The wave packet description [Archive]

masudr

Nov8-06, 09:07 PM

For a hydrogen atom we assume the electron and nucleus to be point charges

Well, technically speaking, the Hydrogen atom is treated as a system with Hamiltonian (I'll write it in Cartesians and their conjugate momenta since they are the usual canonical variables in the electrostatic case, although it'd be more concise in spherical polar co-ordinates):

\hat{H}(
\hat{x}_1,
\hat{p_x}_1,
\hat{y}_1,
\hat{p_y}_1,
\hat{z}_1,
\hat{p_z}_1,
\hat{x}_2,
\hat{p_x}_2,
\hat{y}_2,
\hat{p_y}_2,
\hat{z}_2,
\hat{p_z}_2) =

\frac{\hat{p_x}_1^2+
\hat{p_y}_1^2+
\hat{p_z}_1^2}
{2m_1}+
\frac{\hat{p_x}_2^2+
\hat{p_y}_2^2+
\hat{p_z}_2^2}
{2m_2}-
\frac{1}{4\pi\epsilon_0}
\frac{e^2}
{\sqrt{
(\hat{x}_1 - \hat{x}_2)^2+
(\hat{y}_1 - \hat{y}_2)^2+
(\hat{z}_1 - \hat{z}_2)^2}}

You haven't assumed anything of the system apart from the fact that it has the above Hamiltonian. To get to that expression, you might use some classical physics of point particles and the Coulombic interaction between charged particles. However, note that the quantum mechanics of the system starts here, at the Hamiltonian.

You haven't assumed anything more, specifically, you haven't talked about particles - you've talked about systems. I'm not being pedantic: in QFT, you don't deal with particles directly, you deal with oscillating fields, where particles happen to emerge.

P.S. You usually eliminate 6 of the variables by transforming to so-called "centre-of-mass" and "relative" co-ordinates, and while this has physical content in this case, it didn't have to.

FunkyDwarf

Nov8-06, 11:45 PM

there are no particles, there are only waves
particle physics would disagree

quetzalcoatl9

Nov9-06, 12:51 PM

particle physics would disagree

really? i dont think so

tell me what happens to your particles when their average seperation is on the order of the de broglie thermal wavelength? are they still "particles"?

ueit

Nov9-06, 04:21 PM

Well, technically speaking, the Hydrogen atom is treated as a system with Hamiltonian (I'll write it in Cartesians and their conjugate momenta since they are the usual canonical variables in the electrostatic case, although it'd be more concise in spherical polar co-ordinates):

\hat{H}(
\hat{x}_1,
\hat{p_x}_1,
\hat{y}_1,
\hat{p_y}_1,
\hat{z}_1,
\hat{p_z}_1,
\hat{x}_2,
\hat{p_x}_2,
\hat{y}_2,
\hat{p_y}_2,
\hat{z}_2,
\hat{p_z}_2) =

\frac{\hat{p_x}_1^2+
\hat{p_y}_1^2+
\hat{p_z}_1^2}
{2m_1}+
\frac{\hat{p_x}_2^2+
\hat{p_y}_2^2+
\hat{p_z}_2^2}
{2m_2}-
\frac{1}{4\pi\epsilon_0}
\frac{e^2}
{\sqrt{
(\hat{x}_1 - \hat{x}_2)^2+
(\hat{y}_1 - \hat{y}_2)^2+
(\hat{z}_1 - \hat{z}_2)^2}}

You haven't assumed anything of the system apart from the fact that it has the above Hamiltonian.

Then please tell me what is the meaning of x1, px1 and m1? What is their physical significance?

To get to that expression, you might use some classical physics of point particles and the Coulombic interaction between charged particles.

Is there any other way?

However, note that the quantum mechanics of the system starts here, at the Hamiltonian.

Indeed.

I'm not being pedantic: in QFT, you don't deal with particles directly, you deal with oscillating fields, where particles happen to emerge.

