B What does a Penning trap say about the electron?

I am in the midst of a discussion with someone who feels very confident that an electron is always and forever a point particle and never a wave; any wave-like behavior that is observed must be attributed to a pilot wave that guides the path of the electron.

I have sought to argue that this gets us into the question of the interpretation of what's going on under the hood in quantum mechanics, and that all successful interpretations that have survived give the same predictions and are empirically indistinguishable, effectively speaking (apart from the corner case of quantum non-equilibrium). My position, then, is agnosticism about what an electron is. My discussion partner has countered that the Penning trap is an example of an experiment that shows that the electron is a point particle and that the elementary charge cannot in any reasonable understanding be spread out over an extensive electron wavefunction. What assumptions go into this reasoning? Does he have a point, or is he overlooking something?
 
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someone who feels very confident that an electron is always and forever a point particle and never a wave; any wave-like behavior that is observed must be attributed to a pilot wave that guides the path of the electron.
This is the de Broglie-Bohm interpretation of QM; it's a logically valid interpretation, but it's just an interpretation. It makes the same predictions as all of the other intepretations, so there's no way to "prove" it experimentally.

the penning trap is an example of an experiment that shows that the electron is a point particle and that the elementary charge cannot be spread out over the electron wavefunction. What assumptions go into this reasoning?
You would have to ask him. But if he really thinks this is an example of an experimental proof of his interpretation, he should be able to show you how other interpretations make different predictions. That will be difficult since they all use exactly the same math to make their predictions.
 

Mentz114

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Quantum mechanics, ie the wave function does not say that the charge nor the electron is spread out. The wave function gives the probability of finding the electron at a specified range of positions.
 
Quantum mechanics, ie the wave function does not say that the charge nor the electron is spread out. The wave function gives the probability of finding the electron at a specified range of positions.
I don't disagree. But my understanding is that one interpretation of the available experiments is that the electron is a wave, at least in certain contexts, and that the point you make does not invalidate that understanding. I am not prepared to weigh in on this specific take on things and simply say, "I don't know. Maybe." My discussion partner says this is an untenable position. Do you agree that your point about what information the measurement of the electron wavefunction gives does not decide this question?
 
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The wave function gives the probability of finding the electron at a specified range of positions.
Strictly speaking, the wave function in the position basis (i.e., the wave function with the position operator applied) gives the probability of finding the electron at a specified range of positions.

the measurement of the electron wavefunction
You don't measure the electron wavefunction (or any other wave function, for that matter). You measure a number which is an eigenvalue of some observable. Applying an operator that represents the observable to the wave function for the electron (or whatever object you are measuring) gives you the probabilities of the different possible eigenvalues, i.e., measurement results.
 
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my understanding is that one interpretation of the available experiments is that the electron is a wave
What does "the electron is a wave" mean? If all it means is that something called a "wave function" appears in the math, and happens to appear in an equation that looks like a wave equation, that's not an "interpretation"; it's just a description of the math. If it means something more, then the person who is arguing for the interpretation needs to tell you what it means--and if the person is claiming that some experiment proves that his interpretation is right and all the others are wrong, then, as I said before, that person needs to show how the math is different, and leads to different predictions, for all the other interpretations as compared to his. Which will be difficult since they all use the same math.
 
What does "the electron is a wave" mean? If all it means is that something called a "wave function" appears in the math, and happens to appear in an equation that looks like a wave equation, that's not an "interpretation"; it's just a description of the math. If it means something more, then the person who is arguing for the interpretation needs to tell you what it means
I'm thinking specifically of this and similar descriptions I have come across on Wikipedia:
The relative state formulation makes two assumptions. The first is that the wavefunction is not simply a description of the object's state, but that it actually is entirely equivalent to the object, a claim it has in common with some other interpretations. The second is that observation or measurement has no special laws or mechanics, unlike in the Copenhagen interpretation which considers the wavefunction collapse as a special kind of event which occurs as a result of observation. Instead, measurement in the relative state formulation is the consequence of a configuration change in the memory of an observer described by the same basic wave physics as the object being modeled.
My contention is that without an experiment to sift between the competing possibilities, a position such as this one can only be assessed on the basis of intuition and taste and cannot as such be excluded as a possibility.
 

Mentz114

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I don't disagree. But my understanding is that one interpretation of the available experiments is that the electron is a wave, at least in certain contexts, and that the point you make does not invalidate that understanding. I am not prepared to weigh in on this specific take on things and simply say, "I don't know. Maybe." My discussion partner says this is an untenable position. Do you agree that your point about what information the measurement of the electron wavefunction gives does not decide this question?
The question appears to be about wave/particle distinctions which is not a fruitful subject to pursue.

