Is this explanation of "space itself expanding" correct?

[michelcolman]

TL;DR Summary

I came up with a layman's explanation of what it means for "space itself" to be expanding faster than light. But is it correct?

Hi,

I always used to struggle with the concept of "space itself expanding" (didn't Einstein say that the aether did not exist?) until one day an idea struck me that seemed to explain it all, without any need for complicated math. After talking about it with others, I got some great feedback from people profusely thanking me for finally explaining it to them in a way that they could understand, but a couple of days ago I also got a totally opposite reaction from someone claiming to be a theoretical astrophysicist on Slashdot. He or she was posting as "Anonymous Coward" but basically said I did not understand what I was talking about, I was just throwing jargon around as if it meant something, and I was suffering from the Dunning-Kruger effect.

So I thought I'd try my theory description of the way I understood established science here. What do you think, does it make any sense or is it completely off the mark? I do understand that it may be simplistic, and insufficient to explain some of the finer points and recent discoveries of cosmology (it neglects gravity, for example, which would kinda sort of seem like an important thing to miss), but I really do feel it does a great job explaining where this concept of "space itself" comes from. So, here it goes:The way I see it, "space itself" is an artefact of the co-moving coordinates that are usually used in cosmology. Those coordinates have the advantage of making the universe look homogenous at a large scale, and independent of the choice of any particular reference point. But the disadvantage is that they violate the axioms of Special Relativity, requiring General Relativity and this concept of "space itself".

It is perfectly possible to describe the universe with a different reference frame that does obey Special Relativity. You need to pick some point as the central, stationary reference point (for example some point in our immediate neighbourhood that appears stationary relative to the cosmic radiation background) and define coordinates so that the speed of light is constant everywhere (relative to us).

In this reference frame, distant galaxies are moving away from us at great speed (but always less than the speed of light) so that they are Lorentz contracted and time dilated. Time is moving more slowly at those distances, and has been moving more slowly ever since the big bang, so those objects are also younger than us (less evolved after the big bang). They don't just look younger because their light took a long time to get to us, they actually are younger right now even if we take the travel time of light into account. ("Right now" being defined as "the events having the same time coordinate as us with this particular choice of reference frame").

If we "look" at distant objects using an infinitely fast way of looking that can only exist in a theoretical model, without needing to wait for light to get to us, we see the universe getting younger and younger the further we "look", and also more Lorentz contracted. When we reach a distance equal to the age of the universe multiplied by the speed of light, things are moving away from us at light speed and the big bang is just beginning at this moment, stuck in time forever (as an asymptotic limit, or a singularity, or whatever you want to call it). This means the entire infinite universe (not just the observable part, but all of it, everything after the big bang) actually fits inside a finite sphere expanding around us. An infinite amount of stuff fits in a finite sphere thanks to Lorentz contraction which approaches infinity near the edge.

Of course this view of the universe can hardly be called objective. If, instead of our own location, you would have taken some other distant galaxy as the reference point, they would suddenly be the oldest while our part of the universe would be much less evolved, in fact our civilisation would not even exist yet in their reference frame. That's not a contradiction, it's perfectly OK for different observers to disagree on which events happen "now", in the past, or in the future.

To avoid this kind of subjectivity, though, co-moving coordinates were invented, precisely tailored to our expanding universe. They redefine time at any point of the universe to be the local time as experienced by a local observer traveling together with the expansion of the universe. Space coordinates are defined so that the universe looks about the same everywhere, which can be achieved by requiring that the speed of light is c relative to those same moving observers. This reference frame by definition gets rid of time dilation and Lorentz contraction from the expansion of the universe. Everything now looks the same age and the same size everywhere, and the universe is truly infinite. Of course time dilation and Lorentz contraction still exist for local movements relative to local space, but not for the general movement of the expanding universe.

The disadvantage is that the speed of light is no longer constant relative to us. Instead, it is c relative to "space itself", which is expanding and even makes things move away from us faster than the speed of light. That doesn't mean "space itself" is a real, physical thing. It's just a result of using coordinates that don't comply with Special Relativity. Fortunately General Relativity works on just about any coordinate system you can come up with, as long as you apply the appropriate corrections for the metric of the resulting "space".

