What does the probabilistic interpretation of QM claim?

[unusualname]

By the way, the url in your profile is spelled incorrectly.

thanks! probably just as well since I haven't constructed M yet (need linear groups and propagation of states throughout the universe ;) )

 

[meopemuk]

You are confusing assumptions and knowledge.

We never ''look at an electron experimentally'' - we only infer its presence from a measured current or ionization track. Mott shows that this track is produced by a classical spherical wave impinging on the cloud chamber from a certain direction, which will determine the direction of the track produced at the atom that happens to fire. There is nothing counterintuitive about that. The uncertainty in the charge density inside the detector is much larger than the charge of one electron.

You _assume_ instead that this is caused by a single electron. And then you say that you find it because of the track. This is a simple instance of a self-fulfilling prophecy. http://en.wikipedia.org/wiki/Self-fulfilling_prophecy

Instead of a cloud chamber bombarded by a dense electron flow I would like to think about a cleaner setup in which definitely one and only one electron was emitted and then captured by an array of tiny detectors, such as CCD device. After the measurement we can be sure that only one detector in the array has "clicked" and the entire electron charge has been deposited inside this detector. If I apply your "charge density field" theory to this situation, I'll get a surprising conclusion that the extended charge distribution has collapsed to the volume of one micrometer-size detector all by itself and against the resistance of the Coulomb repulsion. I find this rather amazing.

Eugene.

 

[strangerep]

Instead of a cloud chamber bombarded by a dense electron flow I would like to think about a cleaner setup in which definitely one and only one electron was emitted and then captured by an array of tiny detectors, such as CCD device. [...]

You still haven't given a reference to an actual experimental setup that does this.
I.e., emits definitely one and only one electron, presumably with a momentum uncertainty
corresponding to a small solid angle that exactly encompasses the CCD device.

 

[strangerep]

[...] there are no no-go theorems against deterministic field theories
underlying quantum mechanics. Indeed, local field theories have no
difficulties violating Bell-type inequalities. See
http://arnold-neumaier.at/ms/lightslides.pdf ,
starting with slide 46.

On slide 49, you begin a hidden-variable analysis of a particular
experiment with the following assumptions:

(i) The source of beam 1 produces an ensemble of photons which is in
the classical (but submicroscopic) state \lambda with
probability density p(\lambda).

(ii) Whether a photon created at the source in state \lambda reaches
the detector after passing the kth filter depends only on B_k and
\lambda. (This is reasonable since one can make a beam
completely dark, in which case it carries no photons.)

(iii) The conditional probability of detecting a photon which is in state \lambda
and passes through filter k when B_k = B and B_{3 − k} = 0 is given
by a functional expression p_k(B,\lambda).

Later (after a QM analysis, etc), you say on slide 57:

The experiment can be explained by the classical Maxwell
equations, upon interpreting the photon number detection rate as
proportional to the beam intensity. This is a classical description,
not by classical particles (photons) but by classical waves.

I didn't see where you "explained the experiment by the classical
Maxwell equations" in these slides. (Or are you implicitly referring
to the arguments given in Mandel & Wolf?)

You go on to say:

Thus a classical wave model for quantum mechanics is not ruled out
by experiments demonstrating the violation of the traditional hidden
variable assumptions.

Therefore the traditional hidden variable assumption only amount
to a hidden point particle assumption.

And the experiments demonstrating [Bell inequality] violation
only disproves classical models with point particle structure.

It's not clear to me where, in the hidden variable assumptions you
listed, one has assumed point particle structure.

 

[meopemuk]

emits definitely one and only one electron,

I am not an experimentalist, so I can be mistaken. But I think that it should be possible to arrange emission of exactly one electron in a controlled fashion. For example, one can use a single radioactive nucleus, which experiences beta-decay.

