Does quantum mechanical definition of momentum require movement ?

[feynmann]

Does quantum mechanical definition of momentum require "movement"?

If quantum mechanical definition of momentum does not require "movement", then why "white dwarf star" won't collapse? How can it resist the pressure of gravity in the star?
http://en.wikipedia.org/wiki/White_dwarf

The quantum mechanical definition of momentum does not require "movement" since as f95toli said, the concept of "moment" is not well defined for particles on the quantum scale. Instead, the momentum of a particle is defined in terms of an operator on the wave function of the particle.

 

[whybother]

I'm not sure what this has to do with "movement" really, but white dwarfs stars only don't collapse if they are held up by the appropriate http://en.wikipedia.org/wiki/Electron_degeneracy_pressure" for full details though, because White Dwarfs can collapse/supernovae.

 

[feynmann]

I'm not sure what this has to do with "movement" really, but white dwarfs stars only don't collapse if they are held up by the appropriate http://en.wikipedia.org/wiki/Electron_degeneracy_pressure" for full details though, because White Dwarfs can collapse/supernovae.

But how can it resist the pressure of gravity if no "movement" is involved?
For example, the reason balloons won't collapse is that the gas molecules inside it are moving, so the momentum resist the pressure in it

 

[whybother]

But how can it resist the pressure of gravity if no "movement" is involved?

Read what I just wrote about electron degeneracy pressure.

 

[feynmann]

Read what I just wrote about electron degeneracy pressure.

I already knew electron degeneracy pressure.
The question is the electron degeneracy pressure involve the "movement" of electrons or not.

 

[whybother]

It did not explain anything, I already knew electron degeneracy pressure.

Then what is your question? Why are you assuming that movement is needed? What kind of movement are you thinking about?

 

[feynmann]

Then what is your question? Why are you assuming that movement is needed? What kind of movement are you thinking about?

Like the "movement" of the gas molecules inside the balloon

 

[whybother]

Yes, but that's not the kind of pressure that is holding a white dwarf up. The matter is too close together to be moving like that, the thing that is keeping it apart is the Pauli Exclusion principle. No motion needed, or possible, really.

 

[feynmann]

Yes, but that's not the kind of pressure that is holding a white dwarf up. The matter is too close together to be moving like that, the thing that is keeping it apart is the Pauli Exclusion principle. No motion needed, or possible, really.

The calculation of <degenerate matter> does involve "movement" or speed of the electrons.
See this link:
http://books.google.com/books?id=P_...Goa&sig=ZkzEIBINItUiFyMW5-uvjt1kMus#PPA143,M1

 

[alxm]

If quantum mechanical definition of momentum does not require "movement"

Says who? Quantum mechanical particles most certainly do move. While they do not have the same properties as a classical particle, as in an exactly defined position or momentum, that doesn't mean they do not move.

Quantum mechanical particles have momentum, they have kinetic energy, they display all the dynamical effects of motion. It's simply wrong to think that, for instance, a particle in a bound state doesn't move. It's analogous to saying that a classical standing wave isn't moving.

 

[Halcyon-on]

Quantum mechanical objects have no rest, thez are always in "motion". Think to the quantum harmonic oscillator which has no zero energy mode.

 

[feynmann]

See this link, https://www.physicsforums.com/showthread.php?t=304954

As I sad above, "movement" is not well defined on the quantum scale. Classically, one could say a particle moves if at time x it is at position y and at time x' it is at y'. However, in quantum mechanics, one never knows precisely where the particle is. The best you can do is say that at time t, the particle has a certain probability of being at position x.

An important point to realize is that the wave function does not correspond to any physically meaningful/observable quantities. When we say a wave function, it doesn't mean that the particle follows the path defined by the wave function, or that the particle oscillates like the wave function.

The wave function is merely a mathematical tool for describing a system of particles.

 

[ExactlySolved]

I think that the term 'movement' is unnecessary and vague when talking about phenomena that are dominated by quantum effects. In this regime the wave nature of matter is important, and so it is not clear what is moving (it's not a particle, it's not a fluid) so it just makes more sense to give a description in terms of waves (scalar fields) that are a function of space and time.

 

[Halcyon-on]

I think that the term 'movement' is unnecessary and vague when talking about phenomena that are dominated by quantum effects. In this regime the wave nature of matter is important, and so it is not clear what is moving (it's not a particle, it's not a fluid) so it just makes more sense to give a description in terms of waves (scalar fields) that are a function of space and time.

