Shape of Universe - What would a very long stick do

[CMaso]

if it were extended out from Earth, was perfectly straight, and could be any length desired? If I understand the prevailing theories it would either A) Just keep going forever (assuming infinite mass were possible), or B) Seem to travel in a straight line as far as we could tell, but eventually return to Earth from the opposite direction. Going with the popular "balloon surface" analogy, B seems the more likely of the two. 2-dimensional beings on the surface of a balloon would perceive its surface as a flat plane, and perceive their very long stick to be extending away in a straight line, but it would eventually go around the balloon and return to its point of origin.

 

[HiggsBoson1]

That is fascinating!

 

[PeterDonis]

Going with the popular "balloon surface" analogy, B seems the more likely of the two.

That analogy is misleading in this respect (and also in a number of other respects, which have been discussed in plenty of other threads in this forum). The current best-fit model of our universe says that it is spatially flat, which means the stick would just go on forever.

 

[Chalnoth]

And if it got large enough, it'd get ripped apart by the cosmological constant.

 

[timmdeeg]

The current best-fit model of our universe says that it is spatially flat, which means the stick would just go on forever.

Is the 3-torus which is spatially flat too already ruled out? But apart from that it is my impression that cosmologist indeed prefer the 3-plane.

 

[Chalnoth]

No, a 3-torus isn't ruled out. I don't think it can be.

 

[CMaso]

The shape of the universe is widely discussed on this forum and elsewhere -- my apologies for creating a new thread, I just wanted to approach the question from a different angle. It gets a little confusing when scientists describe the big bang, saying the universe expanded to be x wide in the first y seconds, as though the universe has some central point of origin, which it does not. Another way to ask the question might involve lowering the bridge rather than raising the river, so to speak -- if one were here on Earth observing this very long stick extending straight outward into space during a big crunch event, what would the stick be doing...would it still appear to be stretching on forever, even though all objects in the universe were in much, much closer proximity to each other? (assuming it were physically invulnerable to the immense heat and gravity...)

 

[marcus]

if it were extended out from Earth, was perfectly straight, and could be any length desired? If I understand the prevailing theories it would either A) Just keep going forever (assuming infinite mass were possible), or B) Seem to travel in a straight line as far as we could tell, but eventually return to Earth from the opposite direction. Going with the popular "balloon surface" analogy, B seems the more likely of the two. 2-dimensional beings on the surface of a balloon would perceive its surface as a flat plane, and perceive their very long stick to be extending away in a straight line, but it would eventually go around the balloon and return to its point of origin.

Hi Maso, welcome to PF!
I think that's a good basic "thought experiment" type question. to make it work you should imagine that you temporarily PAUSE expansion of distances (or contraction if distances happened to be shrinking).
Then what you find is there are two popular ideas of large-scale spatial geometry A) flat infinite and B) slight overall positive curvature, analogous to a balloon surface but 3d instead of 2d
So you freeze the geometry of space at a particular instant and A) you find there is no limit on how long and straight the stick can be, it goes "forever". OR you find that it is analogous to the balloon picture and B) the stick comes around and rejoins from the opposite direction.

There are other more complicated possibilities but those models of spatial geometry are probably the most commonly considered and cosmologists keep MEASURING the large scale spatial curvature in the hopes of getting a decisive answer. You might ask how they do it, sometime, there are clever ways to judge overall large scale curvature. but so far what they get is that SPATIAL curvature is either exactly zero or very small===so small that it is "as good as zero". I think lot of people would be willing to admit that it might be case B) with a very small curvature but they don't BOTHER to include it in calculations because all the calculations wouldn't change very much.

The other thing to mention is that if you don't pause the expansion process then it would wreck the stick.
If the stick were a fixed 14.4 billion LY long, then its tip end would find itself in local space that was getting farther away from us at speed c. So for the stick to remain intact that tip end would have to be moving towards us (thru its local surroundings) at speed c. but material things don't do that. so the tip end couldn't make it, and the stick would come apart.
14.4 billion LY is called the "Hubble radius". It is the size of distances which are growing at exactly the speed of light. Other cosmic scale distances are growing in proportion. One 7.2 billion LY long would be growing at speed c/2.

