# B What does a Penning trap say about the electron?

#### jarekduda

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.
So what kind of evidence could convince you?
This is not a place for interpretations, but an objective yes or no question: do particles have simultaneously both natures, or only one at the time?

Claiming that only one leaves us with many questions which are not only unanswered, but also seem impossible to answer (e.g. due to Rydberg atoms), like the conditions and mechanisms for switching the nature, the problem with objectively smeared indivisible elementary charge ...

All these issues seem to vanish (?) if accepting that they are simultaneously both. Additionally, particles are similar to solitons, for which having internal clock (periodic process) generating a coupled wave is quite natural (e.g. breathers).
Do you have any experimental evidence against particles being simultaneously both: corpuscles (e.g. indivisible elementary charge) and coupled waves?

If not, please explain your agnosticism: between being satisfied with lack of answers, requiring controversial and experimentally unsupported smearing of elementary charge ... and a view which allows to provide them?

That's true. There's a "huge sociological inertia in physics" throughout, not just QM. Major "paradigm shifts" will occur one of these decades.
It is happening right now as resolution of experiments starts allowing us to look inside the quantum probability clouds, like 50pm resolution of electron microscope or the photos of orbitals above.
We now need to break this "sociological inertia" so that physicists start asking questions about details and dynamics hidden behind the probability clouds - instead of just being satisfied with "shut up and calculate" and lots of unanswered questions.

Unfortunately that "Low Energy Nuclear Reactions" (i.e. "Cold Fusion") stuff is considered "fringe" physics. Certainly not convincing.
I have very mixed feelings about this topic, I have looked closer at it only because considering electron trajectory could make it non-negligible ... also the high tritium release from volcanoes seems highly suspicious: it decays in 12 years to He3, and fission is extremely ineffective in producing tritium ... and there are lots of serious people and institutions (e.g. NASA, US Navy, MIT) claiming observation of such effects: <off topic reference removed>

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.
Indeed superposition of elementary charges leads to many questions and problems.
For example there is this huge 1um Rydberg molecule ( http://physicsworld.com/cws/article/news/2016/aug/25/giant-two-atom-molecules-are-the-size-of-bacteria ) - imagine there is a charged particle flying nearby, how its trajectory would be affected by this bond electron?

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#### PeterDonis

Mentor
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
In contrast, being objectively smeared over the atom means ~10^-10m, or even ~10^-6m in Rydberg molecules
All of these are different physical scenarios, with different Hamiltonians (different potentials), so you would expect them to have different behavior. So size limitations that apply to one scenario won't apply to others. The potential in an atom is very, very different from the potential in a Penning trap; that's why the latter confines the electron wave function (and, for that matter, its "elementary charge") much more than the former. That means you can't use the "size" of an electron in a Penning trap to "prove" anything about the "size" of an electron in an atom, or any other system. You have to model each system based on its actual physics.

#### PeterDonis

Mentor
why can't we just assume that electron has both natures simultaneously?
Because there is no way to experimentally distinguish that interpretation from all the others. All the interpretations use exactly the same math and make exactly the same predictions for all experiments. So experimentally they are all identical. Physics is an experimental science; models that make identical experimental predictions are identical as far as physics is concerned.

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.
If you think these experiments are going to enable us to distinguish between the different interpretations of QM, then you should be able to show us some references that explain how the different interpretations will make different predictions about the results of these experiments. Can you?

This is not a place for interpretations, but an objective yes or no question: do particles have simultaneously both natures, or only one at the time?
This does not exhaust the possibilities; it could be that quantum objects are neither particles nor waves, but something else.

But the real question is, how can you determine this by experiment? If you think this can be done, show us the math. Show us how your interpretation makes concrete predictions, using the math of QM, that are different from the predictions made by all other interpretations, for some experiment. As I've already commented several times in this thread, that will be very difficult since all the interpretations use exactly the same math.

#### jarekduda

All of these are different physical scenarios, with different Hamiltonians (different potentials), so you would expect them to have different behavior. So size limitations that apply to one scenario won't apply to others. The potential in an atom is very, very different from the potential in a Penning trap; that's why the latter confines the electron wave function (and, for that matter, its "elementary charge") much more than the former. That means you can't use the "size" of an electron in a Penning trap to "prove" anything about the "size" of an electron in an atom, or any other system. You have to model each system based on its actual physics.
Sure, but the question seems quite objective: what is the size of elementary charge of electron?
And I think you agree that the consensus is that it is below 10^-15m.

What is many orders of magnitude smaller than sizes of quantum probability clouds - so the question is if the elementary charge of electron is objectively smeared to this huge probability cloud?
Or maybe wavefunction only describes wave coupled with the elementary charge, like in Couder's picture?

#### PeterDonis

Mentor
LENR is off topic for this thread; however you might feel about it, it is not mainstream science. And in any case it's not necessary to bring it up here; you have made claims about plenty of experiments that are mainstream science, and the discussion should focus on those.