You can say that the emitted electron flies in a random direction, so, most likely, it will not be found in our measuring device. But if we are persistent and prepare another radioactive nucleus, then another one... Eventually, we will be able to catch the electron and perfrom the experiment.

presumably with a momentum uncertainty
corresponding to a small solid angle that exactly encompasses the CCD device.

If this electron passes through a crystal, then the effect of "electron diffraction" occurs, which is basically similar to the occurence of interference picture in the famous double slit
experiment. There are probability peaks in certain directions of electron propagation. The preferential angles depend on the (1) initial electron's momentum, (2) type of the crystal lattice, (3) orientation of the crystal. So, it should not be difficult to arrange all components in such a way that the diffraction (or interference) picture covers the entire surface of the CCD device.

Eugene.

 

[strangerep]

[...] I think that it should be possible to arrange emission of exactly one electron in a controlled fashion. For example, one can use a single radioactive nucleus, which experiences beta-decay.

You can say that the emitted electron flies in a random direction, so, most likely, it will not be found in our measuring device. But if we are persistent and prepare another radioactive nucleus, then another one... Eventually, we will be able to catch the electron and perform the experiment.

This is almost the "preparation" arrangement assumed in Mott's analysis (except
he uses alpha particles instead of electrons).

But you have not specified a way to observe the electron on its way from nucleus
to target (and I'm not sure what you meant by "catch the electron").

Instead, you're relying on random emission by nuclear decay. I don't see how this
is practical except by having a sample of the radioactive material with many nuclei,
and this leads to an ensemble of emitted electrons, with nonzero probability of
more than 1 electron in any given time interval.

 

[meopemuk]

But you have not specified a way to observe the electron on its way from nucleus
to target (and I'm not sure what you meant by "catch the electron").

There is no need to observe the electron on its way from nucleus to target. "Catching the electron" means registration of the hit by one detector in the CCD array.

Instead, you're relying on random emission by nuclear decay. I don't see how this
is practical except by having a sample of the radioactive material with many nuclei,
and this leads to an ensemble of emitted electrons, with nonzero probability of
more than 1 electron in any given time interval.

This is not easy, but in principle possible. One can make sure that the radioactive sample contains one and only one nucleus of the desired unstable type. As an exotic possiblity I can suggest using C60 buckyballs. Currently there are techniques allowing to place one foreign (e.g., radioactive) atom inside the buckyball sphere. Then, I guess, it might be possible to deposit just one such "stuffed" buckyball on the surface of the sample. This would arrange a "single electron" emitter.

Eugene.


EDIT: I've googled for "single electron source" and found a number of interesting references. So, I guess that preparation of one-electron states is a solved technical problem. See, for example,


J.-Y. Chesnel, A. Hajaji, R. O. Barrachina, and F. Frémont, Young-Type Experiment Using a Single-Electron Source and an Independent Atomic-Size Two-Center Interferometer. Phys. Rev. Lett. 98, 100403 (2007). http://prl.aps.org/abstract/PRL/v98/i10/e100403 [/URL]

 

[strangerep]

I've googled for "single electron source" and found a number of interesting
references. So, I guess that preparation of one-electron states is a solved
technical problem.

Although such papers are indeed interesting I came to the opposite
conclusion about it being a "solved technical problem" in the way you seem
to mean. I think such a description is an over-claim indeed.

The various setups I saw appear quite elaborate, specific to particular
applications that don't correspond easily to what you wanted (imho).

See, for example,

J.-Y. Chesnel, A. Hajaji, R. O. Barrachina, and F. Frémont,
"Young-Type Experiment Using a Single-Electron Source and an Independent
Atomic-Size Two-Center Interferometer."
Phys. Rev. Lett. 98, 100403 (2007).
http://prl.aps.org/abstract/PRL/v98/i10/e100403

Umm,... did you actually read this paper?
As usual, the devil is in the detail...

