Following a recent interesting question about the collapse of the wave function (link at the bottom).
It seems that the wave function is just a mathematical way to give predictions of various outcomes for a quantum system, that can occur with various probabilities...the 'collapse' part seems to be another way of saying that later we'll know which one actually occurred.
Would any answers please correct any misconceptions here...
So given that one outcome occurs, but our best theories can't predict which, we are faced with an 'intrinsic uncertainty' in nature, or with the possibility that there are 'hidden variables' - apparently David Bohm and others have proposed these.
Many physicists e.g. Einstein would prefer not to admit an intrinsic uncertainty, so regarding hidden variables:
Have experiments yet decided whether hidden variable theories (HV) are viable?
Is there a difference between 'knowable' HVs and 'unknowable ones' (in terms of which have been checked by experiment)?
Answers to 1-2) are welcome and any discussion on how deeply the 'intrinsic uncertainty' is believed (at the moment) to be embedded in physics, i.e. are HV theories of any type still actively debated in quantum theory?
A note on the terms 'knowable' and 'unknowable':
Knowable HV: caused by either: An undiscovered particle or quantity that could transmit effects (historically for example, the existence of electric fields were once not known, the neutrino, etc...) or by fine details of the original setup of an experiment.
Unknowable HV. A change to our universe beyond our ability to detect, that however causes one outcome to be preferred, i.e. that provides a reason for the outcome - thus meaning that the 'intrinsic uncertainty' can be avoided.
An example of an UHV is the total mass or charge of our visible universe, our knowledge of these quantities is limited by what happens at the cosmological horizon (e.g. in the next minute more mass and charge may enter our universe) - due to time delay, the knowledge of these quantities can't be known by us for billions of years. More detail on this approach is at the bottom - and there may well be other UHVs that we are not aware of.