Would this experiment disprove Bohmian mechanics?

[john taylor]

Bohmian mechanics claims that although it is deterministic, randomness emerges from the fact that we cannot know the initial conditions of the particle due to Heisenberg's uncertainty principle. However this experiment can put that to the test and determine whether randomness in quantum mechanics is due Heisenberg's uncertainty principle(not being able to know the position and momentum of the particle at the same time).The experiment is a variation of the double slit experiment, except for before the particles pass through the slit they travel through a type of detector which detects it's position, as it continues traveling it travels to another detector, where again its position is detected. From the time it took to get from first detector to the second, it could then be deduced the momentum at which the particle was traveling when it went through detector number 1. Now at that instance both the position and momentum of the particle were known when it was traveling. This would be repeated as the particles travel through the double slit. Once the experiment has finished, one could calculate trajectories using bohmian mechanics of the particle and determine whether bohmian mechanics was able to predict accuratley where the particles would land on the detector screen. As this experiment gets repeated more and more one would be able to determine whether the retroactive calculations made from bohmian mechanics are more accurate than the already accurate quantum mechanics. It would also be best to perform this experiment in a vaccum, and calculations could be made before the particle lands by potentially a computer if it was fed the data and the particle was traveling at slow speeds. Would this experiment work conceptually?

 

[tnich]

Bohmian mechanics claims that although it is deterministic, randomness emerges from the fact that we cannot know the initial conditions of the particle due to Heisenberg's uncertainty principle. However this experiment can put that to the test and determine whether randomness in quantum mechanics is due Heisenberg's uncertainty principle(not being able to know the position and momentum of the particle at the same time).The experiment is a variation of the double slit experiment, except for before the particles pass through the slit they travel through a type of detector which detects it's position, as it continues traveling it travels to another detector, where again its position is detected. From the time it took to get from first detector to the second, it could then be deduced the momentum at which the particle was traveling when it went through detector number 1. Now at that instance both the position and momentum of the particle were known when it was traveling. This would be repeated as the particles travel through the double slit. Once the experiment has finished, one could calculate trajectories using bohmian mechanics of the particle and determine whether bohmian mechanics was able to predict accuratley where the particles would land on the detector screen. As this experiment gets repeated more and more one would be able to determine whether the retroactive calculations made from bohmian mechanics are more accurate than the already accurate quantum mechanics. It would also be best to perform this experiment in a vaccum, and calculations could be made before the particle lands by potentially a computer if it was fed the data and the particle was traveling at slow speeds. Would this experiment work conceptually?

The problem I see with your experiment is that to detect the position of a subatomic particle, you essentially have to cause it to collide with something. That effectively stops it from continuing through the slit. Can you think of a way to detect its position while still allowing it to continue in motion?

 

[john taylor]

Yes. Having an arrangement of magnets, and then deducing the way that the magnets are affected by the position the electron was at.

 

[richrf]

Bohmian mechanics claims that although it is deterministic, randomness emerges from the fact that we cannot know the initial conditions of the particle due to Heisenberg's uncertainty principle.

I believe Bohm's position on this is more subtle. I will quote from his book, Science, Order, and Creativity in which he discusses his Causal Interpretation Of Quantum Theory.

"Although the interpretation is termed causal, this should not be taken as implying complete determinism. Indeed it will be shown that this interpretation opens the door for the creative operation of underlying, and yet subtler, levels of reality".

No mention is made of the Uncertainty Principle as being the source of the probabilistic behavior of Quantum Theory. The book was written in 1987, so it represents his thoughts in the latter years of his life.

Thus your experiment is unrelated to Bohm's Causal Interpretation since it doesn't claim to be deterministic. I am aware that in very early writings, he did use cite his model as being deterministic. He changed his views over subsequent decades.

 

[mfb]

The uncertainty principle is not about our knowledge of the particles. It is a property of the particles. Measuring repeatedly won't change that.

Besides: dBB makes the same predictions as all other interpretations in all experiments. It was designed to do so. You cannot experimentally distinguish between interpretations, otherwise they wouldn't be interpretations.

 

[PeterDonis]

Bohmian mechanics claims that although it is deterministic, randomness emerges from the fact that we cannot know the initial conditions of the particle due to Heisenberg's uncertainty principle.