I have no training in QFT so I cannot contradict you here, but my understanding was that QFT treats fields as particles and not the other way around.

rlduncan

Nov9-06, 04:56 PM

The SE can't be solved until you specify the potential energy function, U. For the H-atom, U(r) = -e^2/r in which you assume point charges. Is this not a contradiction to current quantum interpretations?

zbyszek

Nov9-06, 08:28 PM

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

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

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

Cheers!

Careful

Nov9-06, 11:16 PM

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

Is this a polish local realist speaking ? :wink:

vanesch

Nov9-06, 11:58 PM

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

What is sure, is that the wave function generates correct probabilities for an ensemble. Now, as whether or not one can give a meaning to the wavefunction of a single quantum object depends on what philosophical preferences one has about ontology.
Personally, I think it is impossible not to consider that a wavefunction describes individual systems, given that there aren't always ensembles.

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

This also has foundational problems of course. Where does the ensemble come from if you only do a thing once ? It gives problems in cosmological considerations. Now of course, without "ensemble", probabilities don't make sense either and hence the "single-event" description is only a description, without predictive value, but at least it is a description.

The question is: is the ensemble, the ensemble of objects, or the ensemble of observers ? If you do a thing only once, but this generates an ensemble of observers, then you have your probabilities there...

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

This is because one has taken as a hidden ontological assumption that determinism of observation should be true, in other words, that it is not possible to generate an ensemble of observers.

masudr

Nov10-06, 04:40 AM

The question is: is the ensemble, the ensemble of objects, or the ensemble of observers ? If you do a thing only once, but this generates an ensemble of observers, then you have your probabilities there...

Hehe, the true vanesch style!

zbyszek

Nov10-06, 05:53 AM

Is this a polish local realist speaking ? :wink:
Yes. Not sure if realist, though.

Cheers!

zbyszek

Nov10-06, 06:21 AM

What is sure, is that the wave function generates correct probabilities for an ensemble.
We agree so far.

Now, as whether or not one can give a meaning to the wavefunction of a single quantum object depends on what philosophical preferences one has about ontology.
Personally, I think it is impossible not to consider that a wavefunction describes individual systems, given that there aren't always ensembles.
I don't care what the philosophical preferences are. The simple question is:
Does QM apply to individual quantum objects or not?

The current state of knowledge is that QM certainly applies to ensembles. If you
claim that it also applies to single objects, justify it.
However, the evidence is against you. Even if a quantum state of a single
object is known perfectly, no one can predict the outcome of a measurement. With
the exeption of several special cases.

The question is: is the ensemble, the ensemble of objects, or the ensemble of observers ? If you do a thing only once, but this generates an ensemble of observers, then you have your probabilities there...

This is because one has taken as a hidden ontological assumption that determinism of observation should be true, in other words, that it is not possible to generate an ensemble of observers.
See, you know so many philosophical concepts and still wasn't able to answer the simple
plain-English question. You just restated it with use of more difficult words.

vanesch

Nov10-06, 09:44 AM

However, the evidence is against you. Even if a quantum state of a single
object is known perfectly, no one can predict the outcome of a measurement. With
the exeption of several special cases.

Why should I have to predict exactly the outcome of a measurement, in order for my description to be "physical" and not just "statistical" ?

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 ?

See, the requirement of determinism and perfect predictability is your requirement, and it doesn't need to be so. It is something we got used to in classical mechanics, and it is a special property of that theory, but I don't see why the argument "you can't tell exactly what's going to happen" is necessarily a proof of the statement that the state description you have is only a description of ensemble, and why it cannot have any physical significance for the single object you consider.

If nature, for one reason or another, is fundamentally non-deterministic, your "current state of knowledge" will remain for ever that you don't have a description of the state of nature, but only of ensembles.

zbyszek

Nov10-06, 11:14 AM

Why should I have to predict exactly the outcome of a measurement, in order for my description to be "physical" and not just "statistical" ?

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 ?

