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In many formulations of Bohmian mechanics, researchers seem to claim that 1) measurements of observables such as spin are just measurements of the position of a pointer variable, such as the Stern-Gerlach experiment apparatus and 2) measurements of position reveal the position of particles. This effectively removes the 'measurement problem', where superpositions of classical pointers can be explained.

However, this explanation seems to be insufficient. There exists the (philosophical) question of why the position is such an important variable - in classical mechanics, the position and the momentum are considered the state of a system. Even worse, position-measuring apparatus, such as the screen in the double slit experiment, obviously perturb physical quantities such as momentum. How is it that we can say measurement reveals the exact position, but perturbs other variables? Isn't it more natural to assume that position measurements are also performed by entangling the system with a classical pointer object (for instance, the screen and the particles become entangled in a double-slit experiment)? For example, weak measurements are performed similarly, by entangling the system with a Gaussian pointer distribution with a high spread. Therefore, position measurement also perturbs particles and therefore cannot reveal the exact position values. A paper by N. Gisin supports this claim, that position measurements in Bohmian mechanics do not reveal exact positions: https://doi.org/10.3390/e20020105.

Qmechanic
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cognition
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  • https://physics.stackexchange.com/a/386154/28512 – alanf Sep 15 '23 at 08:09
  • @alanf I'm confused. It seems like you are arguing against BM, which this question is not concerned with (nor am I concerned with arguing for BM). – cognition Sep 15 '23 at 11:41

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In Bohmian mechanics, the entire trajectory of all particles through space as a function of time is well-defined. So they have both a position and a momentum at all times.

Yes, you are correct that measurements never reveal the exact position or momentum. So what?

Travis
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  • There is a problem because the 'advantage' Bohmian mechanics has lies in this assumption that position measurements simply reveal the positions of particles. In BM, all measurement is reduced to position measurements of 'pointers' which are entangled to the system. If position measurements are also performed by entangling the system with a classical pointer, then the underlying logic becomes circular logic. I have difficulty understanding this extremely fundamental nature of position in BM. – cognition Sep 15 '23 at 11:36
  • That's just not true. Bohmian mechanics does not rely on the assumption that position measurements reveal the positions of particles. All measurements are explained by the positions of the particles that make up the pointer, but the positions of the particles in the pointer is never known with perfect accuracy and doesn't need to be for Bohmian mechanics to work. – Travis Sep 15 '23 at 21:08
  • BM claims that it removes the distinct nature of quantum and classical systems. If position measurements of particles do not match with the actual positions, then doesn't this phenomenon have to happen in the classical, macroscopic world? – cognition Sep 16 '23 at 01:35
  • What do you mean by removing the distinct nature of quantum and classical systems? In a way, Bohmian mechanics has both because it has a wave function and also classical particles that move around in space. – Travis Sep 16 '23 at 02:27
  • I phrased that weirdly; what I was trying to say is that in BM there is no distinction between macro and microscopic systems, but in microscopic systems, the measured position does not correlate to the actual position whereas in macroscopic systems there certainly is a correlation. We do not know the actual positions of particles even after measurement. Doesn't this bring back the need for a distinction between quantum and classical systems? – cognition Sep 16 '23 at 04:06
  • We don't need to know the precise location of particles in macroscopic systems in order to be able to make a measurement. We just need to know the locations of particles in that macroscopic system well enough to be able to say read a dial on an instrument. We could be off by a few microns or so and still be fine. Does that make sense? – Travis Sep 16 '23 at 04:35
  • Yes, I do acknowledge that classical measurements also do not reveal 'exact' positions. I was confused because there were instances in BM where the measured position and the exact position were extremely far apart (for instance in the Mach-Zehnder interferometer example shown in Gisin's paper). Maybe these huge 'errors' go to 0 when the classical limit is performed, but I'm not sure. – cognition Sep 16 '23 at 05:09
  • Yeah, the probability of an entire macroscopic object not being approximately where you measure it to be is essentially zero. – Travis Sep 16 '23 at 06:26