Absolute Zero and the Uncertainty Principle

[Slip_Mahoney]

The comma should have been after the word “exactly”.

[teemingONE]

hold on im confused, is absolute zero a tempature?

[Squink]

This is related to that affect when two plates are brought together, right? (Now I can’t remember that name)

The Casimir effect.

[Achernar]

Slip Mahoney, why do you say it’s not impossible to measure a particle’s momentum exactly? If you did that, then the theoretical uncertainty in position would be infinite. This is not something you can get under normal circumstances.

teemingONE, yes, Absolute Zero is the temperature at which the classical thermal kinetic energy is equal to 0, that is, the temperature something has when it’s absolutely still. (This is only true classically, though. There are quantum effects that prevent anything from being absolutely still.) Thus, there is no temperature below Absolute Zero.

[man779977]

Absolute zero can not be reached for these reasons:

1. If you used something to create absolute zero in anything whatever you used to create it would be using energy, and that energy would create heat, however minimal it might be.

2. You would never be able to observe absolute zero because once you got near it, you would create enough energy just by being there to raise the temperature.

3. There is always energy around so you can never reach absolute zero.

[man779977]

I also agree that you cant measure an objects momentum exactly (unless the object is completely still) because it will always be moving until another force acts upon it.

Example:

Turn on a fan.

Determine the exact position and momentum of any of the blades on that fan at any given second.

[The_Ryan]

*Originally posted by Giraffe *
**For a quantum particle, uncertainty in x is equivalent to how localized the particle is. If you put a particle in a 1 nm-sized bucket, then that is how localized it is, and it’s momentum can not be less than hbar/(1 nm). **

Did you mean to say its uncertainty in mometum can’t be less than habar/1nm? I suppose that there is a mininum momentum, but not because of the Heisenberg principle.

And of course, the Heisenberg uncertainty principle is only comprehensible to someone who understands QM, and if you understand QM then the question of why a particle with zero momentum is spread out equally across space is trivial.

A particle’s state is made up of waves. In free space, each wave is spread equally across space. The only way to have a total state that isn’t spread equally across space is to add several of them together, and there is only one state with zero momentum, so there’s not way to add different states to gether and get zero momentum, so there’s no way to have zero momentum without the wave being equally spread across space.

Lumpy

What about the speed of light limitation? If a particle was so localized that it’s momentum would have to be greater than the speed of light, then what happens?

It’s not the momentum that becomes infinite, it’s the momentum spread. A particle with definite position would have an equal probability of having every momentum. That doesn’t mean it would have an infinite momentum.

[Urban_Ranger]

*Originally posted by Giraffe *
Urban, that is true. However, Heisenburg uncertainty is not just a rule about how well you can do experiments. It is a physical property of a system – a particle with very small uncertainty in its momentum would have very large uncertainty in its position, which means the particle’s position would not just be hard to measure – it would physically occupy a large region of space simultaneously.

My understanding of the Uncertainty Principle is about measurements. That is, the act of measuring directly affects the thing being measured, causing the uncertainty itself.

[Ring]

*Originally posted by Urban Ranger *
**My understanding of the Uncertainty Principle is about measurements. That is, the act of measuring directly affects the thing being measured, causing the uncertainty itself. **

Nope, uncertainty is an inherent aspect of nature. If you precisely know the position then, in principle, the particle does not have a momentum, and this is true for any conjugate pair of observables. It has nothing to do with measurement even though many pop science books and textbooks describe it that way.

[Ring]

Think of this way. Momentum is proportional to frequency and it takes an infinite number of frequencies to produce an infinitely peaked superposition of wavefunctions which gives an exact position for the particle. But if you have an infinite number of frequencies then you can know nothing about the momentum.

[Achernar]

Although the Uncertainty Principle is not an artifact of measurement, I think that the best explanation of just what the heck we mean by delta-x and delta-p (short of whipping out bras and kets) can be achieved by putting it in terms of measurements.

