Impossibilty of hidden variables (Bohm, 1951)

[atyy]

To conclude Bohm's pilot-wave interpretation is definitely realist in nature. It has some problems (for example it requires a reformulation of SR to admit the absolute simultaneity of all inertial systems, fully possible see for example Cushing 'Philosophical concepts in physics') but what interpretation is without problems?

That's a rather subjective type of problem, because there is nothing to say that nature isn't like that - as is often said when explaining relativity or quantum mechanics - "nature doesn't care what we like"*. An objective definition of a problem would be lack of internal coherence or inconsistency or inability to predict known experimental results. Bohmian Mechanics does have an open objective problem: there is no known Bohmian version of chiral fermions interacting with non-Abelian gauge fields.

*unless ultrahardcore Copenhagen is right :)

 

[write4u]

[es,

The meaning here is not philosophical, but the meaning you will find in physics texts on mechanics that determines the force a particle experiences.

You are thinking in terms of the wave-particle duality which isn't actually true - its one of a number of myths about QM:
http://arxiv.org/pdf/quant-ph/0609163v2.pdf

I think you are getting caught up too much in semantics. A wave-function has a very precise meaning in the theory - its the expansion of a pure state in terms of the position observable, but to explain that unfortunately requires a reasonable acquaintance with linear algebra. If you have that its not too hard. The fundamental axiom of QM is the outcomes of observations are described by a resolution of the identity Ei. If we associate the value yi with outcome i then we can form the Hermitian operator O= Σyi Ei called the observation's observable. By the spectral theorem a hermitian operator can be uniquely decomposed into the yi and Ei. From the Ei we can get an orthonormal basis |bi>. A representation of a state |u> in terms of the basis |bi> from an observable O is the representation of the state in terms of that observable.

Its a bit hard to dissect this stuff without delving into its technical detail.

Thanks, Bill

Thank you for you indulgence of my groping around. You have given me plenty of material to research and is much appreciated.

 

[write4u]

A little follow up, which may clarify my confusion.,
The original question was prompted by this statement in wiki,

The wave of the wave function, however, is not a wave in physical space; it is a wave in an abstract mathematical "space", and in this respect it differs fundamentally from water waves or waves on a string.[/quote]

http://en.wikipedia.org/wiki/Wave_function

 

[bhobba]

The original question was prompted by this statement in wiki,

That's true.

The wave-particle duality is a myth - as a link I gave explained.

Thanks
Bill

 

[write4u]

That's true.

The wave-particle duality is a myth - as a link I gave explained.
Thanks
Bill

Please forgive my persistence, but in context of our discussion, what does this mean?

First photograph of light as both a particle and wave.

http://phys.org/news/2015-03-particle.html

and this also prompted a question that, if in the double slit experiment we remove the receptors, what happens to the interference patterns (as observable when the receptors are in place)?

 

[bhobba]

what does this mean?

The authors likely want to be sensationalist - its wrong - or at least its full technical detail is likely far less picturesque. There are threads discussing it.

and this also prompted a question that, if in the double slit experiment we remove the receptors, what happens to the interference patterns (as observable when the receptors are in place)?

What do you mean by receptors?

Thanks
Bill

 

[metacristi]

That's a rather subjective type of problem, because there is nothing to say that nature isn't like that - as is often said when explaining relativity or quantum mechanics - "nature doesn't care what we like"*. An objective definition of a problem would be lack of internal coherence or inconsistency or inability to predict known experimental results. Bohmian Mechanics does have an open objective problem: there is no known Bohmian version of chiral fermions interacting with non-Abelian gauge fields.

*unless ultrahardcore Copenhagen is right :)

One objection heard quite often is that Bohm's theory cannot be made compatible with Relativity in a profound sense, I only stressed that it can at limit if we relax the requirement of Lorentz invariance to apply solely to observations (explicit non locality cannot be used for superluminal transmissions of data). So yes I agree with you, it actually fits very well with my fallibilist philosophy presented in my first post here, maybe there is a preffered reference frame in spite of not being able to corroborate this practically at least at the moment. But as far as I see there is also effort to show that Bohm's theory can be made Lorentz invariant in a more fundamental sense (http://arxiv.org/pdf/1307.1714.pdf).

Never heard about the problem you mention at the end of your post as an objection to the Bohmian program (and as far as I know this a problem affecting alternatives as well), actually there is a surprisingly dynamical research along bohmian lines (http://www.bohmian-mechanics.net/research_papers.html#QFT) so I'd say it is too early for 'no-go' theorems which, we all know well, proved so harmful in the past. The Universe can be very well even superdeterministic in reality, why block unnecessarily still legitimate directions of research?

