What does a Penning trap say about the electron?

[PeterDonis]

I have not asked about size of electron, but about size of its elementary charge.

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]

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]

No, please answer my question in general.

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]

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?

 

[PeterDonis]

Can you please give reference (preferably free link) for actual math of what you are saying?

Any QM textbook. For a quick summary, see here:

https://en.wikipedia.org/wiki/Charge_density#Charge_density_in_quantum_mechanics

 

[zonde]

Any QM textbook. For a quick summary, see here:

https://en.wikipedia.org/wiki/Charge_density#Charge_density_in_quantum_mechanics

Well, yes. But probability density function is not the same as wave function.
Anyways if we use probability density function we get charge probability density, right? But we don't have some kind of Coulomb potential probability density.

 

[zonde]

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]

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]

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]

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]

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]

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

Reference, please?

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]

Reference, please?

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.

You expressed your opinion:

[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]

You expressed your opinion

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]

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.

 

[zonde]

You expressed your opinion

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.

You expressed quite common opinion of mathematical physicist*. Why do you say "No"? Can't you tell apart opinion from something else?

* I will make the point by quoting Feynman's opinion: "And there's a very important thing that a lot of people who study physics that come from mathematics don't appreciate. The physics is not mathematics, and mathematics is not physics. One helps the other."

 

[PeterDonis]

The physics is not mathematics, and mathematics is not physics. One helps the other.

Since we're playing "find the quote", here's another one from Feynman: "If you want to understand Nature, you must learn the language she speaks in." Meaning mathematics. That's all I'm saying: if you want to be precise and describe the physics, you have to look at the math. And if two different "interpretations" both use the same math, then they are both describing the same physics, regardless of how different the ordinary language is that is used.

 

[PeterDonis]

This thread has run its course and is now closed.