How Does Quantum Mechanics Combine Particle and Wave Descriptions?

[zbyszek]

1. If you read it more carefully, you will notice that \psi and \hat{\phi} are not the same objects, despite the fact that they satisfy the same Klein-Gordon equation. In particlar, the former is a c-number function, whereas the latter is an operator. Eq. (3) is just a textbook relation between these two quantities. (Perhaps you was reading some other textbooks than I did.) In other words, this equation is a sort of bridge between first and second qutization and has nothing to do with third quantization.

I know that \phi and \psi are different objects. However, they do not both
satisfy K-G. Operator \phi does, the wave function \psi does not. If you
say that \psi satisfies K-G then \psi MUST be an operator and \phi in (3) is the
third quantized one :).
In case of doubts of what satisfies K-G eq., please refer to the introduction
of your manuscript.

Cheers!

 

[zbyszek]

Zbyszek:” The QM is incomplete in the sense that it is only statistical. … So, where is the progress on foundations of QM? What exactly did Glauber do that qualifies as progress in QM? You seem to distinguish between QM and quantum statistical mechanics.
What's the difference?”

For me Born’s statistical interpretation is counter-intuitive. I don’t understand how single particle may do statistic with itself. Contrary, selfinterference is not only a mystery but self-evident as explained by P.A.M. Dirac and clearly demonstrated experimentally by A.
Tonomura.

Single particles don't do statistic with themselves. In the Tonomura experiment one
electron didn't give any interference. It gave just one spot on a screen.
The interference fringes appeared after many electrons run through the apparatus.

What is conuter-intuitive here? The electrons, despite their time separation, are correlated
by their initial state or by the preparation procedure if you prefer. This is why one
can see the fringes.

The wave packet reduction (as explained by A. Einstein) is necessary in order to satisfy requirements of special relativity in the classical physics.

There is no need for the reduction if you keep in mind that the wave packet describes
an ensemble and not a single quantum object.

By quantum statistical mechanics I mean construction of tensor product states and description of many particle QM systems
( N>4 )using them. Indeed this is inherent part of QM.

In my environment this just Many-Body QM.

My distinction is between QM and the statistical interpretation of QM.

Perhaps you think that there are couple of equally good interpretations of QM like
Copenhagen, many worlds or statistical interpretation and one is free to choose one that he likes the most.

It is not so.

The statistical interpretation gives the physical meaning to QM, that no other interpretation
can deny: |\psi|^2 is a probability density. All other interpretations must have that
built-in to be in agreement with experiments.

On top of that other interpretations assume something extra like "\psi is also associated
with a single quantum object" or "all possibilities are acctually realized in diffrent worlds",
etc.

Since every one has to agree on the Born postulate the distinction you make can be
safely dispossed of.

Cheers!

 

[zbyszek]

Zbyszek, as you clearly do not like the Bohmian interpretation (just as many others), I believe that you might like this anti-Bohmian interpretation of CLASSICAL mechanics:
http://xxx.lanl.gov/abs/quant-ph/0505143

Or but I love BM. One cannot dislike things one understands. I just seriously doubt its usefulness.

Cheers!

 

[Careful]

Here is the Maxwell embeded himself :
http://xxx.lanl.gov/abs/gr-qc/0112041"

The idea is that for He3-A, close to the Fermi points the order parameter (atomic angular momentum for the liquid) satisfies Maxwell's equations.

Cheers!

Thanks, I will take a look at it (but I was more interested in Maxwell theory in general - not in a specific case).

Cheers,

Careful

 

[zbyszek]

Thanks, I will take a look at it (but I was more interested in Maxwell theory in general - not in a specific case).

There is some general idea concerning Maxwell theory in that paper. The electromagnetic
fields can be an emergent phenomenon in our world too. The mechanism is present
not only in He^3 but in the entire universality class with Fermi points (+ isotropic sound
velocity).

Cheers!

 

[ueit]

If I only give you the positions (and the momenta, if you wish) of the particles, in BM, you are unable to calculate the force. This means that there is a dynamical content which is entirely contained in the wavefunction, and the wavefunction alone.

If you give me a system (let's say a molecule) and the relevant parameters (positions, momenta, particle masses and charges) I can give you a realistic picture of what's going on there. The force is calculated from Schroedinger's equation. The ontology is pretty clear.

As in BM, the wavefunction evolves strictly according to the Schroedinger equation, there is no projection, and hence there are exactly the same "branches" present as in MWI. That's why I sometimes say (to enerve Bohmians) that BM is MWI plus a tag

I can calculate the quantum force acting on a particle existing in space. I don't need to assume that the wavefunction itself must evolve somewhere in reality, it's only a mathematical trick to compute the value of the force. For example, in a hydrogen atom, the quantum force equals the electrostatic force. I don't need to give an account for why the two forces act as they act although it would be nice to be able to do it.

No, your brain is aware of its particle positions, but not of the wavefunction that goes with it.

Is a brain aware of the EM force acting on its molecules?

I don't believe those claims.

I cannot contradict you on this issue, as lack the necessary knowledge, but I'll try learn about.

But, 3d space (plus time) is also a mathematical construction...

Yeah, that's true, but it's a necessary construction for our understanding. For me, at least, that's what reality means. If you propose another construction as the basis for reality you should explain why, for example, we "see" 3 dimensions and not 2 or 5, our perception of time and so on. I doubt, however, that MWI can do that.