QT says the electron is an excitation of a quantum field - neither a wave nor a particle.
 
The question appears to be about wave/particle distinctions which is not a fruitful subject to pursue.
I guess I'm trying to get my discussion partner to understand this point, and my discussion partner believes that the matter can be sorted out by referencing the Penning trap and other experiments. If I say to him, "you're essentially getting into philosophy, because there's other ways of looking at it, and no way of experimentally distinguishing between them," he counters that my comparison of his (particle) description of things with other possibilities is equivalent to comparing evolution with creationism. I think it would be anti-intellectual to just say to him, "No. You're wrong."
 
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My contention is that without an experiment to sift between the competing possibilities, a position such as this one can only be assessed on the basis of intuition and taste and cannot as such be excluded as a possibility.
Well, we here all agree with this, so I'm not sure how much point there is in trying to discuss it here.

If I say to him, "you're essentially getting into philosophy, because there's other ways of looking at it, and no way of experimentally distinguishing between them," he counters that my comparison of his (particle) description of things with other possibilities is equivalent to comparing evolution with creationism. I think it would be anti-intellectual to just say to him, "No. You're wrong."
Why? IMO he's being anti-intellectual, or at least anti-science, by not giving any experimental way to distinguish the possibilities. That's how we distinguish evolution from creationism--by looking at the different predictions they make and seeing which way nature votes. Why should he get a free pass?
 
IMO he's being anti-intellectual, or at least anti-science, by not giving any experimental way to distinguish the possibilities.
He's given the Penning trap as an experiment to sort between the various possibilities: a Penning trap, in his understanding, shows that the electron is highly localized in a very small region for an extended period of time. Taken at face value, without further elaboration, that reply of his would seem to rule out descriptions such as that of the relative state formulation quoted above. In other words, he seeks to cite the Penning trap as a counterargument to descriptions along the lines I've quoted. I don't think he can do this, but I don't have enough knowledge of the subject to say anything more than, "I think you're wrong."
 
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He's given the Penning trap as an experiment to sort between the various possibilities
And unless he can show you how the different possibilities actually make different predictions, he's just blowing smoke. It's not enough just to say what is "in his understanding". He needs to show you the actual math being different from one interpretation to another. Which, as I've already said, is going to be difficult.

a Penning trap, in his understanding, shows that the electron is highly localized in a very small region for an extended period of time
So what? No interpretation says this is impossible. "Highly localized" is not the same as "has a definite position". If he were to claim that the experiment showed that the electron had a definite position for an extended period of time, he would be claiming that the experiment contradicts the basic math of QM (which shows that a state of definite position for an electron very quickly evolves into a state that is a superposition of many different possible positions). But the Penning trap does not put the electron in a state of definite position. It just puts it in a state where its wave function is confined to a small region of space.

Taken at face value, without further elaboration, that reply of his would seem to rule out descriptions such as that of the relative state formulation quoted above.
I don't see why. Where does the relative state interpretation say this is impossible? See above.

I don't have enough knowledge of the subject to say anything more than, "I think you're wrong."
Tell him that all interpretations use the same math and make the same predictions, and challenge him to show you a reputable source (textbook or peer-reviewed paper) that says otherwise.
 
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the elementary charge cannot in any reasonable understanding be spread out over an extensive electron wavefunction.
A point charge does extend to infinity ie the classical E field.
 
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I am in the midst of a discussion with someone who feels very confident that an electron is always and forever a point particle and never a wave; any wave-like behavior that is observed must be attributed to a pilot wave that guides the path of the electron.
I am the person from the concerning discussion (I treat LENR only as a hypothetical possibility) and the above statement is not true - I only emphasize that the ELEMENTARY CHARGE of electron is not objectively smeared over the atom - that there is not a single piece of experimental evidence showing that it can be objectively smeared (e.g. to 10^-10m) or divided (?)
Some arguments I have used - limiting its size:
- in Penning trap limited by 10^-22m: http://iopscience.iop.org/article/10.1088/0031-8949/1988/T22/016
- in electron-position scattering by 10^-20m: http://gabrielse.physics.harvard.edu/gabrielse/overviews/ElectronSubstructure/ElectronSubstructure.html
- the above link says that theory limits by 10^-18m
- "classical electron radius" ( https://en.wikipedia.org/wiki/Classical_electron_radius ) is 2.8 * 10^-15m
In contrast, being objectively smeared over the atom means ~10^-10m, or even ~10^-6m in Rydberg molecules ( http://physicsworld.com/cws/article/news/2016/aug/25/giant-two-atom-molecules-are-the-size-of-bacteria ).