See, the requirement of determinism and perfect predictability is your requirement, and it doesn't need to be so. It is something we got used to in classical mechanics, and it is a special property of that theory, but I don't see why the argument "you can't tell exactly what's going to happen" is necessarily a proof of the statement that the state description you have is only a description of ensemble, and why it cannot have any physical significance for the single object you consider.

If nature, for one reason or another, is fundamentally non-deterministic, your "current state of knowledge" will remain for ever that you don't have a description of the state of nature, but only of ensembles.

You are joking, right?

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.

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.

But here is a quick sanity quiz:

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

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

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

Cheers!

lightarrow

Nov10-06, 11:44 AM

If the first is true then how come that electrons appear as points on the screen in Young-like experiment although the their wave functions spread across the whole screen?In 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.

IMO, the problem is to find a physical meaning for the word "electron" (or "particle") because, unless we are talking about an energetic "thing" (and, so, well spatially localized) the "electron" is not a well defined concept and we can only think of it as the "click" of the revelator.

Another, probably similar, problem, is, for example, which precise physical meaning we could give to the word "position" in the case of a wave packet, even for a real wave of any kind. 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.

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.

ueit

Nov10-06, 01:30 PM

But here is a quick sanity quiz:

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

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

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

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

The double slit experiment is explained using not pure QM but a semiclassical approximation of it. The electron is treated as a quantum, but the wall, source and detector not. In order to find out what QM realy 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.

zbyszek

Nov10-06, 01:41 PM

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

Nov10-06, 02:10 PM

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

Nov10-06, 02:27 PM

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 realy 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

Nov10-06, 02:49 PM

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 couldnt resist

zbyszek

Nov10-06, 03:04 PM

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

Nov10-06, 08:52 PM

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

Nov11-06, 08:51 AM

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

Nov11-06, 11:03 AM

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

Nov12-06, 05:28 AM

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

Nov12-06, 11:44 AM

Thank you zbyszek.

ueit

Nov12-06, 03:12 PM

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

Nov18-06, 06:37 AM

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 realy 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

Nov18-06, 08:13 AM

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

Nov18-06, 08:55 AM

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

Nov19-06, 08:46 AM

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

Nov21-06, 06:40 AM

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

Nov21-06, 12:59 PM

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

Anonym

Nov21-06, 02:52 PM

zbyszek

Nov21-06, 04:08 PM

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

Nov21-06, 05:02 PM

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

Nov21-06, 05:05 PM

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

Nov21-06, 05:27 PM

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

Nov22-06, 03:35 AM

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

Nov22-06, 04:01 AM

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

Nov22-06, 04:09 AM

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

Nov22-06, 04:14 AM

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

Nov22-06, 06:39 AM

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

Nov22-06, 09:36 AM

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

Nov22-06, 10:29 AM

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

Nov22-06, 10:49 AM

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

Nov22-06, 12:07 PM

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

Nov23-06, 05:15 AM

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

Nov23-06, 07:09 AM

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

Nov23-06, 07:41 AM

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

Nov23-06, 09:25 AM

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

Nov23-06, 10:14 AM

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

Nov23-06, 11:01 AM

Anonym

Nov23-06, 11:35 AM

Careful

Nov23-06, 11:48 AM

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

Nov23-06, 12:20 PM

(and mind MWI is not realistic).

... for sufficiently naive versions of "realistic" :tongue2:

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

Careful

Nov23-06, 12:26 PM

... for sufficiently naive versions of "realistic" :tongue2:

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

Brilliant !! :biggrin: :biggrin:

ueit

Nov23-06, 03:15 PM

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

Nov23-06, 03:55 PM

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

Nov23-06, 04:07 PM

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

Nov23-06, 06:15 PM

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

Nov23-06, 06:20 PM

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

Nov23-06, 06:40 PM

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

Nov23-06, 06:48 PM

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

Nov24-06, 01:47 AM

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

Nov24-06, 02:20 AM

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 :smile:

