I More double slit experiment questions

[jackjack2025]

TL;DR Summary

Double slit experiment and Feynman lecture comments on it

In the Feynman lectures Chapter 1 on Quantum Behaviour he states:

"We make now a few remarks on a suggestion that has sometimes been made to try to avoid the description we have given: “Perhaps the electron has some kind of internal works—some inner variables—that we do not yet know about. Perhaps that is why we cannot predict what will happen. If we could look more closely at the electron, we could be able to tell where it would end up.” So far as we know, that is impossible. We would still be in difficulty. Suppose we were to assume that inside the electron there is some kind of machinery that determines where it is going to end up. That machine must also determine which hole it is going to go through on its way. But we must not forget that what is inside the electron should not be dependent on what we do, and in particular upon whether we open or close one of the holes. "

The bold parts sound sensible initially, but at the same time I think they need some justification.

So for example the first bold sentence. Is he saying if something contributes to determining where it ends up, then it must determine the whole path it took to get there? What is the justification for that?

And the second bold line, in the chapter he has already explained an experiment where one tries to measure which slit it goes through, and the act of measurement can affect the results and the interference pattern is lost. But now he seems to apply some reasoning that what we do shouldn't affect the inner variables which may contribute to the results.

 

[PeroK]

The assumption is that the machinery is classical in nature. The proton, for example, has internal machinery, that being a certain state of three quarks. But, that machinery is QM in nature.

 

[jackjack2025]

There are theories with 'hidden variables' that seem to match experimental results, e.g. De Broglie-Bohm. So it seems valid to at least consider the possibility. Not to say De Broglie - Bohm is correct, but Feynman seems to quickly dismiss this sort of thing in the quoted passage, but I am not sure why.

To my logic, there could be hidden variables which affect the final position of something, but do not necessarily define the exact path taken.

Analogies get me into trouble on these forums, but:
If I take a Stock price (or particle) S and say that it behaves stochastically according to
dS(t) = u S(t) dt + o S(t) dW(t)
where W is a Brownian motion, u is the drift etc.

I can look at real data to try to estimate 'u', but I can never really get a good estimate for the drift 'u'. It is 'hidden' (from me) as a variable. 'u' certainly should affect the path the Stock takes. But it doesn't tell you the exact path it will take. Even if you knew the value of 'u' and 'o' exactly, you could get a probability distribution of results/paths, but you can't conclude that it determines exactly which path it takes. So why does Feynman suggest that the hidden variable must determine which slit it passes through on its way to the end result?

And the second line I bolded is simpler. How can he show that what we do can affect the results of a quantum experiment and then say something along the lines of: well there can't be hidden variables because those shouldn't be affected by what we do. It makes no sense. If experimental data shows that what we do in terms of observation does affect the results of the experiment, then it is natural it could affect the hidden variables too, no?

Feynman being a genius is perhaps saying something else that I haven't understood, but the statements aren't obvious.

 

[PeterDonis]

There are theories with 'hidden variables' that seem to match experimental results, e.g. De Broglie-Bohm.

The "hidden variables" in that theory are the unobservable particle positions--but those by themselves don't determine what the particles do. The quantum potential is also part of the particle dynamics, and the quantum potential is what, for example, "detects" whether one or both slits are open in the double slit experiment. So it's not quite the kind of model Feynman was describing.

To my logic, there could be hidden variables which affect the final position of something, but do not necessarily define the exact path taken.

Bohmian mechanics doesn't work that way.

 

[Nugatory]

So for example the first bold sentence. Is he saying if something contributes to determining where it ends up, then it must determine the whole path it took to get there? What is the justification for that?

The justification is that any classical model must work that way - that's pretty much what "classical" means - and Feynman's point in this discussion is that classical models don't work.