Anyway, welcome and keep asking questions :D

 

[timmdeeg]

-- if one were here on Earth observing this very long stick extending straight outward into space during a big crunch event, what would the stick be doing...would it still appear to be stretching on forever, even though all objects in the universe were in much, much closer proximity to each other? (assuming it were physically invulnerable to the immense heat and gravity...)

We talk about accelerated motion of those objects towards each other. Which means that there are tidal forces tending to stretch (during expansion) or to squash (during contraction) them. So, what happens to the stick seems to depend merely on its physical properties. In my opinion any thought-experiment should obey the physical laws und thus ideal rigidity of the stick isn't possible then. Note that tidal force is proportional to distance, so the longer the stick ... .

 

[CMaso]

Hi Maso, welcome to PF!
The other thing to mention is that if you don't pause the expansion process then it would wreck the stick.
If the stick were a fixed 14.4 billion LY long, then its tip end would find itself in local space that was getting farther away from us at speed c. So for the stick to remain intact that tip end would have to be moving towards us (thru its local surroundings) at speed c. but material things don't do that. so the tip end couldn't make it, and the stick would come apart.
14.4 billion LY is called the "Hubble radius". It is the size of distances which are growing at exactly the speed of light. Other cosmic scale distances are growing in proportion. One 7.2 billion LY long would be growing at speed c/2.
Anyway, welcome and keep asking questions :D

Thank you very much Marcus, and everyone, for your comments - great forum. :) I really mean the stick to be a virtual one; just a convenient gauge of what's happening to 3-d space. But as a follow-up question - I get that the tip end of a 14.4 billion LY-long stick would be stretching away from us at a rate of c, and eventually come apart, but then, what if someone were at the other end of that stick, pointing an identical stick back at us? Because of relativity, they would perceive *us*, and the tip of their stick, to be stretching away from them at c. So would the stick(s) start coming apart at their end, or ours?

 

[Jorrie]

But as a follow-up question - I get that the tip end of a 14.4 billion LY-long stick would be stretching away from us at a rate of c, and eventually come apart, but then, what if someone were at the other end of that stick, pointing an identical stick back at us? Because of relativity, they would perceive *us*, and the tip of their stick, to be stretching away from them at c. So would the stick(s) start coming apart at their end, or ours?

I think a hypothetical "ideal stiffness stick" of less than the Hubble length will experience a stretching force (in our present universe) between its two ends that depends on both its proper length and the deceleration parameter (q = Ω_m/(2a³) - Ω_Λ). It does not matter to which end ("ours" or "theirs") it is anchored. One cannot say where it will break; I suppose an 'ideal stick' will just be breaking up into many smaller pieces over its length.

 

[TEFLing]

I think you would need to calculate the deviation from geodesic motion for the two ends relative to the middle

Then the geodesic equation would tell you the required force

 

[Jorrie]

I think you would need to calculate the deviation from geodesic motion for the two ends relative to the middle

Then the geodesic equation would tell you the required force

That would be one method, yes. Davis et. al give another approach in their "Tethered Galaxy problem", which is what I based my comment on.

 

[CMaso]

This brings up another question which I haven't found an answer for anywhere online yet -- relative to one's point of reference, how does one distinguish if objects are moving through space vs. moving *with* space as it expands?

 

[Jorrie]

This brings up another question which I haven't found an answer for anywhere online yet -- relative to one's point of reference, how does one distinguish if objects are moving through space vs. moving *with* space as it expands?

It is rather difficult to determine the peculiar velocities of distant galaxies. A good description of the problem and methods is given by Jeffrey Willick of Stanford in MEASUREMENT OF GALAXY DISTANCES: http://ned.ipac.caltech.edu/level5/Willick/Willick_contents.html, specifically
"1.1. Peculiar Velocities versus H0"

 

[TEFLing]

A light bridge between galaxies, composed of photons ( say in a standing wave ), would redshift with expansion so as to keep in connection, yes?

 

[timmdeeg]

This brings up another question which I haven't found an answer for anywhere online yet -- relative to one's point of reference, how does one distinguish if objects are moving through space vs. moving *with* space as it expands?

One can tell that the velocities of galaxies belonging to the local group are obeying Special Relativity, because those galaxies being gravitationally bound can be treated as moving in flat space-time. Thus they don't 'feel' any expansion.
Farther away both, peculiar velocities and influence of expansion will contribute to the observed redshift. However it seems very difficult to distinguish one from the other, if that is possible possible at all.
Regarding galaxies in cosmological distances peculiar velocities are negligible.

