Impossibilty of hidden variables (Bohm, 1951)

[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