Even though these descriptions seem very different, they do yield the same conclusions when you actually try to calculate an observable event or any other testable prediction.

For example, using co-moving coordinates you may say that we will never see certain events that ere happening "now" in some distant galaxy because that part of space is receding faster than light, and its light can never get to us. It's as if this light was trying to move towards us along a cosmic conveyor belt moving the other way at a higher speed. My special-relativistic reference frame explains this differently: with those coordinates, the event has a time coordinate infinitely far in the future, it has not happened yet and never will happen because time in that part of space is moving very slowly and is even slowing down to an asymptotic standstill long before the event ever gets a chance to happen, as the galaxy continues to accelerate away from us.

Two totally different explanations, but with the same result: we will never see it happen.

Another example: will we ever be able to reach that location if we fly towards it? With co-moving coordinates, we can't because space is expanding faster than we can catch up with it. With special-relativistic coordinates, the location seems to be within reach (a finite distance away) but as soon as we start to accelerate towards it, our plane of simultaneity tilts so that they are catapulted into the future and therefore further away and accelerating to even higher speeds. No matter how much we accelerate (shrinking our local surroundings along the axis of our motion), faraway objects will fast forward through time and space so that their distance to us actually increases faster than the Lorentz Contraction of our own speed can shrink it. Again, the same result, we will never reach them.So, what do you think, is this really a totally wrong explanation, or is it actually a pretty good way of explaining what "space itself" means?

 

[gleem]

Be advised that Physics Forum is not a forum for presenting personal theories.

 

[phinds]

I am old and impatient so the fact that trying to wade through your entire post just made my head hurt is probably more my fault than yours and possibly entirely my fault but it seems to be a personal theory so this thread will likely be closed or deleted.

"Space itself" is not a "thing" that can stretch or expand or bend, it's just geometry. I think the expansion is explained in a way that might be helpful to you if you check out the link in my signature (but read it all the way through, and carefully).

 

[michelcolman]

Be advised that Physics Forum is not a forum for presenting personal theories.

It's not so much a "theory" as a "way of describing things". I just want to know whether this is a correct description or not. Meanwhile I seem to have read some other descriptions that resemble mine somewhat (are my "special-relativistic coordinates" actually "Minkowski Space"?) but I may have missed something here and there.

 

[michelcolman]

"Space itself" is not a "thing" that can stretch or expand or bend, it's just geometry. I think the expansion is explained in a way that might be helpful to you if you check out the link in my signature (but read it all the way through, and carefully).

I am familiar with the balloon analogy. I read the article you linked to just to be sure.

It does say the universe "has no center", but that is not the case if you choose to describe it with special-relativistic (Minkowski?) coordinates around a chosen center. We may consider ourselves to be the center of a spherical universe (containing an infinite amount of stuff thanks to Lorentz contraction near the edges), but we are free to choose any other center to end up with an equivalent description of the same universe, but now centered around that place. Both are equivalent to a center-less spatially infinite universe in co-moving coordinates.

The "center" is an artefact of the chosen coordinate system just like "space itself" is an artefact of co-moving coordinates.

Does that make any sense?

 

[PeroK]

The "center" is an artefact of the chosen coordinate system just like "space itself" is an artefact of co-moving coordinates.

Does that make any sense?

I'd say that experimentally there is the concept of "distance" and that's where the concept of space comes from. More generally, we measure "spacetime", with three spatial and one time dimension.

You ought to start with this:

https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/
Which is the real deal.

 

[michelcolman]

You ought to start with this:
https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/Which is the real deal.

Thanks for the link, it's a very nice description of the different phases of expansion of the universe using the usual cosmological co-moving coordinates. (My model only considered simple expansion).

But my question is, what if we use coordinates based on the axioms of special relativity, in which space itself is not expanding but only the stuff inside of it is?

I'm not sure, but it looks like my idea is similar to the Minkowski space described in this link:
https://www.physicsforums.com/insights/coordinate-dependent-statements-expanding-universe/
If I understood correctly, it says that the motion of distant objects can be considered either as a cosmological redshift due to the expansion of space itself, or as a relativistic doppler shift due to their speed in a non-expanding (Minkowski) reference frame, and these two yield the same result.

Did I understand this correctly, or is this something completely different?

