How do we know the universe isn't a loop?

[SamBridge]

So light red-shifts over time as it travels over vast distances of space, eventually to the point where it would be immeasurable by our current technology, but for the faint radio photons we do manage to pick up, how do we determine that it wasn't a photon that traveled in the opposite direction from it's sources and then looped around the universe in a 4 dimensional hyper-sphere?

[ajb]

You mean could the universe have some non-trivial topology? (Say compact, or maybe non-simply connected etc)

 

If the Universe was shaped a bit like a doughnut (compact), then it could be possible to see multiple images of the same galaxy. On compact manifolds, not all geodesic come back to their starting point and so multiple images are possible. I believe people are searching for such image.

[StringJunky]

You mean could the universe have some non-trivial topology? (Say compact, or maybe non-simply connected etc)

 

If the Universe was shaped a bit like a doughnut (compact), then it could be possible to see multiple images of the same galaxy. On compact manifolds, not all geodesic come back to their starting point and so multiple images are possible. I believe people are searching for such image.

 

Did you mean that: On compact manifolds, not all geodesic come back to their starting point and so multiple images are not possible? Have you done a typo?

[imatfaal]

Did you mean that: On compact manifolds, not all geodesic come back to their starting point and so multiple images are not possible? Have you done a typo?

i assumed that if the image came back to it's starting point we wouldn't see two of them - but if the geodesic takes it to a slightly different point then we can see it twice.

 

baseball analogy - you pitch at the worlds greatest hitter, he hits back at a ludicrous speed and it whizzes past your eyes and does an orbit. if the geodesic takes the ball back exactly it will hit the back of the batsmans head and you will only see it once, if the geodesic route did not take it to the same place it would miss the batsmans by a yard or so and you would see it again on its second passage.

 

we look for images of things that we see directly and that we see having done an entire loop - actually I didnt know we did look and I don't understand how the time would allow any light to have made a complete circuit.

[StringJunky]

i assumed that if the image came back to it's starting point we wouldn't see two of them - but if the geodesic takes it to a slightly different point then we can see it twice.

 

baseball analogy - you pitch at the worlds greatest hitter, he hits back at a ludicrous speed and it whizzes past your eyes and does an orbit. if the geodesic takes the ball back exactly it will hit the back of the batsmans head and you will only see it once, if the geodesic route did not take it to the same place it would miss the batsmans by a yard or so and you would see it again on its second passage.

 

we look for images of things that we see directly and that we see having done an entire loop - actually I didnt know we did look and I don't understand how the time would allow any light to have made a complete circuit.

 

I am open to the fact that I'm missing something which is more than possible.

[Arch2008]

For photons to "loop around", the universe would have to be bent into a taurus (doughnut) shape. Mass bends space time, so a sufficiently large amount of mass might do this. For space time to be bent into such a shape, or topology, we have determined that more mass would be required than has been observed. So a photon in the observable universe would not be able to loop.

[ajb]

i assumed that if the image came back to it's starting point we wouldn't see two of them - but if the geodesic takes it to a slightly different point then we can see it twice.

Yes, you could in principle see two images of the same galaxy close to each other. Even without this, assuming that light rays form closed loops, one could in principle observe the same galaxy at two apparent locations in the sky.

 

For photons to "loop around", the universe would have to be bent into a taurus (doughnut) shape.

Technically a tours is flat.

 

It is the global shape of the Universe that is in question here and not the local geometry. General relativity tells us very little about topology.

[Arch2008]

We can only receive photons from the observable universe. GR determines that the observable universe is not a taurus. That is what I addressed.

[Dekan]

 

You mean could the universe have some non-trivial topology? (Say compact, or maybe non-simply connected etc)

 

If the Universe was shaped a bit like a doughnut (compact), then it could be possible to see multiple images of the same galaxy. On compact manifolds, not all geodesic come back to their starting point and so multiple images are possible. I believe people are searching for such image.

 

This is interesting, because how is it possible to see multiple images in a mirror. I mean, suppose you stand in front of a full-length mirror. And look at your legs in it. Your legs appear in the mirror as an image. But if you then look downwards, away from the mirror, you can also see an image of your legs.

 

So, by rapidly flicking your eyes towards the mirror, then away from it, down towards your legs - you can get two separate leg-images.

 

Supposedly, these images are produced by individual photons. Which enter your eye, get focussed by the lens onto the retina, converted into nerve impulses, then sent to your brain, where the visual processing parts of your brain interprete them as images.

