How Does Quantum Mechanics Combine Particle and Wave Descriptions?

[zbyszek]

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.

Yep, Dirac was ok. One of the very few who didn't assume to much about QM.

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?

Classical statistical mechanics and quantum mechanics are analogous descriptions
of classical and quantum world, respectively. You can compare evolution of a classical
Liouville density (distribution over classical trajectories in phase space) and a Wigner
function (a fancy representation a wave function). Namely, you can compare classical
and quantum ensembles. There is no quantum counterpart of classical mechanics.

There is no "quantum statistical mechanics" because world 'statistical' is redundant.

A "statistical interpretation of QM" is a name given to QM by those who believe
that QM is something more than a statistical theory. They (unjustly) ascribe a new meaning to wave functions. They believe it applies not only to an ensemble of quantum
objects but to individual objects as well. And to distinguish themselves from normal
physicist they say they follow the Copenhagen Interpretation (after Bohr) or Many Worlds Interpretation (after Everett and the rest of Wheeler's mafia).
None of those bright minds can show any grounds for such an abuse of a quantum state,
but this is not really required for a religion.

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.

But hey, how many people realize that FDR put the US into a decay mode?

Cheers!

 

[zbyszek]

I thought the point was to get some sort of "classical-style" trajectory out of it using the "other" equation?

There is no "other" equation. There is only Schroedinger equation with an ordinary complex valued wave function written as R(x)*exp(i*S(x)/hbar), i.e. the modulus and
a phase are given separate symbols R and S.
The Schroedinger equation splits then into conservation of probability equation and something that resembles Hamilton-Jacobi one. That's it.
If you know the wave function you can compute some trajectories that follow
the H-J equation :).

Cheers!

 

[vanesch]

No, it's not. There are other interpretations (Bohm's one for example) free from the measurement problem.

Although, for non-relativistic QM, Bohmian mechanics is ontologically clearer, its "clearness" is sometimes overstated, because Bohmian mechanics needs TWO ontological parts:
- the particles, and that's what everybody stresses, and what looks like Newtonian mechanics with an added potential, so this seems at first sight to be very clear
- but there is ALSO, as an independent entity, the wavefunction, which does NOT live in spacetime, but which lives over configuration space all together. It is NOT a classical field, and it contains also all the "ghosts" of MWI.

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.

The other problem with BM of course is the fact that it is not compatible with a relativistic spacetime: there is no geometric formulation of BM possible (which would come down to being able to write BM in a lorentz-invariant way, which is not possible).

Anyway, for a double slit experiment even CI would give a much accurate prediction if a more detailed approach is used. For example it would be interesting to explain the change in momentum at the slits in terms of the interaction between the incoming electron and the field produced by the wall.

There is absolutely no difference between practical calculations in MWI and in CI, so both are just as accurate.

Before we discuss this further, there is something fundamental that escapes me in regards to MWI. QM is defined on a 4D spacetime background.

Not at all. QM is defined in hilbert space, which is the functional space over configuration space. This only coincides with "normal space" in the case of a single point particle.

Here the particles and fields exist, here we calculate the Hamiltonian and so on. What exactly is MWI's background? Do we have a 5D spacetime where the worlds are stacked in a certain way, or what? What is the geometry of this background? It is probably a silly question, but I couldn't find a good answer yet.

There are a lot of misunderstandings about MWI. MWI is simply defined, as in "normal" QM, over Hilbert space. This Hilbert space has a basis which can be "indexed" using a configuration space of a classical system, and that classical system can be a field over spacetime, or a set of particles in Euclidean space, or... whatever.
A given "observer" in MWI corresponds to certain subspaces of Hilbert space which correspond to a certain "history of observations" (just like a given observer state in classical phase space corresponds to certain patches in phase space corresponding to a certain "record of observation"). Now, in classical phase space, we usually consider only ONE point which is wandering around (the "state of the universe") in phase space, following a Hamiltonian flow. This point will enter and leave certain "observer patches" and this will correspond to "experienced observations". Given that these patches, classically, are disjoint (you do not have a patch that corresponds at the same time to "the light bulb was on" and "the light bulb was off"), there is no ambiguity to any observation.

