Particle Movement in Quantum Mechanics

[Islam Hassan]

TL;DR

Is movement of a particle in quantum mechanics assumed/theorized/speculated to be smooth and continuous, or does QM only deal with probabilistic determinations of that particle's location and not address the matter of its movement.

Niels Bohr famously said --and I paraphrase-- that QM is an abstract description of nature and that it can only prescribe what we can say about nature rather than what nature is.

What does QM say about the movement of a particle? Is this movement positively ascertained to be smooth and continuous, or only assumed or theorized or speculated to be so?

I am thinking specifically of an electron's 'orbit' around a nucleus. IH

 

[Halc]

What does QM say about the movement of a particle?

It talks about what is measured, or what might be measured. It says nothing about what goes on between measurements.

I am thinking specifically of an electron's 'orbit' around a nucleus.

The model of electrons orbiting a nucleus was discarded a better part of a century ago.

 

[Islam Hassan]

Thank you Halc...re the electron orbit, that's why I put the word in quotation marks 'orbit'...

If QM says nothing about what goes on between measurements, what do physicists speculate about a particle's movement being smooth and continuous or not...if of course they engage in such speculation...IH

 

[topsquark]

TL;DR Summary: Is movement of a particle in quantum mechanics assumed/theorized/speculated to be smooth and continuous, or does QM only deal with probabilistic determinations of that particle's location and not address the matter of its movement.

Niels Bohr famously said --and I paraphrase-- that QM is an abstract description of nature and that it can only prescribe what we can say about nature rather than what nature is.

What does QM say about the movement of a particle? Is this movement positively ascertained to be smooth and continuous, or only assumed or theorized or speculated to be so?

I am thinking specifically of an electron's 'orbit' around a nucleus.IH

What we think of as a "path" in Classical Physics is a continuous set of points in space (or space-time, if you want to go there). (If you want to get really precise, a path is a map $\gamma : [a,b] \to \mathbb{R}^3$).

However, this ends up violating the Uncertainty Principle because, theoretically, we would be able to exactly know a position and momentum of the particle exactly at any given point.

So however a particle gets from point to point, it is not along a continuous path or, if there is one, the path is somehow hidden to us by some principle that we don't know. (Or that I'm not thinking of at the moment!). Quantum Mechanics doesn't tell us how things get from point to point: it tells us what we can expect when we take a measurement.

-Dan

 

[Islam Hassan]

Thanks Dan, that pretty much sums it up for me!!

Theoretical continuous movement is out of the scope of QM due to the uncertainty principle...at least out of the scope of QM as it is formulated today.IH

 

[PeroK]

If QM says nothing about what goes on between measurements, what do physicists speculate about a particle's movement being smooth and continuous or not...if of course they engage in such speculation...

Orthodox QM goes further than that. Asking what a particle does between measurements makes no sense as a scientific question. For example, only measurements of position make sense. Asking where a particle was when you didn't measure its position is not a scientific question.

There is, however, the Bohmian interpretation of QM, which entails particles have unknown, unmesaureable (and potentially unknowable) trajectories under the surface, as it were.

.re the electron orbit, that's why I put the word in quotation marks 'orbit'...

Note that in the ground state of hydrogen, the electron has zero orbital angular momentum. Which shows that this "orbit" is distinctly non-classical.

 

[vanhees71]

In any energy eigenstate the system "doesn't move" since the energy eigenstates are stationary states. Thus in a hydrogen atom in its ground state nothing moves (or maybe the atom as a whole moves, if the total momentum is not 0).

 

[Dale]

Theoretical continuous movement is out of the scope of QM

On the other hand, both the position and momentum operators produce continuous probability density functions rather than discrete probability mass functions.

 

[vanhees71]

All you can know according to quantum theory are probabilities for the outcomes of measurements, given the state (statistical operator) of the system. The time evolution of the statistical operator is described by differential equations, leading to the corresponding unitary time-evolution operator, i.e., given the quantum state at an initial time you can calculate the state at any other time, and it's a continuous function.

That's not different in classical mechanics: The equations of motion allow you to calculate the state of the system (a point in phase space in the case of complete information) given the initial point in phase space.

