Does the expanding Universe follow Lorentz contraction?

[Staticboson]

TL;DR Summary

Farther objects are receding faster therefore Lorentz contraction effects should increase with distance.

As object separate with a receding velocity proportional to the distance, it would seem appropriate to think that objects and space itself, which are located at a distance sufficiently far away (and beyond) to were recession velocities are large enough that Lorentz length contraction effects would be noticeable.

Following this logic, at distances where recession speeds are close to c, the universe would appear to be flatter in the direction of expansion. At the point where the receding velocity is c, the length of any object (and the space containing it) in the direction of expansion would be zero. This of course seems like it would affect the horizon of the observable universe.

However that is clearly not the way it is. There is depth observed well beyond the point where the receding velocity reaches c, and there is no such flattening.

The only explanation I can come up with is that Lorentz expansion only applies to inertial frames and of course the expanding universe with a velocity differentially increasing with the distance there is no such thing as inertial frames, but still, it seems like relativistic effects should be noticeable in other than redshifts.

Please point me towards where to look for an explanation, thank you.

 

[phinds]

The only explanation I can come up with is that Lorentz expansion only applies to inertial frames and of course the expanding universe with a velocity differentially increasing with the distance there is no such thing as inertial frames,

Exactly (that is, there are no inertial frames that encompass two objects that are far enough away from each other to be experiencing recession velocity)

but still, it seems like relativistic effects should be noticeable in other than redshifts.

Why? "Relativistic effects" have to do with relative movement to two objects and that's already covered by your correct explanation regarding Lorentz contraction.

 

[Staticboson]

Why? "Relativistic effects" have to do with relative movement to two objects and that's already covered by your correct explanation regarding Lorentz contraction.

So basically there is no Lorentz effect due to receding velocities between objects caused by the expansion of space, as opposed to receding velocities between objects in fixed inertial frames assuming a non-expanding space. I did not realize this until now.

Does the use of a comoving distance model of the universe have something to do with being able to use inertial frames and connect the local laws of physics to far away objects? Not sure if the question makes sense.

 

[PeroK]

So basically there is no Lorentz effect due to receding velocities between objects caused by the expansion of space, as opposed to receding velocities between objects in fixed inertial frames assuming a non-expanding space. I did not realize this until now.

Yes.

Does the use of a comoving distance model of the universe have something to do with being able to use inertial frames and connect the local laws of physics to far away objects? Not sure if the question makes sense.

The laws of physics are independent of the coordinates you choose. In classical (Newtonian physics) and Special Relativity the laws are often expressed in terms of inertial reference frames, which form a special set of reference frames where the laws are easier to express. Like F=maF=ma and "the invariance of the speed of light".

There are, however, reformulations of these laws in a coordinate-free form. And in General Relativity the laws have to be written in a coordinate-independent form, as there are no special reference frames and in particular no global inertial frames.

The comoving coordinates in Cosmology also form a special set of coordinates, which simplify the description to some extent. But, the laws of physics do not depend on using comoving coordinates.

Note the important distinction here:

"Special" - reference frame or coordinates in which certain laws may be more simply expressed or phenomena more easily studied.

"Preferred" - reference frame or coordinates in which the laws of physics hold, in preference to all others. There is an underlying hypothesis in modern physics that there is no preferred reference frame.

 

[phinds]

So basically there is no Lorentz effect due to receding velocities between objects caused by the expansion of space, as opposed to receding velocities between objects in fixed inertial frames assuming a non-expanding space. I did not realize this until now.

Correct. Lorentz "effects" are based on proper motion. There is no proper motion on receding objects. Well, to be technically correct, there probably IS some small proper motion between objects that are receding from each other but it is probably not measurable since it is swamped by the recession velocity.

Does the use of a comoving distance model of the universe have something to do with being able to use inertial frames and connect the local laws of physics to far away objects? Not sure if the question makes sense.

I can't help you with that one.

 

[Staticboson]

Thank you for the responses guys.

 

[PeterDonis]

As object separate with a receding velocity proportional to the distance

No, they don't. The correct statement is that "velocity" is not well-defined for objects that are spatially separated in a curved spacetime. The recession velocities that are given in discussions of the expansion of the universe are coordinate velocities, not actual relative velocities that anyone measures.