In Hilbert space, the patches of "states of observers" are subspaces of hilbert space. And the "state of the universe" is a vector in Hilbert space that follows the unitary evolution of the Hamiltonian flow. However, the difference is now that this state of the universe can have components in DIFFERENT observer subspaces at the same time.
In MWI, we simply say that these different and incompatible observations are then taking place in different "worlds", and that you, as an observer, are just experiencing one of these subspaces and not all of them, simply because we can only experience one subspace. The other subspaces then correspond to experiences of "copies". What matters, for a specific subjective observer, is, what is the probability that he will be one of the copies. It is the specific structure of the subspaces which makes us have the illusion of a "theatre that is like spacetime".

You could compare this situation with a classical phase space where there are different points corresponding to different "worlds" wandering around on the Hamiltonian flow. These different points can then be in different "observer patches" at the same time, but you will only experience "one of these patches".

There is no need to assume that every possibility has to exist. Just because a brain has a number of possible states id doesn't follow that it has to exist in all those states simultaneously.

This is not postulated a priori. It is because it follows naturally out of the Schroedinger evolution equation that this consideration is taken. The reason for postulating "many worlds" is not a crazy idea that is imported, it is because it follows from the formalism. One has introduced a specific EXTRA mechanism in quantum theory to GET RID OF IT, which is projection, but that extra mechanism is the core of all difficulties in QM: it is explicitly non-local and not Lorentz-invariant, irreversible, dynamically ill-defined (when exactly does it happen) etc... It is because of all these difficulties *introduced by the patch that is projection* that Everett first considered to get rid of it, and to keep the one and only dynamical law that is well-defined in QM: hamiltonian unitary evolution. But IF you keep that as a universal dynamics, well then you end up *naturally* with a state of the universe where observers occur in superpositions of "macroscopically different observations". It is just because of this natural appearance of different classical observation states in the "state of the universe" that the idea was then to see this as "parallel worlds". There's no more or no less to it. MWI is simply: let us take the unitary dynamics of quantum theory as fundamental and universal, without introducing a patch to make it fit "classical outcomes" which introduces a lot of difficulties.

So MWI is nothing else but: let us take the hilbert space formalism of QM, and its unitary dynamics, for real, and see what it tells, without wanting to force any specific a-priori of what "should" reasonably, come out.

 

[Demystifier]

The other problem with BM of course is the fact that it is not compatible with a relativistic spacetime: there is no geometric formulation of BM possible (which would come down to being able to write BM in a lorentz-invariant way, which is not possible).

Don't be so sure:
http://arxiv.org/abs/quant-ph/0406173

 

[Demystifier]

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]

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]

Statistically it's perfect

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]

Don't be so sure:
http://arxiv.org/abs/quant-ph/0406173

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]

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]

Don't be so sure:
http://arxiv.org/abs/quant-ph/0406173

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

(and mind MWI is not realistic).

... for sufficiently naive versions of "realistic"

(meaning: where events really, and uniquely, happen)

 

[Careful]

... for sufficiently naive versions of "realistic"

(meaning: where events really, and uniquely, happen)

Brilliant !

 

[ueit]

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.

 

[ueit]

Although, for non-relativistic QM, Bohmian mechanics is ontologically clearer, its "clearness" is sometimes overstated, because Bohmian mechanics needs TWO ontological parts:
- the particles, and that's what everybody stresses, and what looks like Newtonian mechanics with an added potential, so this seems at first sight to be very clear
- but there is ALSO, as an independent entity, the wavefunction, which does NOT live in spacetime, but which lives over configuration space all together. It is NOT a classical field, and it contains also all the "ghosts" of MWI.

The wavefunction describes the force acting on the particles. The particles exist in 3D space and the force acts upon them in 3d space as well. We need not to ascribe a fundamental character to the mathematical formalism needed to calculate that force. And what do you mean by ghosts?

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.

The wavefunction describes how the particles move. I don't understand your point about "awareness". Is this like saying that we are aware of the Moon but not of its gravitational force?

The other problem with BM of course is the fact that it is not compatible with a relativistic spacetime: there is no geometric formulation of BM possible (which would come down to being able to write BM in a lorentz-invariant way, which is not possible).

I think there is some debate about this issue.

Not at all. QM is defined in hilbert space, which is the functional space over configuration space. This only coincides with "normal space" in the case of a single point particle.