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

Nov24-06, 04:49 AM

Anonym

Nov24-06, 05:14 AM

Demystifier

Nov24-06, 06:34 AM

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 :smile:

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

Demystifier

Nov24-06, 06:41 AM

Demystifier

Nov24-06, 07:00 AM

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

Nov24-06, 07:17 AM

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

Nov24-06, 07:29 AM

Careful

Nov24-06, 07:57 AM

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

Nov24-06, 09:16 AM

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

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 :cool:

zbyszek

Nov24-06, 09:40 AM

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

Nov24-06, 09:52 AM

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

Nov24-06, 07:22 PM

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

Nov24-06, 07:31 PM

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

Nov25-06, 03:48 AM

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

Nov25-06, 05:44 AM

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

Nov25-06, 07:31 AM

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 :smile:

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

Nov25-06, 08:06 AM

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

Nov25-06, 09:44 AM

“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

Nov25-06, 01:40 PM

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

Nov26-06, 11:39 AM

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

Hen,hen.

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

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

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

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

What wrong with that?

zbyszek

Nov26-06, 01:47 PM

Obviously, you are using circular arguments.

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

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

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

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

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

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

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

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

Cheers!

reilly

Nov26-06, 02:53 PM

Of course it exists. Nothing stops you to perform a fully QM treatment of the entire experimental setup except the lack of a good enough computer.

Classical world is quantum world.

In a double slit experiment it's the wall with the slits. An electron passing near such an object changes momentum. The mechanism behind this change is ignored so we shouldn't expect a good prediction of the individual detection event. So, besides the probable statistical character of the wavefunction itself, we have another approximation regarding the potential at the slits (which is assumed to be 0 although it's only 0 on average).

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

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

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

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

Regards,
Reilly Atkinson

reilly

Nov26-06, 03:17 PM

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

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

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

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

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

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

..........

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

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

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

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

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

Regards,
Reilly Atkinson

Demystifier

Nov27-06, 03:58 AM

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

vanesch

Nov27-06, 05:48 AM

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

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

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

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

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

Demystifier

Nov27-06, 07:08 AM

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

Anonym

Nov27-06, 12:02 PM

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

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

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

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

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

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

ueit

Nov28-06, 11:53 AM

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

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

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

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

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

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

ueit

Nov28-06, 04:37 PM

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

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

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

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

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

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

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

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

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

ueit

Nov28-06, 04:46 PM

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

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

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

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

Regards,
Reilly Atkinson

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

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

Regards,
Andrei Bocan

zbyszek

Nov28-06, 07:37 PM

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

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

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

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

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

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

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

Don't know the problem.

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

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

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

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

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

Cheers!

vanesch

Nov29-06, 06:51 AM

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

:confused:

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

vanesch

Nov29-06, 07:05 AM

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

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

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

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

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

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

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

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

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

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

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

Anonym

Nov29-06, 11:30 AM

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

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

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

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

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

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

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

Zbyszek:” I mean the one by Ballentine.”

Sorry, I did not. I promise I will.

Anonym

Nov30-06, 11:30 AM

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

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

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

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

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

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

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

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

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

reilly

Nov30-06, 02:05 PM

Quote:
Originally Posted by reilly View Post

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

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

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

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

Regards,
Reilly Atkinson

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

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

Regards,
Andrei Bocan
Report Post Reply With Quote

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

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

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

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

Regards,
Reilly Atkinson

zbyszek

Dec1-06, 05:08 PM

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

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

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

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

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

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

Cheers!

ueit

Dec3-06, 12:18 PM

:confused:

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

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

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

vanesch

Dec3-06, 01:39 PM

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

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

ueit

Dec3-06, 04:43 PM

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

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

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

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

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

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

P.S.

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

vanesch

Dec4-06, 07:02 AM

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

http://plato.stanford.edu/entries/qm-manyworlds/

ueit

Dec7-06, 11:32 AM

http://plato.stanford.edu/entries/qm-manyworlds/

Thanks.