No, the degrees of freedom in normal QM are indexed using a Newtonian space (to enumerate the degrees of freedom as "x-position of particle 5"...).

Why not use 2 or 5 variables to describe each particle's position then?

Well, you can simply have a totally different enumeration of the basis vectors in Hilbert space (for instance, N spin-1/2 systems, with no relation to any space !).

Spin is a magnetic moment, existing in space.

Yes, that's because it is put in by hand: you START by saying that you want a quantum system of dots in an Euclidean space. But you could just as well start from something totally different.

In order for math to become physics you need space and time. We can only make experiments in space and time and their results have to appear there.

 

[Anonym]

Zbyszek:” On top of that other interpretations assume something extra like "\psi is also associated with a single quantum object" or "all possibilities are acctually realized in diffrent worlds", etc. “

Thank you. I had suspicion that it is so. I hope one may prove it
rigorously.

“every one has to agree on the Born postulate”

Why? Otherwise you will shoot me?

 

[zbyszek]

“every one has to agree on the Born postulate”

Why? Otherwise you will shoot me?

It's not in my nature to contribute to misery of others :).

 

[vanesch]

If you give me a system (let's say a molecule) and the relevant parameters (positions, momenta, particle masses and charges) I can give you a realistic picture of what's going on there. The force is calculated from Schroedinger's equation. The ontology is pretty clear.

That means that you assume a ground state, or any other specific quantum state.

If you have 2 particles A and B, and I give you the quantum state psi(r1,r2), you can calculate the "quantum force" from BM. But if I don't give you that quantum state, even if you know the positions of A and B, and their velocities, you won't be able to give me the quantum force. You need psi for that. The trick with the molecule is only because you can somehow assume what is its quantum state (probably the ground state of the Hamiltonian, OR a chiral state OR ...).

I can calculate the quantum force acting on a particle existing in space. I don't need to assume that the wavefunction itself must evolve somewhere in reality, it's only a mathematical trick to compute the value of the force. For example, in a hydrogen atom, the quantum force equals the electrostatic force.

Also in the case of a superposition of a few excited states ?

Is a brain aware of the EM force acting on its molecules?

Somehow, the brain is aware of an aspect of its state, right ? It's a philosophical issue to say whether the "essential element" is the EM configuration, or the electron configuration, or the atomic configuration or all of it together or...

Yeah, that's true, but it's a necessary construction for our understanding. For me, at least, that's what reality means. If you propose another construction as the basis for reality you should explain why, for example, we "see" 3 dimensions and not 2 or 5, our perception of time and so on. I doubt, however, that MWI can do that.

I don't think there is a need of explanation (which would in that case make appeal to other fundamental aspects which would then require an explanation in their turn etc...). It is undeniable that certain degrees of freedom in nature come in sets of 3 real numbers, which give us an impression of space. So be it. I don't think everything has an "explanation", we can already be happy with a description. In how much this is a strict necessity that the "space behind it" is real, I let the formalism decide. And the problem is that there is no existing theory as of today (not BM) which is demonstrated equivalent with QM and which can be defined *entirely* as some extra structure over spacetime (which would then be a "local realistic relativistically invariant equivalent to QM"). BM needs also that hilbert space. QM lives ONLY in that hilbert space.

Why not use 2 or 5 variables to describe each particle's position then?

If I knew, I would be famous. And maybe there is no "reason" to it, it just IS so.

Spin is a magnetic moment, existing in space.

No, I didn't mean "spin of a dirac particle" or something. Just abstract 2-dimensional hilbert spaces (that's essentially what is spin-1/2) in a big tensorproduct combination.
Note that it is (extremely clumsy but) possible to write *every* hilbert space that way (also the hilbert space of, say, the hydrogen atom). Enumerate, say, the energy eigenstates in a certain order, and collect them 2 by 2. Call each pair of states a "spin-1/2" system. The unitary time evolution of the free hydrogen atom is then a sum of sigma_z operators (diagonal in the eigenstate basis, and hence in basis of each pair of eigenstates). A perturbation (external field, extra coupling, whatever...) will now result in two kinds of terms:
-sigma-x and sigma-y terms within each 2-dim subspace
-couplings between the different 2-dim spaces (spin-spin couplings :=)
in such a way that the perturbation hamiltonian takes on the right form.

If we now "forget" that we started with a hydrogen atom, we see that we started with a bunch of spin-1/2 systems, that we have a hamiltonian over them coupling them in some peculiar ways, and that this gives you a complicated quantum system. However, a smart guy can come along, and say: "hey, this just looks like a kind of , well, hydrogen atom in 3-dim space with a kind of coulomb force ! You only need to re-interpret your spin-1/2 systems as energy eigenstates of a different system"
==> emerging impression of a particle in a 3-dim space with a potential well.

This is a stretched example, but it shows you how it is in principle possible to have some 3-dim continuous space emerging from a totally different structure.

 

[Anonym]

Zbyszek:” It's not in my nature to contribute to misery of others”

Hen,hen.

Zbyszek:” What is counter-intuitive here? The electrons, despite their time separation, are correlated by their initial state or by the preparation procedure if you prefer. This is why one
can see the fringes.”

