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B What does a Penning trap say about the electron?

  1. Nov 1, 2016 #1
    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?
    Last edited: Nov 1, 2016
  2. jcsd
  3. Nov 1, 2016 #2


    Staff: Mentor

    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.

    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.
  4. Nov 1, 2016 #3


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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.
  5. Nov 1, 2016 #4
    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?
  6. Nov 1, 2016 #5


    Staff: Mentor

    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.

    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.
  7. Nov 1, 2016 #6


    Staff: Mentor

    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.
  8. Nov 2, 2016 #7
    I'm thinking specifically of this and similar descriptions I have come across on Wikipedia:
    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.
  9. Nov 2, 2016 #8


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    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.
  10. Nov 2, 2016 #9
    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."
  11. Nov 2, 2016 #10


    Staff: Mentor

    Well, we here all agree with this, so I'm not sure how much point there is in trying to discuss it here.

    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?
  12. Nov 2, 2016 #11
    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."
  13. Nov 2, 2016 #12


    Staff: Mentor

    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.

    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.

    I don't see why. Where does the relative state interpretation say this is impossible? See above.

    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.
  14. Nov 2, 2016 #13
    A point charge does extend to infinity ie the classical E field.
    Last edited: Nov 2, 2016
  15. Nov 2, 2016 #14
    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.ed...lectronSubstructure/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...t-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

    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?
    Last edited by a moderator: May 8, 2017
  16. Nov 2, 2016 #15
    Excitations of the field in the second quantisation and no more wave particle duality.
  17. Nov 2, 2016 #16
    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
  18. Nov 2, 2016 #17
    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.
  19. Nov 2, 2016 #18
    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.

    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.
  20. Nov 2, 2016 #19
    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.
  21. Nov 2, 2016 #20
    So how does an electron microscope work?
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