Although all worlds are of the same physical size (this might not be true if we take quantum gravity into account), and in every world sentient beings feel as "real" as in any other world, in some sense some worlds are larger than others. I describe this property as the measure of existence of a world.[5] The measure of existence of a world quantifies its ability to interfere with other worlds in a gedanken experiment, see Vaidman 1998 (p. 256), and is the basis for introducing probability in the MWI. The measure of existence makes precise what is meant by the probability measure discussed in Everett 1957 and pictorially described in Lockwood 1989 (p. 230).

Is this "measure of existence" deduced somehow or postulated to be identical with Born's rule?

vanesch

Dec7-06, 01:15 PM

Is this "measure of existence" deduced somehow or postulated to be identical with Born's rule?

That's the big question in MWI. Personally, I think you have to postulate it, and I even think I have the proof that it is logically independent. But some people try to deduce it. They are encouraged by that by things such as Gleason's theorem and similar results which indicate that (with some weak additional assumptions) the only consistent way of assigning probabilities to terms in a wavefunction is through the Born rule (the Hilbert norm in fact).

Personally, I don't think it is a problem that this is an extra postulate, because after all, it is part of the link between the "objective universe state" and the subjective "world experience" which is in any case, in this setting, a postulated relationship.

ueit

Dec9-06, 06:59 AM

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

I've certainly read your post. I may be a little lazy but the reasons for not doing the calculations you suggested are:

1. I have little time (full time job + 1 little kid) and I've forgot much of the math required.

2. There is no chance to explain interference in this way because the pattern changes when we cover a slit. The force the electron "feels" at the slit should depend on the macroscopic structure of the wall so we need a much complicated calculation (including for example the lattice oscillations, which are a function of the wall shape).

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

What other possible explanation could be for the particle's change in momentum if not an interaction with the wall (crystal lattice, whatever)?

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

Sure, momentum conservation is only important to prove that there is interaction between the particles and the wall.

As a matter of fact, there is, I think, another factor that should be taken into account, the influence of the wall on the source, prior to the particle's emission. It's the only way we could explain EPR experiments in a local manner and this probably applies to the double-slit as well.

Regards,
Andrei Bocan

ueit

Dec9-06, 07:17 AM

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

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

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

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

Cheers!

If the source is not known in detail you don't know the electron's original wave function.

If the wall is not known in detail you don't know the electron's wave function before the detector.

If the detector is not known in detail you cannot know where the spot is produced.

I'm not even sure that we can speak about the electron's wave function as it is probably entangled with both the source and the wall.

zbyszek

Dec10-06, 07:38 AM

If the source is not known in detail you don't know the electron's original wave function.

If the wall is not known in detail you don't know the electron's wave function before the detector.

If the detector is not known in detail you cannot know where the spot is produced.

I'm not even sure that we can speak about the electron's wave function as it is probably entangled with both the source and the wall.

You can postulate what the reasonable electron w.f. is. And this is how it is done.

Notice, that if one has a problem with guessing the electron's w.f. then somewhat bigger
issue arises if it comes to the w.f.s of the detectors, walls, etc.. There, one
has to deal with 10^25 or more atoms. How do you propose to determine details of w.f.
for those objects?

The only realistic way is to guess their wave functions.

Why bother then? Since heavy guessing is inevitable, why not to guess just the electron w.f. and focus on its properties?

Otherwise you fall into a circular reasoning:
1. To determine w.f. of an object you have to measure it.
2. You don't know what you measure if you don't know the w.f. of the measuring
apparatus.
3. So, you have to measure the w.f. of the measuring apparatus, and so on ...

I propose to cut this circle in the most convenient point i.e. the one that requires
the least amount of guessing.

Would gladly hear about another way out, though.

Cheers!

ueit

Dec12-06, 09:03 AM

You can postulate what the reasonable electron w.f. is. And this is how it is done.