No, that's not what Bohmian mechanics says. Bohmian mechanics says that particles always have definite positions, but the exact positions are not measurable or knowable. That is not due to the uncertainty principle. It's a postulate of Bohmian mechanics only, whereas the uncertainty principle is part of basic QM (common to all interpretations).

 

[Demystifier]

The uncertainty principle is not about our knowledge of the particles. It is a property of the particles. Measuring repeatedly won't change that.

Besides: dBB makes the same predictions as all other interpretations in all experiments. It was designed to do so. You cannot experimentally distinguish between interpretations, otherwise they wouldn't be interpretations.

In dBB, the uncertainty is about the (lack of) knowledge, and not a property of particles.

 

[Demystifier]

No, that's not what Bohmian mechanics says. Bohmian mechanics says that particles always have definite positions, but the exact positions are not measurable or knowable. That is not due to the uncertainty principle. It's a postulate of Bohmian mechanics only, whereas the uncertainty principle is part of basic QM (common to all interpretations).

In Bohmian mechanics non-measurability of exact positions is not a postulate. It is a derived property valid only in the FAPP (for all practical purposes) sense. Roughly speaking, this is like the 2nd law (the entropy-increase law) in statistical mechanics, which is not a postulate but a derived property valid only in the FAPP sense.

 

[Demystifier]

Bohmian mechanics claims that although it is deterministic, randomness emerges from the fact that we cannot know the initial conditions of the particle due to Heisenberg's uncertainty principle. However this experiment can put that to the test and determine whether randomness in quantum mechanics is due Heisenberg's uncertainty principle(not being able to know the position and momentum of the particle at the same time).The experiment is a variation of the double slit experiment, except for before the particles pass through the slit they travel through a type of detector which detects it's position, as it continues traveling it travels to another detector, where again its position is detected. From the time it took to get from first detector to the second, it could then be deduced the momentum at which the particle was traveling when it went through detector number 1. Now at that instance both the position and momentum of the particle were known when it was traveling. This would be repeated as the particles travel through the double slit. Once the experiment has finished, one could calculate trajectories using bohmian mechanics of the particle and determine whether bohmian mechanics was able to predict accuratley where the particles would land on the detector screen. As this experiment gets repeated more and more one would be able to determine whether the retroactive calculations made from bohmian mechanics are more accurate than the already accurate quantum mechanics. It would also be best to perform this experiment in a vaccum, and calculations could be made before the particle lands by potentially a computer if it was fed the data and the particle was traveling at slow speeds. Would this experiment work conceptually?

It would not work. In the case you describe, the wave function is not an eigenfunction of the momentum operator. In standard QM it means that the momentum is uncertain. In Bohmian mechanics it means that the particle momentum is not a constant, so you cannot deduce the momentum from the time it took to get from first detector to the second.

 

[Demystifier]

I believe Bohm's position on this is more subtle. I will quote from his book, Science, Order, and Creativity in which he discusses his Causal Interpretation Of Quantum Theory.

"Although the interpretation is termed causal, this should not be taken as implying complete determinism. Indeed it will be shown that this interpretation opens the door for the creative operation of underlying, and yet subtler, levels of reality".

No mention is made of the Uncertainty Principle as being the source of the probabilistic behavior of Quantum Theory. The book was written in 1987, so it represents his thoughts in the latter years of his life.

Thus your experiment is unrelated to Bohm's Causal Interpretation since it doesn't claim to be deterministic. I am aware that in very early writings, he did use cite his model as being deterministic. He changed his views over subsequent decades.

It is true that Bohm changed his position, but physicists that study Bohmian mechanics usually consider only his early completely deterministic version of the theory.

 

[stevendaryl]

In Bohmian mechanics non-measurability of exact positions is not a postulate. It is a derived property valid only in the FAPP (for all practical purposes) sense. Roughly speaking, this is like the 2nd law (the entropy-increase law) in statistical mechanics, which is not a postulate but a derived property valid only in the FAPP sense.

In the Bohmian interterpretation of QM, the wave function plays a double role:

1. Its square is interpreted as the subjective probability distribution of the particle.
2. It affects a particle's motion in a nonlocal way (akin to de Broglie's "guiding wave")

What seems weird about this to me is that #1 is interpreted as subjective (we just don't know the particle's position precisely, so we use a probability distribution to describe it) while #2 is interpreted as objective (the wave function has an objective effect on the particle's motion). The subjective and objective roles of the wave function have to be precisely in-sync in order for Bohmian mechanics to make the same predictions as orthodox QM.