The radical difference between classical and quantum theory is that in classical physics all observables always take definite values, and you can construct at least in principle measurement devices for any observable such that you can neglect the influence of this measurement on the measured system, while according to quantum theory there is in general no state, where all observables take determined values, and the influence of the measurement on a small enough object (particularly some elementary particle) is never negligible, i.e., in general when measuring one observable the corresponding interaction of the measurement apparatus with the system will change the state in such a way that observables which took determined values before the measurement, because the system has been prepared in a corresponding state, don't take definite values anymore after the measurement.

For a very thorough discussion, see the introductory chapter of

J. Schwinger, Quantum Mechanics, Symbolism of Atomic
Measurements, Springer, Berlin, Heidelberg, New York (2001).

 

[WernerQH]

Thus in a hydrogen atom in its ground state nothing moves

Does this mean that in the ground state the electron has no kinetic energy? Only potential energy?

 

[vanhees71]

The virial theorem for the hydrogen atom says that
$$\langle T \rangle=-\langle V \rangle/2.$$

 

[WernerQH]

Interesting. So the electron doesn't move, but has kinetic energy?

 

[vanhees71]

The value of the kinetic energy is indetermined for an energy eigenvalue. The same holds for potential energy. That's why I compared expectation values of these quantities. It's a typical phenomenon of "quantum fluctuations".

 

[PeterDonis]

So the electron doesn't move, but has kinetic energy?

The electron is not in an eigenstate of either the momentum operator or the kinetic energy operator (or the potential energy operator), so neither of these statements, strictly speaking, are correct. The best we can do is to give expectation values, as @vanhees71 did. But expectation values alone are not sufficient to say that the electron is in a specific state of motion or kinetic energy.

 

[WernerQH]

In any energy eigenstate the system "doesn't move" since the energy eigenstates are stationary states.

To me the scare quotes indicate that you yourself don't feel quite at ease with your explanation.

 

[PeterDonis]

To me the scare quotes indicate that you yourself don't feel quite at ease with your explanation.

A better phrasing would be that neither "does move" nor "doesn't move" are correct for a state that is not an eigenstate of momentum. "Stationary" when applied to quantum states actually means "doesn't change with time", not "doesn't move in space".

 

[weirdoguy]

with your explanation

It's not "his explanation", it's what is thought to physics students and it's quite basic QM stuff.

 

[WernerQH]

What does QM say about the movement of a particle?

This is an intriguing question. I don't share the view that it is impossible or inappropriate to form mental images. But when it cannot be said whether or not it moves, does the idea of a particle make any sense?

So however a particle gets from point to point, it is not along a continuous path

I agree with that. Perhaps you have encountered Roger Penrose's book "The Road to Reality", in which he depicts the motion of a free Dirac particle as a zig-zag path in spacetime. The uncertainty principle says that the electron cannot be at rest (unless its position is absolutely uncertain). And the velocity operator actually has only two eigenvalues, $\pm c$, so the electron would appear to move with the speed of light! In its (average) rest frame it would go back and forth incessantly, flipping its helicity every time because angular momentum (spin) is conserved. This would happen on a time scale of $\hbar / mc^2$, i.e. on the order of $10^{-21}$ seconds. Penrose draws the path as a zig-zag line, but there is no evidence at all that it is continuous. (Experimentally, the shortest laser pulses have durations much longer than that time scale.) I prefer to think of only the helicity flips as real, semi-regularly separated in space by $\sim 10^{-11}$ cm. At longer time and length scales the world-line would look smooth, but at the smallest scales it's just a dotted line.

I don't think that in an atom you need a completely different picture and "motion just stops". Of course, the dotted line(s) can longer be straight, and in the ground state they would become a tight, roughly spherical twine with no discernible direction of winding.

 

[topsquark]

This is an intriguing question. I don't share the view that it is impossible or inappropriate to form mental images. But when it cannot be said whether or not it moves, does the idea of a particle make any sense?I agree with that. Perhaps you have encountered Roger Penrose's book "The Road to Reality", in which he depicts the motion of a free Dirac particle as a zig-zag path in spacetime. The uncertainty principle says that the electron cannot be at rest (unless its position is absolutely uncertain). And the velocity operator actually has only two eigenvalues, $\pm c$, so the electron would appear to move with the speed of light! In its (average) rest frame it would go back and forth incessantly, flipping its helicity every time because angular momentum (spin) is conserved. This would happen on a time scale of $\hbar / mc^2$, i.e. on the order of $10^{-21}$ seconds. Penrose draws the path as a zig-zag line, but there is no evidence at all that it is continuous. (Experimentally, the shortest laser pulses have durations much longer than that time scale.) I prefer to think of only the helicity flips as real, semi-regularly separated in space by $\sim 10^{-11}$ cm. At longer time and length scales the world-line would look smooth, but at the smallest scales it's just a dotted line.