Notice, that if one has a problem with guessing the electron's w.f. then somewhat bigger
issue arises if it comes to the w.f.s of the detectors, walls, etc.. There, one
has to deal with 10^25 or more atoms. How do you propose to determine details of w.f.
for those objects?

The only realistic way is to guess their wave functions.

Why bother then? Since heavy guessing is inevitable, why not to guess just the electron w.f. and focus on its properties?

Otherwise you fall into a circular reasoning:
1. To determine w.f. of an object you have to measure it.
2. You don't know what you measure if you don't know the w.f. of the measuring
apparatus.
3. So, you have to measure the w.f. of the measuring apparatus, and so on ...

I propose to cut this circle in the most convenient point i.e. the one that requires
the least amount of guessing.

If you want to test the statistical character of QM’s formalism you cannot use statistics in doing the calculations, that's fallacious. At least you should estimate the errors introduced at each step.

If, for practical reasons, you cannot calculate anything without statistics that only means that the problem remains open for debate, not that you are right.

I have an idea of how to do a full QM calculation:

1. Use an as small as possible system (a single anion as the source, a molecule as beam splitter, a few cations as the detector.

2. Use a computer simulation, not a real experiment; use the wave function of the whole system.

3. Visualize the experiment evolving in time for different initial parameters, using perhaps Bohm's approach.

4. See if some interesting correlations appear (for example between the detector's state before the electron's emission, and the detection event).

This way we could see QM's true predictive power as far as this experiment is concerned.

Cheers!

zbyszek

Dec13-06, 03:28 PM

If you want to test the statistical character of QM’s formalism you cannot use statistics in doing the calculations, that's fallacious.

You are right. If I wanted the test that would stupid.

I have an idea of how to do a full QM calculation:

1. Use an as small as possible system (a single anion as the source, a molecule as beam splitter, a few cations as the detector.

2. Use a computer simulation, not a real experiment; use the wave function of the whole system.

3. Visualize the experiment evolving in time for different initial parameters, using perhaps Bohm's approach.

4. See if some interesting correlations appear (for example between the detector's state before the electron's emission, and the detection event).

This way we could see QM's true predictive power as far as this experiment is concerned.

I do similar simulations on the daily basis. Without calculating Bohm's trajectories,
because they do not provide any additional information.
What I have is the full evolution of many-body wave functions for systems with interacting
particles and for different initial wave functions.

What I get at the end of the evolution is another many body wave function. And this
is it for quantum mechanics.

The next step is to take the wave function modulus squared and sample it to generate possible
outcomes of a single run of the experiment.

Sometimes the structure of the wave function is such that only very limited class of single
run outcomes is possible, and they are observed in real life experiments. Mainly with condensates.

Cheers!

reilly

Dec14-06, 03:41 PM

Reilly:....”

You consider only one aspect of the problem. Your description of the measurements fit perfectly the mathematical framework used in the classical physics. It essential feature is the use of analysis (classical,vector and tensor consequently). In the foundation of the analysis lies lim operation which can’t be reduced to addition and multiplication. It means intrinsically that for every predefined epsilon > 0 you may find suitable delta > 0. And thus your notion of accuracy fit it perfectly too.
However, QM do not follow that scenario.
Consider properly calibrated and functioning set of the measurement instruments. You perform the observation and obtain a point. Now you repeat the procedure for the identical system (the standard QM treatment of that notion). Your new observation is legal exactly as the previous. However, it do not always satisfy your requirement. Sometimes one obtain points where delta is arbitrary large. This do not mean that now your measurement equipment is spoiled. This mean that you met new physics (and new mathematics consequently).
Quantum world is not a classical world.

After spending time moving lead bricks around for shielding for electron scattering experiments, and working extensively with data from such experiments, I'll claim that the measurements don't know from quantum or classical. It's all in the eye of the beholder. Perhaps it's not quite a mantra, but "experiments are experiments", and "propagation of errors is propagation of errors." There's nothing quite like computing or measuring the 5th decimal place; tends to make one practical.

Regards,
Reilly Atkinson