 

[Dale]

It is perfectly possible to describe the universe with a different reference frame that does obey Special Relativity

Basically, the paragraph preceding this is fine, but everything from here on goes downhill. It is most decidedly not possible to describe the whole universe in a reference frame that obeys special relativity.

The spacetime of special relativity is flat, but the LCDM spacetime is not flat. You cannot isometrically map a curved manifold onto a flat one.

With special-relativistic coordinates, the location seems to be within reach (a finite distance away) but as soon as we start to accelerate towards it, our plane of simultaneity tilts so that they are catapulted into the future and therefore further away and accelerating to even higher speeds

This doesn’t happen in SR.

But my question is, what if we use coordinates based on the axioms of special relativity, in which space itself is not expanding but only the stuff inside of it is?

Such coordinates do not exist that cover the whole universe.

As was mentioned above, we do not discuss personal theories here. You have said that it is your attempt to describe the standard theory, so I will take you at your word, as long as you seem to be interested in learning instead of in pushing your approach.

 

[Orodruin]

Summary: I came up with a layman's explanation of what it means for "space itself" to be expanding faster than light. But is it correct?

It is perfectly possible to describe the universe with a different reference frame that does obey Special Relativity.

I stopped reading here. This is just flat out wrong. SR deals with a flat spacetime. The Universe is not well described by a flat spacetime.

 

[michelcolman]

This doesn’t happen in SR.

Hmmm, I must have completely misunderstood some part of SR then. Would you mind telling which part I'm getting wrong?

When I accelerate towards a distant object, it moves forward in time, right? You can even make distant galaxies move forward and backward in time by accelerating a little bit towards them and back again, leading to the Andromeda paradox.

But if the object has a certain speed relative to us, surely when it moves into the future, it must also move in space?

If I fly to the Andromeda nebula (M31 for short) at almost the speed of light, it takes 2.5 million years as observed from Earth or from M31, but perhaps only a day as observed by the ship's clock. From my reference frame, the clocks at M31 jumped forward by 2.5 million years during the acceleration and then remained almost stationary during the constant speed part of the flight. (I'm not talking about the images I'm getting, but the actual time as calculated in my reference frame).

But M31 is moving towards us at 110 km/s. So in 2.5 million years, it will be 275 million km closer to earth. Of course that's almost unnoticeable compared to 2.5 million light years, but anyway, it moved. When did it move, as observed from the ship? Surely during the acceleration, it moved to its new location while it was moving into the future?

Now imagine an extremely distant galaxy moving away at very high speed and accelerating. If I accelerate towards it, it moves forward in time and therefore also moves to where it will be at this new time, which is further away. And if it is accelerating, it will be moving faster too.

At which point did I make a mistake?

 

[PeroK]

When I accelerate towards a distant object, it moves forward in time, right?

I'm not even sure what this means!

But if the object has a certain speed relative to us, surely when it moves into the future, it must also move in space?

I definitely don't know what this means.

Put simply, your local acceleration has no influence on any object, distant or otherwise.

If I fly to the Andromeda nebula (M31 for short) at almost the speed of light, it takes 2.5 million years as observed from Earth or from M31, but perhaps only a day as observed by the ship's clock. From my reference frame, the clocks at M31 jumped forward by 2.5 million years during the acceleration and then remained almost stationary during the constant speed part of the flight. (I'm not talking about the images I'm getting, but the actual time as calculated in my reference frame).

There was a long thread about this recently. Although it might be a tenable explanation, it can easily lead you astray and is certainly no preparation for considering GR and cosmology.

Note: Acceleration does not cause time dilation nor differential ageing.

 

[PeterDonis]

When I accelerate towards a distant object, it moves forward in time, right?

No.

At which point did I make a mistake?

Right at the start.

Changing your state of motion does not change where in spacetime some other object is. In fact it doesn't change anything about the other object, it only changes something about you. The change you refer to as leading to the Andromeda paradox is only a change in coordinate convention and makes no difference physically.

Also, you continue to fail to realize that the spacetime of our universe is curved, not flat, and SR only describes flat spacetime. So even if your SR reasoning were correct, which it isn't, you could not correctly apply it to the curved spacetime of our actual universe.