More generally, the concept of Lorentz contraction only makes sense in a flat spacetime--or in a patch of a curved spacetime that is small enough that the effects of spacetime curvature are negligible. So it doesn't make sense for objects that are far enough away from us to be significantly affected by the expansion of the universe.

Does the use of a comoving distance model of the universe have something to do with being able to use inertial frames

No. It is a model of a curved spacetime, for which there are no global inertial frames.

and connect the local laws of physics to far away objects?

I'm not sure what you mean by this. If you're asking if observers in a galaxy a billion light-years away would observe local effects like Lorentz contraction for objects close to them, yes, they would.

 

[Staticboson]

No, they don't. The correct statement is that "velocity" is not well-defined for objects that are spatially separated in a curved spacetime. The recession velocities that are given in discussions of the expansion of the universe are coordinate velocities, not actual relative velocities that anyone measures.

More generally, the concept of Lorentz contraction only makes sense in a flat spacetime--or in a patch of a curved spacetime that is small enough that the effects of spacetime curvature are negligible. So it doesn't make sense for objects that are far enough away from us to be significantly affected by the expansion of the universe.

I learned from the thread responses that Lorentz effects don't apply to recession velocities from expanding space, or as you better state it, recession velocities of coordinates.

I'm not sure what you mean by this. If you're asking if observers in a galaxy a billion light-years away would observe local effects like Lorentz contraction for objects close to them, yes, they would.

I meant applying laws of physics in the sense of using measurements to calculate positions, velocities, and acceleration of distant objects, however I understand your response indicating it is meaningless to do this.

Thank you for the responses!

 

[PeterDonis]

I meant applying laws of physics in the sense of using measurements to calculate positions, velocities, and acceleration of distant objects, however I understand your response indicating it is meaningless to do this.

More precisely, the "positions, velocities, and accelerations" you are describing do not correspond to any actual measurements that anyone can make. They can, however, be useful for further calculations that do correspond to measurements that can be made. So it's not that they're "meaningless"; it' s just that they don't have the simple physical meaning you were thinking they have.

 

[Staticboson]

More precisely, the "positions, velocities, and accelerations" you are describing do not correspond to any actual measurements that anyone can make. They can, however, be useful for further calculations that do correspond to measurements that can be made. So it's not that they're "meaningless"; it' s just that they don't have the simple physical meaning you were thinking they have.

I think I kind of understand what you're saying. We are limited to measurements of red shift and light intensities, which do not correspond directly to positions, velocities, or acceleration of distant objects, but are useful to calculate them.

 

[PeterDonis]

We are limited to measurements of red shift and light intensities, which do not correspond directly to positions, velocities, or acceleration of distant objects, but are useful to calculate them.

We certainly can't measure positions, velocities, or accelerations of distant objects directly. But that's not the issue I'm talking about. The issue I'm talking about is that the "recession speed" you describe, for example, is not an actual speed anyone can measure. It's just a coordinate speed and has no physical meaning. But that coordinate speed can be a useful parameter in a model that can calculate things we can observe--for example, the model can calculate predictions for observed redshifts and light intensities, that can be compared with observations.

 

[Staticboson]

the "recession speed" you describe, for example, is not an actual speed anyone can measure. It's just a coordinate speed and has no physical meaning

I think my problem might come from thinking of it as frames of reference that are incrementally faster in proportion to distance.

 

[phinds]

I think my problem might come from thinking of it as frames of reference that are incrementally faster in proportion to distance.

Inertial frames of reference don't "move". Things that are stationary in one IFR can be moving in a different IFR but that doesn't mean that it is any any way helpful to think of IFR's as "moving".

 

[PeroK]

I think my problem might come from thinking of it as frames of reference that are incrementally faster in proportion to distance.

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.

With a modern perspective we realize that the recessional velocity is coordinate dependent. If you use comoving coordinates, then there is no recessional velocity. In general, the whole concept of what is coordinate dependent and what is not is quite hard to get used to.

There's an excellent Insight here if you interested in learning a bit more:

https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/

 

[Staticboson]

There's an excellent Insight here if you interested in learning a bit more:

https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/

Man what a great article... it will take a few sittings to properly wrap my head around it, but I believe I'm up to the task. Thanks!

