# I Differing first-principle models for Maxwell-Boltzmann statistics?

#### Dale

Mentor
I think even real electrons in a beer-electron-pong set-up would result in the dice model.
If that were true then we would be able to observe substantial departures from equipartition

#### greswd

If that were true then we would be able to observe substantial departures from equipartition
If we fire 9 electrons, one at a time, at a set-up of 6 holes where the electron has a 1/6th chance of entering any one hole, we can see from there that it is no different from beer-pong.

#### Dale

Mentor
If we fire 9 electrons, one at a time, at a set-up of 6 holes where the electron has a 1/6th chance of entering any one hole, we can see from there that it is no different from beer-pong.
If that were true then there would be a violation of equipartition. I don't have any evidence to suggest that is correct, do you?

#### greswd

If that were true then there would be a violation of equipartition. I don't have any evidence to suggest that is correct, do you?
But you can imagine a fair set-up, with a 1/6th chance each, like a fair die.
And the electrons are fired one at a time. It is virtually identical to beer pong.

#### Dale

Mentor
It is virtually identical to beer pong.
With the very big difference of distinguishability, right? You are still envisioning that the electrons are indistinguishable, but ping pong balls are not. That has testable consequences.

#### greswd

With the very big difference of distinguishability, right? You are still envisioning that the electrons are indistinguishable, but ping pong balls are not. That has testable consequences.
But can you imagine how it would differ?
We set it up with a fair 1/6th chance each, or very closely to perfect fairness.
But somehow the electrons behave differently and don't behave according to those odds.
That would be very strange. Electrons can indeed behave very strangely, or non-classically, but not in this manner.

#### DrClaude

Mentor
If I understand correctly, in the dice / beer pong analogy, you want to label the units of energy, distinguishing which is where?

If that is the case, you need to understand that keep track of the energy is only accounting (see the Feynman lectures). The state of the economy does not depend on which dollar is in which bank account.

#### greswd

If I understand correctly, in the dice / beer pong analogy, you want to label the units of energy, distinguishing which is where?

If that is the case, you need to understand that keep track of the energy is only accounting (see the Feynman lectures). The state of the economy does not depend on which dollar is in which bank account.
I mentioned removing all forms of labels in #15, and also mentioned throwing all 9 balls at the same time, albeit "ghostly" balls, in #10.

#### DrClaude

Mentor
I mentioned removing all forms of labels in #15, and also mentioned throwing all 9 balls at the same time, albeit "ghostly" balls, in #10.
Then I must admit I don't understand the discussion.

#### Dale

Mentor
Electrons can indeed behave very strangely, or non-classically, but not in this manner.
I think they do behave non-classically in exactly this manner. At least I am not aware of any evidence of a violation of the equipartition theorem. Are you? You seem very convinced by this, but the consequences would be easily observable.

#### greswd

I think they do behave non-classically in exactly this manner. At least I am not aware of any evidence of a violation of the equipartition theorem. Are you? You seem very convinced by this, but the consequences would be easily observable.
But electrons, no matter how non-classical, can't change the 1/6th odds of the fair setup. And its one at a time so two electrons can't interfere with one another.

So it could be that Maxwell-Boltzmann statistics are right but with the wrong explanation.

Or because they don't refer to electrons, but quanta of energy, which somehow behave differently.

#### Dale

Mentor
And its one at a time so two electrons can't interfere with one another.
If you detect after each electron where it went then that makes it distinguishable. If you fire them in one at a time so there is no interference but don't observe their locations until the end then I think they are indistinguishable and would have the corresponding statistics, not the beer pong statistics.

I don't think it works the way you seem to think, and I am not aware of any evidence suggesting it works the way you suggest which I think would be big-news kind of evidence. And you don't seem to be aware of any such evidence either.

It is certainly also possible that I am misunderstanding or misapplying the equipartition theorem, but as far as I know distinguishability has some pretty dramatic physical consequences.

#### greswd

If you detect after each electron where it went then that makes it distinguishable. If you fire them in one at a time so there is no interference but don't observe their locations until the end then I think they are indistinguishable and would have the corresponding statistics, not the beer pong statistics.
But if its like the double-slit experiment, with the beer cups being like the slits, the electrons just pass right through the slits, and there is nothing to observe at the end.

Kinda like having cups with the bottoms cut off, the ping-pong balls just fall right through, and at the end of the experiment, all we're left with is 6 empty cups.

#### Dale

Mentor
But if its like the double-slit experiment, with the beer cups being like the slits, the electrons just pass right through the slits, and there is nothing to observe at the end.
I didn't say anything about the double slit experiment. It is not the only experiment that invalidates the notion of counterfactual definiteness. There is no counterfactual definiteness in QM, regardless of if you are describing electrons in wells or photons through slits.

#### greswd

I didn't say anything about the double slit experiment. It is not the only experiment that invalidates the notion of counterfactual definiteness. There is no counterfactual definiteness in QM, regardless of if you are describing electrons in wells or photons through slits.
If you detect after each electron where it went then that makes it distinguishable. If you fire them in one at a time so there is no interference but don't observe their locations until the end then I think they are indistinguishable and would have the corresponding statistics, not the beer pong statistics.
noted, not double-slit. what kind of experimental set-up do you think would yield the corresponding statistics?
because I'm wondering what it means to not observe during the firing and observing at the end of it all.

#### Dale

Mentor
noted, not double-slit. what kind of experimental set-up do you think would yield the corresponding statistics?
because I'm wondering what it means to not observe during the firing and observing at the end of it all.
I would think of some sort of potential well created by a circuit where you could turn the individual wells on or off as needed. They would need to be deep enough potential wells that 9 electrons plus or minus would not alter the probabilities. Then you can turn off the wells one at a time and count how many electrons leave each well.

#### greswd

I would think of some sort of potential well created by a circuit where you could turn the individual wells on or off as needed. They would need to be deep enough potential wells that 9 electrons plus or minus would not alter the probabilities. Then you can turn off the wells one at a time and count how many electrons leave each well.
That means that somehow the electrons are defying the setup that every well has a 1/6th chance. Interesting, someone should totally conduct this experiment.

#### Dale

Mentor
That means that somehow the electrons are defying the setup that every well has a 1/6th chance.
Actually, no it doesn't mean that. If you go to all of the 2002 distinct configurations you still find that each well is equally likely to contain any given amount of energy. The 1/6 chance is not violated. All that is changed is the distinction if a well with one unit of energy got the first unit or the last unit. In either case it still had the same 1/6 chance to get it but those two scenarios are actually the same scenario.

"Differing first-principle models for Maxwell-Boltzmann statistics?"

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