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Author Topic: Is there an infinity problem here?  (Read 6078 times)

Offline jeffreyH

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Is there an infinity problem here?
« on: 31/01/2015 17:15:12 »
If we choose a finite distance from a point A to a spatially different point B that we wish to move an object and then put the constraint on the system that it has to take an infinite amount of time to move from point A to point B at a constant velocity then we can never find a solution that will work. We could argue that the interval of time could be infinitely short. However we do not want to violate the laws of physics in order to solve the problem. In this situation it looks like the object can never move from point A at all because any initial velocity would be finite and so could not take an infinite amount of time.


 

Online chiralSPO

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Re: Is there an infinity problem here?
« Reply #1 on: 31/01/2015 17:56:14 »
Yes, the problem was defined in such a way that there was an infinity problem. If I read your question properly, I translate it as:

let d be a finite distance and v be a finite, non-zero velocity,

d/v = ∞

solve for v.

The is no non-zero value that v can have to satisfy the equation. Infinity should usually be dealt with as a limit anyway...

Now there are a few tricky ways out of your proposed problem:

For instance, you can leave point A at any finite velocity headed away from point B, and never get there.

 

Offline jeffreyH

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Re: Is there an infinity problem here?
« Reply #2 on: 31/01/2015 18:39:50 »
Yes, the problem was defined in such a way that there was an infinity problem. If I read your question properly, I translate it as:

let d be a finite distance and v be a finite, non-zero velocity,

d/v = ∞

solve for v.

The is no non-zero value that v can have to satisfy the equation. Infinity should usually be dealt with as a limit anyway...

Now there are a few tricky ways out of your proposed problem:

For instance, you can leave point A at any finite velocity headed away from point B, and never get there.

A good use of lateral thinking. Well consider this then. We say that infinity is unreachable. You can never arrive at infinity. Consider your response "For instance, you can leave point A at any finite velocity headed away from point B, and never get there." is this the correct view of infinity. That you can't even head in its direction let alone get there.
 

Offline alancalverd

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Re: Is there an infinity problem here?
« Reply #3 on: 31/01/2015 18:45:00 »
No.

You have already assumed a definition of infinity by "put the constraint on the system that it has to take an infinite amount of time...." and then abandoned it by making AB finite and d/dt (AB) finite. In other words, your question is self-inconsistent.
 

Online chiralSPO

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Re: Is there an infinity problem here?
« Reply #4 on: 31/01/2015 19:09:26 »
Consider your response "For instance, you can leave point A at any finite velocity headed away from point B, and never get there." is this the correct view of infinity. That you can't even head in its direction let alone get there.

No, you can head in the direction of infinity, but still will never get there (even on the most direct path). That's what's so special about it.
 

Offline jeffreyH

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Re: Is there an infinity problem here?
« Reply #5 on: 31/01/2015 19:42:44 »
OK lets restate the initial problem without the set velocity but make the distance between the points 1 Planck length with the time for the journey still infinite. How do we proceed?
« Last Edit: 31/01/2015 19:45:57 by jeffreyH »
 

Offline jeffreyH

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Re: Is there an infinity problem here?
« Reply #6 on: 31/01/2015 20:00:53 »
BTW You forgot to mention zero velocity which is itself a constant velocity but makes the equation undefined.
 

Online chiralSPO

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Re: Is there an infinity problem here?
« Reply #7 on: 31/01/2015 20:03:49 »
Ah. I misread your question, and thought you had already ruled out the zero velocity solution.
 

Online chiralSPO

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Re: Is there an infinity problem here?
« Reply #8 on: 31/01/2015 20:04:53 »
OK lets restate the initial problem without the set velocity but make the distance between the points 1 Planck length with the time for the journey still infinite. How do we proceed?

Velocity is meaningless on this scale.
 

Offline jeffreyH

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Re: Is there an infinity problem here?
« Reply #9 on: 31/01/2015 20:10:13 »
No.

You have already assumed a definition of infinity by "put the constraint on the system that it has to take an infinite amount of time...." and then abandoned it by making AB finite and d/dt (AB) finite. In other words, your question is self-inconsistent.

Yes I know it is.
 

Offline jeffreyH

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Re: Is there an infinity problem here?
« Reply #10 on: 31/01/2015 20:21:59 »
The problem here is two fold. A Zeno's paradox type of situation and an object that approaches a black hole and is observed from a remote frame.
 

Offline jeffreyH

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Re: Is there an infinity problem here?
« Reply #11 on: 31/01/2015 20:34:41 »
We can restate the equation e63bfa073d7eafc1fc5ab2e448b99520.gif as 6134d47f33cba4cc4665c991f752968d.gif where the distance has an infinite number of divisions. This equates to Zeno's paradox and mirrors the situation that a remote observer sees when an object approaches an event horizon.
« Last Edit: 31/01/2015 20:37:48 by jeffreyH »
 

Offline evan_au

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Re: Is there an infinity problem here?
« Reply #12 on: 01/02/2015 11:10:05 »
There is another solution that works if the distance between A & B is of a cosmological scale.
If you set off from A at a finite velocity >0, the (accelerating) expansion of the universe will make it take an infinite time to reach B (ie it will never reach B in the lifetime of the universe).

