A physics question from a conversation I had

Originally posted by kbaumen
This brings my mind to a question. How would it be with sound in absolute zero temperature (-273 oC or so). As far as I know absolute zero is when the particles have stopped their movement completely. Or would it not be possible to have sound in AZ because the sound waves would oscillate particles so that the temperature increases a little?

Absolute 0 temperatures are impossible to achieve because of quantum dynamics. As the the temperature lowers quantum dynamical effects have to be taken into account and because of the uncertaintity principle you can't have 0 temperature. The thing is if the velocity was zero than you could pinpoint exactly were the particles were. But if you could do that than the uncertaintity on their momentum would have to be infinite. Which is to say that would have to be moving a lot. Since you started the reasoning assuming that weren't moving at all and non of the other steps are wrong than the only problem must be that your initial premise is wrong.

Originally posted by adam warlock
Absolute 0 temperatures are impossible to achieve because of quantum dynamics. As the the temperature lowers quantum dynamical effects have to be taken into account and because of the uncertaintity principle you can't have 0 temperature. The thing is if the velocity was zero than you could pinpoint exactly were the particles were. But if you could do th ...[text shortened]... of the other steps are wrong than the only problem must be that your initial premise is wrong.

I don't get it. If velocity is zero for a discrete amount of time, then momentum (during that period) should be zero. By the Uncertainty Principle then position should be unknown.

No?

Originally posted by Palynka
I don't get it. If velocity is zero for a discrete amount of time, then momentum (during that period) should be zero. By the Uncertainty Principle then position should be unknown.

No?

If the velocity is 0 the particle is localized, thus the position is known with certain.
Edit: This reasoning seems almost like a tautology. Are you familiar with the proof by contradiction argument?

Originally posted by adam warlock
If the velocity is 0 the particle is localized, thus the position is known with certain.
Edit: This reasoning seems almost like a tautology. Are you familiar with the proof by contradiction argument?

Why can't the velocity be zero and position uncertain?

Originally posted by Palynka
Why can't the velocity be zero and position uncertain?

If the position is 0 the particles doesn't move. So can its position be uncertain?

Originally posted by adam warlock
If the position is 0 the particles doesn't move. So can its position be uncertain?

Did you mean if momentum was 0?

Why not? I'm a layman in physics, but wouldn't the attempt to localize it generate momentum?

Originally posted by Palynka
Did you mean if momentum was 0?

Why not? I'm a layman in physics, but wouldn't the attempt to localize it generate momentum?

The theory of measurement in quantum mechanics is a pretty tricky field and to be honest with you I'm not very comfortable talking about it.
But the first thing I'll tell you is that our conversation is a little bit wrong. First of all you know that p=mv. But in quantum mechanics v has no sense whatsoever! The thing is thatv=dx/dt but on quantum mechanics you can't specify simultaneously both dx an dt so that division is out of bounds. In quantum mechanics we can only talk about things we mesure, again that tricky stuff, and momentum, or rather the change in momentum, can be mesured. So let's just talk about p. The thing is if you say p=0 than we have to say that the particles don't move at all. So Dx (the uncertaintity in position mesurement is 0). But we know that Dx.Dp=h (approximate relationship here...) so if Dx=0 than Dp must be infinite. But the only for Dp to be infinite is that the particles have some very crazy movement. And that contradicts our initial assumption.So it means the initial assumption is wrong.
I can't really explain this much better than this. 😞

edit: I meant momentum was 0. i'm a little bit dyslexic. It runs in the family.

And on measurement in quantum mechanics:
http://www.mtnmath.com/faq/meas-qm.html

Originally posted by adam warlock
The theory of measurement in quantum mechanics is a pretty tricky field and to be honest with you I'm not very comfortable talking about it.
But the first thing I'll tell you is that our conversation is a little bit wrong. First of all you know that p=mv. But in quantum mechanics v has no sense whatsoever! The thing is thatv=dx/dt but on quantum mechan is. 😞

edit: I meant momentum was 0. i'm a little bit dyslexic. It runs in the family.

I appreciate you taking the time to explain this.

I still have trouble understanding why you say that if Dp is infinite is for the particles to have some very crazy movement. I read Dp being infinite as complete ignorance about the particle's position. If you will, that would imply that the particle could be anywhere in the universe. Which would logically mean random teleportation but not necessarily momentum. Am I making any sense at all?

