Can someone please explain to me the motion of an electron?

[Musti425]

TL;DR Summary

Need some clarity about some aspects of the double slit experiment and it’s results.

Hello everyone. I am not a physics major or anything but have recently started finding it very fascinating and have been reading up on some of physics most popular experiments.

I recently started reading about the double slit experiment to learn more about QM concepts like wave particle duality, superposition etc. I think I have a pretty clear understanding of what the experiments goal is and how it goes about proving it. But while getting into the details of the experiment, like what electron source is used and how it works and how measurements are made as to which slit the electron goes through, one thing I discovered is that a standalone electron occupies a cloud like space which is specified by its wave function and that function just gives us a probability of finding the electron somewhere within that tiny space.

Unless we measure or observe it we cannot know exactly where in that small space the electron is. I also read that the electron is constantly in motion. But not the classical kind of motion that follows any kind of path. What I want to understand better is:

1> if it’s not classical motion, what kind of motion is it?

2> How and why does the electron move?

3> If the electron is always moving within its wave function, is the act of measurement actually stopping that motion to observe where exactly it is at that point in time?

4> Once we have measured an electron and it’s wave function collapses and it starts behaving like a particle, does it forever stay locked in a particle state or does it go back to being a wave?

5> It is my understanding that to ‘observe’ an electron, we cannot yet do so without interacting with it directly, and this interaction is what causes the wave function to collapse. Is this correct?

6> How should I imagine an electron? I know that after observation it behaves like a particle, but does the wave function collapse and reveal a small marble like object? Is it just a packet of negative energy floating around? I can’t seem to make sense of it.

Thanks in advance to anyone who takes out the time to answer my questions.

 

[anuttarasammyak]

For your questions, Feynmann https://www.feynmanlectures.caltech.edu/III_01.html would give you a good insight.

 

[PeroK]

TL;DR Summary: Need some clarity about some aspects of the double slit experiment and it’s results.

Hello everyone. I am not a physics major or anything but have recently started finding it very fascinating and have been reading up on some of physics most popular experiments. I recently started reading about the double slit experiment to learn more about QM concepts like wave particle duality, superposition etc. I think I have a pretty clear understanding of what the experiments goal is and how it goes about proving it. But while getting into the details of the experiment, like what electron source is used and how it works and how measurements are made as to which slit the electron goes through, one thing I discovered is that a standalone electron occupies a cloud like space which is specified by its wave function and that function just gives us a probability of finding the electron somewhere within that tiny space.

That's all roughly correct.

Unless we measure or observe it we cannot know exactly where in that small space the electron is.

This is not correct. The electron has no position. QM is an entirely different description of nature, where the electron is described by its wave function; not by a position. When we think of a particle in classical physics, then it must be somewhere at all times. A particle in QM is something different - and in general it doesn't have a well-defined position.

I also read that the electron is constantly in motion. But not the classical kind of motion that follows any kind of path. What I want to understand better is:
1> if it’s not classical motion, what kind of motion is it?

The motion is described by the wavefunction, which tells you where you are likely to find the particle if you "measure its position".

2> How and why does the electron move?

Classically, the electron moves in response to an electromagnetic field; interaction with other particles; and, following Newton's laws of motion.

All of this is "upgraded" in QM, where the classical picture emerges as a special case and an approximation.

In QM, the wavefunction evolves under the Hamiltonian - which includes its interaction with the electromagentic field. The electron interacts with other particles. The QM calculations for scattering are much more complicated than the equivalent classical scattering.

3> If the electron is always moving within its wave function, is the act of measurement actually stopping that motion to observe where exactly it is at that point in time?

No. Nothing like that.

4> Once we have measured an electron and it’s wave function collapses and it starts behaving like a particle, does it forever stay locked in a particle state or does it go back to being a wave?

The electron is always a particle described by a wavefunction. It's a popular science myth that it varies from wave to particle and back again.

5> It is my understanding that to ‘observe’ an electron, we cannot yet do so without interacting with it directly, and this interaction is what causes the wave function to collapse. Is this correct?

Essentially, yes. Note that when the wave function collapses, it only means that the wave function transforms to one that is highly localized. It's still a wavefunction and it still obeys the HUP (Heisenberg Uncertainty principle). It's just as much a wavefunction as it ever is. It's just a different shape.

We can interact with and monitor a macroscopic object (like a car) continuously by shining light on it, without significantly influencing the dynamics of the car. You can't do this for an electron.

6> How should I imagine an electron?

Don't try. This is why, ultimately, you need to grasp the mathematics.

I know that after observation it behaves like a particle, but does the wave function collapse and reveal a small marble like object? Is it just a packet of negative energy floating around? I can’t seem to make sense of it.