 

[michelcolman]

I stopped reading here. This is just flat out wrong. SR deals with a flat spacetime. The Universe is not well described by a flat spacetime.

What if I just define a coordinate system as follows:

- We (or rather a point close to us, stationary relative to the CMB) are the stationary origin.
- The time coordinate at any point of the universe, stationary relative to us (zero redshift) is defined by the Einstein synchronization theorem.
- Speed of light relative to us is c at any point in the universe

Surely I can define a coordinate system like that? Or would that be impossible?

Maybe it wouldn't be the most practical system, maybe it would lead to complicated calculations, but I can still define it that way, right?

 

[PeterDonis]

Surely I can define a coordinate system like that?

Yes, you can (actually I'm not 100% sure that the third property will hold, but I'll leave that aside for now), but it won't satisfy all the properties of an inertial frame in SR. Except for the object at the spatial origin, objects at rest in these coordinates will not be in free fall--it will require nonzero proper acceleration to stay at rest in these coordinates. And "comoving" objects, which are in free fall, that are at other spatial points except the origin will be moving away from the spatial origin at different velocities that change with time, even though they experience no proper acceleration. So you can't use these coordinates the way you would use an inertial frame in SR.

 

[michelcolman]

Changing your state of motion does not change where in spacetime some other object is. In fact it doesn't change anything about the other object, it only changes something about you. The change you refer to as leading to the Andromeda paradox is only a change in coordinate convention and makes no difference physically.

OK, forget about the curved universe for a minute, let's first clear this up.

Lorentz contraction is indeed "just a change in coordinate convention", and so is time dilation. Still, they lead to very real and measurable results.

When I say "M31 moves into the future during this acceleration", I mean "after the acceleration, our new moving reference frame assigns a different time coordinate to M31". Which explains why it's 2.5 million years in the future (5 million years later than the last observed image) when we get there after only 1 day of travel (ship's time). That's a real effect resulting from a change in coordinates.

Now it may well be that our universe cannot be described by a flat spacetime (for reasons I don't quite understand yet), but I fail to see how the part of my logic about not being able to catch up with distant galaxies was wrong. When we try to catch up with a very distant moving object that's accelerating away from us, we will not be able to catch it because

- from a stationary frame, it outruns us as it takes a very long time for us to get there, and it will have a lot of time to accelerate away before we get there
- from our accelerating frame, even though we can cross any arbitrary distance in a very short amount of ship's time when traveling near the speed of light, we still cannot catch up with it because it moves to future positions during our acceleration.

These are two perfectly equivalent descriptions.

 

[PeterDonis]

Lorentz contraction is indeed "just a change in coordinate convention", and so is time dilation. Still, they lead to very real and measurable results.

No. "Lorentz contraction" in the sense of a change in coordinate convention does not lead to any measurable results. You can't change the results of any experiments by changing your coordinate convention.

"Lorentz contraction" in a different sense does lead to measurable results: for example, if you measure the length of a body at rest relative to you using a ruler at rest relative to you, then accelerate the body so it's moving relative to you, and then measure its length again using a ruler at rest relative to you, the second length measurement will be shorter than the first. But that has nothing whatever to do with any coordinate convention; the two measurement results will be the same no matter what coordinates you use to calculate them. So this sense of "Lorentz contraction" is different from the sense of "Lorentz contraction" in which that just means a change in coordinate convention.

When I say "M31 moves into the future during this acceleration", I mean "after the acceleration, our new moving reference frame assigns a different time coordinate to M31".

And this has nothing whatever to do with any measurement result. It changes nothing about M31, and changes nothing about any actual measurement you make on M31. It's just a change in coordinate convention and has no physical meaning.

Which explains why it's 2.5 million years in the future (5 million years later than the last observed image) when we get there after only 1 day of travel (ship's time). That's a real effect resulting from a change in coordinates.

No, it's a real effect resulting from how the clocks on M31 and Earth were synchronized prior to your trip. That clock synchronization is a real physical process involving real physical events, and those events are the same regardless of what coordinates you use to describe them.

Now it may well be that our universe cannot be described by a flat spacetime (for reasons I don't quite understand yet)

Any universe that contains matter and energy will not be a flat spacetime. Nor will any universe that has a nonzero cosmological constant (aka dark energy). Flat spacetime is only a solution of the Einstein Field Equation if the stress-energy tensor is zero (i.e, no matter or energy anywhere) and the cosmological constant is zero.