 

[Demystifier]

In the Bohmian interterpretation of QM, the wave function plays a double role:

1. Its square is interpreted as the subjective probability distribution of the particle.
2. It affects a particle's motion in a nonlocal way (akin to de Broglie's "guiding wave")

What seems weird about this to me is that #1 is interpreted as subjective (we just don't know the particle's position precisely, so we use a probability distribution to describe it) while #2 is interpreted as objective (the wave function has an objective effect on the particle's motion). The subjective and objective roles of the wave function have to be precisely in-sync in order for Bohmian mechanics to make the same predictions as orthodox QM.

I see nothing weird with this. For an analogy, consider a dice.
1. Its inverse number of faces is interpreted as subjective probability.
2. The shape of the dice with faces affects the objective rolling of the dice.

 

[stevendaryl]

I see nothing weird with this. For an analogy, consider a dice.
1. Its inverse number of faces is interpreted as subjective probability.
2. The shape of the dice with faces affects the objective rolling of the dice.

But the probabilities for dice are not really facts about the dice, alone. The unknown is about the environment--the precise shape of the surface the dice is rolling on, and the precise nature of the mechanism doing the tossing. Those facts are not specified by the definition of "rolling the device", so there is an inherently underspecified component to the problem. Presumably, if you could nail down the surface and the rolling mechanism in enough detail, the dice results would be predictable, in which case the probabilities of 1/6 per face would no longer apply.

 

[atyy]

What seems weird about this to me is that #1 is interpreted as subjective (we just don't know the particle's position precisely, so we use a probability distribution to describe it) while #2 is interpreted as objective (the wave function has an objective effect on the particle's motion). The subjective and objective roles of the wave function have to be precisely in-sync in order for Bohmian mechanics to make the same predictions as orthodox QM.

Yes, that's weird. I like Antony Valentini's proposal that this condition of "quantum equilibrium" does not hold in general, but is rapidly established by the dynamics in many cases (similar to how Newtonian dynamics establishes thermal equilibrium in many cases).
https://www.sciencedirect.com/science/article/pii/037596019190116P
https://www.sciencedirect.com/science/article/pii/037596019190330B

There is also a brief, but interesting, comment by Wood and Spekkens about this weirdness or fine tuning needed in dBB, as well as on Valentini's approach in https://arxiv.org/abs/1208.4119 (p21).

 

[richrf]

With Bohmian Mechanics it is easy to be led astray if I've simply looks at it as a series of abstract mathematical functions. There is real meaning in each of the functions that has to be understood in order to grasp the math. Bohm and Hiley spent a great deal of their lives trying to understand the meaning. The theory has to be rooted in reality before it is tinkered with. Too often scientists are quick to critique without spending the necessary effort to understand. To attempt to understand Bohmian Mechanics, as finally realized by Bohm before his death, from the math, is equivalent to attempting to understand a great novel from Cliff Notes.

 

[Demystifier]

But the probabilities for dice are not really facts about the dice, alone. The unknown is about the environment--the precise shape of the surface the dice is rolling on, and the precise nature of the mechanism doing the tossing. Those facts are not specified by the definition of "rolling the device", so there is an inherently underspecified component to the problem. Presumably, if you could nail down the surface and the rolling mechanism in enough detail, the dice results would be predictable, in which case the probabilities of 1/6 per face would no longer apply.

Again, this is completely analogous to Bohmian mechanics. If you could nail down the initial particle positions of the system and its environment in enough detail, then the outcomes of quantum measurements would be predictable and the probabilities $|\psi|^2$ would no longer apply.

 

[richrf]

It is true that Bohm changed his position, but physicists that study Bohmian mechanics usually consider only his early completely deterministic version of the theory.

I do not believe Bohm every changed his position, but rather his nomenclature. The Quantum Potential is still governed by Schrodinger's Equation, thus describing it as deterministic is misleading. Bohm describes his interpretation succinctly in his paper, "An ontological basis for the Quantum Theory", which he co-authored with Hiley.

