A body traveling for infinte time

1. Mar 27, 2014

Varun Bhardwaj

Hi,
Consider a body is traveling with a velocity in a direction for infinite time.
If anything does not disturb that body.
It will come to its initial position for a time ?

2. Mar 27, 2014

sugeet

by direction of time you mean increasing right? Are you asking if the space-time is curved? yes it is

what do u mean by position, with respect to what?

If you condider an object on the surface of the earth, position defined by latitude and longitude, then yes after a certain interval of time, it should cross the same point!, I hope I helped

3. Mar 27, 2014

Varun Bhardwaj

A body is traveling
in a direction
with a velocity
for infinite time

4. Mar 27, 2014

Staff: Mentor

I think you are asking if an object will travel across the universe and end up back where it started. If the universe were not expanding so fast, yes, it would -- but the universe is expanding too fast for that to happen.

5. Mar 27, 2014

craigi

It depends on the geometry and we don't know the geometry of the whole universe. So the answer is an emphatic maybe.

6. Mar 27, 2014

Bobbywhy

Infinite time does not and cannot exist, so why bother trying making a thought experiment that begins with an impossibility?

7. Mar 27, 2014

A.T.

If the universe is closed, then it could come back. Even in finite time. In infinite time it could come back infinitely many times.

I don’t think the current rate of expansion is relevant, but rather whether the expansion accelerates. If the expansion is constant then you can circumnavigate a closed universe in finite time even if you move slower than the expansion rate.
http://en.wikipedia.org/wiki/Ant_on_a_rubber_rope

8. Mar 27, 2014

Staff: Mentor

As far as I know, there is no boundary for time - it may well proceed forever.

9. Mar 27, 2014

phinds

As far as I've ever heard that absolutely is NOT known to be true and it implies a finite universe, neither of which are known to be true. On what do you base your statement?

10. Mar 27, 2014

Staff: Mentor

Wait, which part are you asking about? Did you mean infinite when you said finite?

Anyway, I'll need to backtrack at least a little based on what AT posted -- I am unsure. But the expansion curve for the ant's rubber band isn't the same shape as for the universe (d/t vs d/t/d), so I'm not sure it is really analogous.

For the ant, since it is linear, with every step the expansion is less in front of him than for the previous step, but for the universe it is geometric, so the distance ahead of him is increasing faster with every step he takes. Another way to look at it is that for the ant he is moving backwards but accelerating forwards(wrt his goal), but with geometric expansion he is accelerating away from it....even without an accelerating expansion rate.

So I still think I'm right, but not completely sure.

Last edited: Mar 27, 2014
11. Mar 27, 2014

phinds

No, I meant finite when I said finite. If the universe is infinite then you'll never get back to your starting point so that's why I said that your description implies finite, which is not known to be true.

I agree that the ant will move faster and faster and farther and farther due to expansion but there will always be more distance to travel if the universe is infinite. There will always be expanding space in front of him.

12. Mar 27, 2014

dauto

Neither of these statements seem correct to me. An event with zero probability will never happen even after an infinite amount of time and right now there are places in the universe that are already unreachable even by a beam of light. They are too far to be reached. Look up "cosmic horizon".

13. Mar 27, 2014

A.T.

I think what you call "geometric expansion" implies an "accelerating expansion rate":
http://en.wikipedia.org/wiki/Accelerating_universe

14. Mar 27, 2014

A.T.

Because the expansion is accelerated, not because those places currently recede at more than c from us.

Last edited: Mar 27, 2014
15. Mar 27, 2014

dauto

No, they are in fact receding faster than c. (or they will be receding faster than c before the light beam ever reaches them). At cosmological distances space doesn't behave as a Minkosky manifold.

16. Mar 27, 2014

dauto

No, even at a constant rate of expansion objects seem to accelerate and eventually superluminal speeds.

17. Mar 27, 2014

A.T.

Yes I know. If a distant galaxy is currently receding at 2c from us, and that receding rate stays constant at 2c, then our light ray send now can reach that galaxy in finite time.

This seems to be a semantic issue (see post #13). By "constant rate of expansion" I mean that a certain galaxy recedes at a constant rate, which doesn't change over time, so it doesn't seem to accelerate.

Last edited: Mar 27, 2014
18. Mar 27, 2014

dauto

No, it won't ever reach it. How could it? the galaxy is moving away at superluminal speeds.
Yes it is semantic. Note that we're talking about constant rate of expansion (which is measure in km/s/megaparsec. We are not talking about constant speed (measured in m/s).

Last edited: Mar 27, 2014
19. Mar 27, 2014

phinds

Yes, because such objects are well inside our light cone. However, all objects that are currently receding from us at, say, 5c and more are outside out light cone and will remain so even if the expansion were to stop accelerating (and they were to continue to recede at the current rate). They can move back into our light cone only in the big crunch scenario and current science says that is no reason for that to happen.

The observable universe is going to get a bit bigger than it is now, in terms of what part of the rest of the universe is encompassed by our light cone, but that is only by a modest amount. It doesn't extend forever.

20. Mar 27, 2014

A.T.

No, the galaxy is not moving at superluminal speeds. It is receding due to metric expansion, which is different than relative motion. If the superluminal receding speed of the galaxy is constant, then the light will reach it, just like the ant reaches the receding end of the rope:

http://en.wikipedia.org/wiki/Ant_on_a_rubber_rope

Last edited: Mar 27, 2014
21. Mar 27, 2014

craigi

Not quite.

Take the the real numbers from 0 to 1. Now choose one at random with infinite precision. What's the probability that you got exactly 0.5? Zero. It's a probability zero event. That's the correct mathematical terminology. Not the terminology I would've chosen, but that's irrelevant. What's the probability that you got any other exact number? Zero. But you did get one of them and if you got it once, you could get it again. If you choose infinitely many times, you're certain to get the same number again and you'll get it infinitely many times.

So the notion that a zero probability event never happens in an infinite number of trials couldn't be further from the truth!

Last edited: Mar 27, 2014
22. Mar 27, 2014

Staff: Mentor

No, geometric is a constant multiple instead of a constant addition. The length of the ant's rope (before considering his motion) is:
1+1=2
2+1=3
3+1=4

But our universe, if not accelerating is:
1+1*1=2
2+2*1=4
4+4*1=8

Accelerating (linear) changes the multiplier:
1+1*1=2
2+2*2=6
6+6*3=24

23. Mar 27, 2014

Staff: Mentor

OK....I also said "if". I was suggesting a scenario under which you could get back where you started, but I wasn't saying that our universe looks that way; I was saying it doesn't. It sounds like a disagreement, but I'm not seeing a point we disagree on.

I think it is pretty obvious that in an infinite universe you can't get back where you started. But the conditions of an expanding but finite universe that may allow it are less clear to me.

24. Mar 27, 2014

A.T.

Yes, I know what you meant. The use seems a bit inconsistent. The Wiki article for example seems to identify "accelerating universe" with "velocity at which a distant galaxy is receding from us should be continuously increasing with time", which would apply to your "our universe, if not accelerating".

25. Mar 27, 2014

dauto

That's wrong. Specially the part where you say
The chance of getting it again is zero