Regarding the wave nature, I am emphasizing the wave-particle duality: that electron is simultaneously corpuscle (e.g. indivisible elementary charge) and coupled ("pilot") wave.
For atom I use intuitions from Couder's experiments with classical object having wave-particle duality ( https://en.wikipedia.org/wiki/Hydrodynamic_quantum_analogs ) - quantization ( http://www.pnas.org/content/107/41/17515.full ) is explained that the coupled wave has to find a resonance - create a standing wave to avoid synchrotron radiation. I see this standing wave as what QM is describing:

https://dl.dropboxusercontent.com/u/12405967/qantization.png [Broken]

So the discussion is not about particles being a point, but about understanding the wave-particle duality: if they are both simultaneously, or maybe only one at the time.
Example of experiment for being simultaneously both is Afshar's: https://en.wikipedia.org/wiki/Afshar_experiment
375px-Afshar-experiment-1.png


Is there an experimental evidence that wave-particle duality means having only one of these natures at the time?
If so, what are the conditions and mechanisms for switching between these two natures?

For example imagine free electron traveling through empty space (as corpuscle/localized wavepacket) - finally it gets to a vicinity of proton and becomes smeared as orbital of atom (change nature corpuscle -> wave).
When exactly this smearing happens? What is its mechanism?
 
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Excitations of the field in the second quantisation and no more wave particle duality.
 
Excitations of the field in the second quantisation and no more wave particle duality.
Solitons are examples of field excitations and the simplest model (Sine Gordon: phi_tt - phi_xx = sin(x)) already has solitons with internal periodic motion, creating coupled waves around: having wave-paricle duality
https://en.wikipedia.org/wiki/Breather
 
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Not sure why a localised wave has to have a wave particle duality in the way I think you mean. It's just a wave with a decaying amplitude in space, hence localized.

BTW, your equation is not in a readable form.
 
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I am in the midst of a discussion with someone who feels very confident that an electron is always and forever a point particle and never a wave; any wave-like behavior that is observed must be attributed to a pilot wave that guides the path of the electron. ... the Penning trapis an example of an experiment that shows that the electron is a point particle and that the elementary charge cannot in any reasonable understanding be spread out over an extensive electron wavefunction.
Your friend's argument is:

1) Penning trap confines electron (or other ion) to a very small "point-like" space and can keep it there for a long time (years).

2) But Schrodinger equation (or, in general, the wave model of an electron) says that the electron "wave" will spread out when left alone. Before long it will cover a large space, bigger than Penning trap.

3) Therefore electron can't be a wave.

Eric Walker said:
Does he have a point, or is he overlooking something?
He's overlooking the fact that Penning trap uses an EM field. When you include an EM field in Schrodinger equation (or Dirac, or QFT, or any other formulation) the wave doesn't necessarily "spread out".

Consider any atom, like hydrogen. The nucleus (like, a proton) provides an EM field - in this case, just a static electric field - which confines the electron. If your friend has had introductory QM course he's seen Schrodinger's for hydrogen atom and knows how the nucleus centripetal force determines specific electron orbits. Penning trap is similar, although more complicated. Actually, an atom typically confines an electron much tighter than a Penning trap, and for a much longer time - like, billions of years. But of course, the orbit is still considered to be a bound wave (in most interpretations).

Penning traps are not used simply to confine an electron, you can do that much easier with a hydrogen atom. A Penning trap allows us to control and manipulate the electron, to study it.

Tell your friend that in this room there are about a million trillion trillion electrons, all confined about 10,000 times tighter than a Penning trap! And, of course, the founders of QM knew that. So if such confinement proved it was a point particle, they didn't need a Penning trap to figure it out.

Finally - tell him to come to PF himself. There are a couple very knowledgeable pilot-wave proponents here. They believe, as he does, that the electron is a particle, not a wave. But even they know that a Penning trap doesn't prove their position. In fact, as you say, pilot wave is just another interpretation, which can't be proven or disproven at this time. Anyway, let him argue with them - see who wins.
 
Not sure why a localised wave has to have a wave particle duality in the way I think you mean. It's just a wave with a decaying amplitude in space, hence localized.
For wave-particle duality we need a localized corpuscle (droplet, elementary charge, soliton), coupled with waves it creates around.
These waves travel all paths in double slit - acting on the corpuscle and leading to interference.
They have to find resonance for e.g. atom to avoid synchrotron radiation.
See Couder's experiments, like

secur, "Therefore electron can't be a wave." is completely not my point.
Instead, I am emphasizing that they are simultaneously both waves and corpuscles.
 
