Exploring U: Can We Return to Earth Travelling at Light Speed?

[narrator]

If we headed directly into space traveling at many times the speed of light (ignoring for a moment that you can't travel that fast), maintaining exactly the same course for the whole trip, would or could we eventually find ourselves heading back to Earth?

I got a reply elsewhere, suggesting I start a fresh thread. Here's what was said:

This would depend entirely on the topology of U. If Euclidean and infinite then not as you would just travel indefintely.

If U was an n-sphere then yes.

I am sure someone can elaborate further...

 

[Dmitry67]

Interpreting 'many times the speed of light' as spacelike trajectory,
then asnwer depends on the topology of spacetime.

In flat spacetime - NO
YES - in 'closed' Universe.

 

[firavia]

why it is a yes in a closed universe ? , wouldn't you reach the boundary of space ??

 

[Dmitry67]

there is no such thing as "boundary of space" in any GR solutions.
closed is like a sphere - when you go into one direction, you make a full cirlce and return from an opposite one.

 

[Vanadium 50]

"If I violate the laws of physics, what would be the result?" is not a question with a well-defined answer.

 

[Cosmo Novice]

"If I violate the laws of physics, what would be the result?" is not a question with a well-defined answer.

Although FTL in a direct sense breaks the laws of GR, there are a number of scientific stipulations and theories that deal with superluminal travel while attempting to stay within the laws of physics (albeit dealing in unknown sciences) an example being the Alcubierre drive.

I think the original author is more concerned with this as a thought experiment regarding topology and characteristics of open/closed topological models and physical attributes - I do not expect the OP expects a well-defined answer.

 

[Cosmo Novice]

there is no such thing as "boundary of space" in any GR solutions.
closed is like a sphere - when you go into one direction, you make a full cirlce and return from an opposite one.

An n-sphere is only one cosmological model for a closed universe, the Torus is also one - I think that mathematically there are others too, if anyone can elaborate.

 

[Ryan_m_b]

You can take away the FTL nature of this thought experiment and I think it still works. In a closed universe after a certain amount of time traveling you would come back to your start point. Heres some useful wiki entries http://en.wikipedia.org/wiki/Shape_of_the_Universe#Open_or_closed

 

[Nabeshin]

In flat spacetime - NO.

Ah, same mistake I just made in a similar thread! You could have a torus, for example.

 

[BillSaltLake]

I think the question can be restated as what would we see along a "straight" line if we could observe from comoving time 13.7 Gyr at each point along the line.
It's possible that the statistics of the Universe would be about the same no matter how far you went. Maybe you would encounter the Milky Way again a very long way out, but given recent acceleration, that's unlikely. Also, maybe there's some kind of boundary or a change way out, instead of sameness.

 

[Chalnoth]

"If I violate the laws of physics, what would be the result?" is not a question with a well-defined answer.

Well, in this case, as long as you ignore energy requirements and the lack of existence of exotic matter, it is possible to do this with a Warp drive while remaining consistent with General Relativity.

That said, whether or not you come back to your starting point depends upon the overall topology of our universe, which is distinct from the curvature. Curvature is a local property: it describes how curved (or not) our own observable region is. Topology is a global property, describing the overall shape of the entire universe far beyond our observable horizon. For obvious reasons, we don't know much about the topology of our universe. Our local observable region could easily have positive or negative curvature, and it would say basically nothing about the overall topology, because what lies beyond our cosmological horizon is so much larger than the stuff inside it we can observe: that curvature could be rather different outside our horizon, and we'd have no way to know.

 

[narrator]

You can take away the FTL nature of this thought experiment and I think it still works. In a closed universe after a certain amount of time traveling you would come back to your start point. Heres some useful wiki entries http://en.wikipedia.org/wiki/Shape_of_the_Universe#Open_or_closed

I wondered about this when considering the question. As in, if you travel at <C in the expanding universe, even though the path could lead back towards your point of origin, expansion may be growing faster than your progress along that line, meaning you would never get there - you may have to travel many times FTL to not be losing ground (so to speak). But yes, the spherical (or other) nature is what I was getting at rather than the need to break the speed limit.

 

[narrator]

... what lies beyond our cosmological horizon is so much larger than the stuff inside it we can observe: that curvature could be rather different outside our horizon, and we'd have no way to know.

Good point. Could it be that rather than spherical or torus shaped, it could have so many curves it becomes a kind of infinite honeycomb?

 

[Chalnoth]

Good point. Could it be that rather than spherical or torus shaped, it could have so many curves it becomes a kind of infinite honeycomb?

Sure. At this point, we just don't know. Though I think naively we would tend to expect that it's probably a relatively simple shape. My personal expectation is that it would most likely be some sort of amorphous bubble. Sort of like these air bubbles in water:
http://www.istockphoto.com/stock-photo-12041902-blue-air-bubbles-floating-under-water-surface.php

Now if our universe starts out like one of these bubbles, it is conceivable that the laws of physics will naturally push the amorphous shape into a sphere, but I strongly suspect that isn't possible, so that it will always remain just as amorphous as it began. In this picture, our observable universe would be a microscopic dot on some part of the surface of the bubble, so tiny that we can't get any hint as to the overall curvature.

Of course, this is just a general expectation that it will be something simple and irregular. It could be quite different, since we don't yet know the physics which produce new regions of the universe, so we can't really say what the overall shape is likely (or not likely) to be. It could be something vastly more complicated.