Speed of Light & Expanding Universe: Does Hubble's Law Violate Rule?

[docnet]

TL;DR

how do scientists reconcile the fact distant galaxies recede away from us at speeds greater than light, while things can't travel faster than light?

Hubbles law states the rate of recession of galaxies increases proportionally with distance, and the cosmological horizon is where distant galaxies recede away at the speed of light. Does this not violate the rule of faster than light speed travel?

 

[PeterDonis]

Hubbles law states the rate of recession of galaxies increases proportionally with distance, and the cosmological horizon is where distant galaxies recede away at the speed of light. Does this not violate the rule of faster than light speed travel?

No. The "speed" in the Hubble's law calculation is a coordinate speed, not a physically measured speed. If you take a galaxy that is right at the cosmological horizon, and look at the coordinate speed of a light ray emitted by that galaxy directly away from us, that light ray will be moving away from us faster than the galaxy itself. (In our best current model, in which the universe is spatially flat, the light ray's coordinate speed away from us will be $2 c$, if the galaxy's coordinate speed away from is is $c$.)

This all illustrates that looking at "speed" is not the correct way to generalize to curved spacetime (GR) the rule in flat spacetime (SR) that "nothing can go faster than light". The correct way is to look at the light cones: all timelike objects (objects with nonzero rest mass) must move inside the light cones, and all lightlike objects (objects with zero rest mass) must move on the light cones. Or, to put it another way, no timelike object can move faster than a light ray moving in the same direction.

 

[Ibix]

The rule is that nothing can overtake a light pulse, and nothing does overtake a light pulse. Light pulses in far distant galaxies will overtake any matter nearby.

 

[docnet]

No. The "speed" in the Hubble's law calculation is a coordinate speed, not a physically measured speed. If you take a galaxy that is right at the cosmological horizon, and look at the coordinate speed of a light ray emitted by that galaxy directly away from us, that light ray will be moving away from us faster than the galaxy itself.

So things cannot travel faster than the speed of light in region of space, but the coordinates within space are expanding across far distances that allows objects to move apart at speeds faster than c?

 

[phinds]

So things cannot travel faster than the speed of light in region of space, but the coordinates within space are expanding across far distances that allows objects to move apart at speeds faster than c?

Yes, but it's not called "moving" because that implies proper motion, which it is not. It is called "recession". They RECEDE from one another, not move. It's more than a semantic distinction.

You might find this interesting

 

[PAllen]

Yes, but it's not called "moving" because that implies proper motion, which it is not. It is called "recession". They RECEDE from one another, not move. It's more than a semantic distinction.

You might find this interesting

Please define proper motion in GR terms. As far as I know, relative motion in GR only has invariant meaning locally, and there is then obviously no notion of rest versus motion except in a relative sense. There is no sense in which it is correct to say a comoving body is not moving; only that it sees the CMB as isotropic.

At a distance, since there is no unambiguous way to compare velocities, all velocities are coordinate dependent, and thus do not have any invariant physical meaning. It is just as meaningful to say comoving galaxies are moving apart (as they are in Fermi Normal coordinates) , as it is to say they are not moving as in FLRW coordinates.

 

[PeterDonis]

Please define proper motion in GR terms.

In the context of cosmology, "proper motion" generally means "motion relative to a comoving observer at the same spatial location".

 

[PAllen]

In the context of cosmology, "proper motion" generally means "motion relative to a comoving observer at the same spatial location".

But that has no meaning in GR terms, except for seeing anisotropy of CMB. I reject that there any sense in which proper motion is real motion, and a comoving body is not really moving. I consider these notions a violation of GR.

 

[PeterDonis]

that has no meaning in GR terms

Certainly it does. The inner product of a comoving observer's 4-velocity and the 4-velocity of some other object at the same spatial location is perfectly well-defined.

I reject that there any sense in which proper motion is real motion, and a comoving body is not really moving.

I agree that there is no such thing as absolute motion. However, I think @phinds did not intend to claim that there was, and if he takes a step back, he will realize that he made a poor choice of words.

