The wave packet description

zbyszek

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

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).

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

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.

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".

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

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

Demystifier

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

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

ueit

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).

vanesch

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

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

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

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

Going with the herd? That's the scientific spirit!
Nice answer to a detailed argument, too.

Cheers!

Demystifier

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

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.