How Does the Statistical Interpretation Address Quantum Interference Effects?

[reilly]

I am not sure if we connect. I say that in statistical interpretation the fringes in the double
slit experiment come from the preparation procedure and not from some assumptions
about wavelike nature of the electrons.
In other words: from the fact that the ensemble of electrons is prepered in some
wave function that exhibit fringes under position measurement.
Let me emphasize that the wave function describes an ensemble and not a single member
in that interpretation.

No need for any communication between any two electrons or a to-be-send electron and the detector.

If this doesn't help, could you formulate a specific question?

Cheers!

Wow. I never knew that initial preparation is responsible for double-slit electron diffraction. Gee, I always thought that the restriction of the wavefront was the major cause. So, I wonder how electron microscope manufactures guarantee that their electrons are properly prepared?

Perhaps you would be so kind as to enlighten us on what constitutes proper preparation for electron diffraction?

Also, would you be so kind as to show us how to compute the correlation between electrons in a XX-slit experiment of any kind. Usually we assume that the incident electrons are independent, hence they cannot be correlated . (There is one correlating factor, the Pauli Exclusion Principle, but, as I'm sure you know, single particle matrix elements of fermions don't create any noticable corrrelations. Further, bosonic objects will also show diffraction patterns.) Most would agree that there is a correlation pattern at the detecting screen. You, unless I'm mistaken, suggest that the correlation is in the preparation. Doe this mean that with proper preparation, we can get electron diffraction without a screen?

I hope that you can enlighten us on these matters -- then I'll be able to revise my thesis on electron diffraction from protons --, which I always thought was right. Also, you might clue us in on the proper way to deal with many issue in solid state physics, conducting, superconducting, and non-conducting materials for example, or in dealing with cascades of cosmic rays.

Also, re probability and ensembles -- see a few books on probablity theory, preferably those that deal with measure theoretic approaches and events, and, perhaps look at ergodic theory-- to understand why you are less than correct on this issue.

But, no matter, in spite of your doubts, QM and particle diffraction are alive and well, conform to the strictures of QM, and make this very forum possible.

Regards,
Reilly Atkinson

 

[zbyszek]

Not quite!
In the Bohmian approach, the wave function has a double role. It is associated with an ensemble just as you said, but it also determines the trajectory of a single particle. You may, of course, argue that these trajectories are useless, meaningless, or whatever you want, but you cannot say that, in this particular interpretation, the wave function is not associated with properties of single particles.

Hi Demystifier,
The wave function is as much associated with a single particle as an external potential.

It is like saying that periodic potential of a crystall lattice is a property of an electron
in a Bloch band.

Thank you for the contribution!
Cheers!

 

[zbyszek]

Wow. I never knew that initial preparation is responsible for double-slit electron diffraction. Gee, I always thought that the restriction of the wavefront was the major cause. So, I wonder how electron microscope manufactures guarantee that their electrons are properly prepared?

Perhaps you would be so kind as to enlighten us on what constitutes proper preparation for electron diffraction?

Also, would you be so kind as to show us how to compute the correlation between electrons in a XX-slit experiment of any kind. Usually we assume that the incident electrons are independent, hence they cannot be correlated . (There is one correlating factor, the Pauli Exclusion Principle, but, as I'm sure you know, single particle matrix elements of fermions don't create any noticable corrrelations. Further, bosonic objects will also show diffraction patterns.) Most would agree that there is a correlation pattern at the detecting screen. You, unless I'm mistaken, suggest that the correlation is in the preparation. Doe this mean that with proper preparation, we can get electron diffraction without a screen?

I hope that you can enlighten us on these matters -- then I'll be able to revise my thesis on electron diffraction from protons --, which I always thought was right. Also, you might clue us in on the proper way to deal with many issue in solid state physics, conducting, superconducting, and non-conducting materials for example, or in dealing with cascades of cosmic rays.

Also, re probability and ensembles -- see a few books on probablity theory, preferably those that deal with measure theoretic approaches and events, and, perhaps look at ergodic theory-- to understand why you are less than correct on this issue.

But, no matter, in spite of your doubts, QM and particle diffraction are alive and well, conform to the strictures of QM, and make this very forum possible.

Regards!

Before I start the enlighment tell me what exactly you are questioning.
Is it:
1. statistical interpretation of QM you are not comfortable with or,
2. is it my understanding of the interpretation that is not sufficient?

I cannot help on 1. but will be happy to improve in case of 2.

Same regards!

 

[Anonym]

Marlon:” We need duality because we look at QM through "classical eyes".

Perfect explanation.

Careful:” Your point is merely the standard Copenhagen view, which brings you into trouble with relativity and reality.”

