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The wave packet description

by flowerew
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Demystifier
#55
Nov22-06, 04:09 AM
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Quote Quote by vanesch View Post
You still have an interpretational problem, in the following sense: somehow, an "observer", although that observer has TWO ontological parts (its "particle" part, and its "wavefunction" part), can only be "aware" of its "particle part", and not of its "wavefunction" part, because if he were so, there wouldn't be any probabilistic part to it, and hence the predictions of BM wouldn't coincide with QM.
This problem is not (much) more difficult than the same "problem" in classical physics. In the Hamilton-Jacobi approach you have the function S(x,t), on which observer cannot be aware. In classical statistical mechanics (in the configuration space) you have the probability density rho(x,t) on which the observer also cannot be aware.

For a quantum-like interpretation of classical mechanics see also
http://arxiv.org/abs/quant-ph/0505143
Demystifier
#56
Nov22-06, 04:14 AM
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Quote Quote by zbyszek View Post
So, using Bohmian formulation is like going deer hunting with an accordion. You have to cope with a wave function first, then you can plot trajectories that have no use whatsoever.
... The only information you have is the one already contained in a wave function. Nothing more.
Don't be so sure:
http://arxiv.org/abs/quant-ph/0406173
ueit
#57
Nov22-06, 06:39 AM
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Quote Quote by ueit
Statistically it's perfect
Quote Quote by Anonym View Post
That what I said. We are now in the classical world. There is no macroscopic object formed by single QM particle. From that point of view any improvement do not exist.
Of course it exists. Nothing stops you to perform a fully QM treatment of the entire experimental setup except the lack of a good enough computer.

In addition, in classical world how do you describe the extentent object by single coordinate point experiment?
Classical world is quantum world.

What do you mean wall in "wall's Hamiltonian"? Lossless beam-splitter?
In a double slit experiment it's the wall with the slits. An electron passing near such an object changes momentum. The mechanism behind this change is ignored so we shouldn't expect a good prediction of the individual detection event. So, besides the probable statistical character of the wavefunction itself, we have another approximation regarding the potential at the slits (which is assumed to be 0 although it's only 0 on average).
vanesch
#58
Nov22-06, 09:36 AM
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Quote Quote by Demystifier View Post
Interesting. I just scanned through it, very quickly.

My impression is that it is indeed possible to generate lorentz-invariant trajectories (that's the entire crux) for free scalar particles, because in that case, indeed, there's nothing that really needs to be transmitted superluminally. I should take a deeper look to see if interactions, which have a genuine superluminal effect in BM, can also be formulated in a lorentz invariant way, as I was under the impression that this was impossible. That is, are there still lorentz-invariant world lines (which are the same, no matter in what reference frame they have been obtained) of Bohmian particles, when we consider interactions ?
If that's really the case (and I thought it was genuinly impossible), then this makes BM way way more attractive. But I doubt it.
Demystifier
#59
Nov22-06, 10:29 AM
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Quote Quote by vanesch View Post
My impression is that it is indeed possible to generate lorentz-invariant trajectories (that's the entire crux) for free scalar particles, because in that case, indeed, there's nothing that really needs to be transmitted superluminally.
You are wrong. The particles are free in the sense that there is no classical force between them, but they are entangled, which, indeed, is the source of EPR action-at-a-distance and related stuff and induces the Bohmian quantum force. The point is that there ARE superluminal influences between particles, but it is made in a relativistic covariant way. Contrary to a common misconception, superluminal signals by themselves are NOT in contradiction with relativity. (The best known counterexample is a tachyon.)
zbyszek
#60
Nov22-06, 10:49 AM
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Quote Quote by Demystifier View Post
Demystifier, you are a nice guy, but in that eprint you didn't know what you were doing.
In particular, you didn't understand, so called, second quantization.

In the introduction you notice that the object that satisfies Klein-Gordon equation is not
a wave function but a field operator. However, in the third section you call it a wave
function anyway and even worse you introduce in eq. 3 a third quantized operator
on the right hand side. Do you realize that?
The left hand side of eq. 3, \psi, is already a "second quantized" operator and to get a wave function for a Fock state |n> you should have put \psi in place of \hat \phi in the RHS!

As to you remark on BM, I see you agree that it is a useless curiosity at best as
far as QM is concerned. The domain of your objection is relativistic QM. But even
there how do you pick initial conditions for the Bohmian trajectories (defined correctly
i.e. not as you did it)?
Don't you have to draw them from some probability density? If the answer is
afirmative then you have your "statistical transparency".

To sumarize, the eprint has nothing in it.

