Hi Sorry I haven't posted for a while (over 2 years) I have not been as focused as I should have been so apologies. I hope you are all surviving the COVID lock down about which the least said the better and the sooner it is over the best for all of us.
I found myself reviewing a book on the Foundations of quantum mechanics for Amazon which is fine as far as it goes but I do think it is fundamentally flawed
The book is
https://link.springer.com/book/10.1007/978-3-319-65867-4
and you can download it for free for now via the springer website which is really helpful anyway here are my thoughts on the book
On the whole this is a pretty good survey of the foundations of quantum mechanics and the alleged problems associated with it's Interpretation and the ways out of it. However it is arguable that all one needs to interpret quantum mechanics successsfully are the Born Rule and the link between the eigenvalues of the Schrodinger equation and the energy levels of the system under consideration
If the Born rule is taken seriously, then it implies that the solution to Schrodinger's equation, the so called wave function is in effect the square root of a probability density function or probability amplitude. However unlike most square roots of a probability density functions, in some cases this may be a complex function and one can only get a measurable quantity by taking the modulus squared of the solution to Schrodinger's equation. If there is more than one possibility then to get the overall probability for a given situation one must add theprobability amplitudes for the two or more possibilities together before taking the modulus squared of the wavefunction to get the overall probability density function for the situation. As these can be complex functions then there is interference between the two or more possibilities and this interference is seen in many quantum systems. All of this is explained (or described) in Feynman's lectures on quantum mechanics, which surprisingly the author does not mention.
The author does a good job in describing the ignorance interpretation of Born, Einstein and Schrodinger which essentially claims that the wave function is not a physical entity but more a reflection of possible outcomes on measurement. He also goes onto show problems with interpreting the wave function as something physical. However for reasons which he does not really clarify goes onto reject the ignorance interpretation. This is despite the fact that it avoids all the problems with the collapse of the wavefunction, if taken literally as a physical phenomenon and one does not need to invoke spooky action at a distance to explain the violation of the Bell inequalities. Indeed the latter half of the book is the most disappointing, having shown the problems with interpreting the wave function as a physical entity he then embraces a literal interpretation of Bohm's version including the rather tendentious claim that in situations such as the Aspect experiment, really does involve a causal influence from one part of the system to another at speeds faster than the speed of light.
This is not really plausible despite the claims of many people in the popular literature. From the ignorance interpretation, the explanation is really quite simple. Prior to making a measurement observer A will have a 50% of measuring a photons or electrons spin in one direction but does not know which, so his wave function is constructed in such a way to reflect this 50% chance. However after his measurement he will know that his spin is in one direction, and he instanteanously knows that another observer will measure the spin of the other particle to be in the opposite direction. But until B makes his or her measurement B will not know the outcome of his measurement/ There is no signalling, the other particles spin was set at the moment of emission due to the law of conservation of angular momentum and to deny otherwise is to make a mockery of the conservation of angular momentum which plays such a major part in understanding particle physics today. As there are no hidden variables A or B will never know on a given measurement what he or she will measure, only that if a sufficient number of measurements are made 50% of the time A will measure the spins to be up and 50% of the time they will down and vice versa for B, It does puzzle me greatly that this simple solution is claimed to be ruled out by Bell's analysis by many books including this one. But does this interpretation of the wave function for situations actually violate the quantum mechanical predictions. of course not as it is using the wave function that makes the correct prediction.
Looking at the assumptions behind the proof of Bell's inquality as many people do, doesn't shed any light on why the quantum mechanical explanation works as we know Bell is analysing the phenomenon in a classical manner. Despite the overblown rhetoric by Bell and others, all he managed to show was that the joint probability distribution for the particles spins could not be separated into a product of the probability distributions of the individual particles spins. But it is well known in statistics that if a probability distribution for a multivariable system cannot be factorised into a product of the individual variables probability distribution functions then the variables are not independent. But we know this for the particles spin components as the total spin must obey the conservation of angular momentum. If there were signalling as Bell claims why doesn't any signalling (a Green's function say) term appear in the actual maths which predicts the measured correlation.
Bell himself at the end of his 1964 paper claimed to have shown that it is only if one wishes to go beyond a purely statistical intepretation of quantum mechanics then superluminal signalling must be involved in situations such as the Aspect experiment. This may or may not be true, however if one wishes to avoid invoking superluminal signalling then one is stuck with a statistical interpretation to which there has been no experimental refutation
For this reason I can only give the book 3 stars despite the fact that it is extremely well written and probably is one of the most accessible accounts of the various positions informing the current debate today
I am currently working on completion of my calculation of neutrino proton scattering which was the final piece of the jigsaw in establishing the quark model and I will hopefully publish my results by the end of June. Even though no one has yet liberated a quark the results from these experriments carried out in the early 1970's gave evidence that quarks had fractional charge which is really quite amazing.
Also I have some thoughts on the two slit experiment which I will publish soon. One of the things that most accounts miss is that the characteristic interference pattern is in the far field, However in the near field there is no interference, thus the idea that a photon or electron passes through both slits simultaneously is clearly incorrect.
In the mean time keep sane