?

zbyszek:” Ballentine's paper "The statistical interpretation of QM" (1970) would be a good start. Preferably, before any further discussion on the subject.”

L.E. Ballentine (p.359): “The primitive concepts are those of state and of observable. … This implies that any state operator may be diagonalized in terms of its eigenvalues and eigenvectors.”

This is like to say that the proton is the elementary particle which is the QM ground state of the three bounded point-like fermions called quarks.
L.E. Ballentine presentation is obscure, tedious, didactic, eclectic and old turkey style. In addition, it is simply wrong, since the writer reject the experimental evidence.

Quantum River:” could you recommend more readings of statistical interpretation of QM besides Bellentine's review?”

The clear presentation and discussion of the problem is given by E.P.Wigner in the paper “The problem of Measurement” (AJP,31,6 (1963)).
For me the key statement of the paper is:
“The misgivings, which are surely shared by many others who adhere to the orthodox view, stem from a suspision that one cannot arrive at valid epistemological conclusions without a careful analysis of the process of the acquisition of knowledge. … We are facing here the perennial question whether we physicists do not go beyond our competence when searching for philosophical truth.”
Recent investigations performed by A. Zeilinger and others moved that issues from the area of philosophy to the standard experimental and theoretical treatment (see for example quant-ph/0212084) used in the physics. The theory of measurement must be accompanied by the description of the process of the acquisition of knowledge. The density matrix and the projection operators seems to provide suitable dynamical variables. Whether the Born interpretation is necessary for the description we will see in the future.

 

[Careful]

Careful:” Your point is merely the standard Copenhagen view, which brings you into trouble with relativity and reality.”

I meant realism.

 

[zbyszek]

L.E. Ballentine presentation is obscure, tedious, didactic, eclectic and old turkey style. In addition, it is simply wrong, since the writer reject the experimental evidence.

So you are the man of your word. You have read it.

Could you explain in more detail what experimental evidence has been rejected
by Ballentine, please?

Cheers!

 

[Anonym]

Zbyszek:” Could you explain in more detail what experimental evidence has been rejected by Ballentine, please?”

The “collapse of the wave function” . We already discussed that in the “wave packet description” session.

The “collapse of the wave function” is not a postulate and it is not interpretation dependent. The collapse is universally valid firmly established experimental result connected with the transition from Quantum world to Classical world (E. Schrödinger cat). The collapse is a key problem of the measurement theory and therefore also is called “The Measurement Problem”. The theoretical description of the natural phenomena is groundless without consistent and adequate measurement theory. There are and always will be people that claim that a quantum world is a classical world or a classical world is a quantum world, that the measurement problem do not exist, AB phenomenon do not exist,quarks do not exist, etc. These are the people that have no problems in their world. God bless them. But it is not interesting world.

 

[Careful]

Zbyszek:” Could you explain in more detail what experimental evidence has been rejected by Ballentine, please?”

The “collapse of the wave function” . We already discussed that in the “wave packet description” session.

The “collapse of the wave function” is not a postulate and it is not interpretation dependent. The collapse is universally valid firmly established experimental result connected with the transition from Quantum world to Classical world (E. Schrödinger cat).

The world in which the experiments you consider to be conclusive are accepted as such must be very poor minded indeed.

 

[zbyszek]

The “collapse of the wave function” is not a postulate and it is not interpretation dependent.

Is the collapse also required in the interpretation where the wave function is not associated
with any single object but only with ensembles?

The collapse is universally valid firmly established experimental result connected with the transition from Quantum world to Classical world (E. Schrödinger cat).

I might have some insides, not discussed in QM textbooks yet, as to the quantum to classical transition, and to the Schrodinger cat problem in particular.
For example, the lack of observed superpositions of macroscopic objects can be derived from a structure of the many-body wave functions of those objects.

If you mock up the measurement process by sampling (can be approximate) of the many-body probability density (the wave function modulus squared) you will find that the
density itself prevents macroscopic superpositions from happening in the results of measurements.

No reduction of the wave function required.

Cheers!
zbyszek

 

[Anonym]

Careful:” The world in which the experiments you consider to be conclusive are accepted as such must be very poor minded indeed.”

But I am happy to be there. In addition, I have plenty of tools in my restaurant.

 

[Anonym]

Zbyszek:” Is the collapse also required in the interpretation where the wave function is not associated with any single object but only with ensembles?”

The theory should explain the results of experiments. That all.
In the wave-packet description session you stated that the Born interpretation is exception, may be more than interpretation. L.E. Ballentine reduced it to just another interpretation. As I stated above, I made my mind. You helped me to do that. I am grateful to you for that. I do not intent to convince anybody. I try to understand.