Now you are ready to sacrifice the standard treatment of the identical particles that lies even in foundation of classical statistical mechanics. I would like to continue our discussion on that question later. But now let me say a few words about “interpretations”. I had in my mind the analysis of H.D. Zeh.

Obviously, you are using circular arguments. J. von Neumann did work simpler. He postulated the reduction phenomenon and developed the theory of measurements under assumption that the statistical interpretation is correct. J. von Neumann was outstanding mathematician and physicist. He honestly pointed out that these two assumptions lead him to absurd.
When we discuss the A.Tonomura results you simply refuse to accept what you see right in front of your eyes. When I started to study physics I never dreamed that I will see such a picture. You see properly amplified image of the single electron. And it is most beautiful picture I ever seen. It is highly regular. One may describe it completely using only three parameters. Apparently, it has nothing to do with statistic. No room for the mystery at all. It is well known during the centuries picture of the physical field. Field mathematically as well as physically means: extended object. And as I mentioned above you cann’t obtain picture of your face using only one pixel. As Careful said if you are going to restaurant it is more reasonable to use all available tools.
The reduction of wave packet can’t be accepted as a postulate. In general, the postulate must be simple, clear, self-obvious and universally valid. The reduction is not simple, clear and by no means self-obvious. Most importantly, it is the inherent property of the QM mathematical formalism. Since the measurement instruments are macroscopic, it therefore have to have natural explanation within the classical physics. And it does not. Therefore, the classical physics is not complete. But this is a trivial statement. Until now nobody explain the wave mechanical nature of HJ formulation, which allow to formulate the most important principle postulate of the physics:
Principle of Least Action. Without that explanation all of the classical physics has no foundation.
I use to explain the content of the Least Principle in the Fermat version: suppose somebody sink and cry for the help. You are located somewhere on the beach at some distance from the water. What is the best way you choose in order to help? As you said :” It's not in my nature to contribute to misery of others”. I guess that you also too modest.
And now we arrived to the interconnection between physics, mathematics and biology. It is clear that they are different aspects of the integrated human activity called development of humam culture. But you need also to differentiate them. It seems to me that the proper distinction will be achieved if you will define the physics as an empirical science (axiomatically considered as an auxiliary definition). Thus no room for the solipsism will be left.


Zbyszek:” In my environment this just Many-Body QM”

What wrong with that?

 

[zbyszek]

Obviously, you are using circular arguments.

Could you be more specific? I mean, list the arguments and show that they are circular?

J. von Neumann did work simpler. He postulated the reduction phenomenon and developed the theory of measurements under assumption that the statistical interpretation is correct. J. von Neumann was outstanding mathematician and physicist. He honestly pointed out that these two assumptions lead him to absurd.

Did it lead him to a contradiction? If that it is what you mean, which of the premisses
is invalid?

When we discuss the A.Tonomura results you simply refuse to accept what you see right in front of your eyes. When I started to study physics I never dreamed that I will see such a picture. You see properly amplified image of the single electron. And it is most beautiful picture I ever seen. It is highly regular. One may describe it completely using only three parameters. Apparently, it has nothing to do with statistic. No room for the mystery at all.

Anonym, you act as if you knew something I still don't. If that is really so, I honestly
would love learning it.
Could you guide me to the enlighment, please? I am serious.

From descriptions of the Tonomura experiment, electrons pass the double slit setup, one electron at the time, and their position is recorded some distance from the slits. All electrons are prepared the same way. One electron produces one spot. Many spots
group into interference fringes.
Are we talking about the same experiment, at least?

The reduction of wave packet can’t be accepted as a postulate. In general, the postulate must be simple, clear, self-obvious and universally valid. The reduction is not simple, clear and by no means self-obvious. Most importantly, it is the inherent property of the QM mathematical formalism. Since the measurement instruments are macroscopic, it therefore have to have natural explanation within the classical physics. And it does not. Therefore, the classical physics is not complete. But this is a trivial statement. Until now nobody explain the wave mechanical nature of HJ formulation, which allow to formulate the most important principle postulate of the physics:
Principle of Least Action. Without that explanation all of the classical physics has no foundation.

Here, I don't know what you are talking about.
First, I don't need the reduction postulate and never did.
Second, how come "it is the inherent property of QM". I have never seen a wave
packet reduced in QM calculations. I have seen only unitary evolutions.
Third, is it possible to talk QM without solving all shortcomings of the classical mechanics?
One theory at the time, please!

Cheers!

 

[reilly]

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.



Classical world is quantum world.



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).

.........
Yes, but. You suggest that the wall and slit boundaries have an important dynamical role in the double slit experiment. That's not so clear. Don't see many backscattered electrons from the slits.

Look at the physics: as an electron goes through a slit, it forces electrons in the wall away from the slit boundary. Both the electrons and nucleii are subject to thermal bouncing about. In my view, this is suficient to say that 1. the forces on a passing electron are small ( left balances right), and 2. average to zero over all but the shortest of times.

A somewhat more sophisticated approach is to treat the wall as composed of
nuclear-electron dipoles, which in turn are created by the fields of the passing electrons. This approach makes the handling of magnetism a bit easier.

The translation into QM is to get the "actual" potential seen by a passing electron, and include this in the Schrodinger Eq. (Not to worry about feedback of forces in this problem). Also a helpful fact: the dwell time of an electron in the wall's potential will generally be quite short.

