I think I have heard that a beam of light (if this was feasible) which was emitted by an observer would ,eventually(well under strictly defined circumstances I imagine) return and strike the back of his head.

 

So that ,perhaps the observer might look at the back of his neck whilst staring straight ahead by the time the universe had come to an end

 

Ignoring the impossibility of this scenario (if I have not misremembered it) there seems to be some fundamental principle involved ,perhaps connected with the underlying geometry of the universe . Can anyone explain it to me?

 

Or at least explain some of it.

 

I have never heard of that and would very much love an explanation too.

If the universe has a slight positive curvature. Two parallel light beams will gradually converge. The light path will not be straight but slightly curved. A perfect flat universe, the light beams will stay parallel. In a negative curvature the light beams will diverge.

 

Now assuming expansion stopped, with the current miniscule deviation from a flat universe in the Planck dataset. If you fire an ideal laser beam. It would take roughly 880 Billion light years for the laser beam to return to its original point.

 

Of course we know its highly unlikely expansion will stop lol.

 

Key note, at one time it was once thought that if you have a positive universe, the universe would be bounded. This however isn't true due to the cosmological constant. The universe can be bounded or unbounded.

Edited November 4, 20169 yr by Mordred

If the universe was completely flat would the theoretical laser stiĺl return to its starting point?

 

If it did not, what would it do?Just get further and further away?

 

Follow the expansion of U?

It would never return in a perfectly flat scenario. Just continue a straight line path. A return path is only viable under positive curvature.

Edited November 4, 20169 yr by Mordred

What circumstances might have produced a universe with a negative curvature?

 

Would it affect the " looking at the back of your own head" scenario?

 

Would it rule out that ever happening even by chance?(the possibility would be "unstable")?

light beams only return to origin on positive curvature. Fairly cut and dry, your back of the head scenario is only viable on that scenario.

Edited November 4, 20169 yr by Mordred

SO if you shoot a blaster and stand there for the next trillion years(pretty much) you'll get hit in the back of the head? And does this mean the universe IS curved, as of now that we know, or its a theory?

SO if you shoot a blaster and stand there for the next trillion years(pretty much) you'll get hit in the back of the head? And does this mean the universe IS curved, as of now that we know, or its a theory?

Too close to flat, that it could be either negative or positive. Its that close that an exact determination is tricky. Though the datasets at present indicate a leanings towards the positive side.

 

The best indicator is CMB distortions which is tricky to exactly determine

Edited November 4, 20169 yr by Mordred

I think I have heard that a beam of light (if this was feasible) which was emitted by an observer would ,eventually(well under strictly defined circumstances I imagine) return and strike the back of his head.

 

So that ,perhaps the observer might look at the back of his neck whilst staring straight ahead by the time the universe had come to an end

 

Ignoring the impossibility of this scenario (if I have not misremembered it) there seems to be some fundamental principle involved ,perhaps connected with the underlying geometry of the universe . Can anyone explain it to me?

 

Or at least explain some of it.

 

If this would happen, we need to conclude that the universe is a sphere and there lies a finite limit to it.

If this would happen, we need to conclude that the universe is a sphere and there lies a finite limit to it.

incorrect this can happen in both the finite or infinite case.

If geometry is positive:

 

Would it be correct to say the universe is bounded and finite at any moment in time? That is, the surface of a (hyper)sphere is finite.

 

But due to expansion over time, it is unbounded and could be infinite in size? That is, the volume of the (hyper)sphere can inflate to any size.