A Would this experiment disprove Bohmian mechanics?

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1. Sep 2, 2018

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?

2. Sep 2, 2018

tnich

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?

3. Sep 2, 2018

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.

4. Sep 2, 2018

richrf

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.

5. Sep 2, 2018

Staff: Mentor

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.

6. Sep 2, 2018

Staff: Mentor

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).

7. Sep 3, 2018

Demystifier

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

Last edited: Sep 3, 2018
8. Sep 3, 2018

Demystifier

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.

Last edited: Sep 3, 2018
9. Sep 3, 2018

Demystifier

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.

10. Sep 3, 2018

Demystifier

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.

11. Sep 3, 2018

stevendaryl

Staff Emeritus
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.

12. Sep 3, 2018

Demystifier

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.

13. Sep 3, 2018

stevendaryl

Staff Emeritus
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.

14. Sep 3, 2018

atyy

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).

15. Sep 3, 2018

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.

16. Sep 3, 2018

Demystifier

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.

17. Sep 3, 2018

richrf

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”.

Last edited: Sep 3, 2018
18. Sep 4, 2018

Staff: Mentor

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

19. Sep 4, 2018

Alex Torres

Do you mean hidden variables??....

20. Sep 4, 2018

Yes.