As a side note (i'm sure not very appreciated here) I do not claim that hidden variables programs are the way ahead, they are not even very high currently on a list of alternative scientific approaches, but (unfortunately for those who think that science can only progress, some even think algorithmically, toward truth) there is sufficient reason to be sceptical of the mainstream interpretations of today, we can still be very well on 'the wrong branch', finally even seemingly degenerative scientific programs can become progressive later when the 'background' assumptions (rational ones, nothing linked with politics) are prepared for them. As Popper put it plastically (paraphrased) some very good ideas can even be lost forever if we are constantly told that they are impossible or meaningless.

 

[write4u]

The authors likely want to be sensationalist - its wrong - or at least its full technical detail is likely far less picturesque. There are threads discussing it.

What do you mean by receptors?
Thanks
Bill

I named the plates which show the interference patterns behind the double slits "receptors' for want of a better name. I suppose they are photographic plates,
I wondered what would happen to the interference patterns if these plates were removed. Seems to me these wave patterns would still exist, even if the are not observed (collapsed). Do these patterns eventually dissipate? If so, would there be an effect on the photons also?

From a previous link, I read this, which seems to pose a somewhat similar question.

[QUOTE] In a 1964 book de Broglie gave a detailed statement of the Einstein’s Boxes thought experiment.10
“Suppose a particle is enclosed in a box B
with impermeable walls. The associated wave
is confined to the box and cannot leave it.

The usual interpretation asserts that the particle
is “potentially” present in the whole of
the box B, with a probability ||2 at each
point. Let us suppose that by some process
or other, for example, by inserting a partition
into the box, the box B is divided into
two separate parts B1 and B2 and that B1
and B2 are then transported to two very distant
places, for example to Paris and Tokyo.

[See Fig. 1.] The particle, which has not yet
appeared, thus remains potentially present in
the assembly of the two boxes and its wave
function consists of two parts, one of which,
gives no information about this.

“We might note here how the usual interpretation
leads to a paradox in the case of experiments
with a negative result. Suppose that
the particle is charged, and that in the box B2
in Tokyo a device has been installed which enables
the whole of the charged particle located
in the box to be drained off and in so doing to
establish an observable localization. Now, if
nothing is observed, this negative result will
signify that the particle is not in box B2 and
it is thus in box B1 in Paris. But this can
reasonably signify only one thing: the particle
was already in Paris in box B1 prior to
the drainage experiment made in Tokyo in
box B2. Every other interpretation is absurd.

How can we imagine that the simple fact of
having observed nothing in Tokyo has been
able to promote the localization of the particle
at a distance of many thousands of miles
away?”11 [/QUOTE]
http://www.bohmian-mechanics.net/research_papers.html#QFT

 

[bhobba]

I wondered what would happen to the interference patterns if these plates were removed. Seems to me these wave patterns would still exist,

You are falling into a VERY common trap. QM is a theory about observations. The primitive of the theory is an observation, like point particle is a primitive a classical mechanics, like event is a primitive of probability theory etc etc. What properties a quantum system has when not observed the theory is silent about. The state is simply a device to help predict the probabilities of observations. It says nothing about if it's real or not. We have interpretations where its real, others where its subjective knowledge, and others where it applies to an ensemble. Again the theory is silent on the issue.

The screen at the back of the slits is an observation. Remove it and the theory says nothing since its about observations. It says nothing about waves dissipating etc etc. You can use the state to figure out what would happen if it was there but that doesn't mean there is anything going on. In fact, since the wave particle duality is wrong that explanation of the double slit experiment is wrong. Here is a correct quantum one:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

The explanation of the double slit is each slit 'scatters' the particle at an unpredictable angle because of the uncertainty principle. Note scatter in inverted commas - it doesn't mean it has a real trajectory that's scattered - simply that if you measured its momentum it will be scattered. Just behind the slits the state is the superposition of the state just behind each slit. And when you chug through that math as per the paper above you get an interference pattern on the screen. No screen - no observation - and the theory says nothing.

That quote from Bohm is philosophical waffle - which Bohm rather enjoyed rambling on about - and Feynman for example chided him on that tendency (I recall reading about an interesting exchange along those lines when he explained BM to Feynman - I think it was Surely Your Joking - he said, or at least its my recollection, something like Dave - we have this perfectly valid theory that predicts things perfectly well so what's the point). The theory does not say 'The usual interpretation asserts that the particle is “potentially” present in the whole of the box B, with a probability ||2 at each point.' That's Bohm's interpretation of Copenhagen - his use of the word potentia is his own - Copenhagen doesn't say that. In Copenhagen the state is subjective knowledge.

