How Does Quantum Mechanics Combine Particle and Wave Descriptions?

[zbyszek]

In which other way could it appear on the screen? The screen is made of many single revelators, and each of them can only make a "click" or not making it.

If many revelators, let's say 1000, on a spread area on the screen, would click at the same time, this wouldn't be interpreted as "the electron has been revelated on a spread area of the screen" but, instead: 1000 electrons have arrived at the same time.

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 ? .
No one has seen such wonder yet.

The physical meaning is made by the act of measuring in some way. If the measuring process means to make the wave interact with revelators that can "click" in any instant of time when the wave hits them, then, by definition the "position" of the wave cannot have a more precise value.

Does, for instance, an 'event horizon' have any physical meaning? If it does, who measured it?

I mean, IMO, it's not because of some strangeness of physical word, but just because we have given that meaning to that physical property/concept.

Our set of concepts evolves. There is still hope :).

Cheers!

 

[vanesch]

In a single run of an electron through slits it ends up in a spot on a screen. Do you
have a theory predicting the spot? Don't do exactly, do it with an arbitrary precision.
If you cannot do that (despite the fact that you know all the states exactly) I say you have no theory of single objects.

As I said elsewhere, in an MWI setting, the single electron, after interaction with the screen, the photodetector, the electronics and all that, generates an *ensemble of observers* for that single event (aka "branches" for that observer). Because "you" are only one of them, you can't predict what you'll observe, because you only have the law for the ensemble of observers. So yes, quantum theory is not a theory of a single observer, but only of an ensemble of observers. Nevertheless, it can perfectly well describe a single *object*.

Ok, you don't have to adhere to that view, but to me it is a perfectly sensible one, for two reasons. The main reason is that this is what comes out of the formalism itself, if you consider that everything in the universe is described by QM (and hence has a quantum state, including human bodies and all that) and that you consider that there is only one genuine dynamical law. The second reason is that it allows you to give some ontological status to the formal elements of quantum theory.

What you actually can do, you can tell me the distribution of spots that can be recovered after many repetition of the same experiment with an arbitrary precission, a statistical average over an ensemble. In my dictionary that constitutes a statistical theory.

It very well might be that in Nature there is no theory of single objects. It still does not give
us freedom to put monsters in the uncharted area or stretch known maps to hide them.

I find it more difficult to conceive that *there is no theory of single objects* (and hence that there is no theory of the universe as a whole), than to make a few assumptions that fit perfectly well with the formalism that we have at hand.

1. Do you agree that QM does not reveal the spot?

Yes.

2. How would you call a hypothetical theory that does?

If it works, a better theory of course.

3. If such a theory appears, would you still consider QM applicable to individual objects?

That will depend on the new theory, with its new ontology and how it relates to the older QM (how the older QM is emergent from the newer one). Maybe the new theory will tell you *how to pick the observer* from its ensemble!

If we change theory, we change of course ontology, and the entire world picture changes completely.

 

[vanesch]

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.

That "ridiculously complex calculation" is nothing else but an MWI view on things. The "problem" with it is the following: if *everything* is described by quantum theory (ie, has a quantum state, a state in Hilbert space), then there's no "outside" which can make an "observation", and the only thing that's left is applying the Schroedinger equation to that quantum state, in which the Hamiltonian includes all the physical interactions between the electron, the screen, the photodetector, the computer, the computerscreen, your eyes, your brain and everything. Indeed at first sight ridiculously complex.
But we know that the Schroedinger equation, no matter how complicated the hamiltonian, is a linear equation.

That means that superpositions of solutions are also solutions.

Now, "electron through the left slit" is the starting state |left>, and if we take this as the starting situation, and solve this tremendiously complicated equation, we will find that the screen, the computer, your eyes, your brain ... will be in a certain quantum state, which we will symbolically represent by |observed-left>.

Similarly for "electron through the right slit", |right> ... which will result in the final quantum state |observed-right>

Well, what will now be the result when we allow for interference ?
Due to the linearity of the Schroedinger equation:

from |left> + |right> will simply follow:

|observed-left> + |observed-right>

In other words, "you" now appear TWO TIMES in the final state, with two *different* observations. This is when, in MWI, we say that "the observer has branched", which means, he now appears in two different states, with each a different outcome.
Or, we say that we now have "two copies" of the observer.
Or, we can say that we have now an "ensemble of observers" with two possibilities.

We didn't do anything special here. We didn't introduce any extra formal elements, we didn't change any equation... we simply assumed the axioms of quantum theory valid "all the way", and applied the Schroedinger equation, which contained all physical interactions (at a ridiculously detailled level). That's why I say that the "multiplication of observers" or the "appearance of an observer-ensemble" appears naturally in the quantum formalism, if you use it rigorously all the way.

Now, it turns out that we, subjectively, don't experience this "multitude of copies". So where does the "statistical aspect" of quantum mechanics seem to reside ? In the fact that we have to repeat the experiment somehow ? That doesn't appear nowhere in the formalism: we did everything for one single incident electron. We didn't start out with a hilbert space of states of several electrons.
No, we saw that, upon this single-electron event, there appeared an ensemble of observers "out of the single one that was present", through the use of the Schroedinger equation.

