# Question concerning superposition

I have a question regarding superposition and its relation with interpretations/counterfactual definiteness. I've seen this question brought up a few times when browsing through forums although I don't think it has ever been fully addressed.

I've heard that counterfactual definiteness is not related to superpositions. According to one member of PF, "all superposition is is pure states form a vector space. It has nothing to do with CFD". This doesn't make sense to me, as I've been taught that in interpretations that preserve CFD superpositions don't exist. Take pilot wave theory for example, it claims that superpositions are not real and the phenomena observed in the double slit experiment are explained an invisible wave that "guides" the particles. As a result, CFD is preserved. In an interpretation that claims counterfactual definiteness is true, such as in pilot wave theory, it is even even possible to have probabilistic attributes of particles and not definite ones? A CFD interpretation is predicated upon determinism (or so I've been told), and so how can you have determinism with superposition?

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Wiki says that counterfactual definiteness is "the ability to speak meaningfully of the definiteness of the results of measurements that have not been performed (i.e. the ability to assume the existence of objects, and properties of objects, even when they have not been measured)."
If this is true, even if we drop counterfactual definiteness, we're still assigning the property of probability to the individual particles.

Perhaps I'm reaching conclusions derived from misconceptions. ):

bhobba
Mentor
Perhaps I'm reaching conclusions derived from misconceptions. ):
The best way to proceed in that case is to take it step by step.

First lets have an understanding of superposition.

For that have a read of the first chapter of the classic Dirac - Principles Of Quantum Mechanics. Its not perfect - without detailing its issues (I recall some threads discussing this if you want to look them up) - but as an explanation of the principle of superposition is rather good.

Once you have done that we can have a chat.

Thanks
Bill

Nugatory
Mentor
I've been taught that in interpretations that preserve CFD superpositions don't exist.
Superposition is a fundamental part of the mathematical formalism of quantum mechanics and no interpretation says otherwise. Some interpretations propose an underlying superposition-free model to explain how superposition appears in QM - but that's not the same thing as saying that superposition doesn't exist.

An analogy: When you're in high school you learn about ideal gases and how they have these properties called "pressure" and "temperature" that obey Boyle's ##PV=nRT## but don't seem to have much of anything to do with Newton's laws or any of the rest of physics. Then in your second year of college or thereabouts you encounter statistical mechanics, which explains how individual atoms have neither temperature nor pressure but that a very large number of them bouncing around in accordance with Newton's laws will explain the behavior of ideal gases.

The (non-local realistic hidden variable) interpretations that preserve CFD are doing for quantum superposition what statistical mechanics does for temperature and pressure: explaining why they appear, not denying their existence.

bhobba