Imagine you have a machine that flicks a classical coin and then makes either one wavefunction or another based on the coin toss. Your ordinary ignorance of the coin toss, and the quantum stuff with the wavefunction can be rolled together into an object called a density matrix.
There is a one-to-one mapping between density matrices and Wigner functions. So, in fact there are zero redundant parameters when using Wigner functions. In this sense they do one-better than wavefunctions, where the global phase of the universe is a redundant variable. (Density matrices also don’t have global phase.)
That is not to say there are no issues at all with assuming that Wigner functions are ontologically fundamental. For one, while Wigner functions work great for continuous variables (eg. position, momentum), Wigner functions for discrete variables (eg. Qubits, or spin) are a mess. The normal approach can only deal with discrete systems in a prime number of dimensions (IE a particle with 3 possible spin states is fine, but 6 is not.). If the number of dimensions is not prime weird extra tricks are needed.
A second issue is that the Wigner function, being equivalent to a density matrix, combines both quantum stuff and the ignorance of the observer into one object. But the ignorance of the observer should be left behind if we were trying to raise it to being ontologically fundamental, which would require some change.
Another issue with “ontologising” the Wigner function is that you need some kind of idea of what those negatives “really mean”. I spent some time thinking about “If the many worlds interpretation comes from ontologising the wavefunction, what comes from doing that to the Wigner function?” a few years ago. I never got anywhere.
Another issue with “ontologising” the Wigner function is that you need some kind of idea of what those negatives “really mean”. I spent some time thinking about “If the many worlds interpretation comes from ontologising the wavefunction, what comes from doing that to the Wigner function?” a few years ago. I never got anywhere.
Wouldn’t it also be many worlds, just with a richer set of worlds? Because with wavefunctions, your basis has to pick between conjugate pairs of variables, so your “worlds” can’t e.g. have both positions and momentums, whereas Wigner functions tensor the conjugate pairs together, so their worlds contain both positions and momentums in one.
Imagine you have a machine that flicks a classical coin and then makes either one wavefunction or another based on the coin toss. Your ordinary ignorance of the coin toss, and the quantum stuff with the wavefunction can be rolled together into an object called a density matrix.
There is a one-to-one mapping between density matrices and Wigner functions. So, in fact there are zero redundant parameters when using Wigner functions. In this sense they do one-better than wavefunctions, where the global phase of the universe is a redundant variable. (Density matrices also don’t have global phase.)
That is not to say there are no issues at all with assuming that Wigner functions are ontologically fundamental. For one, while Wigner functions work great for continuous variables (eg. position, momentum), Wigner functions for discrete variables (eg. Qubits, or spin) are a mess. The normal approach can only deal with discrete systems in a prime number of dimensions (IE a particle with 3 possible spin states is fine, but 6 is not.). If the number of dimensions is not prime weird extra tricks are needed.
A second issue is that the Wigner function, being equivalent to a density matrix, combines both quantum stuff and the ignorance of the observer into one object. But the ignorance of the observer should be left behind if we were trying to raise it to being ontologically fundamental, which would require some change.
Another issue with “ontologising” the Wigner function is that you need some kind of idea of what those negatives “really mean”. I spent some time thinking about “If the many worlds interpretation comes from ontologising the wavefunction, what comes from doing that to the Wigner function?” a few years ago. I never got anywhere.
Wouldn’t it also be many worlds, just with a richer set of worlds? Because with wavefunctions, your basis has to pick between conjugate pairs of variables, so your “worlds” can’t e.g. have both positions and momentums, whereas Wigner functions tensor the conjugate pairs together, so their worlds contain both positions and momentums in one.