# How does Bohmian mechanics explain the effect of information in the double-slit experiment?

De Broglie and David Bohm found a method (1952) that explains the double-slit experiment and its variations, which are so central to QM, in an intuitive way without appeal to probability, wave-function collapse, the "measurement problem", or invoking the consciousness of the experimenter. Although recognition of Bohm's work was not timely for sociological reasons, John Bell praised it as early as 1987.

I can almost understand that the experimental configuration can determine a nonlocal equation that guides the path of particles through the apparatus, such that blocking one slit causes the interference pattern to disappear, but I don't understand at all how detecting which slit the particle went through (in such a way that the motion of the electron is not disturbed) can also cause the pattern to disappear. Can someone please try to explain this latter effect, using the Bohmian interpretation, and using a minimum of mathematics?

In Bohm's 1952 paper, part I, page 174, he says that measuring which slit the particle went through (WWM) disturbs the trajectory of the particle, causing the pattern to disappear. He further says that being able to measure WW without disturbing the particle would cause the interference pattern to be seen. This, however, is not what is observed in actual experiments. The following reference implies there is a Bohmian explanation: https://advances.sciencemag.org/content/5/6/eaav9547.full#:~:text=In%201991%2C%20Scully%2C%20Englert%2C%20and%20Walther%20%28SEW%29%20proposed,to%20the%20correlations%20between%20particles%20and%20the%20detectors .

• Do you have a reference for De Broglie and Bohm's method you mention? Jul 27, 2020 at 15:16
• This question was already answered here, at physics.stackexchange.com/questions/429767/… . Jul 27, 2020 at 16:22

Since I'm not getting any answers (possibly because Bohmian mechanics are still being ignored by physicists?), I thought I'd post my own answer, based on Observing momentum disturbance in double-slit “which-way” measurements, a link to which paper is in my question.

It turns out that those physicists who have been speculating that information is at the heart of QM, and that particles turn into waves and then back to particles again in the double-slit experiment are probably wrong, as theory and experiment have confirmed Bohmian mechanics in this 2019 paper.

In particular, there is no need for esoteric discussions about abstract information, wave-like or probabilistic eigenstates, or any kind of nondeterminism in the particle's trajectory.

The paper shows that the momentum transfer to the particle from any apparatus to measure its location relative to the slits is nontrivial, and that there is a linear relationship between the degree of certainty of the position measurement and the degree to which the interference pattern disappears, which depends on the degree of momentum transfer only.

To put this in simple language, measuring the position of a tiny particle is similar to blocking one of the slits. It causes the interference pattern to disappear, in direct relationship with the degree of blockage. This blockage is to be understood to affect the path of the particles exactly as though the wave function were a nonlocal force (Bohm called it the quantum potential). The nonlocal nature of this guiding force implies that closing a slit (or measuring the passage of the particle) instantly changes the nonlocal quantum force field associated with the experimental configuration, which in turn changes the degree to which particles are gradually pushed into an interference pattern.

Remarkably, there is no all or nothing effect at work here, no need for mysticism or ambiguity, non nondeterminism, no need to imagine a "wave function collapse" into classical eigenstates, and no need to worry about Heisenberg's Uncertainty Principle, which still holds for all measurements.

To the extent that we believe in Occam's Razor, then, Bohmian mechanics would appear to be a more correct, intuitive, explanatory, and practical interpretation of QM than Bohr's orthodox Copenhagen Interpretation, at least when applied to the double-slit experiment, which is considered to be quintessential.

If I have made any mistakes in my question or this answer, I ask that they be corrected here, as this seems to be an important understanding in physics today.

• Classically we think of interference as 2 photons arriving out of phase creating a dark spot, this is a violation of energy conservation. I'm a fan of Feynman, which says that photons want to travel n times their wavelength (n = integer) from source to absorption, that's a key part of the photon wave function. There is no way of measuring a photon on its way without absorbing it, for the electron disturbance results in the original wave function being altered/destroyed. Feynman and Bohm would agree, some how there is a guiding EM force the guides the electron of photon. Jul 31, 2020 at 23:37
• Yes, the fundamental explanation of quanta is in the requirement of an integral number of wavelengths (originally, to fit an elliptical orbit). However, a dark spot (destructive interference) is not a violation of energy conservation, since the energy is contained in the wave itself (it requires energy to create a wave of radiation). It is true that inside superimposed waves there may be dark spots and bright spots, in which the instantaneous or standing wave energy appears to be zero or twice the amplitude or more, but the total energy in a wave packet is always conserved. Aug 2, 2020 at 11:57
• In so-called "weak measurement" it is possible to measure a fundamental particle without absorbing ("destroying") it through the use of statistics, and when this is done we can see the effect that measurement has on the experimental results. However, I'm not sure that I see how your observations relate specifically to my question or answer. Aug 2, 2020 at 11:59
• Your statement that Feynman and Bohm would agree that there is a guiding force needs more details, as Feynman simply integrated along all paths, which is more or less a probabilistic argument, while Bohm showed that the Born probability hypothesis is not required at all. Bohm's use of part of the wave function as a guiding force ("quantum potential") is unique and produces the same results as the probability hypothesis with a lot less mysticism and complexity. Aug 2, 2020 at 12:03
• Yes the EM field is "magical" holding, superimposing and transmitting energy but we can never observe it directly .. only once the quanta are absorbed from the field can we make observations. There are no quanta in the dark areas of the interference pattern .... and hence no energy or field there. The pilot wave is common to Bohm and Feynman, the photon's path is determined before it ever begins to travel. Feynman's use of all paths eventually boils down to the shortest path that is integer multiples. Aug 5, 2020 at 13:17