#### PeterDonis

Mentor
but the question seems quite objective: what is the size of elementary charge of electron?
And I think you agree that the consensus is that it is below 10^-15m.
No, I don't. I think that the "size" of an electron depends on the physical situation (and on how you define "size", but the obvious definition, something like the characteristic spatial spread of the wave function, is what you are implicitly using, whether you realize it or not). In a Penning trap it can have one size; in an ordinary atom it can have another. That is what the math of QM says, and the math of QM makes correct predictions about the experimental results.

What is many orders of magnitude smaller than sizes of quantum probability clouds
No. The "size" of the electron--the numbers you quoted for the various experimental situations--is the "size" of the "quantum probability clouds" (i.e., the characteristic spatial spread of the wave function).

the question is if the elementary charge of electron is objectively smeared to this huge probability cloud?
The electron's charge can only be localized to the extent that the electron's wave function can; the "size" of the electron is the "size" of its charge distribution. At least, that's what the math of QM says, and the math of QM makes correct predictions about the experimental results.

#### zonde

Gold Member
Because there is no way to experimentally distinguish that interpretation from all the others. All the interpretations use exactly the same math and make exactly the same predictions for all experiments. So experimentally they are all identical. Physics is an experimental science; models that make identical experimental predictions are identical as far as physics is concerned.
There are many things that experimentalists describe classically.
So would you say that interpretations that are consistent with other models used in descriptions of experiments are equivalent with interpretations that are not consistent with other models used in descriptions of experiments?

#### PeterDonis

Mentor
There are many things that experimentalists describe classically.
Yes, because the classical description is a good enough approximation for the situation they are describing.

would you say that interpretations that are consistent with other models used in descriptions of experiments are equivalent with interpretations that are not consistent with other models used in descriptions of experiments?
Please give a specific example of an experiment and descriptions using different interpretations that you think are inconsistent.

#### jarekduda

No, I don't. I think that the "size" of an electron depends on the physical situation (and on how you define "size", but the obvious definition, something like the characteristic spatial spread of the wave function, is what you are implicitly using, whether you realize it or not). In a Penning trap it can have one size; in an ordinary atom it can have another. That is what the math of QM says, and the math of QM makes correct predictions about the experimental results.
I thought about various experiments as providing various upper bounds - we should finally take minimum of them.

So you claim that elementary charge can grow above let say 10^-15m?
Standard one has electric field proportional to 1/r^2, how does it look for such smeared elementary charge?
I thought elementary charge is indivisible - is there any experimental evidence suggesting that it can be objectively smeared?

#### zonde

Gold Member
Indeed superposition of elementary charges leads to many questions and problems.
For example there is this huge 1um Rydberg molecule ( http://physicsworld.com/cws/article...t-two-atom-molecules-are-the-size-of-bacteria ) - imagine there is a charged particle flying nearby, how its trajectory would be affected by this bond electron?
Your argument is rather weak. You are assuming trajectory - so basically this is "assuming the consequent" fallacy.
So it would be rather more correct to ask your opposition for alternative model, see what is proposed and then look for flaws (inconsistencies) in proposed alternative model.

#### PeterDonis

Mentor
What's the difference? Have you looked at the actual math? Do you understand that, according to the math of QM, the "elementary charge" of the electron is just the physical constant $- e$ (the "charge on the electron") times the electron's wave function? So mathematically they're the same thing.

I thought about various experiments as providing various upper bounds - we should finally take minimum of them.
What is your justification for thinking that?

So you claim that elementary charge can grow above let say 10^-15m?
Standard one has electric field proportional to 1/r^2, how does it look for such smeared elementary charge?
I thought elementary charge is indivisible - is there any experimental evidence suggesting that it can be objectively smeared?
You appear to be mixing up the classical and quantum models of the electron. The classical model, where the electron is a point particle with an electric charge that produces a $1/r^2$ Coulomb field, is an approximation. (Even classically it's only an approximation, because such a point charge does not yield a nonsingular solution of Maxwell's Equations for the electromagnetic field.) It breaks down when quantum effects become important. The quantum model of the electron is what I described above: the electron has a wave function, and its charge distribution is just the physical constant $- e$ times the wave function.

In fact, even the QM model I just described is a non-relativistic approximation; to get a better, relativistically correct model, you need to look at quantum field theory.

#### zonde

Gold Member
Please give a specific example of an experiment and descriptions using different interpretations that you think are inconsistent.
No, please answer my question in general. Is the experiment the only thing that can make us discard some model? If a model can not be scientifically tested should we discard such model?

#### PeterDonis

Mentor
I can't, because I don't know of any cases that satisfy your criteria. That's why I asked you for a specific example.

Is the experiment the only thing that can make us discard some model? If a model can not be scientifically tested should we discard such model?
The various interpretations of QM are not "models" in the scientific sense. They are different ways of describing a single model--the math of QM--in ordinary language. If someone comes up with a way to have different interpretations make different experimental predictions, then they will be different models and we can test them against each other.

