I’ve written a whole book on this subject in great detail, going into all the mathematics and all the major papers on the subject.
The issue actually comes down to an underdetermination problem in the mathematics. If you claim that the systems have definite states in the real world even when you’re not looking, you have to answer, what those states are. The intuitive solution is to say that the state of the system is in some configuration with non-zero probability in the Born distribution, but then this would imply that every non-communicating observable has a configuration in that probability distribution, which the Kochen-Specker theorem shows leads to an algebraic contradiction, so it cannot possibly be true.
The way out of the Kochen-Specker theorem is to privilege a certain measurement basis. The system has a pre-existing configuration on a particular basis, not all bases at once. When you take this approach, then the mathematics already automatically fixes functions of how the other measurement outcomes arise when you go make a measurement; they end up being emergent properties that only have reality in the physical process of measurement, but that physical process is well-defined and is a function of the system’s pre-existing configuration on the privileged basis.
The issue, however, is that all bases are symmetrical in quantum mechanics, so nothing actually tells you which basis to privilege, and since your choice of privileged basis defines what the physical properties of your system even are, then the physical properties of the system become ambiguous.
A materialist thus has to take one of two approaches.
An conventionalist approach. Admit we can’t know what the actual ontology of the world is, but that doesn’t mean we cannot talk about the world’s ontology. We can speak of it under certain materialist frameworks conventionally, based upon what makes intuitive sense to think about and describe a certain experimental context, but with no claim that this is definitively the true ontology. This does not mean the ontology is subjective: you would still be acknowledging a true one exists, but you just can’t know it.
A non-empirical approach. If you are comfortable with making arguments that go beyond what can directly be observed or detected, then you can justify the choice of a particular basis on grounds other than pure empiricism.
To expand on #2, I said all bases are mathematically symmetrical. This is true, although only Heisenberg’s original formalism of quantum mechanics actually treats them all the same. Schrodinger’s wave mechanics specifically gives privilege in representation to the position basis, because people find this way more intuitive, and so there is a strong non-empirical argument to justify the position basis, which then is how you end up with models like Bohmian mechanics. Relativistic quantum field theory also is intentionally formulated to privilege the configuration of fields, so you could argue for that as the basis as well. (Whether or not particles are “fuzzy” or not depends upon the basis representation chosen as privileged.)
Technically, yes, all bases are mathematically symmetrical, so your choice isn’t empirically detectable, but nobody treats them that way because there are obviously ways to think about the system that make sense and ways that do not. If you represent the system on the energy basis for example, the system could clearly be moving in observable ways yet would be static in the description if the total energy content of the system remains the same.
The positivist hates both #1 and #2, so they argue that we should just give up on the idea that things have definite configurations at all when nobody is looking. But no one has shown how you can make this consistent without descending to idealism. Most physicists either embrace the idealism or resort to a kind of instrumentalism, some claim that it can be made to work, mainly the Many Worlds’ proponents, but none have demonstrated any methodology of making it work; it is always self-contradictory or outright circular.
The conventionalist approach is also great for quantum computing, because it is incredibly rare for anyone to talk about changing basis representations in quantum computing. You pretty much always represent the system on the computational basis throughout; so the conventionalist approach, for a person working with quantum computers, can just take the computational basis of the computer as the privileged basis, and then you can represent it quite trivially easily as just a stochastic process whereby the qubits are just bits that have bit values at all times, and the logic gates are just stochastic perturbations upon those bit values.
The issue was pointed out decades ago by the Soviet physicist Dmitry Blokhintsev, that ψ is quite obviously a description of ensembles of systems. If you have large numbers of systems, the configurations, sampled over many runs of the same experiment, form clear physical patterns. But, given a single run of the experiment, you cannot predict how they will behave, and so then ψ becomes subjective, just referring to your “best guess” as to how they will behave based on previous knowledge of how they behave over an ensemble.