 

But couldn't these images could be multiplied without limit? Suppose you weren't just standing in front of one mirror, but a series, or array, of mirrors. Angled so that each sends an image to your brain.

 

Your brain would process, and have to accept as real, a multiplicity of images - but would the actual photons be multiplied?

[MigL]

Correct me if I'm wrong AJB.

I can see how a flat torus, where the top of the manifold is identified with the bottom and the left side with the right side, would be possible.

From what I remember about simply connected manifolds versus non-simply connected, doesn't the latter imply a 'preferred direction'? And with a preferred direction comes violation of a very important conservation law.

Yes, I do remember that GR doesn't specifically have a mass-energy conservation law, but I always assume it to be valid.

[SamBridge]

I'm not understanding this "geodesic" thing. I understand manifolds and extra dimensional shapes, but why wouldn't you see the baseball if it looped around exactly to it's starting point if you were merely a by-stander and not the pitcher? From the way I think of it the universe would have to be 5 dimensional because the universe would have to loop 3 dimension coordinates around which wouldn't be possible without an extra dimension to warp those 3-D coordinates, then that whole hyper torus would have to be relative from every frame of reference, which would require an extra dimension to bend the 4 dimensional hyper-torus into that sort of shape from every 4 dimensional surface.

Edited January 31, 2013 by SamBridge

[ajb]

This is interesting, because how is it possible to see multiple images in a mirror. I mean, suppose you stand in front of a full-length mirror. And look at your legs in it. Your legs appear in the mirror as an image. But if you then look downwards, away from the mirror, you can also see an image of your legs.

 

So, by rapidly flicking your eyes towards the mirror, then away from it, down towards your legs - you can get two separate leg-images.

So some other observer takes a photo of you and then separately your image in the mirror. He sees that the two photos he taken are of the same object, or for sure two things very similar. Either there are two of you, identical or at best nearly identical, or there is only one of you and the light is getting bent somehow to create another image.

 

So, if an astronomer found two identical images in different parts of the Universe he would wonder if something similar is going on. Either there are two identical galaxies out their, or we have imaged the same object twice.

 

We can only receive photons from the observable universe. GR determines that the observable universe is not a taurus. That is what I addressed.

I don't think that is quite true. General relativity says nothing about topology, it only talks about the local geometry. It is possible, as far as I know, to have nontrivial topology at scales smaller than the observable Universe. We know from the CMBR that the observable Universe is flat, but nothing about the topology. Signals of the topology could be in the CMBR; but this is much more technical than just looking for multiple images.

 

I don't know the state of the art data on this. I am sure a hunt through the literature would help.

 

From what I remember about simply connected manifolds versus non-simply connected, doesn't the latter imply a 'preferred direction'? And with a preferred direction comes violation of a very important conservation law.

A space that is connected, but not simply connected has holes in it. You cannot fully contract loops. I don't know how this gives a preferred direction.

 

People have considered GR with such a thing, for example Einstein aether theory.

 

Typically in cosmological models people assume simply connected manifolds from the off.

Yes, I do remember that GR doesn't specifically have a mass-energy conservation law, but I always assume it to be valid.

You have a local form of energy-momentum conservation and a global one for "nice" space-times.

 

I'm not understanding this "geodesic" thing. I understand manifolds and extra dimensional shapes, but why wouldn't you see the baseball if it looped around exactly to it's starting point if you were merely a by-stander and not the pitcher?

You can do, but if you do the mathematics carefully you see that the paths of light do not necessarily form closed loops on a compact manifold in general. But as I said, you don't really need this to get multiple images. In essence if you look right and see the same object as looking left, you have to wonder if your world is compact.

[LaurieAG]

My avatar is a feedback loop image with 0.5m in air (between CRT and CCD) and 0.5m in vacu running at 25 fps.

 

That's why I wonder why we don't try to make astronomical observations without (1) planetary rotation, (2) earths orbit around the sun and (3) the suns rotation around our galactic center to see what our universe really looks like without the spin.

[Dekan]

My avatar is a feedback loop image with 0.5m in air (between CRT and CCD) and 0.5m in vacu running at 25 fps.

 

That's why I wonder why we don't try to make astronomical observations without (1) planetary rotation, (2) earths orbit around the sun and (3) the suns rotation around our galactic center to see what our universe really looks like without the spin.

 

This business of "spin" seems quite puzzling. Everything seems to be spinning round. Eg, the Earth spins on its axis. The Moon spins round the Earth. Both of them spin round the Sun, which itself spins on its axis. And the Sun is in the Galaxy, which also spins.