Edit - Or, that the particle asymptotically slows down to zero and therefore will take an infinite time to reach zero, even if devoid of further stimuli. This could (depending on the functional form) mean that the particle would travel to anywhere in the universe after the last measurement, leading to a diverging increase in standard deviation of position. Even less sense?

Originally posted by Palynka
I appreciate you taking the time to explain this.

I still have trouble understanding why you say that if Dp is infinite is for the particles to have some very crazy movement. I read Dp being infinite as complete ignorance about the particle's position. If you will, that would imply that the particle could be anywhere in the universe. Which would logically mean random teleportation but not necessarily momentum. Am I making any sense at all?

I appreciate you taking the time to explain this.
No problem. 🙂

I still have trouble understanding why you say that if Dp is infinite is for the particles to have some very crazy movement. I read Dp being infinite as complete ignorance about the particle's position. If you will, that would imply that the particle could be anywhere in the universe.
If Dp, the uncertaintity on momentum, is infinite then the momentum has to be changing wildly at every moment. For instance if Dp=0 P is a constante; if DP=10 P changes somewhat; if Dp=1000 p is changing a lot; Dp=1000000 p is changing like crazy; but if Dp=infinite!!!, in what way would describe the particle's motion?

Which would logically mean random teleportation but not necessarily momentum.
I'm not sure I fully understand this.

I think the reason of this mess up is the word uncertainty. In QM it doesn't mean clumsyness on the part of experimantalist. It means a real and inerent fuzyness of what's being measured. I think a safe to visualize it (I don't really like visualisation on QM more often than not they are misleading) is imagining a kind of variation of the value of what's being measured. So Dp=infinite means that p is changing. And a change of momentum is equivalent to a change in motion. So this contradicts p=0 that means no motion at all.

Edit: Just seen your edit. But a change in position contradicts p=0 you see? p=0 means no movement and a change in position is movement.

Originally posted by adam warlock
[b]I appreciate you taking the time to explain this.
No problem. 🙂

I still have trouble understanding why you say that if Dp is infinite is for the particles to have some very crazy movement. I read Dp being infinite as complete ignorance about the particle's position. If you will, that would imply that the particle could be anywhere in the tion contradicts p=0 you see? p=0 means no movement and a change in position is movement.[/b]

Mmm...

I think Dp here isn't the change (the traditional sense of differentiation) in p, but the standard deviation of its probability distribution. An infinite Dp, doesn't imply an infinite rate of change in p, but total uncertainty about where the heck p is (infinite standard deviation for its probability distribution).

Originally posted by Palynka
Mmm...

I think Dp here isn't the change (the traditional sense of differentiation) in p, but the standard deviation of its probability distribution. An infinite Dp, doesn't imply an infinite rate of change in p, but total uncertainty about where the heck p is (infinite standard deviation for its probability distribution).

It isn't. I said it was a kind of change to see if I could explain things better. Obviously I couldn't! 😞
I didn't want to dweell on interpretation of QM but what does a probability distrinution means for a single particle? You see what I mean.
Things like standard deviation, means, and probability definition are very well understood if we have a collection of particles, just like in the standard model of a gas in a container. But if you have only one particle what does all of that means?

Originally posted by adam warlock
It isn't. I said it was a kind of change to see if I could explain things better. Obviously I couldn't! 😞
I didn't want to dweell on interpretation of QM but what does a probability distrinution means for a single particle? You see what I mean.
Things like standard deviation, means, and probability definition are very well understood if we have a co ...[text shortened]... model of a gas in a container. But if you have only one particle what does all of that means?

I see what you mean. Sort of.

I'll just let it go, with the feeling I can't really grasp the concepts and I'm just clutching at straws. Thanks for the patience, anyway.

Originally posted by Palynka
I see what you mean. Sort of.

I'll just let it go, with the feeling I can't really grasp the concepts and I'm just clutching at straws. Thanks for the patience, anyway.

Feynman was once said that nobody really understands QM so you're not alone. Some of us know how to work with it, but if anyone thinks that they really understand it they're just playing with them selves.
If you have the time and patience try to an introductory book on QM. But please leave out the Gradive books. Get a realtechnical book on it. And if you do read it try to solve its exercises. I have a book on QM by J. J. Sakurai (Modern Quantum Mechanics) that says on the preface that the student who has read the book but can't do the exercises has learned nothing.