Explaining Curved Space-Time to a Friend

  • Thread starter Mark_W_Ingalls
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In summary, the conversation is about the idea that if the universe is spatially finite, an observer traveling in one direction at a speed greater than that of the expansion of the universe will eventually return to their starting point. However, this idea relies on certain assumptions and theories, such as a closed universe and the general theory of relativity. It is also important to consider the expanding nature of the universe and the possibility of a cosmological event horizon, which may make it impossible to circumnavigate the universe. Overall, there is still much unknown and debated about the shape and boundaries of the universe.
  • #36
I see. I naively assumed that t' will become negative for some large value of tau.
 
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  • #37
Mathematically, it can never be negative. Although it could be imaginary. Imaginary time is, however, hard to conceptualize.
 
  • #38
Mathematically, it can never be negative. Although it could be imaginary. Imaginary time is, however, hard to conceptualize.
I said that I assumed that t', (i.e,[itex]\frac{dt}{d \tau} [/itex] ) would eventually become negative even for a time-like geodesic. I never though that t itself would become negative, I thought that it would go to 0.
 
  • #39
I got myself confused a while ago on a very similar issue. One thing I want to add in addition to the the specific solution I quoted for a specific expansion function a(t) is that we know in general that t' could not pass through zero for a timelike geodesic. This follows from the requirement of a timelike geodesic that

a^2(t) dx^2 - dt^2 < 0

after dividing both sides by d lambda^2 we get

a^2(t) (x')^2 - (t')^2 < 0

t' can never be zero and make the interval timelike, the best we could do is to make it lightlike (and that would be a boring, pointlike solution).
 
  • #40
Like what infinitetime said, how can the universe be finite and flat? That would mean the universe has an edge. What's beyond the edge? That would also mean the universe has a center which violates relativity because there is now an absolute reference frame. The only way the conditions exists where there is no absolute reference frame is either
1. the universe is infinite or 2. the universe is closed.
 

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