The Hilbert space is a mathematical construct. The derivation of the wavefunction involves the assumption of point particles existing in a 3d space + 1d time background.

There are a lot of misunderstandings about MWI. MWI is simply defined, as in "normal" QM, over Hilbert space. This Hilbert space has a basis which can be "indexed" using a configuration space of a classical system, and that classical system can be a field over spacetime, or a set of particles in Euclidean space, or... whatever.

Normal QM is defined on a Newtonian background, QFT on a Minkowski spacetime. The particles with their masses and various charges exist in this background. As MWI is only an interpretation it should be defined on the same background, isn't it?

A given "observer" in MWI corresponds to certain subspaces of Hilbert space which correspond to a certain "history of observations" (just like a given observer state in classical phase space corresponds to certain patches in phase space corresponding to a certain "record of observation"). Now, in classical phase space, we usually consider only ONE point which is wandering around (the "state of the universe") in phase space, following a Hamiltonian flow. This point will enter and leave certain "observer patches" and this will correspond to "experienced observations". Given that these patches, classically, are disjoint (you do not have a patch that corresponds at the same time to "the light bulb was on" and "the light bulb was off"), there is no ambiguity to any observation.

In Hilbert space, the patches of "states of observers" are subspaces of hilbert space. And the "state of the universe" is a vector in Hilbert space that follows the unitary evolution of the Hamiltonian flow. However, the difference is now that this state of the universe can have components in DIFFERENT observer subspaces at the same time.
In MWI, we simply say that these different and incompatible observations are then taking place in different "worlds", and that you, as an observer, are just experiencing one of these subspaces and not all of them, simply because we can only experience one subspace. The other subspaces then correspond to experiences of "copies". What matters, for a specific subjective observer, is, what is the probability that he will be one of the copies. It is the specific structure of the subspaces which makes us have the illusion of a "theatre that is like spacetime".
You could compare this situation with a classical phase space where there are different points corresponding to different "worlds" wandering around on the Hamiltonian flow. These different points can then be in different "observer patches" at the same time, but you will only experience "one of these patches".

Again, the hilbert space is a derived concept. What could be the meaning of the configuration space without first defining the background? The position of a particle depends on the number of dimensions in which the particle exists so it doesn't seem to me that the "theatre that is like spacetime" follows from quantum formalism but the other way arround.

This is not postulated a priori. It is because it follows naturally out of the Schroedinger evolution equation that this consideration is taken. The reason for postulating "many worlds" is not a crazy idea that is imported, it is because it follows from the formalism. One has introduced a specific EXTRA mechanism in quantum theory to GET RID OF IT, which is projection, but that extra mechanism is the core of all difficulties in QM: it is explicitly non-local and not Lorentz-invariant, irreversible, dynamically ill-defined (when exactly does it happen) etc... It is because of all these difficulties *introduced by the patch that is projection* that Everett first considered to get rid of it, and to keep the one and only dynamical law that is well-defined in QM: hamiltonian unitary evolution. But IF you keep that as a universal dynamics, well then you end up *naturally* with a state of the universe where observers occur in superpositions of "macroscopically different observations". It is just because of this natural appearance of different classical observation states in the "state of the universe" that the idea was then to see this as "parallel worlds". There's no more or no less to it. MWI is simply: let us take the unitary dynamics of quantum theory as fundamental and universal, without introducing a patch to make it fit "classical outcomes" which introduces a lot of difficulties.

So MWI is nothing else but: let us take the hilbert space formalism of QM, and its unitary dynamics, for real, and see what it tells, without wanting to force any specific a-priori of what "should" reasonably, come out.

I have a hard time understanding how can you write down a wavefunction without first assuming point particles in a 3d background. And if you assume that as real, then how can the wavefunction be real and the spacetime an illusion?

 

[karfiol]

there are no particles, there are only waves

When energy is spreading through space it has form of wave. That is default form of energy.

But when energy come in contact with something, it cease to be wave and become particle.

 

[zbyszek]

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?

No, I'm not. We are talking QM here, right? No relativistic extensions.
The QM is incomplete in the sense that it is only statistical. No single events
theory at all. How many quantum physicist realize that today?
In the first half of 20th century, there was no MWI. Do you need a stronger
argument? :)
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?