QM says precisely nothing about when it's not observed. Remove the screen and the theory says nothing. Interpretations may say something - Bohm's picturesque language may suggest things, but the theory says nothing.

Thanks
Bill

 

[write4u]

You are falling into a VERY common trap. QM is a theory about observations. The primitive of the theory is an observation, like point particle is a primitive a classical mechanics, like event is a primitive of probability theory etc etc. What properties a quantum system has when not observed the theory is silent about. The state is simply a device to help predict the probabilities of observations. It says nothing about if it's real or not. We have interpretations where its real, others where its subjective knowledge, and others where it applies to an ensemble. Again the theory is silent on the issue.

The screen at the back of the slits is an observation. Remove it and the theory says nothing since its about observations. It says nothing about waves dissipating etc etc. You can use the state to figure out what would happen if it was there but that doesn't mean there is anything going on. In fact, since the wave particle duality is wrong that explanation of the double slit experiment is wrong. Here is a correct quantum one:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

The explanation of the double slit is each slit 'scatters' the particle at an unpredictable angle because of the uncertainty principle. Note scatter in inverted commas - it doesn't mean it has a real trajectory that's scattered - simply that if you measured its momentum it will be scattered. Just behind the slits the state is the superposition of the state just behind each slit. And when you chug through that math as per the paper above you get an interference pattern on the screen. No screen - no observation - and the theory says nothing.

That quote from Bohm is philosophical waffle - which Bohm rather enjoyed rambling on about - and Feynman for example chided him on that tendency (I recall reading about an interesting exchange along those lines when he explained BM to Feynman - I think it was Surely Your Joking - he said, or at least its my recollection, something like Dave - we have this perfectly valid theory that predicts things perfectly well so what's the point). The theory does not say 'The usual interpretation asserts that the particle is “potentially” present in the whole of the box B, with a probability ||2 at each point.' That's Bohm's interpretation of Copenhagen - his use of the word potentia is his own - Copenhagen doesn't say that. In Copenhagen the state is subjective knowledge.

QM says precisely nothing about when it's not observed. Remove the screen and the theory says nothing. Interpretations may say something - Bohm's picturesque language may suggest things, but the theory says nothing.

Thanks
Bill

Thanks for your patience with my uninformed questions. I won't waste any more of your time and do some more studying, before I jump into deep water again..

 

[metacristi]

By the way I was reading a few days ago the comments to this blog post (https://tjoresearchnotes.wordpress.com/2013/05/13/guest-post-on-bohmian-mechanics-by-reinhard-f-werner/), a lot of disagreement there something which could only reinforce in me that perennial question 'Do we really understand Quantum Mechanics' (see also http://arxiv.org/abs/quant-ph/0209123)? I would say that in the current state of affairs openness toward a pluralistic approach is the best way ahead*, in the words of John Bell (talking about how to teach Relativity in 'Speakable and unspeakable in quantum mechanics'):

'There is no intention here to make any reservations whatever about the power and precision of Einstein's approach. But in my opinion there is also something to be said for taking students along the road made by Fitzgerald, Larmor, Lorentz and Poincare. The longer road sometimes gives more familiarity with the country'.

*bolstered by my incursions in the philosophy and history of science which show quite clearly that the demise of the old positivistic and logical positivist perspectives (which informed the operantionalism of Bohr and Heisenberg) was fully justified

 

[bhobba]

*bolstered by my incursions in the philosophy and history of science which show quite clearly that the demise of the old positivistic and logical positivist perspectives (which informed the operantionalism of Bohr and Heisenberg) was fully justified

Personally I think people over think it.

I spend a lot of time explaining something utterly trivial. QM is a theory about observations. Its deceptively simple but very hard to internalise. It took me a long time. I remember going on long walks thinking about things like Schroedinger's Cat - how could it collapse when opened - all the usual stuff, I did it for years. But slowly it sunk in - its about observations.

Once you accept that it fits together once its understood as the simplest probability model that allows continuous transformations between pure states:
http://arxiv.org/pdf/quant-ph/0101012.pdf

Thanks
Bill

 

[ddd123]

You are thinking in terms of the wave-particle duality which isn't actually true - its one of a number of myths about QM:
http://arxiv.org/pdf/quant-ph/0609163v2.pdf

I wasn't really convinced by the (very short) treatment this article gives on the wave-particle duality. It seems to me a straw-man argument. I've always considered the wave-particle duality not to be much about the behavior of a single entity in space that can be either smeared or localized, which is associated to a wave-function, but the fact that we speak of a single entity at all instead of a continuum. We speak of photons, we can count the photons, instead of light as being a continuum, in principle infinitely divisible: this is what is very classically assumed when talking about waves, not just a spatial distribution property which is "wave-like".