I fail to see how the part of my logic about not being able to catch up with distant galaxies was wrong. When we try to catch up with a very distant moving object that's accelerating away from us

Distant objects are not "accelerating away from us". They are in free fall. The fact that their redshift as seen by us increases with time is a manifestation of the curvature of spacetime in our universe (in this case the curvature caused by the nonzero cosmological constant).

Your reasoning about distant galaxies implicitly assumes that "acceleration" means the only kind that can cause a change in relative velocity (as measured by redshift) in flat spacetime, namely nonzero proper aceleration (firing a rocket, for example). But in our actual universe, with its curved spacetime, that's not the case.

 

[PeroK]

OK, forget about the curved universe for a minute ...

In which case there is no expansion and certainly no objects "receding at faster than the speed of light".

The "Special" in SR means "special case" where there is no gravity, spacetime is flat and there is no concept of the universe expanding.

That's why, regardless of the details, you cannot do cosmology using SR.

 

[Dale]

When I accelerate towards a distant object, it moves forward in time, right? You can even make distant galaxies move forward and backward in time by accelerating a little bit towards them and back again, leading to the Andromeda paradox.

No, this is not correct and is based on an invalid concept of non-inertial frames. The naive approach of formulating a non-inertial frame is to simply stitch together the momentarily co-moving inertial frames. This is invalid because it leads to a non-invertable mapping.

This is discussed by Carroll in chapters 1 and 2 of his Lecture Notes on General Relativity. It is also discussed and a different method of constructing non-inertial frames is provided by Dolby and Gull. There are, in fact, an infinite number of valid ways to define a non-inertial reference frame (and none are “standard”), but the naive approach is invalid.

http://arxiv.org/abs/gr-qc/0104077

But if the object has a certain speed relative to us, surely when it moves into the future, it must also move in space?

This is not something that I recognize as being part of SR, except in the trivial fact that everything moves to the future at a rate of one second per light second of spacetime.

When did it move, as observed from the ship?

Unfortunately, there is no standard reference frame for a non inertial object, but the naive one you are trying to describe is invalid. It is not your fault, the Andromeda paradox is a perennial favorite of pop-sci authors. Such authors deliberately avoid telling their audience about the mathematical issues in favor of dramatic anecdotes.

 

[Dale]

What if I just define a coordinate system as follows:

- We (or rather a point close to us, stationary relative to the CMB) are the stationary origin.
- The time coordinate at any point of the universe, stationary relative to us (zero redshift) is defined by the Einstein synchronization theorem.
- Speed of light relative to us is c at any point in the universe

Surely I can define a coordinate system like that? Or would that be impossible?

Maybe it wouldn't be the most practical system, maybe it would lead to complicated calculations, but I can still define it that way, right?

You could do that but it would not cover the entire universe as you claim. Also, spacetime would still be curved so this would not be SR and the resulting coordinate system would not have all of the properties of an inertial frame.

When we try to catch up with a very distant moving object that's accelerating away from us

Distant objects don’t accelerate away in SR unless they are undergoing proper acceleration.

 

[PAllen]

I'm not sure, but it looks like my idea is similar to the Minkowski space described in this link:
https://www.physicsforums.com/insights/coordinate-dependent-statements-expanding-universe/
If I understood correctly, it says that the motion of distant objects can be considered either as a cosmological redshift due to the expansion of space itself, or as a relativistic doppler shift due to their speed in a non-expanding (Minkowski) reference frame, and these two yield the same result.

Did I understand this correctly, or is this something completely different?

The non-cosmological coordinates describe in this link are not Minkowski, and they can't be, because the spacetime is not flat. Only local (very small in extent and time) are possible in general relativity. The coordinates used in this article share certain features with Minkowski coordinates in SR, but they are just not the same thing. Specifically, the metric being Minkowski and the vanishing of the connection coefficients holds true only at the spacetime origin. That is, formally, there is one spactime point where they are identical to SR Minkowski coordinates.

They do show that cosmological redshift's explanation is coordinate dependent (it can be considered as a generalization of SR Doppler), as is the expansion of space (versus motion in said coordinates).