I completely agree with you.

 

[alxm]

I think that the term 'movement' is unnecessary and vague when talking about phenomena that are dominated by quantum effects. In this regime the wave nature of matter is important, and so it is not clear what is moving (it's not a particle, it's not a fluid) so it just makes more sense to give a description in terms of waves (scalar fields) that are a function of space and time.

What 'makes sense' depends entirely on the context. Referring you to the recent post on Hartree-Fock, I'd challenge you to give a rationalization of electronic (Coulomb) correlation that doesn't rely on using the idea of 'motion'. Moreover, electrons do not self-interact; which they would if they were simple semi-classical 'density fields'.

I said it before but I'll say it again: Neither the 'particle' or 'wave' description is correct. And if you tell people that 'quantum particles don't move', then you're setting them up for other misunderstandings farther down the road.

 

[f95toli]

I said it before but I'll say it again: Neither the 'particle' or 'wave' description is correct. And if you tell people that 'quantum particles don't move', then you're setting them up for other misunderstandings farther down the road.

I think we are arguing about semantics here. The reason why I don't think one should talk about "motion" in this case is that people will inevitably think of the classical concept. One advantage with the concepts such as momentum, kinetic energy etc is that they are quite abstract (and more "mathematical) even in classical physics, meaning there is less risk of misunderstanding about what they mean in QM. There is-as far as I know- no obvious reason why one would need to keep the link between motion and momentum/kinetic energy that exists in classical physics when we move to QM.

The point is that we must -in my view- always remember than ANY form of "visualization" of concepts in QM (and physics in general) can never be more than tools to help us understand what is going on (i.e. predict the outcome of experiments) and I think one should emphasise this when teaching QM; there is no reason to believe that the pictures we draw have anything to do with an underlying reality (whatever that means).

 

[feynmann]

I think it's wrong to say that quantum particles do not move. For example, the double-slit experiment, The electrons must "move" from the source and pass through both slits, then reach the screen, in order to generate interference pattern. However we do not know the exact path it takes. So we do not know how electrons move from point A to point B if they are not observed, but that does not mean electrons do not "move" in space, otherwise, how can the interference pattern show up?

 

[sokrates]

See this link, https://www.physicsforums.com/showthread.php?t=304954

The same story again...Hootenanny's that post is a little misleading as stated by himself later in that post.

Concept of movement not only makes perfect sense in the quantum sense, but also is absolutely ESSENTIAL in understanding QUANTUM TRANSPORT.

Guys, please, I am doing my Ph.D on quantum transport, where there's ALWAYS movement. The whole field is built on dynamics, movement, current flow operators etc... The computer you are using right now is governed by MOVING electrons.

The fact of the matter is, whether you treat it classically or quantum mechanically, gate capacitors of the transistors in your laptop is being charged right now by MOVING electrons.

Doesn't matter your abstract Hilbert space formulation shows it or not.

This is the reality.

For more info:
See my post in that link above. And if you are going to refer to a previous post, at least do justice to it and read the whole thing.

 

[f95toli]

Concept of movement not only makes perfect sense in the quantum sense, but also is absolutely ESSENTIAL in understanding QUANTUM TRANSPORT.

I agree that it makes sense (or at least is useful) when dealing with transport phenomena (which I also wrote in the other thread). But the question was if the definition of momentum requires movement, i.e. even when dealing with electrons in an atom. I would argue that the idea of something "moving" is more of a hindrance than a help in the latter case.

However, it is worth noting that even in electronic circuits it is not always obvious what is actually moving. I did my PhD working with components where the quantized phase is the most "fundamental" variable (since charge isn't well defined because of the charging energy being so low). In most of the models I used (and sometimes still use) the equations of motions describe a phase "particle" moving around a potential landscape. One could of course argue that this is just a formal analogy, but this phase particle nevertheless behaves more or less the the same way electrons do in equivalent charge system (it can tunnel etc).

 

[alxm]

I agree that it makes sense (or at least is useful) when dealing with transport phenomena (which I also wrote in the other thread). But the question was if the definition of momentum requires movement,

I would say that yes, it does. I would say that movement does not require having an exactly defined position or momentum. (analogies abound) Something is 'moving' relative you if it has kinetic energy relative your frame of reference, and obeys Newton's laws of motions. This is true whether you're talking about classical or quantum mechanical particles. It's also implicit in how the QM definition/derivation of the momentum operator.

