Does the expanding Universe follow Lorentz contraction?

[PAllen]

Note that this statement says two things:

1) It says something about the theory of GR and Cosmology.

2) It says something about Rees and Weinberg. What it says about Rees and Weinberg is that they can't understand why everyone else doesn't adopt the same conventions for talking about Cosmology as they do. They have their own rules and pet peeves and they can't understand why everyone else isn't pedantic to precisely the same degree and in precisely the same way as they are.

They even go so far as to say Cosmologists should "know better".

The only solution would be for Rees and Weinberg to publish a definitive guide to terminology in Cosmology and insist that everyone follow their precise convention. For example, presumably the term "metric expansion of space" would be out and replaced by something else of their choosing.

Note that no one would argue with the underlying mathematics or physics. In the same way that no one can argue that the Solar System is absolutely heliocentric. But, if you tried to describe the Solar System in purely coordinate independent terms it becomes cumbersome to the point where communication breaks down.

I agree Weingerg's phrase "cosmologists should know better" is poor in the same way as stating that expansion of space is the correct way to describe the physics. The expanding space description is not wrong, only the claim that it is the unique correct view is wrong. I hemmed and hawed about whether to include the reference at all, since it wasn't strictly necessary to my point, which was responding to your statement:

"... The galaxies appear to be moving away, but the redshift is caused by the expansion of space. "

This is wrong precisely to the extent that it insists expansion of space is the only correct view of the cause of redshift. My invariant description of the redshift in terms of motion was sufficient to refute this. This is a pet peeve of mine, because some (nowhere near all) cosmologists claim cosmological redshift is a different physical phenomenon than Doppler, which I view as nonsensical. There is only one valid way to generalize SR doppler to GR, and that way covers all redshifts with complete generality. If your physical situation can be well approximated using an everywhere isotropically expanding congruence, it is extremely convenient to introduce the notion of cosmological redshift proportional to distance (with a suitable definition), but this doesn't make it a separate physical phenomenon (note that such a congruence is possible in SR as well as GR). Similarly if your physical situation is well approximated by a stationary, noninertial, congruence (surface of planet, accelerating rocket, rotating space station) it is extremely convenient to introduce the notion of gravitational redshift proportional to potential difference, but that again doesn't introduce a new physical phenomenon (in either the SR cases or the GR cases).

 

[PeroK]

I agree Weingerg's phrase "cosmologists should know better" is poor in the same way as stating that expansion of space is the correct way to describe the physics. The expanding space description is not wrong, only the claim that it is the unique correct view is wrong. I hemmed and hawed about whether to include the reference at all, since it wasn't strictly necessary to my point, which was responding to your statement:

"... The galaxies appear to be moving away, but the redshift is caused by the expansion of space. "

This is wrong precisely to the extent that it insists expansion of space is the only correct view of the cause of redshift.

With respect, you are quoting me out of context and putting words in my mouth. I'm not insisting that anything is the only correct view. What I said was:

The observed recessional velocity of distant galaxies was the key to Hubble discovering the expansion of the universe. However, what Hubble really measured was red-shift. And, once you accept the universe is expanding, you realize that it was only an apparent recessional velocity. The galaxies appear to be moving away, but the redshift is caused by the expansion of space.

I was trying to put Hubble's discovery in some context. I can see now how it could be better phrased. Although, there's still something of an issue that one has to say something to explain what Hubble discovered and what it meant.

 

[PeterDonis]

First, however, you would have to define "expanding" - which, in any case, is probably impossible in a coordinate independent way.

No, it's not impossible. I referred to the coordinate independent definition in post #28: the congruence of worldlines that describes comoving observers--observers who always see the universe as homogeneous and isotropic--has a positive expansion scalar.

 

[PeterDonis]

How you split it into "space" and "time" is (to an extent) up to you. One obvious way to do it has spatial slices where galaxies are not moving, but nevertheless grow further apart. Another way is to pick a slicing where you are stationary and everything has the velocity a straight reading of its redshift would imply. Neither is right or wrong.