I don't think that in an atom you need a completely different picture and "motion just stops". Of course, the dotted line(s) can longer be straight, and in the ground state they would become a tight, roughly spherical twine with no discernible direction of winding.

I don't think you are being "severe" enough about the path thing.

I haven't actually read Penrose's work, so I'm not quite sure what his model or argument is here, but bear in mind that even "zig-zag" isn't a good representation, either. It still implies a path of some sort. An electron in an orbital has a position, it has a momentum, it has an energy, etc. but these properties are subject to a probability distribution and we cannot predict anything about their specific values at any given time. Even a "path" that is discontinuous at every point isn't quite enough because we know that the particle stays in a local area to the path. The electron could be at a point in the electron cloud one instant and be measured somewhere completely different the next, not locally close. The probability it will be near it's original position the next instant is quite high, but we can calculate a non-zero probability that it's on the other side of the atom as well. Or even in the Andromeda galaxy. (Though highly unlikely!)

As has been said before this, we know nothing about what goes on between measurements. We can only make predictions based on a probability density about what the result of the next measurement will be.

-Dan

 

[PeterDonis]

when it cannot be said whether or not it moves, does the idea of a particle make any sense?

If you insist on taking "particle" to mean "a little ball with a definite position and velocity", then no, that idea never makes sense in QM. But QM does not use the word "particle" to mean that.

Perhaps you have encountered Roger Penrose's book "The Road to Reality", in which he depicts the motion of a free Dirac particle as a zig-zag path in spacetime.

Yes. Now go look in the literature to see if anyone ever made this picture work with a bound particle, such as an electron in an atom, which is what we are talking about here.

I don't think that in an atom you need a completely different picture

Before making such claims you should check the literature.

"motion just stops".

...is not what others have been saying.

 

[vanhees71]

Well, Penrose's zigzag picture falls again somehow into the "overpopularization category". It's somehow trying to describe the "oscillation" of left- and right-handed Weyl fermions due to the mass term, i.e., he treats the mass term in a hand-waving way as the perturbative interaction between two massless Weyl fermions (one left-handed, one right-handed) and in this way describing how mass comes about through this "zigzag picture". Then he introduces weak interactions and somehow "explains" parity violation within this "zigzag picture".

The book falls into the usual category of trying to avoid the true math, although it's an exeption in the sense that Penrose actually introduces a lot of math, which however he tries to somehowe describe in intuitive ways, but it's of course his intuition, and to learn his intuition is maybe more difficult for most people than to learn the true math and then build an intuition for your own.

 

[Username34]

If QM says nothing about what goes on between measurements, what do physicists speculate about a particle's movement being smooth and continuous or not...if of course they engage in such speculation...

You are referring to the pioneers of QM who were witnessing a paradigm shift. There wasn't even a Schrödinger equation originally.

Isolated Quantum Mechanics is deterministic, but makes no sense in terms of classical physics. It has no adherence to classical mechanics.

The measurement process is deterministic too, but the exact outcomes are statistically distributed.

Todays physicist can talk about both states meaningfully. But Bohr is right that QM is a model of reality, and not actual reality, until we know the right interpretation.

 

[WernerQH]

I don't think you are being "severe" enough about the path thing.

You misunderstood my point. I'm trying to get rid of paths. Instead of talking about "measurements" I'm looking for a microscopic picture and interpret paths (and electrons!) as something that we read into sequences of microscopic events.

I haven't actually read Penrose's work, so I'm not quite sure what his model or argument is here, but bear in mind that even "zig-zag" isn't a good representation, either.

I only browsed it in a bookstore once, and I don't take the zig-zag literally either. But mental images can be helpful.