Cheers!

 

[zbyszek]

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) ?

Yes, you can. One can get relativistic equations out of nonrelativistic QM.
Here is an example.
Effective theories for low energy corner of nonrelativistic quantum liquids tend
to have Lorentz invariance, among other symmetries. Moreover, one can get something like Einstein's equations for propagation of excitations with, so called, acoustic metric.
c is replaced with the speed of sound in the liquid. See works of Volovik or
his book "The Universe in a helium droplet".

In short you have an absolute frame of reference (the one of the
center of mass of the liquid) and Lorenz invariance (for low energy excitations) in one system.

Cheers!

 

[zbyszek]

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.

Thanks for the explanation!
I find my arguments viable and I am a part of the public. I hope. Or am I?

More, I've even read the manuscript publicly recommended by you with some
level of comprehension. Do I deserve an answer?

Forgive me my curiosity, but I cannot help wondering what "more scientific"
means in that case. Please, don't let me down!



Cheers!

 

[masudr]

Normal QM is defined on a Newtonian background

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

Again, the hilbert space is a derived concept. What could be the meaning of the configuration space without first defining the background? The position of a particle depends on the number of dimensions in which the particle exists so it doesn't seem to me that the "theatre that is like spacetime" follows from quantum formalism but the other way arround.

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.

 

[Careful]

Yes, you can. One can get relativistic equations out of nonrelativistic QM.
Here is an example.
Effective theories for low energy corner of nonrelativistic quantum liquids tend
to have Lorentz invariance, among other symmetries. Moreover, one can get something like Einstein's equations for propagation of excitations with, so called, acoustic metric.
c is replaced with the speed of sound in the liquid. See works of Volovik or
his book "The Universe in a helium droplet".

In short you have an absolute frame of reference (the one of the
center of mass of the liquid) and Lorenz invariance (for low energy excitations) in one system.

Cheers!

Euh, I don't think anybody is worried about how to rewrite a non relativistic theory as an approximately relativistic one for the low energy modes (given for example the fact that Lorentz invariance is so well tested at high energies). I don't know about this reference but it sounds like saying that for sufficiently small x a Lorentz boost B(x) doesn't differ much from the corresponding rotation R(x). It would be much cooler to have a Galileian theory which allows for some coarse graining which *is* Lorentz invariant for *all* modes. This is achieved (but not entirely to my liking) by Holland amongst others in his paper about the hydrodynamic interpretation of Maxwell's theory (which has nothing to do with the old eather models I must add).

Careful

 

[vanesch]

The wavefunction describes the force acting on the particles. The particles exist in 3D space and the force acts upon them in 3d space as well. We need not to ascribe a fundamental character to the mathematical formalism needed to calculate that force.

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.

And what do you mean by ghosts?

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

The wavefunction describes how the particles move. I don't understand your point about "awareness". Is this like saying that we are aware of the Moon but not of its gravitational force?

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

I think there is some debate about this issue.

I don't believe those claims.

The Hilbert space is a mathematical construct. The derivation of the wavefunction involves the assumption of point particles existing in a 3d space + 1d time background.

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

Normal QM is defined on a Newtonian background

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"...).

Again, the hilbert space is a derived concept. What could be the meaning of the configuration space without first defining the background?

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 !).

The position of a particle depends on the number of dimensions in which the particle exists so it doesn't seem to me that the "theatre that is like spacetime" follows from quantum formalism but the other way arround.

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.

I have a hard time understanding how can you write down a wavefunction without first assuming point particles in a 3d background. And if you assume that as real, then how can the wavefunction be real and the spacetime an illusion?

As I said, you can consider a set of spin-1/2 systems, define a unitary dynamics over it, and go ahead.

 

[Anonym]

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. The wave packet reduction (as explained by A. Einstein) is necessary in order to satisfy requirements of special relativity in the classical physics.
QM describes physics of the massive wave packets (not in the coherent basis). R.J. Glauber demonstrated that
<alpha|H|alpha>=omega*(alphasquare+1/2)
with alpha continuous. Glauber contribution is establishing the connection between quantum and classical statistical mechanics by using E.Schrödinger preliminary result. However, I don’t consider that story complete (therefore, I asking questions).
Foundations of non-relativistic QM were established by J.von Neumann through unification of the Heisenberg-Dirac theory of dynamical observables and Schrödinger theory of states. I consider that story complete. 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. My distinction is between QM and the statistical interpretation of QM.