Regards,
Reilly Atkinson

 

[reilly]

zbyszek:Why not? One can control how many electrons enter a double slit experiment. It can be just one. If 1000 revelators click simultaneously that would mean that the electron is apporprieatelly spread (like its wave function ? ."
Why simultaneously? And 70000 will give you better image.
"No one has seen such wonder yet."
A.Tonomura et al. and P.A.M.Dirac in Principles explained it some 70 years ago.

zbyszek:"There is no difference. Repeated observations, as you stated above, is just another name for the observation of the ensemble.

I know that in microscopic (as oposed to statistical) theories I can predict, given initial conditions, with a certainty an outcome of a single run of an experiment. Clearly QM does not qualify as microscopic in that sense. If it did, results of the single runs would be no mystery.

All of this is to point out that no one justified, so far, that a wave function can be viewed as a description an individual quantum object. Thus, it is save to say that we have no theory for these objects."

Sorry,I do not understand your answer. Formulated differently, my question was: what are the interconnection between classical statistical mechanics, quantum statistical mechanics and statistical interpretation of QM or in more compact way: What is the wave packet description?

A. Einstein in his 1928 discussion presented breaf summary of that problem. Today one can say something new?

...

The connection between repeated measurements and ensembles only works for ergodic systems.

However, it is a frequent assumption in physics, and statistics, not unrelated to the often used idea that distributions are Gaussian's.

Here's a simple fact: in this real world of ours we can't predict anything with certainty. Measurement error is a fact of Nature. Thus everything is uncertain, to a greater or lesser degree. Brownian motion occurs in 'classical systems'. That means, of course, that there is no theory of certain events.

That's why we use in experiments the largest sample possible so as to get info about the distribution of measurements with as much accuracy as possible. There are lot's of things that are virtually certain: a gallon of gas in New York is the same as a Boston gallon. The price of gas is another matter: there's virtually no way at present to say what you will pay for your next fill-up.



So, if that's so, why do you single out QM for having a problem that is virtually a universal one?

Regards,
Reilly Atkinson

 

[Demystifier]

And honestly, I have difficulties believing that you can formulate the particle dynamics in a relativistically invariant way. If you can do that, I'll become a bohmian too

I already gave a link, but here it is again:
http://arxiv.org/abs/quant-ph/0406173

 

[vanesch]

I already gave a link, but here it is again:
http://arxiv.org/abs/quant-ph/0406173

Yes, and I responded to that too: you consider free particles, and then introduce the "n-particle wave function" as the n-point correlation function of the free theory, which is a tensor product of solutions of the free KG equation.

But you know very well that once you introduce interactions, that you cannot do that anymore (otherwise, standard QFT would be really easy to solve !).

So of course you can solve for particle trajectories in this free situation, because they all correspond to free world lines of point particles, and you can formulate all that in a relativistically invariant way. But the devil is in the interactions (as is the case in standard QFT too).

There is no simple set of partial differential equations for an "n-particle wavefunction" in this case. So this paper proves nothing in my eyes. It only indicates that a free field theory can have a lorentz-invariant particle trajectory interpretation.

 

[Demystifier]

Vanesch, you are right. But I have also studied the interacting case in
http://arxiv.org/abs/quant-ph/0208185
http://arxiv.org/abs/quant-ph/0302152
Things can be done at least in principle. Unfortunately, you will notice that the interactions are not treated covariantly. Instead, it seems that a preferred coordinate frame is needed. In another paper
http://arxiv.org/abs/hep-th/0601027
I propose that the preferred frame is picked up in a covariant dynamical way. Of course, you may argue that all these theoretical constructs are somewhat artificial and make the theory less elegant. I certainly agree with that, but the results demonstrate that it is not impossible to construct a theory that works, even if it is not very simple. I also try to construct a simpler theory too.

 

[Anonym]

Zbyszek:” One cannot dislike things one understands. I just seriously doubt its usefulness”

“Could you be more specific? I mean, list the arguments and show that they are circular?”

“Here, I don't know what you are talking about.
First, I don't need the reduction postulate and never did.
Second, how come "it is the inherent property of QM". I have never seen a wave packet reduced in QM calculations. I have seen only unitary evolutions.
Third, is it possible to talk QM without solving all shortcomings of the classical mechanics?
One theory at the time, please!”


1.I referred to classical paper by H.D.Zeh for example (Foundations of Physics 1,69 (1970). You may find more in QT and Measurement edited by J.A. Wheeler and W.H.Zurek
2.Spectral Decomposition Theorem. Wave packet is not observable. You may see only indirectly that system is in the pure state.
3.I do not act. I present (I hope consistently) so called “Orthodox QM (quant-ph/0004077).
4.I was involved into discussion of statistical interpretation. Really it is not interested me.” I just seriously doubt its usefulness”.
5.What I try to understand here is whether the coherent state provide the adequate description of the Newtonian “ball” used in classical statistical mechanics and if it is so how to make this basis orthonormal as it should be (J.v.Neumann, Zs.f.Phys.,57,30(1929).

“Anonym, you act as if you knew something I still don't. If that is really so, I honestly would love learning it.
Could you guide me to the enlighment, please? I am serious.”