 

[PAllen]

I agree that there is no such thing as absolute motion. However, I think @phinds did not intend to claim that there was, and if he takes a step back, he will realize that he made a poor choice of words.

It’s a little more than just the question of absolute motion. It is whether in standard GR there is anything at all different about comparing two distant comoving world lines versus two arbitrary distant world lines. In neither case can you justify any statement about whether they are not moving relative to each other or are moving, in any unambiguous way.

 

[phinds]

I agree that there is no such thing as absolute motion. However, I think @phinds did not intend to claim that there was, and if he takes a step back, he will realize that he made a poor choice of words.

Yes, I certainly did not mean to imply in any way that there is any such thing as absolute motion and I tend to forget that proper motion (by which I always intend what you said in post #7) cannot be applied objects that are receeding from each other. I always think of them as having recession velocities (potentially HUGE amount) and proper motion (small amounts and zero if they are both co-moving) but that latter part is not well defined and is an inappropriate use of the term.

 

[vanhees71]

But that has no meaning in GR terms, except for seeing anisotropy of CMB. I reject that there any sense in which proper motion is real motion, and a comoving body is not really moving. I consider these notions a violation of GR.

You can measure locally whether you are "moving or not" already at the level of the homogeneous and isotropic FLRM metric given that space is filled with the blackbody CMBR. You only need to measure the "apparent temperature" as a function of direction of observation. That's the "dipole part" of the measured CMBR anisotropies, which is usually subtracted in the pictures the COBE, WMAP, and Planck collaborations show, because it's just the motion of our local group against the "rest frame" of the CMBR. The latter is the frame of a "fundamental or comoving observer". The rest frame of the CMBR defines physically special local frames of reference as any "fluid" in local thermal equilibrium does.

 

[haushofer]

Does this not violate the rule of faster than light speed travel?

Let me ask you the other way around, keeping in mind the reason why particles in a static, flat spacetime cannot cross the lightbarrier: why would it? :)

 

[PeterDonis]

It is whether in standard GR there is anything at all different about comparing two distant comoving world lines versus two arbitrary distant world lines.

Yes, there is no meaningful "relative velocity" for objects that are not spatially co-located in a curved spacetime.

 

[PAllen]

You can measure locally whether you are "moving or not" already at the level of the homogeneous and isotropic FLRM metric given that space is filled with the blackbody CMBR. You only need to measure the "apparent temperature" as a function of direction of observation. That's the "dipole part" of the measured CMBR anisotropies, which is usually subtracted in the pictures the COBE, WMAP, and Planck collaborations show, because it's just the motion of our local group against the "rest frame" of the CMBR. The latter is the frame of a "fundamental or comoving observer". The rest frame of the CMBR defines physically special local frames of reference as any "fluid" in local thermal equilibrium does.

It is the term "moving or not" that is wrong. The measurement of CMBR isotropy simply says you have a particular state of motion, no different (as motion) than any other, not that you are "not moving". Especially bad is the notion that distant comoving bodies are not moving relative to each other. Correct is that their relative motion is inherently ambiguous in exactly the same way as any other distant bodies in curved spacetime (due, of course, to the path dependence of parallel transport).

It is just as correct to say you are moving with a fluid as at rest relative to the fluid. Just depends on who is looking at the fluid.

 

[vanhees71]

I talked about local observations, which are the only well-defined ones in GR. On the large-scale average the universe is well described by a Friedmann-Lemaitre-Robertson-Walker spacetime, where you have a class of preferred frames of reference, defined by the comoving observers, for whom "space" is homogeneous and isotropic. Operationally it is defined as the local (!) rest frame of the CMBR. Nowhere do you need any description of relative motion of far-distant objects in defining these local co-moving frames.

From the Einstein equations for the FLRM metrics it follows that at this scale of coarse graining the matter is described as a perfect fluid, which of course distinguishes the same preferred local rest frames as the CMBR.