Cheers!
Loren Booda
#61
Nov22-06, 12:07 PM
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One of myriad descriptions of the wavepacket might be as a probabilistic representation of an entity's complementary measurements excluded from each other by the magnitude of Planck's constant.
Demystifier
#62
Nov23-06, 05:15 AM
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Quote Quote by zbyszek View Post
1. Demystifier, you are a nice guy, but in that eprint you didn't know what you were doing.
... bla bla bla ...
To sumarize, the eprint has nothing in it.
As far as quantum mechanics is concerned, you actually disagree with almost everything said by almost everybody. I am glad to see that I am not an exception.
zbyszek
#63
Nov23-06, 07:09 AM
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Quote Quote by Demystifier View Post
As far as quantum mechanics is concerned, you actually disagree with almost everything said by almost everybody. I am glad to see that I am not an exception.
Going with the herd? That's the scientific spirit!
Nice answer to a detailed argument, too.

Cheers!
Demystifier
#64
Nov23-06, 07:41 AM
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Quote Quote by zbyszek View Post
Going with the herd? That's the scientific spirit!
Nice answer to a detailed argument, too.
The idea of a public forum is to write something that will be interesting to many people reading it, not just to one person. If anybody else here finds out that some of your arguments are viable, I will give a more scientific answer. If, one the other hand, you want to argue only with me, send me a private message.
Anonym
#65
Nov23-06, 09:25 AM
P: 451
ueit:"In a double slit experiment it's the wall with the slits. An electron passing near such an object changes momentum. The mechanism behind this change is ignored so we shouldn't expect a good prediction of the individual detection event. So, besides the probable statistical character of the wavefunction itself, we have another approximation regarding the potential at the slits (which is assumed to be 0 although it's only 0 on average)."

You did not answer my question: Do you agree that lossless beamsplitter is real life realization of the "wall"?
Anonym
#66
Nov23-06, 10:14 AM
P: 451
Zbyszek:” I don't think there has been much progress since Einstein. If anything it would be rather a regress. These days Bohr is perceived (unjustly again) as a winner of the duel with Einstein over the meaning of QM. So, not many guys are even aware that we are still missing a quantum theory of single objects and that QM is incomplete indeed.”

You are kidding. I am asking seriously. For example, investigations of R.J. Glauber and others established the connection between classical and quantum statistical mechanics. On the other side, the single particle approach also led to enormous progress in QT: QED, local gauge abelian and non-abelian interactions, electroweak unification, quarks, QCD, etc. However, in that game the role of “interpretations” is not clear. Looks like something stand alone.
May you present coherently what is the content of the “normal physicist” criticism of the standard approach to QM?
Careful
#67
Nov23-06, 11:01 AM
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Quote Quote by Anonym View Post
You are kidding. I am asking seriously. For example, investigations of R.J. Glauber and others established the connection between classical and quantum statistical mechanics. On the other side, the single particle approach also led to enormous progress in QT: QED, local gauge abelian and non-abelian interactions, electroweak unification, quarks, QCD, etc. However, in that game the role of “interpretations” is not clear. Looks like something stand alone.
May you present coherently what is the content of the “normal physicist” criticism of the standard approach to QM?

QFT has no realistic, local single event interpretation, period (and mind MWI is not realistic).
Anonym
#68
Nov23-06, 11:35 AM
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Careful:"QFT has no realistic, local single event interpretation, period (and mind MWI is not realistic)."

I agree. I claim that non-relativistic QM is complete. I don't claim that QFT is complete. And this is not a question. We discuss the description of the statistical ensembles in terms of wave packets.
Careful
#69
Nov23-06, 11:48 AM
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Quote Quote by Anonym View Post
Careful:"QFT has no realistic, local single event interpretation, period (and mind MWI is not realistic)."

I agree. I claim that non-relativistic QM is complete. I don't claim that QFT is complete. And this is not a question. We discuss the description of the statistical ensembles in terms of wave packets.
You cannot discuss physics without taking into account special relativity, that is like going to restaurant and eat with bare hands (which might still be a habit in some parts of the world). I will reverse the question to you, what makes you think that nonrelativistic quantum mechanics has a sensible single event interpretation (there are some ``options'' so it is simply more efficient to ask you) ?
vanesch
#70
Nov23-06, 12:20 PM
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Quote Quote by Careful View Post
(and mind MWI is not realistic).
... for sufficiently naive versions of "realistic"

(meaning: where events really, and uniquely, happen)
Careful
#71
Nov23-06, 12:26 PM
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Quote Quote by vanesch View Post
... for sufficiently naive versions of "realistic"

(meaning: where events really, and uniquely, happen)
Brilliant !!
ueit
#72
Nov23-06, 03:15 PM
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Quote Quote by Anonym View Post
You did not answer my question: Do you agree that lossless beamsplitter is real life realization of the "wall"?
It may be, the electron interference experiments I know of were performed with copper gratings, magnetic fields, or crystallization planes.


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