[erislover]

*Originally posted by Ring *
**Think of this way. Momentum is proportional to frequency and it takes an infinite number of frequencies to produce an infinitely peaked superposition of wavefunctions which gives an exact position for the particle. But if you have an infinite number of frequencies then you can know nothing about the momentum. **

Wow, that is a very good description. I like this a lot.

[Don_Roberto]

*Originally posted by Ring *
**Nope, uncertainty is an inherent aspect of nature. If you precisely know the position then, in principle, the particle does not have a momentum, and this is true for any conjugate pair of observables. It has nothing to do with measurement even though many pop science books and textbooks describe it that way. **

Don’t be so hasty here–I believe it does have something to do with measurement, and that this idea is at least as fundamental as the other picture you describe (superposition of frequencies). It’s the difference between the Heisenberg formulation of quantum mechanics (which describes measurements) and the Schrodinger formulation (which uses waves).

The problem with the pop science books and textbooks is that they are misleading in what they define as a measurement. These books often convey the idea that “measurements” are carried out by experimenters–but quantum measurements (at least, those that describe the state of a system) can be carried out by anything–even the system itself–or space itself (i.e. the quantum field).

None of this to take away from what Ring has recently posted–excellent descriptions from a wave mechanical point of view; but, I do think they shortchange the measurement/operator point of view.

RE: Achernar’s post:
The uncertainty principle is not just an artifact of measurements carried out by human experimenters, but it is fundamentally related to the broader concept of “measurement”.

These misunderstandings are an unfortunate (though common) consequence of an ordinary term being appropriated by scientists in a specific way.

As far as a less technical description goes, I think others on this thread have that well in hand.

[FordPrefect]

*Originally posted by Giraffe *
**Urban, that is true. However, Heisenburg uncertainty is not just a rule about how well you can do experiments. It is a physical property of a system – a particle with very small uncertainty in its momentum would have very large uncertainty in its position, which means the particle’s position would not just be hard to measure – it would physically occupy a large region of space simultaneously. **

Does the particle actually occupy this reqion physically, or does the particle’s probability wave form occupy the region? Which in the end is probably the same thing in quantum terms. But to interested non-physicists as myself what I think of when I hear that a particle would occupy an entire region is that an electron would grow in size and should be visible, and this cannot be what you said.

[Ring]

*Originally posted by FordPrefect *
**Does the particle actually occupy this reqion physically, or does the particle’s probability wave form occupy the region? Which in the end is probably the same thing in quantum terms. But to interested non-physicists as myself what I think of when I hear that a particle would occupy an entire region is that an electron would grow in size and should be visible, and this cannot be what you said. **

An electron, for example, is a point particle and it therefore has no spatial extension. So, in principle, you cannot say that it occupies any region whatsoever and it certainly cannot grow in size.

If you precisely know an electron’s momentum then the subsequent uncertainty in the particle’s position just means that the probability of finding the electron is spread over a large volume.

To go one step further the only knowledge we have of a particle, in between measurements, is the wavefunction, and the wavefunction is not considered to be real. This leads to the inescapable conclusion that the electron has no classical reality except when a measurement is performed. Of course you can say this about macro objects as well. Reality is a very hard thing to pin down.

[Giraffe]

*Originally posted by FordPrefect *
**Does the particle actually occupy this reqion physically, or does the particle’s probability wave form occupy the region? Which in the end is probably the same thing in quantum terms. But to interested non-physicists as myself what I think of when I hear that a particle would occupy an entire region is that an electron would grow in size and should be visible, and this cannot be what you said. **

The two are the same thing in quantum terms – you can’t talk about a delocalized particle as a point object. Certain interactions will cause it to behave like a point object, but when it is delocalized, it behaves like a fuzzy smear, rather than a single tiny hard sphere.

It’s not just a matter of the particle having equal chances of being in multiple places. It’s not just that we don’t know where it is. A ball in a shell game has an equal chance of being under a given shell – this is not the same as quantum uncertainty. A delocalized particle will interact with other delocalized particles as if it were a fuzzy smear. You can observe interference between fuzzy smears that can’t be explained in terms of point-like objects interacting. It simply doesn’t behave like a hard sphere, like we’re used to thinking about from living in the macroscopic world.