This is true. However, in the first description, if you then go on to say "the expansion of space is pushing galaxies apart", that is wrong. There is no "push"; the galaxies do not have any force exerted on them. That is why the "expanding space" terminology is confusing--it makes people, like the OP in this thread, think that "space" is actually pushing galaxies apart, when no such thing is happening.

 

[PeterDonis]

I'm going to qualify my use of the word expansion as nothing more than it will take a longer time for a photon to cross a distance at time t+n than it will at time t.

More precisely, that it will take longer for a photon to go from galaxy A to galaxy B if it starts at time t+n than if it starts at time t. (And then you have to carefully define what "take longer" means--that if galaxy A and galaxy B are both comoving and both measure time from the Big Bang, the difference between emission and reception times will be longer for the second photon.)

 

[Ibix]

What are Milne's spatial slices? $t^2-(x^2+y^2+z^2)=T^2$, where $T$ is the Milne cosmological time and the rest is regular inertial coordinates?

 

[Nugatory]

It's a fairly common shorthand to consider a reference frame "moving" with respect to another.

Indeed it is - people take these linguistic shortcuts all the time because it’s just not reasonable to use the accurate lomg form every time. Who is going to say “using coordinates assigned by an inertial reference frame in which the spaceship is at rest” when they say “the frame of the spaceship”? Or “using an inertial frame in which objects that are at rest relative to me have a non-zero coordinate velocity” when they can say “the moving frame”?

However...

It's hardly a source of confusion.

Not for you, me, and everyone else who already understands the concepts. But I submit that it is a source of confusion for anyone who does not already have a firm grasp of what coordinate transformations do and do not do.

 

[PeterDonis]

What are Milne's spatial slices? $t^2-(x^2+y^2+z^2)=T^2$, where $T$ is the Milne cosmological time and the rest is regular inertial coordinates?

Yes. And note that this only works in Minkowski spacetime, i.e., in a universe with zero Riemann curvature, zero stress-energy and zero cosmological constant.

 

[Ibix]

Yes. And note that this only works in Minkowski spacetime, i.e., in a universe with zero Riemann curvature, zero stress-energy and zero cosmological constant.

I was going to draw a diagram, but I already did. If you are interested, go to my interactive Minkowski diagrams page ibises.org.uk/Minkowski.html.

Scroll down to near the bottom and click the "Make grid" button. Horizontal lines are what Minkowski would call "space at one time" and vertical lines are the worldlines of Minkowski-stationary objects. You can enter a velocity and click "Boost" to see it transform.

Then scroll right to the bottom and click the "Make hyperbolae and spokes" button. Ignore everything except the red lines in the upper half. The hyperbolae are what Milne would call "space at one time" and the straight lines are the worldlines of Milne-comoving observers. The boundary between the red lines and the green is the "Big Bang singularity" - only a coordinate singularity for Milne. Again, you can boost to see how things change (or not!).

 

[Staticboson]

In short, in modern physics you have to let go of the absolute descriptions of things. And "The universe is expanding" is one such absolute description. You would just end up driving yourself crazy trying to justify that description above all others.

Understood, although it is a very difficult thing to do.
You have the real physicists who spend a lifetime working with and developing the mathematical models, gain the insight from within the models themselves, and sometimes adventure into making a spoken word interpretation that the common folk can relate to... by using a language designed to only cover the narrow range of human experience. Of course this can only be accomplished with subjective props and embellishments and reducing the phenomena to poetry.

But there is a middle ground of curious folk who don't have a lifetime to master mathematical theory to the level of second nature that stems insight without the need for interpretation. Using my "hobby time" to develop a working level of calculus, tensors, and geodesics to pursue interests in cosmology has been fun and rewarding, but it barely begins to scratch the surface of the basics, and only makes the colossal gap of understanding between "here" and the point of "insight" more obvious.

In the meantime all I have is the best effort from the educated folks to paint a picture and point to good sources. In the short time I've been here I've learned quite a bit, It's a good forum.