 

[Tanelorn]

If the stick were fixed at our end then space at other end of the stick would be hurtling away from that end at superluminal velocities and such local velocities are not allowed.
Perhaps we are not allowed to something like this except perhaps as a thought experiment to demonstrate the fact.

 

[timmdeeg]

If the stick were fixed at our end then space at other end of the stick would be hurtling away from that end at superluminal velocities and such local velocities are not allowed.

In that case the other end of the stick would move with superluminal velocity relative to the CMB. That isn't forbidden, provided the stick survives its length.
You have a similar situation, if you imagine a stick dipped into a black hole.

 

[PeterDonis]

In that case the other end of the stick would move with superluminal velocity relative to the CMB

No, it wouldn't. Each point of the stick would be moving slower than light, relative to the CMB in its local vicinity.

You have a similar situation, if you imagine a stick dipped into a black hole.

No, you wouldn't. You would find that the stick would have to either fall into the hole or break; but in either case, each point of the stick would be moving slower than light, relative to light in its local vicinity.

 

[Nugatory]

In that case the other end of the stick would move with superluminal velocity relative to the CMB. That isn't forbidden, provided the stick survives its length.
You have a similar situation, if you imagine a stick dipped into a black hole.

In both situations you describe, there's no "provided the stick survives". It will break, as the stress in the stick increases without bound as the velocity of the far end approaches $c$ relative to its local surroundings.

 

[timmdeeg]

No, it wouldn't. Each point of the stick would be moving slower than light, relative to the CMB in its local vicinity.

Yes, agreed and thanks. Perhaps one should distinguish between real and imagined, regarding the stick in this discussion. The length of a real stick grows with a velocity $< c$ and therefore remains shorter than Hubble length. Whereas an imagined stick has arbitrary length and besides talking about proper distance speculations regarding the velocity of his end are of no use. Would this make sense?

 

[timmdeeg]

In both situations you describe, there's no "provided the stick survives". It will break, as the stress in the stick increases without bound as the velocity of the far end approaches $c$ relative to its local surroundings.

Well, I think that the far end of a "physically real stick" can't approach $c$ and whether it gets broken or not depends on material properties and tidal forces. In my opinion (today) it makes no sense to discuss an imagined stick in a physical context like this one.

 

[Tanelorn]

I meant the stick being long enough to reach space moving away from us at superluminal velocities..

 

[timmdeeg]

I meant the stick being long enough to reach space moving away from us at superluminal velocities..

Yes, understood. Therefore I started reasoning about the 'nature' of that stick.

 

[PeterDonis]

The length of a real stick grows with a velocity $< c$ and therefore remains shorter than Hubble length.

It depends on how long the stick is, and how strong the inter-atomic forces in the stick are. It's quite possible for one end of the stick to be moving "faster than $c$" relative to the other end of the stick, if the stick is long enough. But this "relative speed" is not a relative velocity in the sense of Special Relativity, so there's nothing preventing it from being faster than $c$. A light beam emitted at one end of the stick, in the direction away from the other end, would recede faster than the end of the stick itself does--so the light beam would also be moving "faster than $c$" relative to the other end of the stick. (See further comments below.)

The important "relative speed" in determining how the stick behaves is the relative speed between neighboring parts of the stick, parts close enough together that a single local inertial frame can cover them both. This relative speed will always be less than $c$--how much less depends, again, on how strong the inter-atomic forces in the stick are. Those forces have to resist some amount of tidal gravity, due to the universe's expansion, that is "trying" to pull the neighboring pieces of the stick apart. If the forces are strong enough, the neighboring pieces of the stick will not move apart at all--they will just experience some internal stress. In this limiting case, then the opposite ends of the stick will not be moving apart either; the proper distance between the ends will be constant--because each small piece of the stick is keeping a constant proper distance from neighboring pieces, and the proper length of the stick as a whole is just the sum of all those small proper distances between neighboring pieces.

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.