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So how does an electron microscope work?
 
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secur, "Therefore electron can't be a wave." is completely not my point.
Sorry, I didn't notice your post said you were the "discussion partner". I was responding to @Eric Walker's version of your argument, which, apparently, was incorrect. Still, some of my comments are applicable.

I only emphasize that the ELEMENTARY CHARGE of electron is not objectively smeared over the atom - that there is not a single piece of experimental evidence showing that it can be objectively smeared (e.g. to 10^-10m) or divided (?)
Of course it can't be divided (ignoring the quasiparticles of fractional quantum Hall effect).

jarekduda said:
No. According to that reference they determined that electron radius is no greater than 10^-20 cm. That's impressive. But they didn't confine it to that radius! They achieved "a tenfold suppression of the natural width of the cyclotron resonance" which (I think, not sure) gets it down to around 10^-5 cm.

jarekduda said:
Regarding the wave nature, I am emphasizing the wave-particle duality: that electron is simultaneously corpuscle (e.g. indivisible elementary charge) and coupled ("pilot") wave.
Fine. There's no proof of that interpretation, but I can't say your intuition is wrong.

jarekduda said:
For atom I use intuitions from Couder's experiments ...
It's an intuitive analogy, not a proof

jarekduda said:
Example of experiment for being simultaneously both is Afshar's: https://en.wikipedia.org/wiki/Afshar_experiment
As you know most experts disagree with Afshar's conclusion, for various reasons (admittedly, I haven't studied it much).

jarekduda said:
So the discussion is not about particles being a point, but about understanding the wave-particle duality: if they are both simultaneously, or maybe only one at the time. ... what are the conditions and mechanisms for switching between these two natures? ... For example imagine free electron traveling through empty space (as corpuscle/localized wavepacket) - finally it gets to a vicinity of proton and becomes smeared as orbital of atom (change nature corpuscle -> wave). ... When exactly this smearing happens? What is its mechanism?
Nobody knows whether it "switches between the two natures", or the answers to any of these questions. After all pilot wave is a viable interpretation, and it says the two natures are quite separate and both applicable at once. That shows no one has proven otherwise.

Look at it this way. You're claiming these experiments, which have been well known for a decade, prove pilot wave. If that were true, then the physics community would all agree with pilot wave. But they don't. Therefore it must not be proven. QED. What's wrong with that logic? It seems the only possible response is: thousands of physicists, including the best in the profession, are wrong - but you're right. Is that your claim?
 
So how does an electron microscope work?
They usually use transmission or reflection of electron beam: https://en.wikipedia.org/wiki/Electron_microscope
So they focus rather on corpuscular nature of electrons, especially that they can reach resolution below 50pm: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.102.096101 what is smaller than radius of most of atoms.

According to that reference they determined that electron radius is no greater than 10^-20 cm. That's impressive. But they didn't confine it to that radius! They achieved "a tenfold suppression of the natural width of the cyclotron resonance" which (I think, not sure) gets it down to around 10^-5 cm.
Ok, Penning trap is a subtle system, safer limitations can be obtained from electron-positron scattering experiments.
Here is some review saying 2*10^-20m limitation: http://gabrielse.physics.harvard.edu/gabrielse/overviews/ElectronSubstructure/ElectronSubstructure.html
Anyway, even resolution of electron microscope shows that they are much smaller than probability cloud of electron orbital, especially taking Rydberg atoms into consideration.
Nobody knows whether it "switches between the two natures", or the answers to any of these questions. After all pilot wave is a viable interpretation, and it says the two natures are quite separate and both applicable at once. That shows no one has proven otherwise.
If
- nobody knows whether it "switches between the natures",
- nor can propose any conditions (including Rydberg atoms) nor mechanism for it,
- it seems there is no experimental evidence that e.g. elementary charge is objectively smeared,
why can't we just assume that electron has both natures simultaneously?