In terms of the electron itself, there is no wave-particle duality. There is only a quantum particle described by a wavefunction at all times.

Instead, wave-particle duality is an experimental term to fit quantum behaviour into the two classical categories of wave-like and particle-like behaviour.

I have two text books on QM (by Griffiths and by Sakurai). Wave-particle duaility is mentioned once in Griffiths, as a historical footnote. And, it's not mentioned at all by Sakurai.

This is probably the biggest difference between the popular science treatment of QM and the real academic subject. The former raises wave-particle duality into a mystical principle; and, in the latter it hardly gets a mention.

 

[Musti425]

Hi there, thanks for your answer, very helpful. Just a follow up question. Are there things in QM that are impossible to understand without knowing the math?

 

[PeroK]

Hi there, thanks for your answer, very helpful. Just a follow up question. Are there things in QM that are impossible to understand without knowing the math?

It's about the level of understanding. And also the level of mathematics. A poor analogy is the extent to which you can understand the game of chess without learning the rules and how the pieces move.

The mathematical structure of QM is necessary to have the context for physical understanding.

Also, learning mathematics develops your brain in terms of being able to reason logically and deal with complex, abstract concepts.

The difference between a serious chess player and someone reading about a chess match in a newspaper isn't just that the former knows a set of rules. The chess player not only has experience and knowledge of their own games, but their brain has developed and they can think in ways that the non-player cannot.

 

[PeroK]

Hi there, thanks for your answer, very helpful. Just a follow up question. Are there things in QM that are impossible to understand without knowing the math?

The most accessible treatment of QM that I know that gives you a genuine insight with a minimum of mathematics is these notes. It's still undergraduate level material and not casual reading, but there is a wealth of insight contained here:

https://www.e-booksdirectory.com/details.php?ebook=6153

 

[weirdoguy]

The most accessible treatment of QM that I know that gives you a genuine insight with a minimum of mathematics is these notes.

When I click on the download link I get this:

 

[PeroK]

When I click on the download link I get this:

View attachment 350455

It looks like Cresser has left Macquarie University in Australia for the warmer climate of Glasgow, Scotland. It's a shame if his notes are no longer available online.

 

[weirdoguy]

It's a shame if his notes are no longer available online.

Well I couldn't find them elsewhere, maybe he'll upload them again in the future.

 

[Steve4Physics]

It looks like Cresser has left Macquarie University in Australia for the warmer climate of Glasgow, Scotland. It's a shame if his notes are no longer available online.

I guess this is the document (238 pages, pdf): https://physics.mq.edu.au/~jcresser/Phys304/Handouts/QuantumPhysicsNotes.pdf

 

[Nugatory]

I guess this is the document (238 pages, pdf): https://physics.mq.edu.au/~jcresser/Phys304/Handouts/QuantumPhysicsNotes.pdf

Yep, that’s it. Highly recommended.

 

[bhobba]

After looking through the thread, I think mentioning that QM is a theory about the results of interactions will help. When not interacting, it does not really say much.

There is an extension of basic QM called Quantum Field Theory (QFT). In QFT everything is a field. All those interested in QM should aspire to study QFT, but unfortunately, studying QFT without first learning basic QM is not a good idea. Rodney Brooks did write a book at the popular level called Fields of Color that attempted such (although how well he succeeded is debatable):
https://arxiv.org/abs/1311.0205

At a more technical level:
https://arxiv.org/vc/arxiv/papers/1710/1710.10291v4.pdf

Reading that may help, although I am not in 100% agreement with what he says. But then again, I am not in 100% agreement with what popularisations usually say. He was influenced by the great Julian Schwinger, who does not get the press of, say, Feynman, although he is also one of the greats. I use Schwinger's book on Electromagnetism as my reference, even though Jackson is more common. I really should have both. I must also mention the source theory of Schwinger that Rodney mentions never really took off because the approach of a guy called Wilson (Effective Field Theory) is considered more general.

It is such a pity you need QM to do QFT because many misconceptions about QM are seen as trivial in QFT e.g. what is the motion of particle when not observed - as excitations of a quantum field that exists everywhere in the universe - the idea of a definite motion is not applicable. As a theory of interactions, QM is about the results of interactions of excitations in the Quantum Field. Interestingly, when one takes the limit of QFT, QM, as it is usually taught, is not obtained - strangely, it has aspects of the language of QFT.
https://arxiv.org/abs/1712.06605

There are several equivalent ways of expressing QM:
https://faculty1.coloradocollege.edu/~dhilt/hilt44211/AJP_Nine formulations of quantum mechanics.pdf

It could be argued formulation F is the best one - but as the paper says, they are all equivalent (or maybe not EXACTLY the same?)

Thanks
Bill