Sometimes your way to express yourself disturb me. If you already know and understand everything, I can’t help you.
Perhaps, I can tell you something different, some way that you did not consider before. If you are interested, I will send you private message.

 

[ueit]

By that I imagine you mean 3 space + 1 time dimension. This is incorrect. It comes from Hamiltonian phase space.

You forget that there are elements of Q.M. that have absolutely no classical analogue. e.g. spin degrees of freedom. What are the "position co-ordinates" of that?

If you feel that the Q.M. is not defined on an abstract Hilbert space, then you are not talking about standard quantum mechanics here, you are talking about something else.

One should distinguish between what QM is about, its ontology, and the mathematical tools used to describe that ontology.

In classical mechanics, we can use Hamilton's equations or Newton's laws. Still, the theory describes the same thing, say the motion of a pendulum. We don't say that we have a theory describing an abstract phase space.

So, QM certainly uses an abstract Hilbert space, but the theory describes quantum systems existing in space and evolving in time. What do you think is the meaning of time evolution in the absence of spacetime?

 

[ueit]

That means that you assume a ground state, or any other specific quantum state.

If you have 2 particles A and B, and I give you the quantum state psi(r1,r2), you can calculate the "quantum force" from BM. But if I don't give you that quantum state, even if you know the positions of A and B, and their velocities, you won't be able to give me the quantum force. You need psi for that. The trick with the molecule is only because you can somehow assume what is its quantum state (probably the ground state of the Hamiltonian, OR a chiral state OR ...).

The universe, as a whole, cannot be in an excited state as no energy can be added to it. So, we can be certain that it is in a ground state.

An excited molecule, on the other hand, is a subsystem, and it is to be expected that a full description cannot be found by just specifying the momenta and position for its particles. It's like asking for the law of motion of a pendulum without giving the gravitational acceleration.

In order to compensate for the lack of knowledge regarding the whole system (universe) of which the molecule is but a part we need psi.

I don't think there is a need of explanation (which would in that case make appeal to other fundamental aspects which would then require an explanation in their turn etc...). It is undeniable that certain degrees of freedom in nature come in sets of 3 real numbers, which give us an impression of space. So be it. I don't think everything has an "explanation", we can already be happy with a description. In how much this is a strict necessity that the "space behind it" is real, I let the formalism decide. And the problem is that there is no existing theory as of today (not BM) which is demonstrated equivalent with QM and which can be defined *entirely* as some extra structure over spacetime (which would then be a "local realistic relativistically invariant equivalent to QM"). BM needs also that hilbert space. QM lives ONLY in that hilbert space.

If I knew, I would be famous. And maybe there is no "reason" to it, it just IS so.

I certainly agree that any theory has to be based on some postulates and it's meaningless to ask it to justify them. However, in the case of MWI, 3D space does not seem to be postulated, it should be a consequence of the theory.

Let's say I accept a universal wavefunction as the ultimate reality. The question is then, how do we get from there to what it seems to be reality for us. Why a hydrogen atom does not look like a "bunch of spin-1/2 systems" to us?

 

[ueit]

Yes, but. You suggest that the wall and slit boundaries have an important dynamical role in the double slit experiment. That's not so clear. Don't see many backscattered electrons from the slits.

Look at the physics: as an electron goes through a slit, it forces electrons in the wall away from the slit boundary. Both the electrons and nucleii are subject to thermal bouncing about. In my view, this is suficient to say that 1. the forces on a passing electron are small ( left balances right), and 2. average to zero over all but the shortest of times.

A somewhat more sophisticated approach is to treat the wall as composed of
nuclear-electron dipoles, which in turn are created by the fields of the passing electrons. This approach makes the handling of magnetism a bit easier.

The translation into QM is to get the "actual" potential seen by a passing electron, and include this in the Schrodinger Eq. (Not to worry about feedback of forces in this problem). Also a helpful fact: the dwell time of an electron in the wall's potential will generally be quite short.

Regards,
Reilly Atkinson

I think there is no doubt that the electron interacts with the slits, otherwise what part of the experiment is responsible for momentum conservation? The source? The detector?

The big question is how the interference fringes appear as a result of those interactions.

Regards,
Andrei Bocan

 

[zbyszek]

1.I referred to classical paper by H.D.Zeh for example (Foundations of Physics 1,69 (1970). You may find more in QT and Measurement edited by J.A. Wheeler and W.H.Zurek

I've read it. As to quality of this paper it is enough to consider the authors classification
of differrent views on the measurement problem in QM. How would you classify the
statistical interpretation of QM (saying that QM does not describe the measurment at all)
according to the classification scheme introduced by Zeh?

[QOUTE=Anonym]
3.I do not act. I present (I hope consistently) so called “Orthodox QM (quant-ph/0004077).
[/QUOTE]

You list the postulates of QM. All of them, but last, after Ballentine. The last one is the "measurement" postulate Eq.(14). Right after that you claim that everybody agrees
with the list. Well, not everybody. If you read Ballentains work more cerfully you would see that
your last postulate is certainly not a part of the statistical approach to QM.
Especially you could profit from the distinction made by Ballentain between the state
preparation and the measurement.

4.I was involved into discussion of statistical interpretation. Really it is not interested me.” I just seriously doubt its usefulness”.

