View Full Version : How does the curvature of space affect travel?

2006-Apr-02, 07:39 AM
If the universe has no boundaries, then there are eight possibilities, or seven, if the possibility that would be the eighth isn't possible. I'm going to argue that all eight are possible, however, argue against it if you'd like.

The possibilities are a composition of three possibilities: The universe is/isn't finite, the universe is/isn't flat, and the universe is/isn't metaisotropic.

By finite I mean simply that, excluding black holes, and assuming that the universe is not fractal, there exists a finite amount of space.
By flat, I mean as flat as possible given the other two conditions, even if this means I can be only locally flat and not globally flat, or vice versa.
By isotropic I mean that for each point in that universe, there exists a velocity for which universe, by that frame of reference, is radially symmetric.

These definitions really don't work that well, but please do the best you can with them, and don't just assume that they don't work, even if your judgment is backed up with evidence. Just assume that I didn't word them correctly. Don't assume that I don't understand what I'm saying either.

Imagine, for each universe, I go a certain distance, and with minimum curvature. I return to where I started. Aside from acceleration with respect to local curvature, how am I going to be affected by global curvature?

Imagine a non-flat, finite universe, whether it is metaisotropic doesn't matter but sometimes it's easier to get the full impact of this question if it's metaisotropic. Two twins go on journies. One travels from their home planet, and goes around in a figure eight or an infinity. At the same time, the other travels from their home planet and goes around the entire universe. Then they both go home. Their departure and arrival time is the same. Now this is a relatively small universe and the twins are practically immortal. Let's assume they both accelerate the same amount. Which one ends up older and which one ends up younger?

2006-Apr-09, 06:54 PM
You have to know the twin's speed relative to one another because each twin represents one frame of reference. I don't think D makes a difference here, it's only c relative to two or more frames of reference. You have three. One for each twin and that of earth. If you're traveling faster than something relative to you then you experience longer units of time relative to the slower moving object. This means that, while 10 years feels the same as 10 years for someone traveling slower than you, they will have experienced a greater period of time for each unit of time you experience.

Let's make some assumptions: Not accounting for acceleration one sister travels at .5c and the other at .99c relative to the earth for 10 years and then come back. Their flight patterns don't matter so long as they are traveling at a constant velocity. I believe there is an actual equation out there that can estimate more accurately the actual difference in time shift but I'll add some figures just to illustrate what happens, not actual figures though.

So both sisters leave at the same time and don't come back for 10 years. The one traveling at .5c returns 10 years older but for the people on earth, they experienced 20 years in her abscence. The first sister waits for the second sister who returns 20 years after the first sisters arrival. The second sister has still only experienced 10 years but for her sister it's been 30 and for the people of earth, it has been 50. The figures are wrong but actual figures would make this same general pattern.

2006-Apr-09, 07:35 PM
There is something wrong about this thinking. This curvature idea has need of some evolution. Who said space is curved and limited. I would not be alone in my side ways look at this idea. Or is it me that is in the wilderness.?

2006-Apr-09, 07:39 PM
There is something wrong about this thinking. This curvature idea has need of some evolution. Who said space is curved and limited. I would not be alone in my side ways look at this idea. Or is it me that is in the wilderness.?Not space, spacetime. There are mathematical ways of computing the curvature of paths. The path of a bullet is less curved than the path of a batted baseball, in space, but when you calculate the curvature in spacetime the curvature turns out to be the same.