# Shape of Universe - What would a very long stick do

1. Feb 11, 2015

### 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.

2. Feb 11, 2015

### HiggsBoson1

That is fascinating!

3. Feb 11, 2015

### Staff: Mentor

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.

4. Feb 11, 2015

### Chalnoth

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

5. Feb 12, 2015

### timmdeeg

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.

6. Feb 12, 2015

### Chalnoth

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

7. Feb 12, 2015

### 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...)

8. Feb 12, 2015

### marcus

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

9. Feb 13, 2015

### timmdeeg

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 ... .

Last edited: Feb 13, 2015
10. Feb 13, 2015

### CMaso

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?

11. Feb 15, 2015

### Jorrie

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 = Ωm/(2a3) - ΩΛ). 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.

Last edited: Feb 15, 2015
12. Feb 19, 2015

### 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

13. Feb 19, 2015

### Jorrie

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.

14. Feb 19, 2015

### 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?

15. Feb 19, 2015

### Jorrie

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"

Last edited: Feb 19, 2015
16. Feb 24, 2015

### 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?

17. Feb 24, 2015

### timmdeeg

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.

18. Feb 24, 2015

### 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.

19. Feb 24, 2015

### timmdeeg

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.

20. Feb 24, 2015

### Staff: Mentor

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

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.

21. Feb 24, 2015

### Staff: Mentor

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.

22. Feb 25, 2015

### timmdeeg

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?

23. Feb 25, 2015

### timmdeeg

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.

24. Feb 25, 2015

### Tanelorn

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

25. Feb 25, 2015

### timmdeeg

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