise to the "expansion of space" hypothesis.

With this in mind I wish to ask what the difference is between:
- increasing distance between signal source and observer
and
- increasing space between signal source and observer

Thanks in advance,
B

 

[mfb]

It is my understanding that a Doppler shift is the result of a change in wave frequency due to a change in distance of a signal source, relative to the observer.

In special relativity, you have to consider time dilation as well - something like "change in distance in spacetime" (and not just in space).

I assume that the change in distance must be continuous

Motion is always continuous in special relativity.

frequency increase = decreasing distance / time
frequency decrease = increasing distance / time

Not necessarily.

Assuming this simple explanation is correct, and that the velocity of light is constant for all inertial frames of reference, then no Doppler shift should be observed.

Why?

However, a Doppler shift (redshift) is apparent.

The Doppler shift from the expansion of space comes from general relativity, and its contribution is independent of relative motions.

It is my understanding that the apparent cosmological redshift has given rise to the "expansion of space" hypothesis.

Indeed.

With this in mind I wish to ask what the difference is between:
- increasing distance between signal source and observer
and
- increasing space between signal source and observer

Two different words, both are ambiguous in general relativity.