I Does the expanding Universe follow Lorentz contraction?

[PeroK]

But isn't the notion of expansion the result of physical measurements?

The problem here is that in GR the laws of physics can be expressed in coordinate independent way. Let's take the solar system for example.

If you are navigating by the stars, then your navigational charts are by necessity drawn for the Earth's frame of reference. This involves complicated annual motions of the planets. And, the motions of the moons of Jupiter relative to Earth are even more complicated.

If, however, you describe the solar system from the Sun's frame of reference, then everything simplifies. The planets move in ellipses about the Sun and the moons orbit their planets likewise.

Moreover, if you use Newton's law of gravitation, then you can explain the heliocentric solar system. It's tempting, therefore, to say that the solar system really is heliocentric in some absolute sense. However:

In GR, you can describe the solar system similarly in terms of the Schwarzschild coordinates for the spacetime geometry about a spherical star, like the Sun. But, in GR it is clear that your choice of Schwarzschild coordinates is arbitrary. The same spacetime geometry can be described in any other coordinate system and no system has absolute preference. If you wrote down what you know about the solar system, I'd bet most of those statements turn out to be coordinate dependent. E.g. that "the Earth spins on its axis" is a coordinate dependent statement.

In terms of Cosmology you have the same issue. Almost anything you want to say to describe the universe is coordinate dependent. Even the age of the universe is taken to mean in a reference frame where the CMB radiation is isotropic.

Likewise, that the universe is "expanding" is coordinate dependent. First, however, you would have to define "expanding" - which, in any case, is probably impossible in a coordinate independent way. If we go back to the solar system, we can decide that the heliocentric model is sufficiently useful that by convention we'll use it without excessive explanation each time. We might even call it the standard model of the solar system.

The expanding universe in the FLRW model is also sufficiently useful that Cosmologists will use it without unduly emphasising that it is, after all, only one of infinitely many coordinate-dependent descriptions of the universe. And, indeed, this has become something of the de facto standard model.

But, being the standard model is not the same as being absolutely real in some sense.

 

[Staticboson]

The problem here is that in GR the laws of physics can be expressed in coordinate independent way. Let's take the solar system for example.

If you are navigating by the stars, then your navigational charts are by necessity drawn for the Earth's frame of reference. This involves complicated annual motions of the planets. And, the motions of the moons of Jupiter relative to Earth are even more complicated.

If, however, you describe the solar system from the Sun's frame of reference, then everything simplifies. The planets move in ellipses about the Sun and the moons orbit their planets likewise.

Moreover, if you use Newton's law of gravitation, then you can explain the heliocentric solar system. It's tempting, therefore, to say that the solar system really is heliocentric in some absolute sense. However:

In GR, you can describe the solar system similarly in terms of the Schwarzschild coordinates for the spacetime geometry about a spherical star, like the Sun. But, in GR it is clear that your choice of Schwarzschild coordinates is arbitrary. The same spacetime geometry can be described in any other coordinate system and no system has absolute preference. If you wrote down what you know about the solar system, I'd bet most of those statements turn out to be coordinate dependent. E.g. that "the Earth spins on its axis" is a coordinate dependent statement.

In terms of Cosmology you have the same issue. Almost anything you want to say to describe the universe is coordinate dependent. Even the age of the universe is taken to mean in a reference frame where the CMB radiation is isotropic.

Likewise, that the universe is "expanding" is coordinate dependent. First, however, you would have to define "expanding" - which, in any case, is probably impossible in a coordinate independent way. If we go back to the solar system, we can decide that the heliocentric model is sufficiently useful that by convention we'll use it without excessive explanation each time. We might even call it the standard model of the solar system.

The expanding universe in the FLRW model is also sufficiently useful that Cosmologists will use it without unduly emphasising that it is, after all, only one of infinitely many coordinate-dependent descriptions of the universe. And, indeed, this has become something of the de facto standard model.

But, being the standard model is not the same as being absolutely real in some sense.