An electron in an orbital has a position, it has a momentum, it has an energy, etc. but these properties are subject to a probability distribution and we cannot predict anything about their specific values at any given time.

It is assumed that electrons have a continuous existence, but said that their position, momentum, kinetic energy, etc. can be indefinite between "measurements", without it being clearly defined what a measurement is. Isn't it strange to "measure" properties that these quantum "objects" do not have, but are created by that act of measurement? I think it's clearer to say that these objects do not exist between successive microscopic events where they make their "presence felt". They express the correlations between those events.

As has been said before this, we know nothing about what goes on between measurements.

We can compute correlation functions that say a lot about the behaviour of the systems. But we obviously disagree about what it is that is correlated.

 

[PeterDonis]

It is assumed that electrons have a continuous existence, but said that their position, momentum, kinetic energy, etc. can be indefinite between "measurements", without it being clearly defined what a measurement is. Isn't it strange to "measure" properties that these quantum "objects" do not have, but are created by that act of measurement? I think it's clearer to say that these objects do not exist between successive microscopic events where they make their "presence felt". They express the correlations between those events.

Is this your own personal interpretation of QM? That is off limits here.

If it isn't, can you give a reference for an interpretation in the literature along these lines?

 

[Nugatory]

It is assumed that electrons have a continuous existence….

”Continuous existence” is not an assumption. It’s a reasonable enough informal English language description of something the math says, namely that the probability that the particle will be detected somewhere is unity.

 

[GarberMoisha]

Strictly speaking particles do not exist. There is particle-like behvaior in certain instances while there isn't in others(normally between measurements). Herein comes the so called duality, the complimentary nature of 'particles' acting as waves.
Unambiguously in human language this can be referred to as 'behavior'.
What Bohr said is that the quantum system will do what it "needs" to do and we can only say not much about what it will do or why.
This is why some scientists are not quite happy with QT.

 

[WernerQH]

Is this your own personal interpretation of QM?

It is my opinion that quantum field theories are best viewed as theories describing the correlations between events distributed over spacetime. (Certainly not as a theory about quantum objects and measurements performed on them!) And it is not an outlandish idea that $n$-point functions are the bread and butter of quantum field theories, correlation functions derivable from a path integral by functional differentiation. I've been trying to explain this to someone like @Islam Hassan at a level appropriate to a B-level thread.

 

[WernerQH]

”Continuous existence” is not an assumption. It’s a reasonable enough informal English language description of something the math says, namely that the probability that the particle will be detected somewhere is unity.

Of course it is a reasonable, even compelling assumption. A bit like the idea that light waves cannot exist without an ether carrying them. How do you explain the correlations in Bell-type experiments without photons carrying information from the source to the detectors? I fully understand the motivation. But the idea of photons as carriers of information gets us into unnecessary trouble. If we treat them as containers with some definite state we have to assume that these containers can somehow be "entangled". (And there seems to be no end to discussions on entanglement here on PF.) I think it is more economical to just describe the observed correlations and give up on explaining them in a strange way. (Describing the correlations themselves, rather than the containers.)

 

[Islam Hassan]

”Continuous existence” is not an assumption. It’s a reasonable enough informal English language description of something the math says, namely that the probability that the particle will be detected somewhere is unity.

So if I understand correctly, QM prescribes that if a particle exists in the absolute sense, it can be detected somewhere.

QM does not extend this logic to the particle's movement being continuous or not. Intuitively, people --and especially laymen-- cannot help wondering whether this is the case or not.

 

[PeroK]

So if I understand correctly, QM prescribes that if a particle exists in the absolute sense, it can be detected somewhere.

I don't think QM is concerned with the existence of a particle in this metaphysical sense any more than classical mechanics is. No one would say that if a projectile exists in an absolute sense it moves in a parabolic curve.

Basic QM deals with the properties of a particle through the specification of a wavefunction, rather than a classical trajectory.

It's something of a classical predujice to doubt the existence of a particle because it lacks certain classical properties. In this case, it lacks a well defined position at all times.

QM does not extend this logic to the particle's movement being continuous or not.

To be precise, this is not logic. QM has a different set of basic axioms than classical mechanics. Neither is more logical than the other.

Intuitively, people --and especially laymen-- cannot help wondering whether this is the case or not.

Maybe so. But, laymen do not determine the nature of QM.