The other limiting case is that in which the forces between neighboring pieces of the stick go to zero--the inter-atomic bonds are so weak that they have a negligible effect on the worldlines of each individual piece of the stick. In this case, each individual piece of the stick will follow a "comoving" worldline--i.e., it will move along with the "flow" of the universe's expansion in its vicinity. In this case, the opposite ends of the stick can indeed be moving apart "faster than $c$", as described in my first paragraph above, if the stick is long enough. There is no limit in this case on the length of the stick (but of course calling it a "stick" in this case is kind of a misnomer, since it does not behave like a single object, it's just a collection of particles).

The case of interest is an intermediate case between these two--neighboring pieces of the stick are moving apart, but not as fast as "comoving" worldlines would, i.e., the inter-atomic forces do affect the motion of the pieces of the stick, but not enough to keep neighboring pieces the same proper distance apart. In this case, the stick does behave more or less like a coherent object, but an elastic one--it's more like a rubber band than a stick, getting stretched as the universe expands. In this case, the opposite ends of the "band" can be more than a Hubble diameter apart, and can be moving faster than $c$ relative to each other (but note that, at the Hubble diameter, they won't be, because the pieces of the stick there are not following "comoving" worldlines). There will still be (I think) a limit on how long the stick can be, the limit will just be larger than the Hubble diameter. (I do not, however, think this limit will be the same as the point where the ends of the stick are "moving at $c$" relative to each other. I haven't had time to do a calculation to confirm this, though.)

 

[Tanelorn]

I meant an extremely long, infinitely stiff, stick. I guess it is very hypothetical :)

What force would be acting on the end in which space is moving near c or superluminal away from us?

 

[PeterDonis]

an extremely long infinitely stiff stick.

There's no such thing; relativity places a finite limit, even in principle, on the structural strength of materials. One way of stating it is that the speed of sound in the material can never be greater than the speed of light. (An "infinitely stiff" material would have an infinite sound speed.)

 

[Tanelorn]

There's no such thing; relativity places a finite limit, even in principle, on the structural strength of materials. One way of stating it is that the speed of sound in the material can never be greater than the speed of light. (An "infinitely stiff" material would have an infinite sound speed.)

What is the force which would be acting on the end of the stick in which space is moving near c or superluminal away from us?
Assuming empty space.

 

[PeterDonis]

What is the force which would be acting on the end of the stick in which space is moving near c or superluminal away from us?

Whatever force is produced by the interactions between the end of the stick and the neighboring piece of the stick. "Space moving" doesn't exert a force on anything.

 

[Tanelorn]

So why does the stick need to be stiff? Consider an extendable stick like a telescopic antenna being extended from earth, how would space eventually tear it apart?

 

[PeterDonis]

Consider an extendable stick like a telescopic antenna being extended from earth, how would space eventually tear it apart?

It wouldn't. As I said, "space moving" doesn't exert a force on anything. If you could somehow make a telescopic antenna that could extend for fifty billion light years, the expansion of space wouldn't stop it from working.

 

[Jorrie]

What is the force which would be acting on the end of the stick in which space is moving near c or superluminal away from us?
Assuming empty space.

Google "Davis Tethered Galaxy problem", where eqs. 12 to 15 give the tidal accelerations between any two free particles over a distance D in empty space. From this you may be able to calculate the stresses on your hypothetical "stick".

My 2cent is that the ends of the stick will always 'join the Hubble flow', minus some local speed differential (< c), depending on the stiffness of the stick against stretching. This means that the two ends can in principle be farther away from each other than the Hubble radius, as Peter has already stated.

If you had the "infinite telescopic stick", it does not have to break at any distance, but if there is some resistance to extending, it would not quite follow the Hubble flow. Does this make sense?

 

[Tanelorn]

Jorrie, Thanks for the tethered galaxy problem paper. Unfortunately I am still not getting this. Is this because the thought experiment is just not valid?

All I am trying to understand is how do we deal with the relative superluminal speeds between the stick and the space and matter at the far end of the stick, with our end of the stick firmly tethered here on earth? The stick is stiff so something has to give right?

 

[PeterDonis]

how do we deal with the relative superluminal speeds between the stick and the space and matter at the far end of the stick

By recognizing that this "relative speed" does not work the way you are thinking it does. As I said in a previous post, it is not a "relative velocity" in the sense of SR. And it is not a "relative speed" that is exerting a force on anything. It's just a coordinate velocity in comoving coordinates. Thinking of it as though it were driving any of the physics will only cause confusion.

The stick is stiff so something has to give right?

Not necessarily. See above and my previous posts.

 

[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.