If you promote ψ, in an individual run of an experiment, to a physical object, then you are elevating something subjective to something physical. The consequence is that you end up with a reality that depends upon people’s subjective knowledge of it, and, as a consequence, it leads to a breakdown of objective reality, and there just isn’t any way to avoid that, other than recognizing that it was flawed to begin with to treat ψ as a complete description of an individual system. It is only a complete description of an ensemble of systems.
I’ve written a whole book on this subject in great detail, going into all the mathematics and all the major papers on the subject.
The issue actually comes down to an underdetermination problem in the mathematics. If you claim that the systems have definite states in the real world even when you’re not looking, you have to answer, what those states are. The intuitive solution is to say that the state of the system is in some configuration with non-zero probability in the Born distribution, but then this would imply that every non-communicating observable has a configuration in that probability distribution, which the Kochen-Specker theorem shows leads to an algebraic contradiction, so it cannot possibly be true.
The way out of the Kochen-Specker theorem is to privilege a certain measurement basis. The system has a pre-existing configuration on a particular basis, not all bases at once. When you take this approach, then the mathematics already automatically fixes functions of how the other measurement outcomes arise when you go make a measurement; they end up being emergent properties that only have reality in the physical process of measurement, but that physical process is well-defined and is a function of the system’s pre-existing configuration on the privileged basis.
The issue, however, is that all bases are symmetrical in quantum mechanics, so nothing actually tells you which basis to privilege, and since your choice of privileged basis defines what the physical properties of your system even are, then the physical properties of the system become ambiguous.
A materialist thus has to take one of two approaches.
To expand on #2, I said all bases are mathematically symmetrical. This is true, although only Heisenberg’s original formalism of quantum mechanics actually treats them all the same. Schrodinger’s wave mechanics specifically gives privilege in representation to the position basis, because people find this way more intuitive, and so there is a strong non-empirical argument to justify the position basis, which then is how you end up with models like Bohmian mechanics. Relativistic quantum field theory also is intentionally formulated to privilege the configuration of fields, so you could argue for that as the basis as well. (Whether or not particles are “fuzzy” or not depends upon the basis representation chosen as privileged.)
Technically, yes, all bases are mathematically symmetrical, so your choice isn’t empirically detectable, but nobody treats them that way because there are obviously ways to think about the system that make sense and ways that do not. If you represent the system on the energy basis for example, the system could clearly be moving in observable ways yet would be static in the description if the total energy content of the system remains the same.
The positivist hates both #1 and #2, so they argue that we should just give up on the idea that things have definite configurations at all when nobody is looking. But no one has shown how you can make this consistent without descending to idealism. Most physicists either embrace the idealism or resort to a kind of instrumentalism, some claim that it can be made to work, mainly the Many Worlds’ proponents, but none have demonstrated any methodology of making it work; it is always self-contradictory or outright circular.
The conventionalist approach is also great for quantum computing, because it is incredibly rare for anyone to talk about changing basis representations in quantum computing. You pretty much always represent the system on the computational basis throughout; so the conventionalist approach, for a person working with quantum computers, can just take the computational basis of the computer as the privileged basis, and then you can represent it quite trivially easily as just a stochastic process whereby the qubits are just bits that have bit values at all times, and the logic gates are just stochastic perturbations upon those bit values.
The issue was pointed out decades ago by the Soviet physicist Dmitry Blokhintsev, that ψ is quite obviously a description of ensembles of systems. If you have large numbers of systems, the configurations, sampled over many runs of the same experiment, form clear physical patterns. But, given a single run of the experiment, you cannot predict how they will behave, and so then ψ becomes subjective, just referring to your “best guess” as to how they will behave based on previous knowledge of how they behave over an ensemble.
If you promote ψ, in an individual run of an experiment, to a physical object, then you are elevating something subjective to something physical. The consequence is that you end up with a reality that depends upon people’s subjective knowledge of it, and, as a consequence, it leads to a breakdown of objective reality, and there just isn’t any way to avoid that, other than recognizing that it was flawed to begin with to treat ψ as a complete description of an individual system. It is only a complete description of an ensemble of systems.