Fair enough. But why are you asking me about those issues if you are not interested?
Am I being interviewed for a job?

5.What I try to understand here is whether the coherent state provide the adequate description of the Newtonian “ball” used in classical statistical mechanics and if it is so how to make this basis orthonormal as it should be (J.v.Neumann, Zs.f.Phys.,57,30(1929).

Don't know the problem.

Sometimes your way to express yourself disturb me. If you already know and understand everything, I can’t help you.
Perhaps, I can tell you something different, some way that you did not consider before. If you are interested, I will send you private message.

Anonym, I try to keep in mind that my brain can be fooled, and that some of the rock solid
foundations of my understanding of QM can be just my misperceptions. Neural networks
have their weaknesses.
Thus, from time to time I recheck all the premises if new evidence shows up.
Our discussion would be one of those occasions. But I have failed to see the new evidence.
I have read very carefully the nice paper by Ballentine, I tryied to understand the Zeh's
view and yours in the preprint, I learned the original work by Tonomura and here is what
I find:
1. I agree with every sentence of the first part of Ballentine's work. The part with hidden
variables is tricky.
2. Zeh didn't have chance to read Ballentine. Otherwise, he might have commented also
on the statistical interpretation.
3. In your work, you give wrong description of Ballentine's paper (section 1.2), you logic
is questionable in the Recapitulation (section 1.6) when it comes to the two alternatives
A and B (you conveniently forget that neither A or B captures the results from Ballentine's work). Namely, there is also C: QM is exact, no need for any reinterpretation, remove the postulate you have added to the Ballentine's list.
4. I didn't see what is so spectacular in the Tonomura's experiment that could have
force someone to take an orthodox point of view on QM.

Did you really read the papers you referred to in the manuscript? I mean the one by Ballentine.
I don't believe you wouldn't understand if you actually read it. Unless, of course, neurons
in your brain make no new connections.

At the moment it looks to me that you have reservations towards the statistical
interpretation because you don't know it.
Or perhaps, my brain is hard wired already and cannot comprehend the obvious.

Thanks for the references! I didn't know them before.

Cheers!

 

[vanesch]

In classical mechanics, we can use Hamilton's equations or Newton's laws. Still, the theory describes the same thing, say the motion of a pendulum. We don't say that we have a theory describing an abstract phase space.

Ah ? I certainly do. I think that Newtonian mechanics (points in 3-dim Euclidean space with forces and so on) and Lagrangian/Hamiltonian mechanics describe different ontologies ! (which are however observationally identical). In other words, when considering Hamiltonian mechanics, I *do* consider that its universe is a 6N dimensional tangent bundle and not a 3-dim Euclidean space, although one can find certainly a 3-dim Euclidean structure in there.

 

[vanesch]

The universe, as a whole, cannot be in an excited state as no energy can be added to it. So, we can be certain that it is in a ground state.

Mmm, that's a pretty dubious statement...

An excited molecule, on the other hand, is a subsystem, and it is to be expected that a full description cannot be found by just specifying the momenta and position for its particles. It's like asking for the law of motion of a pendulum without giving the gravitational acceleration.

In order to compensate for the lack of knowledge regarding the whole system (universe) of which the molecule is but a part we need psi.

You mean that psi is then the summary of the interaction with the rest of the universe ? The "noise that comes from elsewhere" ?

Ok, but I can think of a toy universe just with one molecule in it, and I give it a certain quantum state |psi> which can be just any state (not even a stationary state). Clearly, this is then the "state of the universe" as there isn't anything else around. I can also give you the initial positions and velocities of the electrons and nucleae. And you can STILL not calculate the quantum forces without using psi - nevertheless, there is no "noise coming from elsewhere".

I only say that to show you that in BM, the wavefunction has a life of its own, with its own dynamics, and its own dynamical content which is NOT derivable from the particle positions and velocities elsewhere. As such, it is entirely part of the dynamical description, and hence must have its own ontology in addition to that of the particles.

However, in the case of MWI, 3D space does not seem to be postulated, it should be a consequence of the theory.

MWI is only a way of looking upon a quantum theory, and a quantum theory needs as its inputs the list of the degrees of freedom, the hamiltonian flow, and the link to (subjective) observation. Depending on that, you can put in the 3-dim space rather explicitly (such as is done in non-relativistic quantum mechanics or QFT), or you can hope that it will somehow emerge if you set up a different structure (LQG ?).

Let's say I accept a universal wavefunction as the ultimate reality. The question is then, how do we get from there to what it seems to be reality for us. Why a hydrogen atom does not look like a "bunch of spin-1/2 systems" to us?

That's the entire definition of how we extract subjective experience from the wavefunction ! It's the "shove-it-all-under-the-carpet" part of MWI (but also of GR, to a lesser extend btw). You have to accept that the psycho-physical link is non-trivial, and corresponds to certain subspaces of hilbert space being associated with certain subjective experiences. Which is in any case a to-be-accepted problem for a physical theory ; only, for some physical theories, this aspect "factors out" (like in Newtonian mechanics - but not in Hamiltonian mechanics !) and in others (such as MWI), it forms a crucial part of it.

 

[Anonym]

Zbyszek:” You list the postulates of QM. All of them, but last, after Ballentine. The last one is the "measurement" postulate Eq.(14). Right after that you claim that everybody agrees with the list.”