The experiment consists of an incident beam of alpha particles,
striking a gas of H_2 molecules. There's a particle reaction
chain in which the alpha particle becomes a doubly-excited helium atom
by capturing two electrons from a hydrogen molecule. The two resultant
protons move apart a little, and the doubly-excited helium atom decays,
re-emitting the electrons. Sometimes, one of the electrons is
re-emitted back towards the 2-proton target which acts like a 2-centre
scatterer. The resultant scattering pattern of such back-emitted
electrons is recorded. The "result" of the experiment is thus a
scattering cross section.

The experiment is called "single-electron" only because the probability
is extremely low that more than one electron is scattered by a given
2-proton scatterer. I.e., it's "single-electron" within the lifetime of
the 2-proton scatterer.

On the 2nd page, the authors clarify further that:

Since these individual scattering processes are repeated with
similar initial conditions many times, what is actually measured
here is the ensemble probability of the diffraction of just one single
electron by one single two-center scatterer.

The results seem adequately accounted for by statistical field-theoretic analysis.

 

[meopemuk]

The experiment is called "single-electron" only because the probability
is extremely low that more than one electron is scattered by a given
2-proton scatterer. I.e., it's "single-electron" within the lifetime of
the 2-proton scatterer.

I am not so sure why you insist that only 1 electron must be emitted in 100% of cases? What if there is some non-zero probability of 2 or 3 electrons being emitted? I see no problem with that from the point of view of the corpuscular interpretation. This is still something completely different from the continuous charge density field that you are arguing for.

Eugene.

EDIT: Well, if you don't like single electron sources, then we can return to the discussion of interference experiments with single atoms. I hope, you wouldn't deny that individual atoms can be produced one-by-one and that double-slit-type experiments are possible with them?

 

[Calrid]

It claims MWI is full of crap basically.

Ie that there is no real wave function, hidden variables that are local and that the evolution of the wave is therefore not deterministic.

 

[strangerep]

I am not so sure why you insist that only 1 electron must be emitted in 100% of cases? What if there is some non-zero probability of 2 or 3 electrons being emitted? I see no problem with that from the point of view of the corpuscular interpretation. This is still something completely different from the continuous charge density field that you are arguing for.

The trouble I find with "corpuscular interpretation" is that it's invariably like an
Esher drawing; -- it makes sense when you focus only on pieces of the picture,
but becomes nonsense when viewed as a whole.

The notion of "corpuscular" entails "discrete, indivisible". This has problems in
explaining wave-like phenomena. (If it's "indivisible", then how did it pass through
both slits...? Blah, blah, blah. I won't repeat that ancient debate which I'm sure
you and everyone around here are thoroughly bored with, and which quantum
theory with Ballentine interpretation explains satisfactorily, imho.)

This is still something completely different from the continuous charge density
field that you are arguing for.

For the record, I'm in favour only of QFT with a minimal statistical interpretation.

EDIT: responding to your edit:

EDIT: Well, if you don't like single electron sources, then we can return to the discussion of interference experiments with single atoms. I hope, you wouldn't deny that individual atoms can be produced one-by-one and that double-slit-type experiments are possible with them?

For a full account, field-theoretic analysis is still necessary.

 

[Calrid]

Isn't this a philosophical question though.

I mean what does something claim and what does something prove are mutually exclusive at least in science.

 

[strangerep]

Isn't this a philosophical question though.

I mean what does something claim and what does something prove are mutually exclusive at least in science.

Could you please include at least a little quoted context so that it's clear
what you're actually replying to??

 

[Calrid]

Could you please include at least a little quoted context so that it's clear
what you're actually replying to??

No one so the OP. I am well aware how to use the quote function.

I'm saying that this question probably better suits a philosophical style debate rather than a scientific one as that is what it is.

No science anywhere in interpretation as yet basically. It's all just philosophy isn't it. Not that there is anything wrong with that, especially if you are into strings and branes etc.

Einstein quoted Descartes, Bohr said Kant was important in his realisation of his interpretation. It has always been a matter of taste what flavour of ice cream you like.