What says that we should ask for trajectory hidden behind the quantum wavefunction, which describes the standing wave for the coupled wave like in Couder's experiment, or just average over trajectories.
Like in these literally "photos of orbitals": http://journals.aps.org/prb/abstract/10.1103/PhysRevB.80.165404 obtained by averaging positions of single electrons leaving the carbon atom:
https://dl.dropboxusercontent.com/u/12405967/atomphoto.png [Broken]
Look at it this way. You're claiming these experiments, which have been well known for a decade, prove pilot wave. If that were true, then the physics community would all agree with pilot wave. But they don't. Therefore it must not be proven. QED. What's wrong with that logic? It seems the only possible response is: thousands of physicists, including the best in the profession, are wrong - but you're right. Is that your claim?
The only reason I can see is sociological one - people learn QM with some magical envelope: "shut up an calculate", "if you think you understand QM, it means you don't understand QM".
There is huge sociological inertia in physics, especially that the official view is that nobody understand QM.

Agreeing that particles are simultaneously waves and corpuscles allows to disperse this magical fog and start asking questions about details and dynamics behind the effective picture of QM probability cloud. Especially that experiments are now reaching this resolution.

For example to understand fusion, like the one in our Sun: thermal energy of protons is ~1000x smaller than required to cross the Coulomb barrier - so there is tunneling used for explanation (Gamow).
But tunneling/teleporting through a huge barrier of proton seems kind of magical explanation - it could be repaired if considering trajectory of corpuscular part of electron: it could perform (elongated elliptic) trajectory between the two collapsing nuclei, screening the Coulomb repulsion.
Like p - e - p initial system would like to collapse due to Coulomb.
If such electron-assisted fusion (the original discussion) is possible, maybe it could be also achieved in lower temperatures, for example to explain 10000x larger tritium release from volcanoes that estimated for fission: <<unacceptable reference removed>>
 
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If - nobody knows whether it "switches between the natures" ... why can't we just assume that electron has both natures simultaneously?
You know what happens when we "assume" (makes a donkey out of you and me :-). Other people are equally certain that other interpretations are right. I (and most others at PF) am agnostic, waiting for convincing evidence. Let's revisit the issue in 10 years. If it turns out the evidence supports your view, I'll be very happy to admit it.

jarekduda said:
The only reason I can see is sociological one - people learn QM with some magical envelope: "shut up an calculate", "if you think you understand QM, it means you don't understand QM". ... There is huge sociological inertia in physics, especially that the official view is that nobody understand QM.
That's true. There's a "huge sociological inertia in physics" throughout, not just QM. Major "paradigm shifts" will occur one of these decades.

jarekduda said:
Agreeing that particles are simultaneously waves and corpuscles allows to disperse this magical fog and start asking questions about details and dynamics behind the effective picture of QM probability cloud. Especially that experiments are now reaching this resolution.
Yes, the picture might start to become clear, as experimental technology advances. I'm 100% in favor of asking questions about those details and dynamics. It's the only way to get the answers - which aren't known yet, IMHO.

jarekduda said:
If such electron-assisted fusion (the original discussion) is possible, maybe it could be also achieved in lower temperatures, for example to explain 10000x larger tritium release from volcanoes that estimated for fission: <<unacceptable reference removed>>
Unfortunately that "Low Energy Nuclear Reactions" (i.e. "Cold Fusion") stuff is considered "fringe" physics. Certainly not convincing.

Let me emphasize again: no one is saying pilot wave is wrong, just that the issue is undecided. Let's talk again in 10 years, see if any of this pans out. Until then, good luck, and don't take any wooden nickels!
 

zonde

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I am the person from the concerning discussion (I treat LENR only as a hypothetical possibility) and the above statement is not true - I only emphasize that the ELEMENTARY CHARGE of electron is not objectively smeared over the atom - that there is not a single piece of experimental evidence showing that it can be objectively smeared (e.g. to 10^-10m) or divided (?)
I think the same way that elementary charge of electron can't be smeared out or divided.
But I could not get clear answer if there is or there isn't mathematical framework for describing Coulomb potential of charged particles in superposition.
Here is my attempt at finding that out: https://www.physicsforums.com/threads/quantum-superposition-of-coulomb-potential.886213/
From stevendaryl's answer I sort of conclude that there is no such thing. On the other hand DrClaude says that delocalized charges is nothing unusual.
 
Sorry, I didn't notice your post said you were the "discussion partner". I was responding to @Eric Walker's version of your argument, which, apparently, was incorrect. Still, some of my comments are applicable.
I think my summary of his position was incorrect only on a minor point of terminology. What jarekduda has been referring to as "elementary charge" I referred to as "electron". With that misunderstanding out of the way, I think the heart of my summary of his argument still stands, which is that the Penning trap (and various other experiments) are sufficient to decide the question of what is going on at the fundamental level in favor of his concrete proposal about "elementary charges" having concrete trajectories and being guided by attendant (pilot) waves. And that he believes that a position of agnosticism is untenable in light of his explanation.
 

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