Sorry, I am not S.L.Adler. It is due to my terrible English.
I only quoted Adler’s paper and I meant the first paragraph “Orthodox QM and Issues it Raises”. I meant that point of view I present somehow close to the orthodox QM. I don’t agree with the presented list of “postulates”. It should be obvious since no one of them fit the description of the requirements for postulate that I wrote to you.

Zbyszek:” But why are you asking me about those issues if you are not interested?”

“Or perhaps you misinterpret wave functions? Does a wave function correspond to a single quantum object or to an ensamble of single quantum objects?

If the second is true then QM has nothing to say about particle or wave character of a single quantum object, a single electron for example. QM describes ensambles.

If the first is true then how come that electrons appear as points on the screen in Young-like experiment although the their wave functions spread across the whole screen? In other words if QM applies to single quantum objects then one should be able to predict WITH CERTAINTY (not just probability) an outcome of a single run of an experiment with one electron!”

I tried to understand why you bring statistics into discussion of the wave packet description. For me it is relevant in the discussion of wave packets description.

Zbyszek:” I mean the one by Ballentine.”

Sorry, I did not. I promise I will.

 

[Anonym]

Reilly:” The connection between repeated measurements and ensembles only works for ergodic systems.

However, it is a frequent assumption in physics, and statistics, not unrelated to the often used idea that distributions are Gaussian's. “

Your argument is very convincing for me. I have no doubt that it should be Gaussian’s. However, adequate means unique. And that what I try to see.

Reilly:”Here's a simple fact: in this real world of ours we can't predict anything with certainty. Measurement error is a fact of Nature. Thus everything is uncertain, to a greater or lesser degree. Brownian motion occurs in 'classical systems'. That means, of course, that there is no theory of certain events.

That's why we use in experiments the largest sample possible so as to get info about the distribution of measurements with as much accuracy as possible.”

All classical theoretical physics: Newtonian mechanics, special relativity,electromagnetism, gravitation and even statistical mechanics are “theory of certain events”.

You consider only one aspect of the problem. Your description of the measurements fit perfectly the mathematical framework used in the classical physics. It essential feature is the use of analysis (classical,vector and tensor consequently). In the foundation of the analysis lies lim operation which can’t be reduced to addition and multiplication. It means intrinsically that for every predefined epsilon > 0 you may find suitable delta > 0. And thus your notion of accuracy fit it perfectly too.
However, QM do not follow that scenario.
Consider properly calibrated and functioning set of the measurement instruments. You perform the observation and obtain a point. Now you repeat the procedure for the identical system (the standard QM treatment of that notion). Your new observation is legal exactly as the previous. However, it do not always satisfy your requirement. Sometimes one obtain points where delta is arbitrary large. This do not mean that now your measurement equipment is spoiled. This mean that you met new physics (and new mathematics consequently).
Quantum world is not a classical world.
Now let me add dual deterministic treatment of the repeatability.
It is not sufficient to perform the measurement only in one laboratory. One need confirmation that what was obtained represent the objective reality. That means that in the alternative laboratory one should be able to reproduce the entire picture of the extended object obtained previously. Once again, the identification may be performed only by using the statistical methods of the data processing. I feel here a deep natural connection with the C.E.Shannon theory of communication but I am not prepared enough to enter into discussion.

Zbyszek:” I didn't see what is so spectacular in the Tonomura's experiment that could have force someone to take an orthodox point of view on QM.”

A.Tonomura experiment demonstrated the power of the human intellect which turns out to be able to extract the precise and detailed knowledge of what happens at electron Compton wave length distances.
Apparently, Born interpretation states that quantum physics may be treated only in terms of “potential reality”. From A.Tonomura experiment follows that one do not need any imagination. Everybody simply see the same picture.

 

[reilly]

Quote:
Originally Posted by reilly View PostYes, but. You suggest that the wall and slit boundaries have an important dynamical role in the double slit experiment. That's not so clear. Don't see many backscattered electrons from the slits.#1
Look at the physics: as an electron goes through a slit, it forces electrons in the wall away from the slit boundary. Both the electrons and nucleii are subject to thermal bouncing about. In my view, this is suficient to say that 1. the forces on a passing electron are small ( left balances right), and 2. average to zero over all but the shortest of times.

#1A
A somewhat more sophisticated approach is to treat the wall as composed of
nuclear-electron dipoles, which in turn are created by the fields of the passing electrons. This approach makes the handling of magnetism a bit easier.

The translation into QM is to get the "actual" potential seen by a passing electron, and include this in the Schrodinger Eq. (Not to worry about feedback of forces in this problem). Also a helpful fact: the dwell time of an electron in the wall's potential will generally be quite short.

Regards,
Reilly Atkinson

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>.
ueit
I think there is no doubt that the electron interacts with the slits, otherwise what part of the experiment is responsible for momentum conservation? The source? The detector?

The big question is how the interference fringes appear as a result of those interactions.

Regards,
Andrei Bocan
Report Post Reply With Quote

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>..
With all due respect, I find it hard to believe that you read my post. In fact, I provide an outline of how to compute the effects of of electron-screen interaction. (#1 and #1A) I will agree to laziness; I'm quite sure that this calculation has been done, but I will leave it at that.