It hence seems *more natural* to me, as an interpretation of the quantum formalism, that in as much there is an ensemble (which must appear somehow, given that there are probabilities), that the ensemble is on the observer.

I don't want to ram this through people's throats (although it sometimes may sound like that :-), everybody is free to have his/her own ideas on the matter. But I don't find this view as "evidently untenable" as it is often suggested.

 

[quetzalcoatl9]

If I know that my wife is in the state "she's doing fine", that doesn't mean that I can predict exactly what she's going to do this evening. But does that mean that the state "she's doing fine" only describes an ensemble of wives of me ? Do you really think that there is a description, so perfect, of my wife (or, of any woman, for that matter), that it tells me what she's going to do, and that "she's doing fine" is not related to herself, as a physical description of her individual state ?

my god man, an ensemble of wives?! do you not know that one is quite enough? furthermore, a complete specification of the wife state is an unknowable observable - the exact state can only be known by guessing, and god help you if that guess is wrong.

:)

sorry, i couldn't resist

 

[zbyszek]

As I said elsewhere, in an MWI setting, the single electron, after interaction with the screen, the photodetector, the electronics and all that, generates an *ensemble of observers* for that single event (aka "branches" for that observer). Because "you" are only one of them, you can't predict what you'll observe, because you only have the law for the ensemble of observers. So yes, quantum theory is not a theory of a single observer, but only of an ensemble of observers. Nevertheless, it can perfectly well describe a single *object*.

Oh! Now I get it! You are an MWI guy. I always wanted to understand this branching thing.
Could you help me a little here?

1. Whether a state is a superposition or not depends on the choice of basis. A gaussian
packet can be viewed as a base vector or as a superposition of position eigenvectors.
So, when the branching occures? For one gaussian is there as many worlds as position
eigenstates or just a one, or some other number?

2. Since nobody was able to quantize gravitation it is concivable that it is classical. If it
does not follow the rules of QM then there is just one gravitational field for all the worlds.
Change in one world affects the field so it affects all other worlds.Perhaps we should
be able to detect all other worlds? If the spliting generated enough worlds the gravitation
would be considerable, right?

3. What advantages does MWI provide over other interpretations of QM?

I find it more difficult to conceive that *there is no theory of single objects* (and hence that there is no theory of the universe as a whole), than to make a few assumptions that fit perfectly well with the formalism that we have at hand.

Or you are too modest! You can easily conceive concepts of ontology and, I bet, epistemology and last but not least infinite complexity of MWI. The lack of theory
for single objects is no match for such a flexible imagination.

Cheers!

P.S. If your do not referee for PRL yet, please ask the editor. You will.

 

[lightarrow]

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 appropriatelly spread (like its wave function ? .

You mean that it's possible to establish, before the "click" on the screen, that a single electron has passed through the slit, without modifying completely the electron's wavefunction and so destroying the resulting "spreadness" of it on the screen?

 

[zbyszek]

You mean that it's possible to establish, before the "click" on the screen, that a single electron has passed through the slit, without modifying completely the electron's wavefunction and so destroying the resulting "spreadness" of it on the screen?

Precisely. You can make sure that only one electron enters the chamber with
double slit experiment without any consequences to the wave function of the electron
between slits and the screen.

Cheers!

 

[lightarrow]

Precisely. You can make sure that only one electron enters the chamber with double slit experiment without any consequences to the wave function of the electron between slits and the screen.

Can I ask you to explain me, (briefly, if you prefer) how this is achieved?

 

[zbyszek]

Can I ask you to explain me, (briefly, if you prefer) how this is achieved?

Sure. Here is one way. A single electron can be trapped in an electromagnetic trap
(see Dehmelt 1973) and kept there for years. It is just one electron, because the
trap is to shallow to hold two.
You put the trap with an electron to a chamber with the double slit setup. Turn off
the trap, turn on some small electric field to accelerate the electron towards the slits.

Another way. You use an electron cannon. Electrons don't like to travel too close together.
A set of pinholes, collimators and magnetic fields is sufficient to select only those
electrons of approprieate positions and velocities. If the cannon is weak enough, you
can have just one electron a day in that beam.


Cheers!

 

[lightarrow]

Thank you zbyszek.

 

[ueit]

That "ridiculously complex calculation" is nothing else but an MWI view on things.

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

The "problem" with it is the following: if *everything* is described by quantum theory (ie, has a quantum state, a state in Hilbert space), then there's no "outside" which can make an "observation", and the only thing that's left is applying the Schroedinger equation to that quantum state, in which the Hamiltonian includes all the physical interactions between the electron, the screen, the photodetector, the computer, the computerscreen, your eyes, your brain and everything. Indeed at first sight ridiculously complex.
But we know that the Schroedinger equation, no matter how complicated the hamiltonian, is a linear equation.

That means that superpositions of solutions are also solutions.