 

[Staticboson]

Inertial frames of reference don't "move". Things that are stationary in one IFR can be moving in a different IFR but that doesn't mean that it is any any way helpful to think of IFR's as "moving".

Would you be able to expand on this.

Up until now I had no second thoughts about visualizing all inertial frames as moving with respect to each other. If an object is moving relative to me, the inertial frame in which he is at rest is moving with respect to my inertial frame... no?
Are you saying that I should limit my conceptualization of IFR's to all frames always sharing a common origin (x=x'=0 and t=t'=0) and only differing by the slanting of their axes?

 

[phinds]

When you are working on a problem, you have to pick one IFR and stick with it.

 

[PeroK]

Would you be able to expand on this.

Up until now I had no second thoughts about visualizing all inertial frames as moving with respect to each other. If an object is moving relative to me, the inertial frame in which he is at rest is moving with respect to my inertial frame... no?
Are you saying that I should limit my conceptualization of IFR's to all frames always sharing a common origin (x=x'=0 and t=t'=0) and only differing by the slanting of their axes?

No, you're correct that IRF's move relative to each other. Sharing a common origin and having their x-axes aligned along the direction of relative motion is a condition on using the usual Lorentz Transformation:

$t' = \gamma (t - \frac{vx}{c^2}); \ x' = \gamma(x - vt)$

Where, of course, $v$ and $\gamma$ relate to the relative motion between the frames.

 

[PeterDonis]

If an object is moving relative to me, the inertial frame in which he is at rest is moving with respect to my inertial frame

"Moving" implies changing position in space with respect to time. Inertial frames don't do that. Each frame is a coordinate grid on the entire 4-d spacetime. The grids for different inertial frames are just tilted relative to each other (and possibly offset if the origins are not the same). But neither grid "moves" or "changes"; they're just there.

you're correct that IRF's move relative to each other

Not with the usual definition of "moving"; see above.

One could, of course, just define "moving" for inertial frames to mean what I described above. But that doesn't seem like a good idea to me since that terminology invites confusion.

 

[PeroK]

One could, of course, just define "moving" for inertial frames to mean what I described above. But that doesn't seem like a good idea to me since that terminology invites confusion.

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

 

[PeterDonis]

It's hardly a source of confusion.

I think it is in the case of this thread, in view of post #12.

 

[PAllen]

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

This, itself, is a coordinate dependent statement and definitely not something you can state absolutely. There is, for example, a wholly invariant way to ascribe cosmological redshift to the GR generalization of Doppler (parallel transport the 4-velocity (an invariant geometrical object) of one galaxy at some emission event along the null geodesic along which its light arrives at some reception event along the world line of another galaxy. Then the redshift exactly corresponds to the SR doppler implied by the relative velocity of the transported 4-velocity in the local frame of the reception galaxy at the reception event, i.e. dot product of the two 4 velocities). Nothing about the GR generalization of Doppler involves coordinates.

Note, the notion of expansion itself is coordinate dependent, as argued in the following:

Martin Rees & Steven Weinberg (1993) state
”...how is it possible for space, which is utterly empty, to expand? How can nothing expand? The answer is: space does not expand. Cosmologists sometimes talk about expanding space, but they should know better.“

 

[Staticboson]

Martin Rees & Steven Weinberg (1993) state
”...how is it possible for space, which is utterly empty, to expand? How can nothing expand? The answer is: space does not expand. Cosmologists sometimes talk about expanding space, but they should know better.“

But isn't space not "nothing"? Isn't vacuum an actual thing that is expanding and increasing the distance between objects? I understand that commoving coordinates assume that only the metric expands and therefore there is no change in the relative position between objects, but that would only be a method, an artifice to simplify calculations. The reality would be that there is an actual increase of the time it takes for light to travel between objects as time passes. I'm going to need some kind of explanation, if you can, for Weinberg's quote.
Thanks!

 

[PAllen]

But isn't space not "nothing"? Isn't vacuum an actual thing that is expanding and increasing the distance between objects? I understand that commoving coordinates assume that only the metric expands and therefore there is no change in the relative position between objects, but that would only be a method, an artifice to simplify calculations. The reality would be that there is an actual increase of the time it takes for light to travel between objects as time passes. I'm going to need some kind of explanation, if you can, for Weinberg's quote.
Thanks!

