I was thinking about the problems with local or non local and hidden variables and no hidden variable models in Quantum Mechanics (QM) and came up with a solution to Bell’s inequalities that is both non local and hidden variables or could be non local and no hidden variables too. Could we have our cake and eat it?
What do you think am I being dense or is this possible?
Warning maths heavy quiggles and conjectures ahead, enter at your own peril.
/ramble
If two particles are measured they will be in a spin up or down state that is equally probable ie in spin up or down state: in either non-correlated spin up and spin down or d,d or u,u state though when they are entangled then the result is that at the other end although there original state is u,d d,u or d,d or u,u or vise-a-versa they will always be equally likely to be either exactly correlated u,u or d,d or u,d d,u or vise a versa which results in the non local theory being correct as the initial state bears no relation to the final state of measured entangled particles. In fact it should correlate at about >=.333… or 1/3 in the measured states. Which is Bell’s inequality.
Qm predicts the state will be correlated at about .25% or cos(120/2) so it violates Bell’s inequalities, and experiment agrees with this?
This leads to the conclusion that one particles state may effect the other when it is measured called a non local event or by Einstein spooky action at a distance.
Is that clear so far?
What if it doesn’t matter what the initial state is and we can work out a final state solution that agrees with QMs 1/4 outcome?
I think you can if you assume there is a 50% chance of any one state occurring before entanglement and that once entanglement happens measuring one particle may effect another. Surely this is just 1/2 of all possible states before the entanglement and then 2/8 of all possible states after entanglement according to QM, in this case either way whatever we measure the initial states to be we can predict the final states because it is 1 of 8 and applying the maths we have 1/2 for initial state and 1/8 of final state also, so it doesn’t matter what the final state is, it can be predicted by the initial state to be 1 in 8. Thus there is non locality and hidden variables, it’s just we can’t have our cake and eat it. We have to either have 1/3 preserved, bells inequality or cos(120)=1/2 preserved. Surely though given these assumptions we can in actual fact have our cake and eat it, and non local and hidden but implied variables are perfectly logical within such a framework.
Just an Idle thought about the Alice and Bob outcomes in Bell’s do you think I’m on to something or just talking arse?
en.wikipedia.org/wiki/Quantum_entanglement
en.wikipedia.org/wiki/Bell%27s_theorem
Isn’t it simply a matter of choosing the possible mathematical orientations, and then simply applying the results to derive a 1/8 and cos(120) or 1/4 result? Instead of a >=.333… result or in fact we can have either even though one is not experimentally valid.
(Quantum prediction in detail: When observations at an angle of θ are made on two entangled particles, the predicted correlation is cosθ. The correlation is equal to the length of the projection of the particle’s vector onto his measurement vector; by trigonometry, cosθ. θ is 45°, and cosθ is
, where they are 135° and 
, but this last is taken in negative in the agreed scoring system, so the overall score is (; 0.707.)
or +/- 1/sqrt{2} is preserved and predictable. If we take these assumptions of variables into account at 1/2 for the initial state and =>.250 or cos(120)/2 or =1/4 for the probability rather than Bell’s inequality of =>.333… or 1/3 of the end state.
/ramble
Merry Xmas by the way, hows it going y’all?
Bell’s with easy math, or easyish:
drchinese.com/David/Bell_The … y_Math.htm
By the way I doubt this works or is valid but humour me. 