Differing first-principle models for Maxwell-Boltzmann statistics?

[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]

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]

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]

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]

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.

 

[greswd]

wow, that's pretty interesting. I think most would imagine a "beer-pong distribution" as the simplest method of probabilistically distributing energy among particles. but nature appears to have other ideas.

As long as the balls are indistinguishable and the cups are distinguishable it will work fine.

I've been thinking about this, do you think a system of particles in nature uses a similar model to the "beer-pong scenario" to distribute energies?

it could be a different form of distribution

 

[greswd]

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.

but physically, the electrons land in the wells no differently than the balls in the cups. so I can't imagine how we would be able to arrive at different numerical results