This solution does not involve any problems with infinities.
 

Offline jeffreyH

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Re: Is there an infinity problem here?
« Reply #13 on: 01/02/2015 17:00:37 »
There is another solution that works if the distance between A & B is of a cosmological scale.
If you set off from A at a finite velocity >0, the (accelerating) expansion of the universe will make it take an infinite time to reach B (ie it will never reach B in the lifetime of the universe).

This solution does not involve any problems with infinities.

Wow I didn't even think of that one.
 

Offline Bill S

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Re: Is there an infinity problem here?
« Reply #14 on: 02/02/2015 20:19:21 »
Quote from: Alan
In other words, your question is self-inconsistent.

As is any question that attempts to mix infinity with finite quantities; unless it is specified that infinity is being used strictly as a mathematical concept. 

Infinity + - / or x by a finite quantity = infinity.

Something that starts finite, eg speed, can never become infinite.

Quote from: evan_au
If you set off from A at a finite velocity >0, the (accelerating) expansion of the universe will make it take an infinite time to reach B (ie it will never reach B in the lifetime of the universe).

Obviously this is correct in this particular scenario, but it makes the basic assumption that the Universe is finite.  If the Universe is infinite, the self-inconsistency returns. 

Essentially, there is no problem with infinity, only in the way it is used.
 

Offline jccc

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Re: Is there an infinity problem here?
« Reply #15 on: 03/02/2015 00:25:21 »
Infinity + - / or x by a finite quantity = infinity.
Something that starts finite, eg speed, can never become infinite.

If that stands true, we should be able to predict lot of things.

Still thinking, interesting!
 

Offline phyti39

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Re: Is there an infinity problem here?
« Reply #16 on: 03/02/2015 21:11:21 »
If we choose a finite distance from a point A to a spatially different point B that we wish to move an object and then put the constraint on the system that it has to take an infinite amount of time to move from point A to point B at a constant velocity then we can never find a solution that will work. We could argue that the interval of time could be infinitely short. However we do not want to violate the laws of physics in order to solve the problem. In this situation it looks like the object can never move from point A at all because any initial velocity would be finite and so could not take an infinite amount of time.
You state the task as "moving an object from A to B".
Then state the required time is infinite (without bound), which is equivalent to "NOT moving an object from A to B".
You contradict yourself.
 

Offline jeffreyH

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Re: Is there an infinity problem here?
« Reply #17 on: 03/02/2015 21:22:08 »
Well I was trying to make a point very badly which is my forte it seems.
 

Offline Bill S

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Re: Is there an infinity problem here?
« Reply #18 on: 03/02/2015 21:54:04 »
Quote from: Jeff
Well I was trying to make a point very badly which is my forte it seems.

A hallmark of the free thinker, Jeff.  At least, that’s what I keep telling myself. :)
 

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Re: Is there an infinity problem here?
« Reply #19 on: 05/02/2015 11:54:35 »
Why go for the infinitely small singularity when we may go for the infinitely large universe? Could it be that we do the same mistake we have done before. We adapt the heliocentric point of view. When we look out in space we define physics in universe relatively our own limited world. The coordinates we use as common ground are those of our own backyard. It gets very complex with all systems we define in universe with our own backyard in the middle. Mathematics fail and we end up with a singularity. Perhaps this initial singularity somehow makes us infinitely big anyway?
 

Offline Bill S

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Re: Is there an infinity problem here?
« Reply #20 on: 05/02/2015 17:30:45 »
Quote
Why go for the infinitely small singularity when we may go for the infinitely large universe? Could it be that we do the same mistake we have done before. We adapt the heliocentric point of view. When we look out in space we define physics in universe relatively our own limited world. The coordinates we use as common ground are those of our own backyard. It gets very complex with all systems we define in universe with our own backyard in the middle. Mathematics fail and we end up with a singularity. Perhaps this initial singularity somehow makes us infinitely big anyway?

You highlight an ever present problem in our thinking about infinity.  We have no language (including mathematics) that completely encompasses infinity, so we are obliged to try to work with the uncomfortable “fit” within our vocabulary. 

We are obliged to talk of “infinitely small” and “infinitely large”, in order to convey our ideas; notwithstanding the fact that large and small are quantitative expressions, but infinity is not a quantity, any more than it is a number.
 

Offline phyti39

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Re: Is there an infinity problem here?
« Reply #21 on: 05/02/2015 20:38:06 »
Well I was trying to make a point very badly which is my forte it seems.
But, you are thinking, and that's a good thing!
 

Offline jeffreyH

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Re: Is there an infinity problem here?
« Reply #22 on: 05/02/2015 22:25:35 »
I think therefore I think I am. I think.
 

Offline jccc

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Re: Is there an infinity problem here?
« Reply #23 on: 05/02/2015 22:35:03 »
Bill killed my dream to live forever.

I lived day by day all my life. Only 24 hours a day.
 

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Re: Is there an infinity problem here?
« Reply #23 on: 05/02/2015 22:35:03 »

 

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