Does expanding space affect time dilation etc?

[Dizzle]

In special relativity we have the velocity 'u', being the difference in speed between two objects, from which we work out time dilation, length contraction etc.

But if those objects are separated by some expanding space, but not moving with respect to that space, is there still the dilation effect?

What if both moved towards each other at the same speed as the space expanded between them, so the net effect what they weren't moving with respect to each other? Would there be no time dilation etc then?

 

[phinds]

For expanding space, I think you run into the issue that you cannot define a single IFR that encompasses both objects. That's why speeding tickets are not issued to galaxies which are receding from us at > c.

If they are stationary w/ respect to each other, I can't see how there would be an time dilation between them regardless of other circumstances, but in the absence of their being in the same IFR I'm not as sure about that.

 

[PeterDonis]

if those objects are separated by some expanding space, but not moving with respect to that space, is there still the dilation effect?

This question isn't really answerable, because the concept of "time dilation" is not well-defined if "space" is expanding. ("Expanding space" isn't really the best description of what's going on, but going into that would probably be too much for this thread.)

What if both moved towards each other at the same speed as the space expanded between them, so the net effect what they weren't moving with respect to each other? Would there be no time dilation etc then?

Same answer as above.

You can make the questions well defined by considering, instead of "time dilation", something like the observed redshift/blueshift of light signals exchanged between the two objects. Then the answer would be that in the first case, each object would observe the other's light to be redshifted, and in the second case, each object would observe no redshift/blueshift in the other's light.