Richard wrote:
The words ‘local’ and ‘realism’ are not wishy-washy. You want to blur their meaning! It’s not necessary. Mathematically, I like your ideas.
Hi Richard,
OK. I will tone down. But locality+realism+no_conspiracy is used as an arbitration method when it is too subjective for my liking.
There are a few more points.
1. It is simple to fill in a 2x2 measurement results table for a Bell simulation using a retro-positron method with beams. It starts with one beam of positrons moving backwards in time. That splits into two beams, one goes to Alice and one to Bob. Those researchers make measurements (either +1 or -1) on individual positrons. That makes four polarised beams to keep track of. Those beams are still polarised on getting back to the source and are replaced by four beams of forwards-in-time beams of electrons heading to the other/second researcher. The four electron beams are polarised identically to the positron polarisations. The second researcher make measurements which splits the beams again, from four beams to eight. An individual beam has measurements which all go into one cell of the 2x2 results table. Measurements of positrons are based on unpolarised incoming particles and so the + and - numbers are evenly split. That make four beams of electrons coming from the source with 25% of particles in each beam, on average. These four beams are already polarised on arrival and so their numbers passing and failing the second filter are not 50/50. The Malus's Law formula (adapted for electrons by halving the angle) gives either cos^2 (theta/2) or 1 - cos^2 (theta/2) as the intensity of the beam passing/failing the second detector filter. So the 2x2 cells are filled by these numbers. If the 2x2 cell is then normalised to have total 1, the 2x2 cell will have correlation of - cos theta. Where theta is the difference angles of the two detector settings.
This is so clear that I do not see the worth of making another particle-at-a-time program. I already made a particle-at-a-time simulation for the Malus experiment. My Bell experiment simulation is merely Malus with a time twist.
2. A point about simulations versus real experments. I can see people might be concerned about mystical connections from the Big Bang in a real experiment, but surely this does not apply in a simulation. There are no actual positrons in the simulation travelling backwards in time (subject to correction by computer experts ...). Everything in the simulation is travelling forwards in time. So cannot we rule out suspicious real-world effects during a simulation? And if it can work inside the limited and constrained 'box' of a simulation, then why bother to look for mysticism in the real experiment. (That IMO applies mainly to entanglement, but also to locality.)
3. I see Bell's Theorem as very important in making one look to see how nature works differently from what one expected classically. But I think I now know the answer physically as well as mathematically.
4. In mid 2020 I revised my structure for the electron and photon to make it conform to Malus's Law results. I can now apply my new structure to ask myself 'what is a hidden variable'. As an analogy a hidden variable is like a phase angle. It is like a vector which is continuously changing direction though conforming to a rule. A precession rule or something similar. So the actual direction of the hidden variable depends on time. A measurement at any instant depends on the direction of the hidden variable at that instant. I really have ignored theoretical Bell formulae in my work, but I guess that λ should be replaced by λ(t) to take into account the dynamic nature of the hidden variable. Wiki says that "The idea persisted, however, that the electron in fact has a definite position and spin". I agree that my electron does NOT have a definite static hidden variable direction. 'Spin' is a tricky and distracting word in this context because all electrons have either spin +0.5 or spin -0.5, and these values do not change during time of flight. So 'spin' +0.5 or -0.5 does not help a lot in considering hidden variables. But 'phase' does change during flight and, according to Feynman, variations in phase, at measurements, can lead to interference patterns. If time is taken out of the formulae then what is left is an average value of the hidden variable, i.e. the polarisation angle of the particle. This does not give enough information to determine an individual measurement but does give enough statistical information to determine the average measurement for a group of particles with that polarisation vector. (So the polarisation vector is good enough for Malus's Law and good enough for a retro-positron version of Bell.)
5. You referred me to Gerard t'Hooft.
Slide 5 of his notes at:
http://www.emfcsc.infn.it/issp2017/docs ... tHooft.pdfshows a very interesting analogy with Black Holes. It is mostly beyond my understanding of course. IMO his region III is analogous to our macro space time and his 'local time' is the time of the thermodynamic arrow of time. His region I could be analogous to micro particle time. His region II could correspond to the reversed time direction of antiparticles; he names these time arrows 'distant time'. Just an interesting analogy and possible link between BHs and spacetimes of particles.
Note that if a positron is an electron travelling backwards in time, then the reverse time must be a property of a particle's spacetime and not a property of the particle itself. That is what led me to the importance of particle spacetime and S^3.
Note also that slide #35 has a timelike Moibus strip which is what I am thinking of for my version of S^3. If space is closed with a point at infinity, then time may similarly be closed at infinity.
I had (I have stopped now!) been wondering how to preserve times' arrows if wending one's way round a Moibus timelike strip. Gerard seems (???) to be saying something similar in slide #36
"Demanding that the external observer chooses the point where the Hamilton
density switches sign as being on the horizon, gives us a good practical
definition for the entire Hamiltonian."
Best wishes