# Hubble's constant measured by observer approaching light speed

I recently read about expansion of the universe and I can't figure out if Hubble's law (and other models of expansion of the universe) is compatible with the theory of relativity.

My question is: In which point of reference is recessional velocity between two bodies proportional to the distance between them ($v=HD$) with '$H$', Hubble constant? Imagine two observers moving in relation to each other with great speed. Each observer attempts to measure the local value of Hubble's constant by placing around himself two non-interacting particles and continuously checking distance between them (let's assume that all external fields and forces are somehow eliminated). Hubble's law states that the particles will move away in time with $v=HD$ and the theory of relativity states that each observer will see that the other one's clock slowed down, so the other one's $H$ will seem to be lower than his own.

So far everything seems ok, but from above scenario it seems that the expansion is a feature of particles (matter) instead of the space itself. If the above scenario is correct that means that for example it should be possible to avoid or postpone "big rip" by moving moving very fast and slowing one's clock (and local recessional velocity); but moving fast in reference to what?

On the other hand, if two observers measure different Hubble's constant because of their speed, that would mean that there is some universal point of reference in which $H$ is smallest, and that point of reference would define absolute rest. All observers moving in relation to this point of reference should observe higher $H$ because their clocks run slower. That doesn't seems right either.

When scientists talk about the rate of expansion of the universe, in which point of reference (with whose clock) is this rate measured?

• Are you familiar with the difference between the peculiar velocity and the Hubble flow? It seems like your problem may come from misunderstanding what 'recessional velocity' is. It is quite poorly-named in my opinion.
– Orca
Commented May 24, 2016 at 20:40
• If you place two masses next to each other, they will attract and eventually collide. They will not be moving with the Hubble flow. Commented May 24, 2016 at 20:53
• @Orca I'm not familiar with Hubble flow. As far as I understand, new space is constantly created between any two points. Commented May 25, 2016 at 10:39
• @CuriousOne I know that masses will collide because of gravitational force, but in theory, if masses are small and the H constant high, then the expansion of space could overcome the gravity and they should recede. Why treat galaxies different that small particles? Commented May 25, 2016 at 10:42
• Even in theory, if you place two masses next to each other in your coordinate system, they well simply attract and not float away. The expansion of space in your coordinate system does not separate two gravitationally bound massed, for that you need an increasing cosmological constant. Commented May 25, 2016 at 18:51

## 1 Answer

The preferred frame of reference is that of the co-moving reference frame that defines the Hubble flow. In practical terms that can be defined by correcting any velocity for the observer's motion with respect to the cosmic microwave background. Individual peculiar velocities for galaxies (including our own) are measured in hundreds to thousands of km/s. This is not large enough to make much difference to any practical measurement of the Hubble constant, but of course leads to scatter in the Hubble diagram for galaxies where $H_0 d$ is not much greater than the typical peculiar velocity.

Possibly your confusion arises from the term "recession velocity". As Orca commented, this is a poor nomenclature, implying that things are flying apart from each other. In fact, a better picture is to think of each galaxy embedded in its own little bit of space, each moving with a relatively modest peculiar velocity with respect to the cosmic microwave background. However, the space between the galaxies is expanding. It is this expansion (and also the additional expansion that occurs whilst light travels between galaxies) that gives the impression of relative motion (and indeed the redshift is spectroscopically indistinguishable from a doppler effect caused by relative motion).

Reading this short essay might help.

• So there exists preferred frame of reference? Does cosmic microwave background defines a special frame of reference that is "absolute rest"? Commented Jun 4, 2016 at 20:07