Shape of Universe - What would a very long stick do

[Tanelorn]

Peter thanks for taking the time. Space and matter are still moving away from us at superluminal speeds at these very distant locations though, right?

I am missing something in this discussion.

 

[timmdeeg]

Peter thanks for taking the time. Space and matter are still moving away from us at superluminal speeds at these very distant locations though, right?

I am missing something in this discussion.

Things are moving apart from each other, not space.

 

[PeterDonis]

Space and matter are still moving away from us at superluminal speeds at these very distant locations though, right?

Only in a coordinate sense. Once again, thinking of these "superluminal speeds" as causing other things to happen will only lead to confusion.

 

[Tanelorn]

Things are moving apart from each other, not space.

So things could be moving at superluminal speeds relative to the far end of the stick?

 

[PeterDonis]

So things could be moving at superluminal speeds relative to the far end of the stick?

Same answer as I gave in post #38:

Only in a coordinate sense. Once again, thinking of these "superluminal speeds" as causing other things to happen will only lead to confusion.

 

[timmdeeg]

Thanks for your detailed response!

Note that this means that "comoving" objects at either end of the stick, objects which are moving with the expansion of the universe, will be moving away from each end of the stick. It also means that the stress on a given piece of the stick will get larger as you move towards either end (it will be zero at the center of the stick). So there is a limit in this case on how long the stick can be--basically it can't be equal to the Hubble length (or twice the Hubble length, i.e., the stick's diameter cannot span the Hubble sphere), because if it were, the stress at the ends of the stick would be infinite.

I am a bit curious about the tidal force along the stick and try this:

Let's (i) have test particles along it and release two neighboring particles somewhere. Then I would expect them to accelerate away from each other in the local frame of this small part of the stick, while both are moving in the direction towards the end of the stick. Whereby the value of this acceleration should determine the tidal force acting locally there on the stick. If correct the total tidal force should be obtained by integration over the whole length.

Or (ii) is it sufficient to consider the acceleration of one released test particle relative to the point on the stick, where it was released?

It seems that the local tidal force in the (co-moving) center of the stick is $> 0$ (i) and $= 0$ (ii), resp. , and constant (i) and increasing (ii) towards the end of the stick. Perhaps (i) is negligible compared to (ii).

I am just thinking aloud.

 

[Jorrie]

Unfortunately I am still not getting this. Is this because the thought experiment is just not valid?

It will be invalid if you insist on any end moving superluminal relative to its immediate surroundings (which follow the Hubble flow).

Your 'telescopic stick', say consisting of millions of 'rigid sections' that freely 'slide out', can actually be quite helpful. In our present Lambda-dominated universe, each section will suffer only small tidal stress between its two ends and each successive section will be 'slowly sliding out' relative to its neighbors. Each section's center will keep up with the Hubble flow, provided there is no friction in the sliding mechanism. Nothing will approach local speed of light anywhere.

Your problem seems to come in when there is some friction in the 'sliding out', i.e., some stiffness in the telescopic rod. If you 'anchor' one rod end to some massive object that is following the Hubble flow, the other end will have to acquire peculiar velocity relative to its local Hubble flow and you are wondering whether this peculiar velocity could not exceed local c if the stick is long enough.

I think the solution is that the tidal forces pulling the rod's sections out will increase as peculiar speeds go up and it will always overcome whatever friction there is in the 'sliding out'. The peculiar velocities will stay less than c, because tidal forces will increase without limit near c.

I think it is a rather tricky calculation to prove all this, but to be compatible with relativity theory, it must be the case. Remember that locally to whatever observer, spacetime is very close to flat in your thought experiment. It is only over many sections that the spacetime is curved, giving rise to the superluminal recession rates.

Does this help, or hinder?

 

[Tanelorn]

Peter, I still do not get what you mean by this: "Only in a coordinate sense. Once again, thinking of these "superluminal speeds" as causing other things to happen will only lead to confusion."

Jorrie, I agree the sliding telescopic stick thought experiment helps and allows all LOCAL frames of reference to not exceed relative super luminal speeds. And I agree that as we start to stiffen the stick something has to give, but I am still not sure what.

 

[PeterDonis]

I still do not get what you mean by this: "Only in a coordinate sense. Once again, thinking of these "superluminal speeds" as causing other things to happen will only lead to confusion."

