Isn't the only theoretical proof of momentum conservation (in QM) a statistical one? I don't see this reflected in your response, or am I missing it?
No, the theoretical proof of momentum conservation is not statistical, unless you start with a state that does not have a well defined momentum from the get-go (in which case your initial conditions are statistical, so no theory can get rid of the statistical character of such a situation). Einstein's thought experiments started from a situation of well-defined momentum. Perhaps you are saying that it is impossible for a macro system to have a well defined momentum, and Bohr could have simply made that argument whenever there is coupling, but it would have been viewed by Einstein as circular reasoning. Bohr had to show that adopting Einstein's view that all systems could have well defined momenta still resulted in experiments where there were not well defined momenta (or whatever version of the UP was under dispute). Bohr was not trying to argue a fringe philosophy, he was trying to show that the alternative was internally inconsistent. Neither Bohr nor Einstein at the time seemed aware of the possibility of the Bohmian interpretation, and I do wonder what each of their reactions were when they did find out about that.Isn't the only theoretical proof of momentum conservation (in QM) a statistical one? I don't see this reflected in your response, or am I missing it?
The modern viewpoint is via Noethers Theorem and it is conserved just as much in QM as in classical mechanics. But in QM it is the momentum operator that is conserved - the statistical aspect is the usual statistical interpretation of operators - ie provided the system is in an eigenstate of momentum and it posses spatial symmetry then it remains in that eigenstate. Actually you do not need to invoke Noethers theorem in QM because it is strongly related to the displacement operator:Isn't the only theoretical proof of momentum conservation (in QM) a statistical one? I don't see this reflected in your response, or am I missing it?
Although off topic Einstein was evidently not amused:Neither Bohr nor Einstein at the time seemed aware of the possibility of the Bohmian interpretation, and I do wonder what each of their reactions were when they did find out about that.
IBYP, I'd missed your qualifications and edit as I was composing. I appreciate your desire to rein in the thread and prevent a devolution into debates of interpretation.@ jambaugh: please read post 12! You're telling me nothing new and are mainly discussing things which I've explicitly told (by now) that this thread is not about.
Yes - but remember the hidden assumption - namely they actually have properties independent of measurement. If not you have strange correlations but influence is probably not the appropriate word. It is true QM probably has some sort of non locality inbuilt but it is rather a strange sort since it can not be used to send information.He seems to make a lot of sense.
We've all heard of the Bohr-Einstein debates to some degree (the essence of them being: Einstein tried to convince Bohr that the uncertainty principle is not true by claiming to have found concrete thought experiments that seemed to violate it). Bohr countered Einstein's arguments.
But what I don't understand is why Bohr not simply said "but you're using classical reasoning", since Einstein heavily depended on classical conservation laws, for example that of momentum. Okay conservation of momentum is still true for statistical averages in the QM formalism, but Einstein really used them classicaly: imagining one particle bouncing off a wall imparting momentum to the wall in such a way as to keep the total momentum fixed.
For example, if Bohr hadn't given the conclusive counter-arguments which he did (incidentally also using classical conservation laws), would others have accepted Einstein's reasoning? Or would they simply have countered with "yes but you're using a classical reasoning"? I think the latter. Hence I'm confused why Bohr didn't immediately answer with it.
NOTE: please don't reply with "the UP is merely a statistical statement that can be derived from the formalism and which talks about the standard deviations of the position and momentum distribution": I know this, but this is not in the least what the above question is about.
EDIT: some people apparently, for some reason, interpreted my OP as inviting general comments about Einstein's realistic view, which is not what this thread is about, every sentence I wrote down was supposed to be specific to the two thought-experiments Einstein brought forth in the Bohr-Einstein debates and are not with a greater generality than that. My question is simply why Bohr thought Einstein's reasoning using classical concepts such as conservation of momentum (not averaged) was a serious threat, saying things like "it would be the end of physics if Einstein were right" etc, although these concepts are not really part of quantum mechanics and so can hardly be used to derive a contradiction.
If I argue that A implies B. And you are arguing Not B then you need to point out that Not A is possible (since A implies B = B or Not A.)Hello, I'm just replying to ask whether you've found out the answer for your question. I think even if Bohr had said "but you're using classical reasoning", it would not help his side of the argument very much. I'm not sure if you'll get this analogy but saying "but you're using classical reasoning" is like a laywer saying "but you're a thief" to a thief in a court. The lawyer and the thief both know that the thief if a thief but how will that help the lawyer prove that the lawyer is correct to the jury. In a similar sense, Bohr and Einstein both knew Einstein was using classical reasoning but how will that help Bohr prove that he is correct. I hope you get where I'm coming from but I'm not even in a University yet so I've probably said something wrong. If you have found a more reliable answer to your question as I am genuinely interested in finding out the answer.