This is complicated question with ongoing debates among experts. What I think Weinberg was getting at is that it is no more true to say "space expands between galaxies" than to say "galaxies are moving away from each other". Both are natural in different coordinates.

An invariant statement is that the shape of spacetime allows the possibility of galaxies to be homogenously and isotropically further apart over time. Once you go further, and say "this must be due to expansion of space" or "must be due to motion of galaxies", you are elevating a coordinate dependent statement to absolute.

A very interesting example is provided by Minkowski flat spacetime. It can be described by an FLRW metric with scale factor given by: a(t) = 1, and also by a(t) = t. The former is 'not expanding', the latter is, yet both are just different coordinates on Minkowski spacetime.

Very important to note is that your statement "The reality would be that there is an actual increase of the time it takes for light to travel between galaxies as time passes" is a valid invariant statement. However, the conclusion about whether it is caused by expansion of space or motion is coordinate dependent. [Fine point: I changed 'objects' to galaxies, because it isn't true for all objects. It is only true for comoving objects, for which it always has been true, and truth in the past implies truth in the future. You could have other pairs of inertial world lines that approach each other. ]

On the other hand, your statement that "Isn't vacuum an actual thing that is expanding and increasing the distance between objects" is exactly the misunderstanding Weinberg is arguing against.

 

[Staticboson]

[Fine point: I changed 'objects' to galaxies, because it isn't true for all objects. It is only true for comoving objects, for which it always has been true, and truth in the past implies truth in the future. You could have other pairs of inertial world lines that approach each other. ]

Understood, I was trying to avoid the term "galaxies" because even within clusters gravitational forces trump expansion, so I thought the term "objects in a large scale" might be more appropriate.

On the other hand, your statement that "Isn't vacuum an actual thing that is expanding and increasing the distance between objects" is exactly the misunderstanding Weinberg is arguing against.

Still trying to grasp why Weinberg would see it as a misunderstanding. Isn't the simple fact that a(t) is used in cosmology calculations regarding things like the age of the universe and the size of the observable universe, intrinsically imply the expansion of vacuum is a reality?
Seems like there would be two options, either vacuum is expanding or more vacuum is created between "galaxies" as a function of (t). Seems like the second option would violate the laws of energy conservation, so I don't know what to think.
Thank you for taking the time anyway...

Edited to say I have no doubt that Weinberg knows exactly what he's talking about, where I have no clue. Just trying to grasp it.

 

[PeterDonis]

sn't the simple fact that a(t) is used in cosmology calculations regarding things like the age of the universe and the size of the observable universe

Yes.

intrinsically imply the expansion of vacuum is a reality?

No. $a(t)$ is a coordinate-dependent quantity. One of the most basic rules of GR is that coordinate-dependent quantities are not "reality"; the "reality" is invariants, quantities that are the same in all coordinate systems and which represent actual physical measurements.

 

[Staticboson]

No. $a(t)$ is a coordinate-dependent quantity. One of the most basic rules of GR is that coordinate-dependent quantities are not "reality"; the "reality" is invariants, quantities that are the same in all coordinate systems and which represent actual physical measurements.

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

 

[PeterDonis]

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

Not the "notion of expansion" that you are using, no. That's a misconception that comes from, as I said, thinking of coordinate-dependent quantities as if they were "reality".

There are notions of "expansion" that correspond to invariants--for example, the expansion scalar of the congruence of comoving worldlines in FRW spacetime--but those notions do not have the properties you are implicitly attributing to "expansion", such as "pushing galaxies apart".

 

[PeroK]

Martin Rees & Steven Weinberg (1993) state
”...how is it possible for space, which is utterly empty, to expand? How can nothing expand? The answer is: space does not expand. Cosmologists sometimes talk about expanding space, but they should know better.“

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.

 

[Ibix]

Just a note on coordinate dependent quantities. Imagine sitting at a rectangular table. You say it's long and narrow, I say it's short and wide. You can visualise what's happened - you're sitting on a short side and I'm sitting on a long side. You can also see that debating whether the table is "really" long and narrow or short and wide is pretty pointless, because both descriptions are equally valid and are related by a rotation - a coordinate transformation.

Whether the space between galaxies is growing or the galaxies are moving apart is a similar debate. The "table" is 4d spacetime with the worldlines of galaxies embedded in it. 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.

 

[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.