Now, "electron through the left slit" is the starting state |left>, and if we take this as the starting situation, and solve this tremendiously complicated equation, we will find that the screen, the computer, your eyes, your brain ... will be in a certain quantum state, which we will symbolically represent by |observed-left>.

Similarly for "electron through the right slit", |right> ... which will result in the final quantum state |observed-right>

Well, what will now be the result when we allow for interference ?
Due to the linearity of the Schroedinger equation:

from |left> + |right> will simply follow:

|observed-left> + |observed-right>

In other words, "you" now appear TWO TIMES in the final state, with two *different* observations. This is when, in MWI, we say that "the observer has branched", which means, he now appears in two different states, with each a different outcome.
Or, we say that we now have "two copies" of the observer.
Or, we can say that we have now an "ensemble of observers" with two possibilities.

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

We didn't do anything special here. We didn't introduce any extra formal elements, we didn't change any equation... we simply assumed the axioms of quantum theory valid "all the way", and applied the Schroedinger equation, which contained all physical interactions (at a ridiculously detailled level). That's why I say that the "multiplication of observers" or the "appearance of an observer-ensemble" appears naturally in the quantum formalism, if you use it rigorously all the way.

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.

Now, it turns out that we, subjectively, don't experience this "multitude of copies". So where does the "statistical aspect" of quantum mechanics seem to reside ? In the fact that we have to repeat the experiment somehow ? That doesn't appear nowhere in the formalism: we did everything for one single incident electron. We didn't start out with a hilbert space of states of several electrons.
No, we saw that, upon this single-electron event, there appeared an ensemble of observers "out of the single one that was present", through the use of the Schroedinger equation.

It hence seems *more natural* to me, as an interpretation of the quantum formalism, that in as much there is an ensemble (which must appear somehow, given that there are probabilities), that the ensemble is on the observer.

I don't want to ram this through people's throats (although it sometimes may sound like that :-), everybody is free to have his/her own ideas on the matter. But I don't find this view as "evidently untenable" as it is often suggested.

I know too little about MWI to make a strong claim about it but its greatest problem is, IMHO, its unfalsifiability (shared by the other interpretations as well). So, it makes more sense to me to try supplement QM with hidden variables in order to make it compatible with the local determinism implied by relativity.

 

[Anonym]

zbyszek:"In a single run of an electron through slits it ends up in a spot on a screen. Do you have a theory predicting the spot? Don't do exactly, do it with an arbitrary precision.If you cannot do that (despite the fact that you know all the states exactly) I say you have no theory of single objects.

What you actually can do, you can tell me the distribution of spots that can be recovered after many repetition of the same experiment with an arbitrary precission, a statistical average over an ensemble. In my dictionary that constitutes a statistical theory."

How you define the difference between repeated observations (measurements) of the indistinguishable individual physical systems and the statistical ensemble of the same system? And why you assume that single run of an experiment should be sufficient to recover the required (complete) information?

ueit:"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."

Notice, that doing ridiculously simple calculations (pure QM) one obtains exact prediction of the experimental outcome.Perhaps this means that your treatment is adequate?

--------------------------------------------------------------------------------

 

[ueit]

Notice, that doing ridiculously simple calculations (pure QM) one obtains exact prediction of the experimental outcome.Perhaps this means that your treatment is adequate?

I think that "exact prediction" is an overstatement. Statistically it's perfect, for a single particle is not much better than chance. It is the prediction for such single events that can be, I think, improved by including all the detail in the calculations.

And those "simple calculations" are not "pure QM". For example, can you point me what's the wall's Hamiltonian?

 

[Anonym]

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. In addition, in classical world how do you describe the extentent object by single coordinate point experiment?
What do you mean wall in "wall's Hamiltonian"? Lossless beam-splitter?

 

[zbyszek]

How you define the difference between repeated observations (measurements) of the indistinguishable individual physical systems and the statistical ensemble of the same system? And why you assume that single run of an experiment should be sufficient to recover the required (complete) information?
--------------------------------------------------------------------------------

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.

Cheers!

 

[Demystifier]

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.

We have at least one such theory - the Bohmian one.
What is your opinion on that theory?

 

[Einstein Mcfly]

I just have to say that this is a very interesting discussion. Thanks to all who have contributed.

 

[Anonym]

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?

 

[zbyszek]

We have at least one such theory - the Bohmian one.
What is your opinion on that theory?

Thanks for the question. At some point I have been fascinated by this formulation
of QM. The quick sorbering occured, when I realized that you can do nothing there
without actually calculating a wave function. More, the only thing you get at the
end is another wave function. 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.
They do not help you predicting outcomes of single experiments! The only information
you have is the one already contained in a wave function. Nothing more.
So, why bother?

Cheers!

 

[Einstein Mcfly]

Thanks for the question. At some point I have been fascinated by this formulation
of QM. The quick sorbering occured, when I realized that you can do nothing there
without actually calculating a wave function. More, the only thing you get at the
end is another wave function. 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.
They do not help you predicting outcomes of single experiments! The only information
you have is the one already contained in a wave function. Nothing more.
So, why bother?

Cheers!

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

 

[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!