 

[bhobba]

It seems to me a straw-man argument.

Consider the wave-function of two entangled particles. It resides in six dimensions. Exactly what is it waves of?

Or to put it in a different light, define, precisely, what a particle is, similarly define, precisely, what a wave is, then from the axioms of QM show a quantum particle behaves like one or the other.

Thanks
Bill

 

[ddd123]

Consider the wave-function of two entangled particles. It resides in six dimensions. Exactly what is it waves of?

The article, if I understood it correctly, says that there's no duality because "electrons and photons always behave as waves, while a particlelike behavior corresponds only to a special case". But maybe I'm decontextualizing the sentence. So I'm tempted to reflect that question back at you, what are they waves of? I don't know. For me, they're waves up to a certain point, with waves you shouldn't have discretized energies for monochromatic light. But maybe I'm fixating on a way of thinking.

 

[bhobba]

The article, if I understood it correctly, says that there's no duality because "electrons and photons always behave as waves, while a particlelike behavior corresponds only to a special case"

It said 'Instead, such serious textbooks talk only about waves, i.e., wave functions ψ(x, t).'

There are no waves - wave-functions are expansion of the state in the position observable.

The fundamental thing is the state - not its expansion in an arbitrary basis.

You are falling into another VERY common trap. Ascribing some kind of reality to the state - in the theory its simply a device to help calculate the probability of observations.

Thanks
Bill

 

[ddd123]

Sorry if I'm beating a dead horse but I still have a residual linguistic doubt. I agree that in that sense, there are no waves, but can't we still speak of wave-particle duality not referring to a reality of the state, but to particle-like and wave-like aspects of the phenomenology? Then of course if we only look at the ket in position basis, the particle-like aspect is only a special case and it's just a wave function; but in a broader sense we still have the singular entities called photons, which our intuition ascribes to a particle-like behavior and that is certainly not a special case, it's a general property. So the particle-wave duality still retains an expository value.

 

[write4u]

I can't resist. The abstract but observable probability wave function just fascinates me.

It occurred to me that the wave function of a particle is a form of "potential" (probabiities), which may become expressed and fixed in reality only when the probability wave is collapsed and its potential ability becomes expressed in reality.

If so, then the question presents if all potentials behave in a wavelike manner. Is it possible that the wavelike property of potential can only be observed in particles traveling at SOL and the probability wave of slower moving objects becomes progressively longer relative to their speed, until it is no longer observable to us, even when collapsed.

That seems to fit nicely with Bohm's holomovement, which consists of an infinity of wavefunctions, some physical (mechanical, sound, water), others abstract (potential) in nature.

The fundamental abstract definition of potential may be identified as a "latent inherent ability which may become expressed in reality".
Question: is potential a probability wave form, present in all objects, whether experimentally observable or not?

As I understand Bohm, the Implicate is formed in the potential field.
Question: Is Bohm's Implicate a "set" of abstract probability wavefunctions?

 

[atyy]

I might be wrong, but as far as I understand, Bohm's implicate order is vague ill-defined musings, and has nothing to do with the serious proposal of Bohmian Mechanics. I think it should not be discussed in this forum.

 

[bhobba]

Sorry if I'm beating a dead horse but I still have a residual linguistic doubt. I agree that in that sense, there are no waves, but can't we still speak of wave-particle duality not referring to a reality of the state, but to particle-like and wave-like aspects of the phenomenology?

You have now hit on the exact reason.

It behaves LIKE a wave sometimes and LIKE a particle sometimes, but there are plenty of times it behaves like neither:
https://www.physicsforums.com/threads/is-light-a-wave-or-a-particle.511178/
https://www.physicsforums.com/threads/do-photons-move-slower-in-a-solid-medium.511177/

Indeed for a photon position isn't even an observable.

The trouble is to know what LIKE means you need the full theory and to know when you can use it and when not - the same. So what is its point?

Thanks
Bill

 

[bhobba]

I can't resist. The abstract but observable probability wave function just fascinates me.

Who said you can observe a wave-function?

Its exactly the same as observing, or even determining, the probability of the sides of a dice - you can't do it.