I'm vanilla.

 

[meopemuk]

... which quantum
theory with Ballentine interpretation explains satisfactorily, imho...

I don't think that my views are much different from those of Ballentine. If I remember correctly, Ballentine is associating the idea of *quantum state* with an ensemble of identically prepared systems. He was being careful not to focus on individual events/measurements. But if we do consider such individual events/measurements, we have no other choice but to conclude that modern quantum mechanics cannot say anything definite about them. These events/measurements are governed by pure chance. I don't see anything wrong with it, and actually like this idea.

Of course, one may take the point of view (shared by Einstein and, if I understand correctly, by Dr. Neumaier) that quantum mechanics is not a complete/final theory. That there should be some field-based deterministic approach, which would explain why this particular CCD pixel has fired in this particular instance. Currently such calculations/predictions are impossible. So, we are back to the point where our differences are purely philosophical.

Eugene.

 

[meopemuk]

The trouble I find with "corpuscular interpretation" is that it's invariably like an
Esher drawing; -- it makes sense when you focus only on pieces of the picture,
but becomes nonsense when viewed as a whole.

I like your analogy with Esher drawings, but I don't find it troubling. To the contrary, I find this controversy rather neat. The point is that in experiments we cannot see the entire drawing (=the entire world). We always see one particular aspect of it. One piece of Esher's stair. For example, we measure either momentum or position of a particle, but not both of them together. So, I agree that when we try to imagine the whole drawing in our brain, we find it controversial. But I don't see any particular reason why nature should care about the deficiencies of our imagination. Perhaps, it is impossible to make a full coherent mental picture of the world. So what? The important thing is that there are no contradictions in our (limited) experimental studies of the world. And corpuscular interpretation of quantum mechanics satisfies this requirement. Everything that goes beyond boundaries of experiment is equal to philosophy/religion and has no place at science discussion forums.

Eugene.

 

[strangerep]

I don't think that my views are much different from those of Ballentine. If I remember correctly, Ballentine is associating the idea of *quantum state* with an ensemble of identically prepared systems. He was being careful not to focus on individual events/measurements. But if we do consider such individual events/measurements, we have no other choice but to conclude that modern quantum mechanics cannot say anything definite about them. These events/measurements are governed by pure chance. I don't see anything wrong with it, and actually like this idea.

Now if only you would re-read Ballentine and adopt the mainstream meaning of
the term "collapse" explained therein (i.e., abandon your private meaning of that
term), much miscommunication would be avoided. :-)

Of course, one may take the point of view (shared by Einstein and, if I understand correctly, by Dr. Neumaier) that quantum mechanics is not a complete/final theory.
That there should be some field-based deterministic approach, [...]

I'll let Arnold speak for himself, but I understand Arnold's position to be that
orthodox quantum theory can be more rationally understood using a field picture,
which is a different statement from the above.

BTW, it doesn't hurt to remind people occasionally that the usual Bell theorems
speaking against certain hidden variable theories do not go through in general for
infinite numbers of hidden variables. One integrates over these variables, in an
expression like:

<br /> \int d\lambda_1 \, d\lambda_2 \dots d\lambda_n <br />

where the \lambda_i denote the hidden variables.
For infinite n, the measure in the integral is ill-defined.

And field theories tend to have an infinite number of degrees of freedom ...

 

[Calrid]

Bit of a tangent but I read an article about them having closed all the loop holes in Bell's recently. Which of course made the scientists become ever more clever with their loopholes. There are only one or two left now that haven't been filled in by experiment and I suspect they will become ever more absurd as they are closed, or more bizarrely correct even!

http://www.newscientist.com/article/mg20928011.100-reality-check-closing-the-quantum-loopholes.html

Subscription only I'm afraid, although there is a taster:

Can the universe really be as weird as quantum theory suggests? Ingenious experiments are coming close to settling the issue

WHEN Rupert Ursin stood in the darkness at the highest point of La Palma in the Canary Islands he found it scary. "Really scary," he says. It was less the blackness stretching out towards the Atlantic Ocean some 15 kilometres away. It was more the sheer technical challenge ahead- and perhaps just a little because of the ghosts he was attempting to lay to rest.