That's a good explanation and think I might be getting at what Weinberg was referring to. The Riemanian geometry using covariant derivatives to model movement and position in the universe without the need of an extrinsic dimension, throws the use of vocabulary implicitly implying the existence of an "external" dimension from which such an expansion could be measured, out the window. Words like "expansion" would imply a God's eye view from which such an expansion can be observed.
Not different than using 3-D attributes when referring to a sphere entirely described with a 2-dimensional geometry.

If that is the case then I understand where Weinberg is coming from, however if my impression is correct, I can't help but think his statement comes as a result of locking himself into the box of the theoretical description and loosing perception of what actually appears to be happening, which is that the universe is... expanding?

And in response to PeterDonis affirming that my use of the word expansion implicitly means pushing galaxies apart, 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. But maybe that way to look at it throws a wrench into is just as well, I don't know.

Again, the responses are appreciated.

 

[PeroK]

If that is the case then I understand where Weinberg is coming from, however if my impression is correct, I can't help but think his statement comes as a result of locking himself into the box of the theoretical description and loosing perception of what actually appears to be happening, which is that the universe is... expanding?

It's not quite as dramatic as that. This is more about how to explain things. In the Newtonian world - unless you apply modernist hindsight - there was an absolute explanation for things. In short $F = ma$.

In modern physics generally you have the phenomena, a mathematical model that predicts the phenomena and then an interpretation of the model. This is most notable in QM. In fact, I think it was Heisenberg who first realized that at the sub-atomic level things could only really be described by mathematical properties.

You could stretch this to GR and Cosmology with the phenomena really the invariant things. If you measure the light you get a redshift of $z$ or whatever. The asteroid and the Earth will collide ...

Even if you start with a ball being dropped, there is no single way to explain that. Most notably it's the surface of the Earth that has proper acceleration (an invariant) and the ball is following a geodesic (invariant). Anything more than that is coordinate dependent - or perhaps an interpretation if you prefer.

You can't say that the ball absolutely falls to Earth (i.e. it's the ball that it really moving and affected by gravity). But neither can you say, as a certain popular UK physicist likes to, that the surface of the Earth moves up to hit the ball. (You might prefer one description to another or you might be neutral, but you can't say absolutely that it's either.)

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.

 

[timmdeeg]

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.

I think a counterexample is Ned Wright's FAQ

Are galaxies really moving away from us or is space just expanding?
This depends on how you measure things, or your choice of coordinates. In one view, the spatial positions of galaxies are changing, and this causes the redshift. In another view, the galaxies are at fixed coordinates, but the distance between fixed points increases with time, and this causes the redshift. General relativity explains how to transform from one view to the other, and the observable effects like the redshift are the same in both views. [URL='http://www.sao.ru/cats/~satr/cosmo/cosmo_03.htm#MSTD']Part 3 of the tutorial shows space-time diagrams for the Universe drawn in both ways.[/url]

It leaves open what happens to space as this is a meaningless question.

 

[Ibix]

Words like "expansion" would imply a God's eye view from which such an expansion can be observed.

Not really. If you think of spacetime as a block of wood, you can imagine slicing it into a stack of thin flat sheets, or a stack of nested bowls. That's the best analogy I can come up with for the two approaches of slicing spacetime into "treat redshift as due to velocity" and "treat redshift as due to the expansion of space" view. Neither slicing has any connection to anything outside the wood, but if you look at things embedded within (the wood grain) the slices will look completely different.

There's nothing wrong with the "space expanding" picture - it's just a different slicing of spacetime. And I doubt that Weinberg and Rees have any objection to the use of comoving coordinates in FLRW spacetime, of which "space is expanding" is a common verbal description. I think they are objecting specifically to that verbal description because of the philosophical baggage it brings (how can nothing expand!?). I'm not really sympathetic to that viewpoint (I think we should be aware of this particular chunk of philosophical baggage and explicitly ditch it) although I can see where it comes from.

 

[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.