I mean that this "superluminal speed" you are talking about is not directly measured by anybody. It's just a mathematical result you get when you use a particular system of coordinates, and divide the increase in "distance" in those coordinates over a given time interval in those coordinates, by the time interval. Coordinates don't cause anything.

the sliding telescopic stick thought experiment helps and allows all frames of reference to not exceed relative super luminal speeds.

What does "all frames of reference to not exceed superluminal speeds" mean? Jorrie is only talking about local comparisons--relative velocities between a given piece of the stick and "comoving" objects (objects moving along with the Hubble flow) at the same spatial location. He is not talking about the "relative speed" between opposite ends of the stick (which is the "coordinate speed" I described above). That can still be "superluminal", but that doesn't matter because it's only a coordinate speed. No piece of the stick is moving faster than light rays at the same spatial location, which is what the rule "nothing can go faster than light" actually means, physically.

I agree that as we start to stiffen the stick something has to give, but I am still not sure what.

What "has to give" as you stiffen the stick is that the maximum possible length of the stick decreases.

In the limiting case of zero stiffness (i.e., zero force between neighboring pieces of the stick), the stick's length can be anything; there is no maximum. That's because each piece of the stick just follows a "comoving" worldline--i.e., it moves along with the Hubble flow in its vicinity. To observers looking at a particular local section of the stick, the stick appears to stretch as neighboring sections move further away (as the universe expands). This doesn't cause any force or stress anywhere because the stick has zero stiffness; one part can't restrict the motion of any other part. Also, in this scenario, the piece of the stick that is exactly one Hubble radius away from the Earth is moving "at the speed of light" relative to the Earth end of the stick, in "comoving" coordinates. Pieces further away are moving "faster than light" in those coordinates. (But, as I said, this is just a coordinate speed and nobody actually measures anything moving faster than light beams at the same spatial location.)

If we make the stiffness of the stick nonzero, each part of the stick now exerts some force on neighboring parts. The boundary condition you appear to be assuming is that one end of the stick, the end anchored to the Earth, is moving along with the Hubble flow, i.e., it is "comoving". (The Earth actually isn't exactly "comoving", but we can ignore that here.) So at that end of the stick, there is zero stress. But that end of the stick is now pulling on the neighboring piece, exerting some force, so that neighboring piece is not exactly comoving; it is moving away from the Earth end of the stick, but not as fast as a "comoving" object would. That means the neighboring piece is under some stress, because it is feeling a force pulling it off of a "comoving" trajectory.

As we move further and further along the stick, away from the Earth, we can apply the same argument: the first neighboring piece next to the Earth end of the stick pulls on the second, the second pulls on the third, etc. At each stage, the stress in the stick increases; the motion of each piece of the stick is a little more different from that of a "comoving" object at the same spatial location, and the force the piece feels is larger. So now, when we get to the piece of the stick exactly one Hubble radius away from the Earth, that piece will have a coordinate velocity of less than $c$, relative to the Earth end of the stick, in "comoving" coordinates, because it is moving away from the Earth end of the stick more slowly than a "comoving" object at the same spatial location. And the stress in the stick at this point will be, I believe (but I haven't done the calculation) small enough that the stick can withstand it.

However, if we continue along the stick, we will reach some point, at some finite "comoving" distance from the Earth, where the stress in the stick exceeds the maximum possible structural strength imposed by relativity (i.e., that the speed of sound in the stick would have to be greater than the speed of light for it to withstand the stress). That point determines the maximum possible length of the stick.

As we increase the stiffness of the stick, the force each part exerts on neighboring parts increases, so the speed of a given piece of the stick relative to a "comoving" object at the same spatial location increases faster. In the (unphysical) limiting case of infinite stiffness, no piece of the stick could move at all relative to any other piece; and in this case, the stress in the stick would go to infinity at the Hubble radius (which would be the maximum possible length of the stick). But, as I said, this case is unphysical, because relativity imposes a finite limit on stiffness--an infinitely stiff material would have an infinite sound speed, and the sound speed in any actual material cannot be greater than the speed of light. So any real stick would stretch some as the universe expanded--each piece would move to some extent relative to neighboring pieces, because of the finite limit on stiffness.

