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- #27

Ken G

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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

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- #28

bhobba

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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:

http://en.wikibooks.org/wiki/Quantum_Mechanics/Symmetry_and_Quantum_Mechanics

'However, such a plane wave is invariant under a displacement, except for the multiplicative phase factor, which has no physical consequences since it disappears when the probability distribution is obtained. Thus, we see that invariance under displacement of the wave function and a definite value of the momentum are linked, in that each implies the other: Invariance under displacement ⇔ Definite momentum'

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Bill

- #29

bhobba

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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.

http://arxiv.org/ftp/arxiv/papers/1007/1007.0769.pdf

'Have you noticed that Bohm believes (as de Broglie did, by the way 25 years ago) that he is able to interpret the quantum theory in deterministic terms? That way seems too cheap to me. But you, of course, can judge this better than I.'

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Bill

- #30

Ken G

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I read this thread and get a tension vibe... just saying.

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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.

But you asked potential respondents to get into the head of Bohr (and by implication Einstein) with the form of your question and that does, absent your qualifiers, invite a broad range of speculation. Rereading I still am not clear what answers you are seeking.

It would be helpful if you further qualified what you understand as the alternative to "your using classical reasoning", though that again may open the interpretation can-o-worms.

One point w.r.t. conservation laws. Note that energy-momentum conservation is typically absolute in quantum interactions. One sees this in the mechanisms for producing entanglement, e.g. two quanta are entangled via anti-correlation of their momenta by exact measurement of their total momentum as zero. Typically this is done right before they interact in a way made uncertain by their imprecise positions (e.g. symmetric elastic scattering).

If one is invoking only statistical conservation then the entanglement doesn't occur and one only has classically statistical correlation of the subsequent measurements of the two components.

Uncertainties in the effect of an interaction arise (and this was the gist of Bohr's counter arguments to Einstein) due to (logically)

The EPR thought experiment, of course, moves beyond the issue of uncertainty in the state of the apparatus.

- #33

edguy99

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"Suppose two particles are set in motion towards each other with the same, very large, momentum, and that they interact with each other for a very short time when they pass at known positions.

Consider now an observer who gets hold of one of the particles, far away from the region of interaction, and measures its momentum; then, from the conditions of the experiment, he will obviously be able to deduce the momentum of the other particle. If, however, he chooses to measure the position of the first particle, he will be able to tell where the other particle is.

How can the final state of the second particle be influenced by a measurement performed on the first, after all physical interaction has ceased between them?"

He seems to make a lot of sense.

- #34

bhobba

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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.He seems to make a lot of sense.

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Bill

- #35

bhobba

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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.

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Bill

- #36

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Hello,

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 isnotin 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.

Well this is what Bohr thought: "Albert asked about a photon and a screen and a double slit screen, so my answer must contain a photon, a screen and a double slit screen. Now I just have to think what really happens to the photon, the screen and the double slit screen"

- #37

MusaKusa

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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.)

"You're thinking classically" is saying that one is using implicit assumptions (A's) which should not be accepted

[Edit, an additional comment.]

In your lawyer analogue, it is more like the prosecutor saying "your a convicted thief so your testimony is questionable" while the defense is pointing to evidence that the witness was in fact wrongly convicted and thus not a thief and so we should listen to what he has to say.