All this looks rather unnatural. Shouldn't things just be quiet, and rest steady. Instead of constantly whirling around. Why would they keep moving, unless the movement is only an illusion.

 

Also, what about atoms. They're supposed to consist of smaller sub-atomic particles, which apparently possess the property of "spin". So the atoms would also spin round.

 

Has the rotation of individual atoms been observed?

[SamBridge]

This business of "spin" seems quite puzzling. Everything seems to be spinning round. Eg, the Earth spins on its axis. The Moon spins round the Earth. Both of them spin round the Sun, which itself spins on its axis. And the Sun is in the Galaxy, which also spins.

All this looks rather unnatural. Shouldn't things just be quiet, and rest steady. Instead of constantly whirling around. Why would they keep moving, unless the movement is only an illusion.

 

Also, what about atoms. They're supposed to consist of smaller sub-atomic particles, which apparently possess the property of "spin". So the atoms would also spin round.

 

Has the rotation of individual atoms been observed?

That sounds like a lot of misinterpretation. Objects are definitely moving but how they move depends on the frame of reference. And with "spin" it seems that it is it actual physical spin, it wasn't the right name for that property.

[MigL]

I think you mean to say AJB, that a space which is not simply connected has holes in it and loops cannot be fully contracted. A very simple example ( 3D only ) would be a doughnut shape. Consider the inside curve of the doughnut, it has negative curvature, while the outside curve has positive curvature. Now if you are standing on the surface of the doughnut between these curvatures, you will notice that turning to one side by a given angle is not equivalent to turning to the other side by the same angle. There is no rotational symmetry, and that is a problem for conservation of angular momentum.

[ajb]

I think you mean to say AJB, that a space which is not simply connected has holes in it and loops cannot be fully contracted.

 

Yes, sorry if I was not clear. You can have path connected spaces that are not simply connected. As far as I know, just about all cosmological models will assume simply connected manifolds, but this must be an assumption.

[Dekan]

That sounds like a lot of misinterpretation. Objects are definitely moving but how they move depends on the frame of reference. And with "spin" it seems that it is it actual physical spin, it wasn't the right name for that property.

Thanks, could you explain a bit further please. The word "spin" seems to be pretty much a synonym for "rotate". At least when applied to big objects like planets.

 

For example, we say that the planet Earth "spins", or "rotates" on its axis in a period of about 23h 56m. And all the other planets in the Solar System also spin, or rotate. They do it at individual rates - Jupiter faster, Venus slower, than the Earth.

 

What I was wondering, is whether this also applies to atoms. Do atoms rotate?

 

And do they have individual rates of rotation. For example, does an atom of Hydrogen rotate faster or slower than an atom of Iron?

[SamBridge]

Thanks, could you explain a bit further please. The word "spin" seems to be pretty much a synonym for "rotate". At least when applied to big objects like planets.

 

For example, we say that the planet Earth "spins", or "rotates" on its axis in a period of about 23h 56m. And all the other planets in the Solar System also spin, or rotate. They do it at individual rates - Jupiter faster, Venus slower, than the Earth.

 

What I was wondering, is whether this also applies to atoms. Do atoms rotate?

 

And do they have individual rates of rotation. For example, does an atom of Hydrogen rotate faster or slower than an atom of Iron?

Well spin isn't a physical rotation, it's something to do with conserved angular momentum stored within the oscillation pattern of a particle, there's a topic here that others and I asked many questions of

http://www.scienceforums.net/topic/52810-spin/

Edited February 5, 2013 by SamBridge

[MigL]

I'm sure composite systems like molecules certainly, and atoms probably, have actual rotations ( observationally constrained by the HUP of course ).

Elementary particles, however, have only intrinsic QM spin, which is not a rotation as elementary particles are considered dimensionless points.

 

Just as you would consider e the quantum of charge and h-bar the quantum of energy, consider h-bar/2 the quantum of angular momentum.

[SamBridge]

I'm sure composite systems like molecules certainly, and atoms probably, have actual rotations ( observationally constrained by the HUP of course ).

Elementary particles, however, have only intrinsic QM spin, which is not a rotation as elementary particles are considered dimensionless points.

 

Just as you would consider e the quantum of charge and h-bar the quantum of energy, consider h-bar/2 the quantum of angular momentum.

Well particles can rotate in a physical sense especially when you have things like isomers, but that is not what causes it to have the diffraction properties they have, those are caused by "spin" which as you stated is not physical.