 

[Tanelorn]

Peter do you agree that beyond the edge of the observable universe there are objects that are traveling away from Earth at faster than light velocities?

If so, then a rigid stick fixed on Earth to that point either is not allowed and is torn apart by something(?) or its far end is moving at super luminal velocities relative to objects out there. I can't understand any other alternative to these two possibilities.

We are just repeating. I apologize for not understanding, let's leave it at that.

 

[PeterDonis]

do you agree that beyond the edge of the observable universe there are objects that are traveling away from Earth at faster than light velocities?

I have already answered this, repeatedly.

If so a rigid stick fixed on Earth to that point either is not allowed and is torn apart by something(?) or its far end is moving at super luminal speeds relative to objects out there.

I have addressed this repeatedly too.

We are just repeating.

Yes, we are. But it seems to me that you have not grasped the key thing I have been saying: the concepts of "speed" and "distance" you are using are not direct observables. Nobody measures them. They are just artifacts of a particular coordinate system. They are just numbers that serve as convenient labels. The reason you are having a hard time understanding is that you are failing to realize that; you are assuming that those numbers have a physical meaning that they simply do not have.

 

[Tanelorn]

"Yes, we are. But it seems to me that you have not grasped the key thing I have been saying: the concepts of "speed" and "distance" you are using are not direct observables. Nobody measures them. They are just artifacts of a particular coordinate system. They are just numbers that serve as convenient labels. The reason you are having a hard time understanding is that you are failing to realize that; you are assuming that those numbers have a physical meaning that they simply do not have."

Well the problem is I don't know what that actually means, but it seems like its like saying these superluminal velocities are somehow not actually real or correct, yet they have to be..

 

[PeterDonis]

it seems like its like saying these superluminal velocities are somehow not actually real

"Real" is a problematic word. A better way of saying it would be that these superluminal velocities do not play any causative role in any of the physics.

yet they have to be

Why?

 

[Tanelorn]

Tanelorn said:
yet they have to be
Peter said:
Why?

Red shift measurements? Objects leaving the observable Universe? Theories about dark energy and expansion of the U?

Perhaps I am trying to imagine space as being a continuous thing whereas over large distances its differential velocities no longer make sense.. I don't know.

 

[PeterDonis]

Red shift measurements?

How do those show superluminal velocities? (Bear in mind that the light we see coming from objects at very high redshifts was emitted a long time ago, so that light doesn't tell us anything directly about what those objects are doing "now".)

Objects leaving the observable Universe?

How do we know they are? What observations tell us this?

Theories about dark energy and expansion of the U?

What observations are they based on?

You can see the general pattern here. You are talking about "superluminal velocities" as if we directly observe them, or something that immediately implies them, so they must be "real". I'm trying to get you to examine the actual observations and what they actually imply. The fact that pop science books and articles and TV shows often talk about "distant objects receding faster than light" does not mean that's a good description of the actual physics.

A good online reference for this stuff is Ned Wright's Cosmology Tutorial:

http://www.astro.ucla.edu/~wright/cosmolog.htm

Both the tutorial itself and the "frequently asked questions" are worth reading.

 

[Tanelorn]

Page 40 here is what my understanding of superluminal velocities is based on:
http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf

I mentioned red shift because it shows that things are receding faster the further away they are and extrapolating from this to superluminal velocities.

 

[PeterDonis]

Page 40 here is what my understanding of superluminal velocities is based on

This is a pop science article. It's not a good reference, even though it's written by scientists. "Pop science" does not mean a non-scientist wrote it. It means that whoever wrote it, scientist or not, was not trying to give you an actual predictive model that you can reason from to get valid conclusions about the physics. If you want to learn about the actual physics involved in cosmology, you need to use sources that are actually trying to give you a valid predictive model. The Ned Wright tutorial can give you a start, and gives references that can get you further.

I mentioned red shift because it shows that things are receding faster the further away they are

But that's not what the red shift "shows". The red shift by itself does not tell you how far away something is, and it only tells you "how fast it is receding" if you interpret it as a Doppler shift, and that interpretation is problematic when spacetime is curved.

 

[Tanelorn]

Wow, thanks Peter. I was using that document to clear up other populist ideas and I thought I now had things much clearer now!