For example; the Babinet opposite of the slit is simple, say, a "small" rectangular piece of screen material, or whatever. Scatter electrons from this target, and include the contribution of eddy currents, including polarization and magenetism. This could, for example, be of interest to users of electron microscopes.

Even if you can demonstrate that screen-electron interactions cause electron diffraction, you'll still have to worry about electron & neutron diffraction from crystal lattices. Tough job indeed.

Not to worry about momentum conservation: inspection of the system confirms that it's ok to treat the screen as if it has an infinite mass. That is it takes a huge hit to get the screen to move -- in comparison to an electron boucing from the screen.

Regards,
Reilly Atkinson

 

[zbyszek]

I tend to agree with you that QM is statistics, however, I have an objection to your argument.

The double slit experiment is explained using not pure QM but a semiclassical approximation of it. The electron is treated as a quantum, but the wall, source and detector not. In order to find out what QM really predicts for such an experiment we need a detailed description of the system, that is, the quantum state of the whole system. The result of such a ridiculously complex calculation could give you a much better prediction about the experimental outcome.

ueit,
This reply is late because I didn't notice that you actually referred to my post.

As a side note: the treatment I proposed is not semiclassical. The word semiclassical
usually means that some aspects of a dynamics of a system are treated classically rather
than quantally.
I propose to ignore the screen with the slits and the detector completely not just their quantum
nature. In their stead I recommend focusing on the wave function of the system of interest,
i.e. of the wave function of an electron just before it hits the detectors.

As you said, QM is statistics, so the wave function is just enough to generate outcomes
of an ideal experiment by sampling the corresponding probability density.

This way you escape from the measurement problem and from internal complexity of
the screen and the detectors.

Cheers!

 

[ueit]

Ah ? I certainly do. I think that Newtonian mechanics (points in 3-dim Euclidean space with forces and so on) and Lagrangian/Hamiltonian mechanics describe different ontologies ! (which are however observationally identical). In other words, when considering Hamiltonian mechanics, I *do* consider that its universe is a 6N dimensional tangent bundle and not a 3-dim Euclidean space, although one can find certainly a 3-dim Euclidean structure in there.

In order to calculate the Lagrangian we need potential and kinetic energies. I don't see the meaning of these parameters outside Newton's ontology. Once you use those parameters and everything else you need to calculate them (concepts like mass localized in 3d space, or force) it seems rather odd to claim that another ontology is at base.

A true example of a different ontology would be GR where the gravitational force is replaced with something else.

 

[vanesch]

In order to calculate the Lagrangian we need potential and kinetic energies. I don't see the meaning of these parameters outside Newton's ontology. Once you use those parameters and everything else you need to calculate them (concepts like mass localized in 3d space, or force) it seems rather odd to claim that another ontology is at base.

No, what I mean is that in a lagrangian formulation, the "world" is a single point in a configuration space, and not "multiple points in a 3-dim space". However, as you point out, the lagrangian "cost function" has strangely enough a special structure to it which links certain degrees of freedom with others in such a way as if they were points in a 3-dim space. It is this special structure of the lagrangian function which gives us then, in that single point in configuration space, an illusion of "multiple points in 3-dim space". So yes, in a certain way, there is a kind of "sub-structure" in the langrangian formulation which makes the dynamics in configuration space behave equivalently to a Newtonian formulation in 3 dim space. But this doesn't need to be the case, a priori, in a Lagrangian formulation. In principle, if the manifold of generalized coordinates is given, and a function L(q,q-dot) is given, that's all you need for a "lagrangian universe". Whether or not these q can be functions of a set of points in 3-dim euclidean space is something extra. It is this special structure which gives, to a creature living in a "lagrangian universe" the impression of living in a 3-dim euclidean space.

 

[ueit]

You mean that psi is then the summary of the interaction with the rest of the universe ? The "noise that comes from elsewhere" ?

Ok, but I can think of a toy universe just with one molecule in it, and I give it a certain quantum state |psi> which can be just any state (not even a stationary state). Clearly, this is then the "state of the universe" as there isn't anything else around. I can also give you the initial positions and velocities of the electrons and nucleae. And you can STILL not calculate the quantum forces without using psi - nevertheless, there is no "noise coming from elsewhere".

I only say that to show you that in BM, the wavefunction has a life of its own, with its own dynamics, and its own dynamical content which is NOT derivable from the particle positions and velocities elsewhere. As such, it is entirely part of the dynamical description, and hence must have its own ontology in addition to that of the particles.

Let's say that a universe consists of a single hydrogen atom with the electron in a p orbital. Now, for that universe, that's the only state it can be in. There is no way it can decay to a lower energy state. If a correct quantum theory for that universe exists, it has to predict with certainty its state (p), as any other state has to have 0 probability. Therefore BM doesn't need a separate ontology.

MWI is only a way of looking upon a quantum theory, and a quantum theory needs as its inputs the list of the degrees of freedom, the hamiltonian flow, and the link to (subjective) observation. Depending on that, you can put in the 3-dim space rather explicitly (such as is done in non-relativistic quantum mechanics or QFT), or you can hope that it will somehow emerge if you set up a different structure (LQG ?).

Is it not that structure you have to put by hand that defines the ontology?

P.S.

Can you point me, please, to an article containing a clear formulation of MWI in terms of its postulates?