 

[Anonym]

Careful:"You cannot discuss physics without taking into account special relativity"

I agree with zbyszek answer. Special relativity as well as wave mechanics already resides in HJ formulation. Be careful, what peoples were doing before 1905? With respect to relativistic QM or QFT as you call it, don't worry. " raffinert ist der Herr Gott, aber boshaft ist Er nicht"

 

[Demystifier]

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 am a Bohmian and I also have a saying.
BM is MWI but with only one world. (Other worlds are tags.)

 

[Demystifier]

Yes, you can. One can get relativistic equations out of nonrelativistic QM.
Here is an example.
Effective theories for low energy corner of nonrelativistic quantum liquids tend
to have Lorentz invariance, among other symmetries. Moreover, one can get something like Einstein's equations for propagation of excitations with, so called, acoustic metric.
c is replaced with the speed of sound in the liquid. See works of Volovik or
his book "The Universe in a helium droplet".

In short you have an absolute frame of reference (the one of the
center of mass of the liquid) and Lorenz invariance (for low energy excitations) in one system.

This time I agree with you.
Maybe I will answer your questions, despite your rude qualifications such as that "I was not knowing what I was doing" and alike.

 

[Demystifier]

1. 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!

2. 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".

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.

2. If you read it more carefully, I admit that I do not always know the correct probability density, but the point is that it is not necessary to know it in a deterministic theory. For example, in classical mechanics you also do not know a priori the correct initial position of the particle nor the correct probability density, but classical mechanics still works very well.

 

[Anonym]

Ueit:” It may be, the electron interference experiments I know of were performed with copper gratings, magnetic fields, or crystallization planes.”

Ok,let us consider 50-50 for siplicity. The only thing I should know in order to proceed after “wall” is relative phase between the transmitted and reflected wave fields.It may be obtained from unitarity without knowledge of any details of underlined dynamics (V.Degiorgio, A.Zeilinger). Apparently, you may invent any complicated interaction you can imagine provided that outcome will be as predicted by them. I guess you cannot. I guess that only minimal coupling will do a job.

 

[Demystifier]

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

 

[Careful]

Careful:"You cannot discuss physics without taking into account special relativity"

I agree with zbyszek answer. Special relativity as well as wave mechanics already resides in HJ formulation. Be careful, what peoples were doing before 1905? With respect to relativistic QM or QFT as you call it, don't worry. " raffinert ist der Herr Gott, aber boshaft ist Er nicht"

Euh, Zbyszek merely gave some examples of ``approximate Lorentz invariance'' in the low energy sector (which is unsurprising since any student knows how to switch between the relativistic and Galileian description in this case). So, what are you saying here, that one should not bother about Lorentz invariance in the high energy sector !? Then, I want to see how you can *naturally* embed Maxwell's theory in such framework without being in violation with Michelson Morely.

NOTE : I looked up the reference of Volovik http://ltl.tkk.fi/personnel/THEORY/volovik/book.pdf and indeed it confirms my supicion about giving up Lorentz, Gauge invariance etc... at sufficiently high energies. So relativity goes down the drain, but on the other hand QM isn't complete either (strange enough he doesn't appear to mention that) : embracing Galileian mechanics isn't sufficient to solve the entanglement ``paradox'' (if it needs to be solved in the first place). And of course, you should worry about those things ...

Careful

 

[vanesch]

I am a Bohmian and I also have a saying.
BM is MWI but with only one world.

Yes, the tag is given by the "particle positions", but you still need the wavefunction as a separate, physical and dynamical entity. 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

 

[zbyszek]

Euh, Zbyszek merely gave some examples of ``approximate Lorentz invariance'' in the low energy sector (which is unsurprising since any student knows how to switch between the relativistic and Galileian description in this case). So, what are you saying here, that one should not bother about Lorentz invariance in the high energy sector !? Then, I want to see how you can *naturally* embed Maxwell's theory in such framework without being in violation with Michelson Morely.
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!

 

[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?