#### zonde

Gold Member
Have you looked at the actual math? Do you understand that, according to the math of QM, the "elementary charge" of the electron is just the physical constant $- e$ (the "charge on the electron") times the electron's wave function? So mathematically they're the same thing.
Can you please give reference (preferably free link) for actual math of what you are saying?

Gold Member

#### zonde

Gold Member
The various interpretations of QM are not "models" in the scientific sense. They are different ways of describing a single model--the math of QM--in ordinary language. If someone comes up with a way to have different interpretations make different experimental predictions, then they will be different models and we can test them against each other.
Various interpretations of QM are not theories in the scientific sense. But they are physical models. Math of QM is just math, it's not physical model.

#### PeterDonis

Mentor
probability density function is not the same as wave function.
It's the square of the wave function. That doesn't affect anything I said.

if we use probability density function we get charge probability density, right?
Yes.

we don't have some kind of Coulomb potential probability density.
That's because in QM the potential is part of the Hamiltonian; it's an operator, not a wave function.

#### PeterDonis

Mentor
Various interpretations of QM are not theories in the scientific sense. But they are physical models.
No, they're not. They're interpretations in ordinary language of physical models.

Math of QM is just math, it's not physical model.
A physical model is math: math is the language we use to write down physical models. The math does come with rules about what quantities in the math correspond to what physical measurement results; but that is the same for all interpretations. The interpretations only differ in how the describe, in ordinary language, things that aren't measurement results.

#### zonde

Gold Member
That's because in QM the potential is part of the Hamiltonian; it's an operator, not a wave function.
It's external potential that's part of Hamiltonian. Not the potential from electrons own charge.

#### zonde

Gold Member
A physical model is math: math is the language we use to write down physical models. The math does come with rules about what quantities in the math correspond to what physical measurement results; but that is the same for all interpretations. The interpretations only differ in how the describe, in ordinary language, things that aren't measurement results.
Math with minimum correspondence rules to measurements is phenomenological model not physical model. For physical model you need some irreducible intermediate component in model. That component we would take as representing something physically real.

#### PeterDonis

Mentor
It's external potential that's part of Hamiltonian. Not the potential from electrons own charge.

Math with minimum correspondence rules to measurements is phenomenological model not physical model. For physical model you need some irreducible intermediate component in model. That component we would take as representing something physically real.
I'm not sure what this means, but it doesn't sound like physics, it sounds like personal opinion. Which is off topic here. The key point is that all interpretations of QM make the same predictions for all experiments. If you disagree with that, please provide an example, with references. If you agree, then we don't need to argue about what the definition of a "model" is.

#### zonde

Gold Member
Let's take wikipedia
https://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics)#Electrostatic_or_coulomb_potential
It says there: "If there are many charged particles, each charge has a potential energy due to every other point charge (except itself)."
And the same is reflected in mathematical expression there.

I'm not sure what this means, but it doesn't sound like physics, it sounds like personal opinion. Which is off topic here.
[Interpretations] are different ways of describing a single model--the math of QM--in ordinary language.
I responded with my opinion. Or would you claim that your opinion is not opinion but solid science?

The key point is that all interpretations of QM make the same predictions for all experiments. If you disagree with that, please provide an example, with references. If you agree, then we don't need to argue about what the definition of a "model" is.
Come on, you are putting it in black or white categories - agree or disagree.
For me it's gray. I am skeptical that some interpretations are capable (and able to make predictions) about many charged particle configurations where one way of possible evolution is irreversible (time asymmetric). Can you shed some light on that question? Mathematical model or something?

#### PeterDonis

Mentor
No, I told you what the actual science is: the math of QM. And I said that yes, the math has to include rules for what mathematical quantities match up with what experimental results. But "interpretations" say much more than that, and everything they say beyond that is not science. If anyone ever figures out how to make different interpretations actually make different predictions about some experiment, then we can run the experiment and see, and then that part of "interpretations" will be science too. But that hasn't happened yet.

I am skeptical that some interpretations are capable (and able to make predictions) about...
One more time: all the interpretations use exactly the same math and make exactly the same predictions. Do you understand what that means?

#### PeterDonis

Mentor
Let's take wikipedia
Two points here. First, note that this is talking about an "electrostatic" system with multiple point charges. Which is impossible unless there is something else present to hold the charges static; otherwise they will repel (or attract, if they're opposite charges) each other. So the "Hamiltonian" being shown there is incomplete; it doesn't include the energy associated with whatever is holding the charges static.

Second, why is a potential energy for each charge due to itself not included? Because, if you use the "naive" method being used there (1/r potential), it's infinite. Which would completely break the mathematical model being used. In other words, in this example, we are working in some approximation in which the charge self-energy problem (which is what I just stated) can be ignored. So if you want to actually address the issue you raised, you need to go find an example where the charge self-energy problem is not ignored.

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