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I have studied physics and I'm finishing my postgrad related to Quantum Physics. I'm doing a quick work involving fuzzy setsand I started to study Quantum Logic to direct my work to this field. Now I don't know what to think.

There are many interpretations of Quantum Mechanics. Like everyone (I think), I learned QP in terms of the Copenhagen interpretation (CI), I have read hundreds of papers in terms of the CI, all the people I know, all my teachers, all the advanced theories and fields that are in the context of QP, like solid-state physics or atomic physics, are expressed in terms of the CI.

Until I started this work in Quantum Logic I didn't pay attention to these other interpretations. As I said, right now I don't know what to think about this.

Questions:

Why are there so many references in QP texts about the existence of other QM interpretations If (almost) anybody uses it?

Is there any application of these other interpretations in a no purely euristic field?

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Adding to Deschele Schilder's answer, many physicists aren't satisfied with the Copenhagen interpretation and feel like the interpretation problem has been wrongly ignored. Bell and Einstein were famous exponents of this party. Mentioning that the Copenhagen interpretation is just one of many equivalent, if not arguably better$^1$, interpretations might be a way to bring more awareness to the issue.

On a more personal note, I believe that there are interests in finding a satisfying interpretation other than making correct predictions. Of course, experiments are the ultimate judges, but it can be argued that the physicist's role is to understand, at the most fundamental level possible, what's going on physically and not just be content with correct predictions.


$^1$At least from a philosophical perspective.

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    $\begingroup$ "the physicist's role is to understand, at the most fundamental level possible, what's going on physically" I highly agree! $\endgroup$ Commented Mar 10, 2021 at 0:05
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Why are there so many references in QP texts about the existence of other QM interpretations if (almost) anybody uses it [the CI]?

It's the question if any interpretation of QM is used at all when physicists use it in doing calculations. Of course, the result of calculations is referring to probability distributions but if this distribution is inherent to Nature (as the CI posits) or derivable from hidden variables (as for example Bohm or van 't Hooft posit about the Nature of the reality of QM), or whatever, is mostly a philosophical discussion. I think most physicists are agnostic towards the interpretation. If for example, virtual particles are real or not is not relevant to most of them. If the calculations done with these objects (be they mathematical or real) give the right predictions for observable, then who cares (I do though; I'm inclined toward a hidden variable formulation; maybe because I don't give too much about calculations referring to observables).

Is there any application of these other interpretations in a not purely heuristic field?

As long as the different interpretations give rise to the same observable effects I think that this is not the case.

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In addition to the answers already given, maybe a point of why this topic used to be highly debated in the first half of the past century and isn't much of a point of discussion among researchers today.

In a loose caricature of the history of science, I think physicists came to believe that the language of natural laws is math. Galileo more or less kickstarted that and Kepler and Newton sealed the deal. Thing is, Newton's theory fits rather well with common intuition. Idealizing an object $A$ as a point mass and understanding its interactions with object $B$ as the sources of the object's acceleration via forces exerted by $B$ on $A$ isn't that surprising given our experiences with springs or fistfights. (Side note: interpreting classical Lagrangian mechanics is already a bit harder)

There is a mapping from reality onto mathematical objects, say an arrangement of position vectors, on which you can perform mathematical calculations to get a new arrangement of position vectors, and then you invert that mapping to get back to reality. People got accustomed to the idea that this mapping is somewhat straightforward and that actually, no matter the measurement you perform, you can use the inverse mapping whenever you please to know exactly what's going on. If two billiard balls collide, you can trace their paths and forces at every instant in time, resolving the entire process of their collision.

Turns out that QM isn't that kind to us. You can transform your measurement apparatus into a set of rules and you can deduce (probabilistically, but still) what measurement outcomes you may encounter. But the information that classical physics promised to be available to you at any arbitrary instant during the progression from initial to final state -- like an electron's position, its trajectory -- cannot be retrieved from the mathematical formalism, even if you have definite positions at the beginning and the end.

If you were to come straight out of the 19th century and encountered that situation, that's a huge blow. Because people considered that knowing what really happens entails knowing positions and momenta at each instant of time. And knowing what really happens was kind of the original sales pitch of physics, as opposed to engineering where you put aside abstraction to focus on what can be done with the math. You really would like to know what the reality the math describes is like.

So they came up with different stories of what is actually happening. Some of these tried to reestablish the common ground of classical physics that position and momentum is still independently available information, others came up with new ideas off the beaten path to talk about these phenomena, Deschele Schilder's answer talks about that.

These philosophical discussions are, I think, important. They belong to the original pursuit of physics to muse about what nature is like, and putting this musing aside just because it doesn't appear to have a practical value ditches the, admittedly rather philosophical, original idea of physics in favor of a more application-oriented branch of science. I understand that such discussions eventually took a back seat once researchers realized that they can build weapons of mass destruction with their new theories, and of course technological advancement (and its control and direction) doesn't require much of interpretation musing, while possibly being more vital to our future as a species.

But there's the possibility of wonder in these musings, and since wonder is what drew most of us into the field, I personally like to sometimes ignore application and falsifiability (though some interpretations are falsifiable) in favor of admiring some ideas of what nature could be at a core level.

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