Do Special Relativity effects apply to total recession velocities or to "peculiar velocities"?

Question

I understand (thanks largely to help from this forum) that the primary source for the recession red shift in distant galaxies is the expansion of the space between us and not the relative velocity of the separating objects within that space. It then seems to me that the relativistic effects (time dilation, etc) resulting from this separation apply only to the latter interpretation of the term "velocity" - i.e the peculiar velocity and not the total recession velocity. This would mean that a distant red shift does not necessarily imply significant time dilation differences - only "time cone" perception differences due to the distances involved. Is this correct? Thank you.

Lola F · Accepted Answer

Special Relativity effects don't apply at all to bodies outside your Local Lorentz Frame. All effects on distant bodies are General Relativistic. So the detailed answer to your question is complex, but in real world situations, to obtain the rate of a clock local to another galaxy, you must multiply its rate in the telescope by 1+z.

In other words, a supernova that takes 10 days in the Milky Way can be observed for 20 days in a galaxy at redshift 1.

Whether you consider this to be a time dilation or Doppler Shift correction depends on your choice of coordinates.

Anonymous · Answer

You aren't going to like this very much, but I'll give links to standard theory at the end and maybe you'll like that better.

Recession can be viewed as relaxation of global curvature, which simply affects "local clock rates" everywhere.  Essentially *now*, all "locales" agree on the clock rate, associated sizes, and "the laws of physics".  So no, the recession does in fact represent time dilation between *now* and *then*, and the light we are receiving *now* only just now arrives from very far away... on the light cone.

I like you am *very* unhappy with using the same words for "recession velocity/speed" and "kinematic velocity/speed", as invariably someone will misunderstand.

There is no limitation placed on "clock rate", so there is no "grip" on how our "clock rate" now compares to a "clock rate" at a previous epoch.

Yes to gravitational red shift, in my opinion.  As to where the curvature originates, it was nearly infinite to start with, and has been relaxing, and that it appears to be "paced" or "metered" is only because our consciousness is based / seated in chemical reactions, which are very much paced along with all other "stochastic processes".

No, "reference frames" don't stretch, they are established by clocks and light, and are inertial.  It is as if we are getting smaller... right where we "stand".

http://www.astro.ucla.edu/~wright/cosmolog.htm
... just click on "Enter the tutorial".

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Do Special Relativity effects apply to total recession velocities or to "peculiar velocities"?

2 Answers