A body traveling for infinte time

[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 ?

 

[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

 

[Varun Bhardwaj]

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

 

[russ_watters]

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.

 

[craigi]

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 ?

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

 

[Bobbywhy]

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

 

[A.T.]

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

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

but the universe is expanding too fast for that to happen.

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

 

[russ_watters]

Infinite time does not and cannot exist...

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

 

[phinds]

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.

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?

 

[russ_watters]

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?

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.

 

[phinds]

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.

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.

 

[dauto]

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

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".

 

[A.T.]

but with geometric expansion he is accelerating away from it...even without an accelerating expansion rate.

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

The accelerating universe is the observation that the universe appears to be expanding at an increasing rate. In formal terms, this means that the cosmic scale factor a(t) has a positive second derivative,[1] so that the velocity at which a distant galaxy is receding from us should be continuously increasing with time

 

[A.T.]

right now there are places in the universe that are already unreachable even by a beam of light

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

 

[dauto]

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

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.

 

[dauto]

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

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

 

[A.T.]

No, they are in fact receding faster than c.

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.

even at a constant rate of expansion objects seem to accelerate

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.

 

[dauto]

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.

No, it won't ever reach it. How could it? the galaxy is moving away at superluminal speeds.

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.

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).

 

[phinds]

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.
.

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.

 

[A.T.]

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.

No, it won't ever reach it. How could it? the galaxy is moving away at superluminal speeds.

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

 

[craigi]

An event with zero probability will never happen even after an infinite amount of time.

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!

 

[russ_watters]

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

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

 

[russ_watters]

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.

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.

 

[A.T.]

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

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".

 

[dauto]

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!

That's wrong. Specially the part where you say

and if you got it once, you could get it again

The chance of getting it again is zero

 

[MikeGomez]

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!

Sounds like fuzzy logic to me.

-Choose a random number with infinite precision.
-Can’t be done with infinite precision so there is zero probability.
-But you do get one of them, even though there was zero probability.
-If you got the zero probability event once, you can get it an infinite number of times.
-Therefore zero probability events occur infinitely many times.

Do I have it right?

 

[dauto]

Sounds like fuzzy logic to me.

-Choose a random number with infinite precision.
-Can’t be done with infinite precision so there is zero probability.
-But you do get one of them, even though there was zero probability.
-If you got the zero probability event once, you can get it an infinite number of times.
-Therefore zero probability events occur infinitely many times.

Do I have it right?

Yes, craigi was quite careless in this "calculation". Problems involving infinite are subtle in nature and must be handled with care. In this case he got an infinite answer where he should've gotten zero.

 

[jbunniii]

If your event (choosing a random number) has zero probability, then

$$\begin{align}
P(\text{choosing the same number more than once}) &=
1 - P(\text{choosing it exactly once}) - P(\text{never choosing it}) \\
&=
1 - 0 - 1 \\
&= 0
\end{align}$$

 

[AlephZero]

Just remember than when dealing with infinite sets, events with probability measure zero are not "impossible". They can even happen twice.

And if you don't know what "measure" means in this context, your logic is likely to be wrong, with probability measure 1

 

[Varun Bhardwaj]

I think that infinite of any kind does not exist in presence of time.
because if anything is changing with time than it will never reach to infinite.
it can only reach infinite if it change in zero time.
because now universe is running with time , Universe is not infinite , because it is accelerating.
But the space (in which all 3 Dimensional body with mass exist ) has infinite volume because its mass is zero.
Is that true ?
if the body travel infinite distance than it needs infinite time , but if the universe is not infinite than it will not take infinite time to come back to its initial position?

 

[Varun Bhardwaj]

but the universe is expanding too fast for that to happen.

Mass can neither be created nor be destroyed.
Energy can neither be created nor be destroyed.
They are conserved.
You are wrong. because ( universe is expanding = universe is shrinking )

 

[craigi]

I think that infinite of any kind does not exist in presence of time.
because if anything is changing with time than it will never reach to infinite.
it can only reach infinite if it change in zero time.
because now universe is running with time , Universe is not infinite , because it is accelerating.
But the space (in which all 3 Dimensional body with mass exist ) has infinite volume because its mass is zero.
Is that true ?
if the body travel infinite distance than it needs infinite time , but if the universe is not infinite than it will not take infinite time to come back to its initial position?

Nothing can reach infinity.

One model of the universe is infinite with expansion. You can visualise it as new space emerging in existing space.

The relationship between mass and space is a complex one, we know that there is a relationship but we don't have a full picture of it yet. It's a very active area of research. The old model is that mass exists in space and deforms it, we don't know if this is.going to hold up.

For an object to return to its initial position we would require that the geometry of the universe to be finite and closed, like a sphere but in higher dimensions. It's very difficult, or even impossible to visualise.

We would also require a limit on the expansion (or contraction) of the whole universe, which is distinct from the observable universe. If new space were to be created at a faster rate than you can traverse it then you're certainly not going back to your starting point.

The answer is we just don't know. There are too many unknowns but it is plausible.

 

[phinds]

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.

OK, I guess this is another case of my response getting ahead of my brain (apparently not having understood the post to which I am responding). I think I may be getting old. Yeah, that's it. Getting old. That's my story and I'm sticking with it

 

[craigi]

Mass can neither be created nor be destroyed.
Energy can neither be created nor be destroyed.
They are conserved.
You are wrong. because ( universe is expanding = universe is shrinking )

The model actually introduces expansion driven by the conservation of energy, which is equivalent to mass.

Sounds like fuzzy logic to me.

-Choose a random number with infinite precision.
-Can’t be done with infinite precision so there is zero probability.
-But you do get one of them, even though there was zero probability.
-If you got the zero probability event once, you can get it an infinite number of times.
-Therefore zero probability events occur infinitely many times.

Do I have it right?

You're right that it can't be done. Quantum physics prohibits it. It's completely out of the realms of our experience, which is fortunate because the predictions in this thread vary as much as they possibly could. We need to treat it as a mathematical problem. The only way that it has any physical relevance is if at least one of the dimensions of the universe is infinite, which is exactly what we were talking about. There is an analogue between the cases of bounded with infinite precision and unbounded with finite precision. It just seems, to me at least, a little easier to talk of zero probability events in the context of the former.

 

[dauto]

Just remember than when dealing with infinite sets, events with probability measure zero are not "impossible". They can even happen twice.

And if you don't know what "measure" means in this context, your logic is likely to be wrong, with probability measure 1

No doubt. If craigi had talked about choosing a rational number instead of choosing a real number I wouldn't have been so quick in declaring the probability to be zero. The real numbers are much more dense than the rational numbers.