"Clearly eq. (3) resembles the Hamilton—Jacobi equation except for an additional term, Q. This suggests that we may regard the electron as a particle with momentum p VS subject not only to the classical potential V but also to the quantum potential Q. Indeed the action of the quantum potential will then be the major source of the difference between classical and quantum theories. This quantum potential depends on the Schrödinger field t/i and is determined by the actual solution of the Schrodinger equation in any particular case. Given that the electron is always accompanied by its Schrodinger field, we may then say that the whole system is causally determined; hence the name “causal interpretation”.

 

[mfb]

In dBB, the uncertainty is about the (lack of) knowledge, and not a property of particles.

Technically correct, but the uncertainty is still a property of the guide wave, and that determines the physics.

 

[Alex Torres]

In dBB, the uncertainty is about the (lack of) knowledge

Do you mean hidden variables??...

 

[Demystifier]

Do you mean hidden variables??...

Yes.

 

[Alex Torres]

Yes

Thought quantum non local realism was falsified back in 2007...

 

[Demystifier]

Though quantum non local realism was falsified back in 2007...

No it wasn't. In one paper (I'm not sure if it was in 2007) Zeilinger et al falsified a certain class of non-local realistic theories. More precisely they falsified non-contextual non-local realistic theories, which does not exclude dBB theory which is a contextual non-local realistic theory.

 

[Alex Torres]

No it wasn't. In one paper (I'm not sure if it was in 2007) Zeilinger et al falsified a certain class of non-local realistic theories. More precisely they falsified non-contextual non-local realistic theories, which does not exclude dBB theory which is a contextual non-local realistic theory.

This article states the before-before experiment also refutes Bohm's nonlocal realism...

https://www.google.com.pr/url?sa=t&...FjABegQICRAB&usg=AOvVaw2Kac5fVnRKloyGqrFoLsWj

Besides, if a theory proposes non local hidden variables, as dBB certainly do, and those hidden variables can be ruled out by the violation of certain type of inequalities (Leggett) then it means the theory also is refuted, don't see the fact being contextual has to do here...

 

[Demystifier]

This article states the before-before experiment also refutes Bohm's nonlocal realism...

https://www.google.com.pr/url?sa=t&...FjABegQICRAB&usg=AOvVaw2Kac5fVnRKloyGqrFoLsWj

As far as I can see, it is not published in a peer-reviewed journal.

Besides, if a theory proposes non local hidden variables, as dBB certainly do, and those hidden variables can be ruled out by the violation of certain type of inequalities (Leggett) then it means the theory also is refuted, don't see the fact being contextual has to do here...

Why do you think that violation of Leggett inequalities rules out non-local hidden variables? I've never seen such a statement in a peer-reviewed paper.

 

[atyy]

This article states the before-before experiment also refutes Bohm's nonlocal realism...

https://www.google.com.pr/url?sa=t&...FjABegQICRAB&usg=AOvVaw2Kac5fVnRKloyGqrFoLsWj

Besides, if a theory proposes non local hidden variables, as dBB certainly do, and those hidden variables can be ruled out by the violation of certain type of inequalities (Leggett) then it means the theory also is refuted, don't see the fact being contextual has to do here...

As far as I can see, it is not published in a peer-reviewed journal.

It's published in Foundations of Physics. https://link.springer.com/article/10.1007/s10701-008-9228-y

 

[Alex Torres]

As far as I can see, it is not published in a peer-reviewed journal.

This reference has the correct link..

https://arxiv.org/abs/0708.1997

Why do you think that violation of Leggett inequalities rules out non-local hidden variables? I've never seen such a statement in a peer-reviewed paper

Yep... it refers to "certain class of nonlocal hidden variables theories" ...need to see if dBB fits in that list...think the above papers just did that...

 

[bobob]

As far as I can see, it is not published in a peer-reviewed journal.

That one may not be, but this one was published in phys rev lett
https://arxiv.org/abs/quant-ph/0110117

 

[Demystifier]

That one may not be, but this one was published in phys rev lett
https://arxiv.org/abs/quant-ph/0110117

This paper shows that one particular attempt to make Bohmian mechanics relativistic does not work. It certainly does not exclude the possibility that another approach might work.