Even defining it is tricky due to its gauge freedom. Its not an actual value, but a complex number and one of its defining properties is multiplying it by a phase factor makes no difference.

If |u> is a pure state c*|u> where c is any complex number is exactly the same state. To get around this one moves away from vectors to operators where a pure state is, without any ambiguity, the operator |u><u|.

Thanks
Bill

 

[bhobba]

I might be wrong, but as far as I understand, Bohm's implicate order is vague ill-defined musings, and has nothing to do with the serious proposal of Bohmian Mechanics. I think it should not be discussed in this forum.

Like a lot of Bohms musings its more philosophy than science.

Thanks
Bill

 

[write4u]

Who said you can observe a wave-function?

I have been warned for going off-topic, so I'll just answer the specific question, If I may.

I did not say we can observe the probability wave. I said we can observe the wavelike function of the probability wave by the interference pattern in the dual slit experiment. I used the term function in its broadest sense. The pattern proves a physical and wavelike aspect to whatever function is performed, and without prejudice, IMHO.

Thanks again for your indulgence, I'll sit back for awhile and learn more.

 

[bhobba]

The pattern proves a physical and wavelike aspect to whatever function is performed, and without prejudice, IMHO.

How you reach such a conclusion has me beat.

In physics, like mathematics, a proof requires a logical connection from assumption (in your case pattern) and the conclusion - what I highlighted.

Previously I gave a link to that explains the double slit pattern without waves - did you read it?

Did you see what I wrote before - you can multiply a wave-function by any complex number and it will make no difference.

Exactly how is such physical or even wavelike?

Added Later:
Before going any further I think it would be a good idea to get some proper background rather than going over standard textbook stuff. Susskinds book on QM examines the wave/particle issue in chapter 8:
https://www.amazon.com/dp/0465036678/?tag=pfamazon01-20

'The answer of course is that real quantum mechanics is not so much about particles and waves as about the non-classical logical principles that govern there behaviour'

He carefully explains many of the issues I have basically just skirted, such as what a wave-function is, that's required to see what's going on.

He goes way beyond the typical 'half truths' in popularisations.

Thanks
Bill

 

[write4u]

How you reach such a conclusion has me beat.

In physics, like mathematics, a proof requires a logical connection from assumption (in your case pattern) and the conclusion - what I highlighted.

Previously I gave a link to that explains the double slit pattern without waves - did you read it?

Did you see what I wrote before - you can multiply a wave-function by any complex number and it will make no difference.

Exactly how is such physical or even wavelike?

Added Later:
Before going any further I think it would be a good idea to get some proper background rather than going over standard textbook stuff. Susskinds book on QM examines the wave/particle issue in chapter 8:
https://www.amazon.com/dp/0465036678/?tag=pfamazon01-20

'The answer of course is that real quantum mechanics is not so much about particles and waves as about the non-classical logical principles that govern there behaviour'

He carefully explains many of the issues I have basically just skirted, such as what a wave-function is, that's required to see what's going on.

He goes way beyond the typical 'half truths' in popularisations.

Thanks
Bill

I am not disagreeing with existing science, I am only attempting to narrate my viewpoint in regards to the OP question.

Perhaps I should have quoted this earlier to clarify my position.

A wave function in quantum mechanics describes the quantum state of an isolated system of one or more particles. There is one wave function containing all the information about the entire system, not a separate wave function for each particle in the system. Its interpretation is that of a probability amplitude. Quantities associated with measurements, such as the average momentum of a particle, can be derived from the wave function. It is a central entity in quantum mechanics and is important in all modern theories, like quantum field theory incorporating quantum mechanics, while its interpretation may differ. The most common symbols for a wave function are the Greek letters ψ or Ψ (lower-case and capital psi).

http://en.wikipedia.org/wiki/Wave_function

and

In theoretical physics, the pilot wave theory was the first known example of a hidden variable theory, presented by Louis de Broglie in 1927. Its more modern version, the de Broglie–Bohm theory, remains a non-mainstream attempt to interpret quantum mechanics as a deterministic theory, avoiding troublesome notions such as wave-particle duality, instantaneous wave function collapse and the paradox of Schrödinger's cat.

http://en.wikipedia.org/wiki/Pilot_wave

This is why I intuitively like Bohm's explanation of the properties and behaviors of the universe. One of those universal behaviors IS the wave function. It is an inescapable part of any and all action at all scales, even in the abstract.

I cannot defend this mathematically, de Broglie and Bohm did. But allow me to step aside and study the valuable information I have gained.

Thank you,
Robert