Is time measured at receding objects dilated?

[johne1618]

As far as I understand it Hubble's velocity law says that the velocity v of a distant object with respect to us, at the present cosmological time, is given by

v = H_0 * r

where H_0 is the present Hubble constant and r is the distance to the object.

If a distant object is moving at velocity v with respect to us does that mean that proper time measured by an observer near that object is dilated by a gamma factor 1/sqrt(1-v^2/c^2) when measured in our time coordinates?

 

[Vorde]

[STRIKE]Yes.[/STRIKE]

EDIT: I spoke too soon.

 

[marcus]

As far as I understand it Hubble's velocity law says that the velocity v of a distant object with respect to us, at the present cosmological time, is given by

v = H_0 * r

where H_0 is the present Hubble constant and r is the distance to the object.

If a distant object is moving at velocity v with respect to us does that mean that proper time measured by an observer near that object is dilated by a gamma factor 1/sqrt(1-v^2/c^2) when measured in our time coordinates?

Yes.

I disagree, Vorde.

The present velocities given by Hubble law, for most of the galaxies we can see, are greater than c.
So the gamma factor would involve taking square root of a negative number. It would not make sense as a time dilation factor.

John, the Hubble law as you state it is v = H₀r
where as you say H₀ is the present value of H, and r is the present distance (which you would measure e.g. by radar if you could stop the expansion process) and v is the present rate of change of this present distance.

Most of the galaxies we currently observe have redshift z > 1.5 and any such galaxy would be presently receding at a rate faster than c.

You might find this online calculator interesting
http://www.einsteins-theory-of-relativity-4engineers.com/cosmocalc.htm
Put in a redshift like, for example 1.8 and press "calculate".

Easy to use. Where it says "Distance traveled by the light" this means the distance the light would have traveled in a non-expanding universe, on its own. It is a way of reading off the light travel time. Just read lightyears as years.

Distant galaxies do not normally share the same Lorentz frame---special rel time dilation does not apply to recession rates. It would be terrible if they did since for the most part the rates are superluminal

 

[Vorde]

I can't argue with that logic, but it seems that if that were true, there is an experimental way to discern whether or not an object is moving away from us or the space in between is expanding, which doesn't seem right.

EDIT: Also it seems that if a galaxy were receding faster than the speed of light, a photon from that galaxy would never be able to reach us as space was expanding faster than it was approaching us.

EDIT 2: What I didn't realize until your Marcus's edit however was that a receding galaxy would not be in the same frame of reference as you however, so the SR stuff I was basing this off of is invalid, nevermind, your view is making sense to me now.

 

[Angelos K]

Related paper

An interesting paper on the subject is this one:

Davis and Lineweaver 2004 in Publications of the Astronomical Society of Australia, Volume 21, Issue 1, pp. 97-109

It also deals with the question why light from such superluminarily receding objects could reach us - which I found very suprising!

 

[johne1618]

John, the Hubble law as you state it is v = H₀r
where as you say H₀ is the present value of H, and r is the present distance (which you would measure e.g. by radar if you could stop the expansion process) and v is the present rate of change of this present distance.

I wonder if someone could comment on this thought experiment.

I imagine constructing a very,very long rigid platform in space of length L light-years. I assume that the center of mass of the platform would travel with the "Hubble flow". Thus if I sat at the end of the platform would I see nearby objects, moving with the local Hubble flow, move past me at a velocity H_0 * (L/2) parallel to the platform?

Surely the velocity of these nearby objects relative to me would be "real" and therefore could not be greater than the speed of light?

John

 

[BillSaltLake]

This is a thought-provoking question. I think that even if one could build a super-rigid platform (or a long plank) outward at the speed of light in both directions (that is, the builders in each direction are building furiously just behind an outbound laser pulse), neither end would ever reach a location where the comoving flow (or any flow) exceeded the speed of light.
If there were "outside" builders that prefabricated and waited to join up with the growing platform, they may never be caught up to by the growing platform. That is, these outside builders may not ever be observable by us and vice-versa.