 

[Alex Torres]

This paper shows that one particular attempt to make Bohmian mechanics relativistic does not work. It certainly does not exclude the possibility that another approach might work.

Check out the conclusion: "Giving up the concepts of locality and realism is not sufficient to be consistent with quantum experiments, one has also to abandon time-ordered causality too. This issue has not yet been highlighted in the ongoing discussion about experimental tests of nonlocal realistic theories. This may be a sign that “most working scientists” (the expression appears in [1]) unconsciously still hold fast to the postulate of time-ordered causality: Apparently, the idea that Nature establishes order without time is, after all, the most counterintuitive feature of quantum mechanics."

Wherever we invoke hidden variables aren't we just doing that?... assuming a time-ordered causality?

 

[Demystifier]

Wherever we invoke hidden variables aren't we just doing that?... assuming a time-ordered causality?

No. Hidden variables do not need to be deterministic (causal), they also can be stochastic. The point of hidden variables is not to comply with the Einstein's "God does not play dice". The point of hidden variables is to comply with the Einstein's "The Moon is there even when nobody looks".

 

[vanhees71]

Isn't the validity of the usual conservation laws sufficient to be sure that the moon is indeed there, even when nobody looks? I never understood, how one can come to the conclusion that things that must be there because of conservation laws may not be there only because nobody observes them. Other entities like photons might be there or not, and I have to look for them, because there are no conservation laws forbidding their disappearance, but in fact already energy-momentum conservation tells you that there most be some interaction with something else to make it possible that a photon is absorbed.

Since all physics sense of the quantum formalism finally can be traced back to symmetry principles (which is the only save "correspondence principle" to guess quantum laws from classical laws we have) and the conservation laws are just equivalent to symmetry principles thanks to Noether's theorems, this seems to be the most sensible explanation for the fact that the moon indeed is still there, even if nobody (not even the cosmic microwave radiation) "looks at it".

 

[Alex Torres]

No. Hidden variables do not need to be deterministic (causal), they also can be stochastic. The point of hidden variables is not to comply with the Einstein's "God does not play dice". The point of hidden variables is to comply with the Einstein's "The Moon is there even when nobody looks".

...Bohr never denied the existence of the moon, rather he just tried to tell the moon could be in Einstein's pockets when nobody looks...

...dBB will make sense if the pilot wave is sort of a Max Planck's matrix concept...

 

[Demystifier]

...dBB will make sense if the pilot wave is sort of a Max Planck's matrix concept...

What is Max Planck's matrix concept?

 

[Demystifier]

Isn't the validity of the usual conservation laws sufficient to be sure that the moon is indeed there, even when nobody looks?

No it isn't. It's sufficient to be sure that the Moon's energy is there, but Moon is much more than it's energy. For most physical systems, the number of degrees of freedom is much larger than the number of conserved quantities. An exception (in classical physics) are the integrable systems, but such systems are rare.

 

[Boing3000]

Isn't the validity of the usual conservation laws sufficient to be sure that the moon is indeed there, even when nobody looks?

I hold an identical view, until I learn about QM and especially that it is the most powerful and accurate description of the world. And I am under the impression that QM says that there is a non-null probability that all particles of the moon decide to tunnel away into another galaxy ( or form a brain or whatnot)

I never understood, how one can come to the conclusion that things that must be there because of conservation laws may not be there only because nobody observes them.

Indeed, but as only observation on identically prepared state, in a laboratory, allows you to assign property to "reality", the moon seems to QM as only existing when it is measured (that is: under Born rule almighty power)

Other entities like photons might be there or not, and I have to look for them, because there are no conservation laws forbidding their disappearance, but in fact already energy-momentum conservation tells you that there most be some interaction with something else to make it possible that a photon is absorbed.

Isn't the moon entirely composed of quantum "smeared out" Quantum object ? Or is there is the cut and can you point to its derivation ?

Since all physics sense of the quantum formalism finally can be traced back to symmetry principles (which is the only save "correspondence principle" to guess quantum laws from classical laws we have) and the conservation laws are just equivalent to symmetry principles thanks to Noether's theorems, this seems to be the most sensible explanation for the fact that the moon indeed is still there, even if nobody (not even the cosmic microwave radiation) "looks at it".

So the obvious solution is to explain how it is that quantum object does tunnel without breaking those symmetries.