Redshift and Blueshift tell us something about the motion of far distant galaxies, but it's only a rough approximation. It only says something about the motion directly towards or away from us. Nothing more.

 

Could this method be used to give an accurate measurement of velocity, even from millions of light years away?

 

If an event is timed by a clock that is stationary in it's frame of reference, (call the result T), any other clock that is NOT stationary in that frame will measure a time greater than T for that event, as it' will observe the event happening slower.

 

So, if we find a pulsar in the far different galaxy, and accurately measure the interval for a thousand pulses (for example), then keep repeating the experiment using clocks moving at varying velocities, you will get different times for each different clock, and you should be able to plot a 3d graph of the results, and deduce from the graph, the velocity for the clock that gives the shortest time for the thousand pulses.

 

The point in the graph that gives the lowest value of T must be at rest in the inertial frame for which the pulsar is at rest. So you would have an accurate figure for the ACTUAL direction and speed of the Pulsar.

 

It might be a difficult thing to set up, but would it work in principle?

Edited March 15, 20178 yr by mistermack

That won't work; I have the impression that you forgot about the "classical" Doppler effect.

- https://en.wikipedia.org/wiki/Doppler_effect

 

What is done in practice, is assuming that the redshift is fully due to velocity, and the velocity is estimated from characteristic emission wavelengths in the spectrum.

I don't think that would affect it, because what you are measuring is the velocity of your clock.

I think that the doppler shift would affect all of your readings equally, so it wouldn't change which reading gave the minimum value for T.

Since your various clock readings can be in varying directions as well as various speeds, the clock that gives the smallest value for T should give direction as well as speed.

 

Edit: not so sure having thought about that. Maybe you could compensate for doppler, if you already have a value for redshift?

Edited March 15, 20178 yr by mistermack