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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:

  1. Have experiments yet decided whether hidden variable theories (HV) are viable?

  2. 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.

The Uncertainty Principle and Mach’s principle

When will a wave function collapse if the observer was only a camera and the video was watched later in time?

John Hunter
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    have you read through this https://en.wikipedia.org/wiki/Hidden-variable_theory ? You are asking too many questions for this site. – anna v Jun 19 '21 at 10:40
  • Thanks. Did you mean the 3 questions were too many, answer to no 3. would be interesting. Or did you mean too many questions in general, the answer to question ratio is about 10:1 – John Hunter Jun 19 '21 at 11:16
  • usually questions with questions inside are asked to keep to one question. This question is too much like philosophy for me. – anna v Jun 19 '21 at 11:28
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    @anna v Ok, maybe someone else would find it suited them. If you have any recommendations on how to edit, please post them. – John Hunter Jun 19 '21 at 11:31
  • It's been edited and reduced to one question with two parts – John Hunter Jun 19 '21 at 11:36
  • The uncertainty comes from the randomness. The term hidden variable has become too mystical or mysterious and discussed to the point that it seems impossible. A hidden variable could just be one extra property of a particle. For instance if you include frequency to a linear equation you can correlate to photons to produce the predictions of quantum mechanics. – Bill Alsept Jun 21 '21 at 16:16
  • @ Bill Alsept Many physicists who prefer hidden variables are trying to avoid the randomness. When you say one extra property of a particle, would that count as a local hidden variable theory? Have those now been ruled out by experiment? Do you prefer an apparent randomness caused by an extra unseen property of the particle or pair of particles? – John Hunter Jun 21 '21 at 17:10
  • @JohnHunter Randomness comes with photons whether or not you consider other variables. When I say extra property of a particle I specifically mean frequency of a photon. All the no go theories including John Bell’s do not include an oscillating frequency. This changes everything when considering the linear Coincidence for two photons. They only compare polarization. For example in a multiple polarizer experiment when you add photon frequency to the equation you can derive cos2theta and match all quantum mechanical predictions. – Bill Alsept Jun 21 '21 at 17:43

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The answer to your question 1. is yes. Experiments on quantum entanglement ruled out a class of theories called Local Hidden Variable theories. In these theories, the particles' variables have definite values before measurement, and measurement simply reveals their value. Bell's theorem shows that this class of theories have an upper-bound to the strength of correlations in certain types of experiments, and these upper bounds are now experimentally violated in labs everywhere.

I can't answer your question 2, as I don't really understand the distinction you are trying to make.

Hidden Variable theories are still under investigation, the most notorious being Bohmian Mechanics, where the hidden variables are the positions of the particles. Note that by Bell's theorem, hidden variable theories must have some form of non-locality.

Andrea
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  • Thankyou, you’ve clarified the case for local HV, “the particles' ...have definite values before...”. Before trying to discuss the ‘knowable’ term would you clarify something about ‘local’ and ‘non-local’. Does local refer to pre-existing conditions inside the particle and non local to conditions external to the particle? E.g. say the Sun’s magnetic field varies rapidly and seemingly randomly , if the exact value of the field at earth, at the time of measurement of the particle, influences the outcome. Would this be a non-local cause, or do we also need a ‘faster than light’ effect too? – John Hunter Jun 23 '21 at 08:20
  • there are many, many, many definitions of "locality" in the literature, all partially overlapping. In the case of LHV, local means that the measurements performed on one particles do not affect the values of the variables of the other particle. – Andrea Jun 23 '21 at 17:00
  • Thanks, have experiments ruled out the possibility that some outside fluctuating influence, perhaps one that is hard to measure , so we are not aware of, can influence the particles. So each particle might have some opposite quantity and when measured, interaction of this quantity with the outside fluctuating influence gives a value (e.g. for spin) dependent on the value of the outside influence at the time of measurement? Then 'action at a distance' - or a 'non local effect' may not be required? – John Hunter Jun 23 '21 at 22:09
  • When the measurements on the particles are done at spacelike separated events, this “outside influence” at one event would need to depend on the measurement settings at the other event. You cannot strictly rule out such mechanisms, but they are non-local in the sense that they violate relativistic causality. – Andrea Jun 23 '21 at 23:34
  • Thanks, some final things. If the particles were spacelike separated, say 500m apart and measurements done within 1micro second, but the fluctuating outside influence varied more slowly, e.g a timescale of milliseconds - and both particles were influenced - then it might appear that causality was violated, but the HV would be an external one. It would be knowable if it was in principle possible to measure the outside influence and unknowable if it wasn't possible to measure it, as in the e.g. about cosmological horizon in the main question. Have both these been ruled out experimentally? – John Hunter Jun 24 '21 at 18:55
  • @JohnHunter This “outside influence” would not allow a violation of causality. – Andrea Jun 25 '21 at 09:47
  • What was meant was this: If local HV are ruled out, some people might think that we are left with non-local effects i.e. "measurements performed on one particles [will] affect the values of the variables of the other particle" [at a speed faster than light]. The rapidly fluctuating "outside influence" was suggested as a way to avoid the 'faster then light conclusion', yet still provide a reason for the apparent randomness. – John Hunter Jun 25 '21 at 12:54
  • I don’t see how that helps: it’s the correlations between the two measurements that challenge local causality, not the the randomness! – Andrea Jun 25 '21 at 20:39
  • Here is a thought experiment: Two swimmers A and B in a sea, they meet and agree that if they are at the peak of a wave, A holds up a blue flag and B holds up a red flag. If at a trough A holds up red and B holds up blue. They then swim 5m apart and don’t communicate. Fast waves of wavelength 200m come and we take photos (the measurements) every few minutes. We would record an apparent correlation in the results of the flags. – John Hunter Jun 26 '21 at 09:00
  • @JohnHunter This is exactly the kind of situation that is ruled out by the violation of the Bell inequalities. I recommend you read some literature. May I recommend Bananaworld (for a long read, meant for wide audience) or https://arxiv.org/abs/1503.06413 for a lucid review. – Andrea Jun 26 '21 at 09:35
  • Thankyou, will read. In that case you've answered most things. Has the case also been considered (and ruled out by violation of Bell inequalities), where the 'sea wave' in the comments is not a knowable or measurable quantity, but 'unknowable' as described in the cosmological example in main question. i.e. a fluctuating influence that could in principle provide a reason for the correlations, but that has a value that could never be known or measured by us? – John Hunter Jun 26 '21 at 10:20
  • @JohnHunter Yes. That is the Hidden in the Hidden variable. I wasn’t too clear in my answer.. the LHV does not need to be a property of the particles themselves, it can be also something like you “outside influences”. The LHV can be anything that behaves causally and classically. Often it is denoted with the symbol $\lambda$. Happy reading! – Andrea Jun 27 '21 at 09:19