But you are reading false features into what this article describes.

 

[Orodruin]

I'm not sure, but it looks like my idea is similar to the Minkowski space described in this link:
https://www.physicsforums.com/insights/coordinate-dependent-statements-expanding-universe/If I understood correctly, it says that the motion of distant objects can be considered either as a cosmological redshift due to the expansion of space itself, or as a relativistic doppler shift due to their speed in a non-expanding (Minkowski) reference frame, and these two yield the same result.

I wrote that. The Minkowski space described in the end is just an example of a FLRW universe with a particular scale factor that turns out to be Minkowski space. This does not mean that every FLRW universe is Minkowski space. In particular, it is not our universe because our universe is not empty as the universe described is. Our universe has curvature, that universe does not.

What you can do is to create coordinate patches in a small enough region of spacetime such that the coordinates are approximately Minkowskian. In that local region and those coordinates, cosmological redshift looks like Doppler shift. You can then use several such regions to see the entire cosmological redshift as a series of very small Doppler shifts adding up.

Also note that (as stated in the introduction) the article was written with people who are already quite well versed with GR as the intended target audience. It was not intended for beginners.

 

[michelcolman]

I wrote that. The Minkowski space described in the end is just an example of a FLRW universe with a particular scale factor that turns out to be Minkowski space. This does not mean that every FLRW universe is Minkowski space. In particular, it is not our universe because our universe is not empty as the universe described is. Our universe has curvature, that universe does not.
(...)

Thank you, your post makes a lot of sense.

So, if I understood correctly, my description would work if the universe consisted of massless galaxies that were being pushed apart by an infinite army of equally massless angels. However, because of gravity, dark energy and other effects, the universe is not flat and therefore my coordinates cannot be used.As for the comments of others on my interpretation of special relativity (whether or not certain effects are "real"), I think we'll have to agree to disagree there. It's just a matter of semantics. The way I see it, while I accelerate towards M31, the local clocks over there spin forward very rapidly in my accelerating reference frame. Yes, that's an artefact of the reference frame but so is literally everything. You cannot describe anything without a reference frame. Also, Lorentz contraction is very real as it would allow two 100 meter trains to pass each other in opposite directions on an 80 meter section of double track between two switches. That's as real as it gets. But sure, if you want to use a different definition of "real", be my guest. It's just semantics, nothing more.I'll be away for a while now, lots of stuff to think about, thank you for the interesting links, I will give all of this some more thought to see if I can puzzle together something that makes sense in my head.

 

[Orodruin]

You cannot describe anything without a reference frame.

This is incorrect. Finding and describing things that are invariant (independent of the reference frame) are fundamental to understanding and teaching relativity (both special and general).

Also, Lorentz contraction is very real as it would allow two 100 meter trains to pass each other in opposite directions on an 80 meter section of double track between two switches. That's as real as it gets. But sure, if you want to use a different definition of "real", be my guest. It's just semantics, nothing more.

Lorentz contraction is a frame-dependent thing in its very essence. The "real" thing is that the train passes, not that Lorentz contraction is taking place. Lorentz contraction is just the description in a particular reference frame. The description is going to look very different in the train's rest frame.

 

[atyy]

So, what do you think, is this really a totally wrong explanation, or is it actually a pretty good way of explaining what "space itself" means?

https://www.preposterousuniverse.com/blog/2008/10/06/does-space-expand/
Does Space Expand?
Sean Carroll

https://arxiv.org/abs/0707.0380
Expanding Space: the Root of all Evil?
Matthew J. Francis, Luke A. Barnes, J. Berian James, Geraint F. Lewis

 

[PeterDonis]

As for the comments of others on my interpretation of special relativity (whether or not certain effects are "real"), I think we'll have to agree to disagree there. It's just a matter of semantics.

No, it isn't, it's a matter of you not distinguishing between things that depend on your choice of coordinates and have no physical meaning, and things that do not depend on your choice of coordinates and do have physical meaning.

What clocks on M31 read "now" according to you is an example of the first kind of thing: it depends on your choice of coordinates and your choice has no physical meaning, it's just a convention.

What you actually see in light signals coming from M31 and reaching you here and now is an example of the second kind of thing: it does not depend on your choice of coordinates and it does have a physical meaning.