 

[dextercioby]

There is Einstein's "Reply to criticism" available on-line.

The book "Quantum Theory: Concepts and Methods" by Asher Peres assumes statistical
interpretation and has large parts devoted to hidden variables.

I heard good things about Ballentine's textbook "Quantum Mechanics: Modern developement"
but don't have access to it yet.

Cheers!

Then you should get it really quickly. It' simply splendid. By far, the best book in the field.

Daniel.

 

[dextercioby]

Zbyszek:” Could you explain in more detail what experimental evidence has been rejected by Ballentine, please?”

The “collapse of the wave function” . We already discussed that in the “wave packet description” session.

The “collapse of the wave function” is not a postulate and it is not interpretation dependent.

It is a postulate, it's necessary to merge it with the other axioms, as Ballentine shows. Oh, and yes, it's probably difficult to follow his 1970 article, simply because it's difficult to follow any article of that kind, including Wigner's that you quoted.

Daniel.

 

[zbyszek]

I try to understand.

Anonym,
Let me stick to this sentence of yours.

Our brains trick us into believing things that do not exist and make as blind to plain evidence
residing just in front of us. I am not patronizing you. The same happens to me way too often.

One way to fight that is to employ different parts of our brains when analysing
a problem.

How is it done?
In the case of reading a paper, that you presume to be wrong(right), you try to remember
that your mind is trying to trick you. During the analysis of the paper try to find evidence that
the paper is correct(wrong). The oposite to the presumption.

In my case, I contemplate almost every sentence of the paper and try to dig out its meaning
in relation to preceeding sentences in a way that would contradict my presumptions.

It takes time but often pays off with understanding.

Give Ballentine a chance. If you are really after the understanding, analyse the first 15 pages
of the review temporarilly assuming that Ballentine is right and your brain plays with you.

After that you will either find better evidence supporting your reservations or annihilating them.

As a side remark, such an exercise would help you deal with symptoms of Alzheimer's desease if you are unlucky to suffer from it in the future.

Cheers!

 

[marlon]

Wow. I never knew that initial preparation is responsible for double-slit electron diffraction.

LOL
That makes TWO of us. This is the very point i was objecting against but this guy just doesn't want to hear me out.

Gee, I always thought that the restriction of the wavefront was the major cause. So, I wonder how electron microscope manufactures guarantee that their electrons are properly prepared?

Don't bother i have asked a similar question before.

Also, would you be so kind as to show us how to compute the correlation between electrons in a XX-slit experiment of any kind. Usually we assume that the incident electrons are independent, hence they cannot be correlated .

Exactly, also a question i have asked to him. Yet no answer.

greets
marlon

 

[masudr]

Hmm, I'm pretty confused by zbyszek's comments. I've tried to make sense of them from zbyszek's point of view. I think what s/he means by the preparation of electrons etc. is that, for example, for an intereference pattern to be observed, we need coherence etc.

I'm not sure though; is this really what zbyszek means?

 

[dextercioby]

Try to read the 8-th and 9-th chapters of Ballentine's QM book or the article in discussion to get the idea behind his assertions.

Daniel.

 

[zbyszek]

Hmm, I'm pretty confused by zbyszek's comments. I've tried to make sense of them from zbyszek's point of view. I think what s/he means by the preparation of electrons etc. is that, for example, for an intereference pattern to be observed, we need coherence etc.

I'm not sure though; is this really what zbyszek means?

He means that for an interference pattern to be observed all electrons have to follow the same wave function. In particular, this means the coherence etc.

In order to satisfy this requirement, the electrons have to be carefully prepared. They cannot
be cast into the experimental setup regardless of their energies and momenta.

In the statistical interpretation of QM the preparation procedure of an ensamble of electrons is synonymous to the wave function of the ensemble.

Cheers!

 

[reilly]

LOL
That makes TWO of us. This is the very point i was objecting against but this guy just doesn't want to hear me out.



Don't bother i have asked a similar question before.



Exactly, also a question i have asked to him. Yet no answer.

greets
marlon

Could not agree more. Somehow, all I see is a future in this thread that is full of words, but little concrete substance. That is, don't hold your breath on getting answers to our questions.
Regards,
Reilly

 

[Anonym]

Zbyszek:” Originally Posted by Anonym
I try to understand.
Let me stick to this sentence of yours.”
Careful:”The world in which the experiments you consider to be conclusive are accepted as such must be very poor minded indeed.”

I do not want to go too far beyond my competence. For me understanding means translation into the suitable mathematical language ( here I see three and Born approach is not relevant at least at the beginning). Now a question is how the difference between the information and the information rate is defined. As Careful said it is “very poor minded indeed.”