Ursin and his colleagues from the Institute for Quantum Optics and Quantum Information in Vienna, Austria, were there that night to see if they could beam single photons of light to the 1-metre aperture of a telescope on the island of Tenerife, 144 kilometres away. Even on a fine day, when Teide, Tenerife's volcanic peak, is clearly visible from La Palma, that would ...

I know its not strictly apropo of anything but I thought it was an interesting article anyway.

Seems the God of the gaps is perhaps existing in smaller gaps, or is he..?

 

[strangerep]

[...] corpuscular interpretation of quantum mechanics
satisfies this requirement [of explaining our (limited) experimental studies of the world]

It doesn't explain the observed wave-like behavior.

(Sigh. This after I swore to myself I wouldn't get embroiled in a
wave-particle debate. Time to exit.)

 

[Calrid]

BTW, it doesn't hurt to remind people occasionally that the usual Bell theorems
speaking against certain hidden variable theories do not go through in general for
infinite numbers of hidden variables. One integrates over these variables, in an
expression like:

<br /> \int d\lambda_1 \, d\lambda_2 \dots d\lambda_n <br />

where the \lambda_i denote the hidden variables.
For infinite n, the measure in the integral is ill-defined.

And field theories tend to have an infinite number of degrees of freedom ...

How is this of any predictive of qualitative use though to science?

It's all very well invoking infinities but they really just say that anything can or could happen and that just isn't really conceptually or scientifically viable. There must be a theory that has a value that would produce a result that is within the bounds of reality. Infinity forgoes such a utility even in the wave function.

I'm pretty sure that even in physics the infinite is a limit that is merely defined as the expanse or x of the entire universe.

How are you defining the limit in this equation as all there can be, or anything that you can think of? And does it really mean anything further than say Copenhagen if you do? If not ultimately where is the utility, isn't it just semantics like MWI, ie ultimately indistinguishable.

I'm not saying you may be wrong I am merely saying that this does not distinguish itself and can not ultimately from any other interpretation. The depressing vanilla ice cream is hard to ignore or to be distinguished from.

It doesn't matter what you believe, if ultimately it will never be more than faith, then one God is as good as another god.

I find it kind of depressing that reality is not deterministically predictive, or even qualitative, but what if it just isn't?

 

[strangerep]

How is this of any predictive of qualitative use though to science?

Quantum field theory is the most accurately predictive theory we know.

How are you defining the limit in this equation as all there can be,
or anything that you can think of?

I was pointing out a restriction in the applicability of a mathematical theorem,
which is often overlooked, nothing more.

 

[Calrid]

Quantum field theory is the most accurately predictive theory we know.

I'm not talking about field theory I am talking about how you define infinity. Are we renormalising, using infinity or just chaos? How would you prove any of them had any underlying reality anyway regardless of mathematical form?

Is maths even suited to this problem?

I was pointing out a restriction in the applicability of a mathematical theorem,
which is often overlooked, nothing more.

Yes and I was agreeing, however in terms of interpretation how do we even know that our maths is even apt?

Bohr in particular said that we might have to accept that we simply neither have the language or maths to explain reality as yet. Perhaps its a comprehension issue, can we see the wood for the trees? And if one of them falls over does it make a sound.

Is it because the only way to make sense of reality is to come to a deterministic point in evolution of mind which then makes us only able to understand a mappable theory, and if so does that mean that we are not even able to comprehend reality and that ultimately it is not definable by such terms.

All good philosophical questions.