You are failing to distinguish these two kinds of things and it is leading you to make incorrect claims.

Yes, that's an artefact of the reference frame but so is literally everything.

No. There are quantities that are invariant and do not depend on your choice of reference frame. And those quantities contain everything that has physical meaning.

 

[michelcolman]

https://www.preposterousuniverse.com/blog/2008/10/06/does-space-expand/
Does Space Expand?
Sean Carroll

https://arxiv.org/abs/0707.0380
Expanding Space: the Root of all Evil?
Matthew J. Francis, Luke A. Barnes, J. Berian James, Geraint F. Lewis

Those are extremely interesting links. If I understood correctly, I was not crazy after all, but just neglected to take certain factors like gravity into account. In an empty universe (or a universe containing only massless objects), my description would be more or less valid, FRW with superluminal expansion of "space" being equivalent to a Minkowski-like metric with subluminal expansion of matter through stationary space). Problem is that the curvature of space due to gravity makes it impossible to keep using SR coordinates. And we have yet to decently explain the acceleration of the expansion in any reference frame at all. (Dark energy being a bit too ad hoc to count as a real explanation, no matter how useful it may be for calculations).

Am I at least right when I restrict my description to a massless universe? (which doesn't exist, obviously).

 

[michelcolman]

No, it isn't, it's a matter of you not distinguishing between things that depend on your choice of coordinates and have no physical meaning, and things that do not depend on your choice of coordinates and do have physical meaning.

Still semantics. We use the word "reality" to mean different things.

When I used the term, I really meant "subjective reality", i.e. reality as observed using that reference frame. Einstein said any observer can describe reality with his own coordinates and use the same physical laws to arrive at the same testable conclusions.

You say that a fast train doesn't really shrink.

I say that, in the subjective reality of a stationary observer, the trains "really" shrink. How else could they pass each other in opposite directions on a section of double track that ought to be too short?

Of course the train conductors have a different view, their own train being the normal length, the section of double track being shorter and the other train being even shorter.

Therefore, you are indeed entitled to say that these measurements are not really "reality" (at least not an objective reality) since different observers see different things, and the only "real" thing is that the trains pass each other.

I simply used the term "reality" to mean "reality as described in this particular reference frame". And with that definition, the trains "really" shrink and the clocks at M31 "really" spin forward during my acceleration towards them. Replace "reality" with "observed reality" ("observed" meaning "described as such in our reference frame", not "observed visually") and we basically agree.

 

[PeterDonis]

we have yet to decently explain the acceleration of the expansion in any reference frame at all. (Dark energy being a bit too ad hoc to count as a real explanation

Dark energy is not ad hoc. When you derive the Einstein Field Equation from a Lagrangian, the cosmological constant term appears naturally. What turned out to be ad hoc was ignoring that term for decades simply because our measurements of the universe's expansion were not accurate enough to see its effects.

Am I at least right when I restrict my description to a massless universe?

You are right that for such a universe there is indeed a global inertial frame that works like an SR inertial frame, since the spacetime is just Minkowski spacetime. In fact, there are an infinite number of such frames, each one with a different piece of comoving "matter" (I put "matter" in quotes because it has zero stress-energy, as necessary for the spacetime to be flat) at rest in it.

When I used the term, I really meant "subjective reality", i.e. reality as observed using that reference frame.

There is no such thing as "subjective reality". There is one reality, spacetime. It can be described using any reference frame you like.

You say that a fast train doesn't really shrink.

I have said no such thing. I specifically described actual, physical measurements that correspond to "Lorentz contraction". And I have said multiple times that you can indeed describe the same actual, physical measurements using any frame you like. But I also said you have to be careful to distinguish actual, physical measurements, which have physical meaning, from coordinate-dependent quantities, which don't. That is the distinction you continue to fail to grasp.

with that definition, the trains "really" shrink and the clocks at M31 "really" spin forward during my acceleration towards them.

Nope. The first is an actual, physical measurement that has physical meaning (at least if by "really shrink" you mean what you said earlier, a physical measurement like the trains passing each other on sections of track that would be too short if they were at rest relative to each other). The second is a coordinate-dependent quantity that doesn't.