Classical motion then, like all classical physics, then becomes a limiting case of QM. Classical particles obey Newton's laws of motion because quantum particles do so. 'Motion' in QM is not an analogy, it's the same thing.

Or to put it another way: At which point in the transition from quantum to classical domains would you say that things start moving, then? And in what way is that motion fundamentally different?

i.e. even when dealing with electrons in an atom. I would argue that the idea of something "moving" is more of a hindrance than a help in the latter case.

And I would say the opposite. Electron motion in atomic and molecular orbitals is usually referred to as such. Not 'motion' but as real motion. It's implicit, then, that you're not implying the kind of exact, stable trajectories of the Bohr atomic model. Anyone who's past the level of introductory QM knows that. Throwing out the concept of 'motion' just because the details of the Bohr model concept were wrong is overzealous.

But if you do not think of electrons in an atom as moving, then you will have big trouble understanding the central and still-relevant problem of electron correlation. I.e. the quantum many-body problem. Which is not an analogy to the classical many-body problem. It's the same problem, and difficult for the same reasons. Using wave functions instead of exact coordinates complicates matters, but does not change the fundamental difficulty of it.

This is an analogy: Electrons in a stationary state, have a time-independent location-probability distribution and therefore appear not to be moving, although they have momentum. Likewise, water flowing through a transparent pipe appears to be stationary, but is not.

Defining motion as 'appearing to move' doesn't make sense; it would exclude lots of classical phenomena like standing waves. I see no reason to define 'motion' as requiring exactly-defined positions and momentums.

 

[sokrates]

I agree that it makes sense (or at least is useful) when dealing with transport phenomena (which I also wrote in the other thread). But the question was if the definition of momentum requires movement, i.e. even when dealing with electrons in an atom. I would argue that the idea of something "moving" is more of a hindrance than a help in the latter case.

However, it is worth noting that even in electronic circuits it is not always obvious what is actually moving. I did my PhD working with components where the quantized phase is the most "fundamental" variable (since charge isn't well defined because of the charging energy being so low). In most of the models I used (and sometimes still use) the equations of motions describe a phase "particle" moving around a potential landscape. One could of course argue that this is just a formal analogy, but this phase particle nevertheless behaves more or less the the same way electrons do in equivalent charge system (it can tunnel etc).

I will even go as far as saying that it is required in the definition of momentum. At least in the semi-classical case...

For the exact quantum mechanical formulation, while putting a big question mark, I will admit that I don't know the answer.

You are right, electron is usually described as a wave, which evolves in unitary fashion (as long as transport is coherent) and the velocity of that wave is just the group velocity of the wavepacket.

But apart from all the technicalities, the fact that your laptop is working right now, is clear proof that electrons are MOVING.

So the concept of movement is there and very tightly coupled to the concept of momentum.

But thanks for reframing the discussion and reminding me the original problem. But at any rate, we have to be very careful in abolishing the concept of movement because it can quickly become misleading for the beginners to the subject!

 

[f95toli]

Or to put it another way: At which point in the transition from quantum to classical domains would you say that things start moving, then? And in what way is that motion fundamentally different?

I don't think there is a sharp limit since there is often a crossover regime were both a QM and a classical (or at least semi-classical) description will yield the same answer. When one enters this regime tends to depend on the how affected the system is by decoherence. Atoms are usually quite well protected so then a QM description is needed, electrons in a microprocessors are in the opposite limit and are essentially "classical".

But then there are systems that can be in both regimes such as some qubits.
If we take the charge qubit as an example we have a situation where the electrons on the island are essentially classical at high temperature (since kbT is larger than the charging energy) and it is useful to describe the system in terms of classical transport (i.e. electrons moving), but if we cool the system we reach a point where -for a short period of time (the coherence time)- we can have a superposition of 0 and 1 electrons on the island; in this case the concept of electrons "moving" in and out of the island become quite tricky and is -in my view- no longer useful.

Whether or not there is a "fundamental difference" it a tricky question that I don't think anyone really know the answer to. Since we can be reasonably sure that the classical world is just -as you say- a limiting case of QM there is presumably no real "physical" difference (whatever that means). But this question is also irrelevant if the aim is to simply better understand our models (so that we can use them the predict the outcome of experiments).
It also does not change the fact that the concept of "moving electrons" is are often useful in the classical regime, but not so useful the the QM regime.
And whether or not a concept is useful is ultimately what determines whether or not we should use it.