Ultimately the only thing we have is experiment, if this is flawed by our perception then maybe we need to evolve both scientifically and physically? Perhaps we need an alien perspective. Or just some evidence.

I wasn't at odds with what you are saying I was merely adding an angle.

 

[meopemuk]

I find it kind of depressing that reality is not deterministically predictive, or even qualitative, but what if it just isn't?

I actually find it not depressing but cheerful. If reality is random, as I believe it is, then this relieves us from the necessity to dig deeper for explanations. Random things do not require explanations, because they are ... simply random. So, the seemingly never-ending history of science, in which questions "why?" were answered just to be followed by even deeper questions "why?" has possibly come to an end. So, quantum mechanics could be the natural end of our scientific quest. We have lost our ability to ask "why?" Because the only remaining sensible answer is "I don't know". Kind of neat!

Eugene.

 

[Calrid]

I actually find it not depressing but cheerful. If reality is random, as I believe it is, then this relieves us from the necessity to dig deeper for explanations. Random things do not require explanations, because they are ... simply random. So, the seemingly never-ending history of science, in which questions "why?" were answered just to be followed by even deeper questions "why?" has possibly come to an end. So, quantum mechanics could be the natural end of our scientific quest. We have lost our ability to ask "why?" Because the only remaining sensible answer is "I don't know". Kind of neat!

Eugene.

And you don't find that frustrating?

Science is dead long live Cartesian dualism.

Matter of taste I guess.

 

[meopemuk]

Quantum field theory is the most accurately predictive theory we know.

Except for the missing description of time evolution. https://www.physicsforums.com/showthread.php?t=476412[/URL] (I hope Dr. Neumaier wouldn't notice this post as he would vehemently disagree.)

Eugene.

 

[meopemuk]

And you don't find that frustrating?

For centuries scientists struggled to find the ultimate answer. Now we found it! Time to celebrate with champagne and caviar and not be depressed.

Eugene.

 

[Calrid]

For centuries scientists struggled to find the ultimate answer. Now we found it! Time to celebrate with champagne and caviar and not be depressed.

Eugene.

I'm going to take coke then if you don't minds, I need a pick me up. I picked a bad day to give up methamphetamine.

 

[A. Neumaier]

Except for the missing description of time evolution. https://www.physicsforums.com/showthread.php?t=476412[/URL] (I hope Dr. Neumaier wouldn't notice this post as he would vehemently disagree.)[/QUOTE]
You speak from a position of ignorance about what QFT is and can do.

In the thread [url]https://www.physicsforums.com/showthread.php?t=476412[/url] , I showed that your statement is wrong. But you didn't even find it worth your time to do the little work that would have enabled you to understand my argument and to verify that I am correct.

 

[A. Neumaier]

I didn't see where you "explained the experiment by the classical
Maxwell equations" in these slides. (Or are you implicitly referring
to the arguments given in Mandel & Wolf?)

I used the fact the quantum mechanics of a photon is given by the Maxwell equations.
See p.8. Thus the analysis starting p.51 applies verbatim.

It's not clear to me where, in the hidden variable assumptions you
listed, one has assumed point particle structure.

The properties (i)-(iv) characterize what is expected of a classical elmentary particle.
More precisely, they characterize a particle that preserves a classical identity while moving through the beam splitter. Pointlikeness is not essential here - it is just the usual classical model for an elementary particle. But since this seemed to be the cause of your query, I changed the wording and now speak of a ''hidden classical particle assumption''
isnead of a ''hidden point particle assumption''. Thanks for the correction! (The updated version will probably be on the web an hour from now.)

 

[strangerep]

Is maths even suited to this problem?
[...] in terms of interpretation how do we even know that our maths is even apt?

It's not all-or-nothing.
Maths develops/evolves partly to meet new challenges.

[...]
All good philosophical questions.

Perhaps, but they should probably be taken up in the philosophy forum,
since this seems to be gradually drifting away from the original intent of
this thread.