I might be wrong but I think you misinterpret the meaning of Bell's Inequality and relevant experiments.They state that hidden variables (which assumed to be local) are not sufficient. The 'global' hidden variable would be the same as 'determinism' or 'absence of free will'.

Nikolay Pavlov

All photons and electrons have their predetermined quantum energy states. Through polarization process either by optical polarize lens for photon or magnetic field for electron, subject to the polarization strength based on the polarization angle, an energy barrier (for photon) or a threshold energy (for electron) will be established.

In case of optical polarization, for those photons which have higher energy than the energy barrier (established by the polarization angle) will pass through the polarizer and keep the same polarization direction as the polarizer, or otherwise, they will be blocked by the polarizer.

In case of magnetic polarization, for those electrons which have initial energy higher than the threshold energy (established by the polarization angle) will gain the polarization energy (provided by magnetic field) to overcome the energy barrier and flip to the opposite spin direction, or otherwise, they will maintain the original spin status in the new polarization direction.

In both cases, the quantum energy states of photons and electrons are determined by polarization angle. The probability to find the polarization status of the photons and electrons is dependent on the original quantum energy states and polarization angle of the polarization processes (measurements). In other words, there is no "Superposition" and "Schrodinger's cat can only be either alive or dead but not both". "God didn't play dice" after all.

As far as Bell Inequality, it is really meaningless. Not only it can't explain the mechanism of polarization processes, but also the definition and physical meaning of the analysis is questionable. Just like "Superposition", it is another piece of fancy "King's new cloth".

Wikipedia tells us that "Bell's theorem proves that quantum physics is incompatible with local hidden variable theories". What I would add to this statement is that nature is non-local when it comes to the measurement of entangled systems or even the simple case of the absorption of a photon by an electron.

See Appendix 2 here: https://www.academia.edu/5927513/The_Spacetime_Wave_Theory

The Spacetime Wave theory asserts that electrons, neutrons and protons are looped waves in spacetime and in the context of Bell's theorem you could consider the representation of these waves as hidden variables. However, this does not contradict Bell's theorem because nature is non-local.

Data Prerecording of Conference Presentation on the Unification of Physics

Conference Paper THE UNIFICATION OF PHYSICS (Conference Paper)

You might also find the description of the property "spin" contained within the presentation helpful on this topic.

Richard

Richard Lewis

According to Yangton and Yington Theory, any spinning particle with polarization shall have Wave Particle Duality such as photon and electron. Also according to Particle Radiation and Contact Interaction Theory, any traveling particle with the capability of making contact interaction with the same particles in space will form a field such as graviton and electron. However, not all particles can be a wave or to form a field.

According to Yangton and Yington Theory, gravitational force is generated between two gravitons (a string structure based on Wu's Pairs) with side by side contact. Because of this reason, for two distance objects, a graviton particle must first escape from the parent object, then travel to the target object to make a side by side contact, such that the propagation of gravitational force can be fulfilled. This is called “Particle Radiation and Contact Interaction Theory”.

Like a photon emitted from a heat source by absorbing thermal energy to overcome its energy of separation, graviton can also be emitted from an object by absorbing thermal energy to overcome its gravitational force. It is obvious that the amount of the gravitons (M) emitted from the parent object to the target object should be proportional to the total amount of gravitons in the parent object, as is proportional to the mass of the parent object (m1). Also according to the Inverse Square Law, the amount of the gravitons (M) emitted from the parent object to the target object should be inversely proportional to the square of the distance (r) between parent object and target object. Therefore,

M ∞ m1/r2

Furthermore, the total gravitational force (F) generated from side by side contact between the gravitons (M) emitted from the parent object to the target object should be proportional to both the amount of the gravitons (M) emitted from the parent object to the target object and the total amount of the gravitons on the target object which is proportional to the total mass of the target object (m2). Therefore,

F ∞ (m1/r2) m2

As a result, Newton’s Law of Universal Gravitation can thus be represented as follows:

F = G (m1m2/r2)

Where G is the gravitational constant 6.674×1011 N m2kg-2.

Gravitational field is the summation of the graviton vectors (graviton with direction) generated from all the objects in the universe onto a point in space. Therefore, the gravitational field can be represented as follows:

Fg = G (∑ m/r2 S)

Where Fg is gravitational field, G is the gravitational constant 6.674×1011 N m2 kg-2, m is the mass of an object, r is the distance between the object and the unit mass, S is the unit vector in the same direction of the graviton vector generated by the object and ∑ is the summation of m/r2 S of all objects in the universe.

Furthermore, ∑ m/r2 S represents the summation of the graviton vectors emitted from all the objects in the universe onto a point based on Particle Radiation and Contact Interaction Theory. With the linear relationship and the same directions between gravitational field and the summation of graviton vectors at any point in space, gravitational field can be considered as a “repercute” of the distribution of graviton vectors in space.

Similar to gravitational field, the electrical field is defined as the electron vectors applied from all charged particles in the universe onto a point in space. Therefore, based on Particle Radiation and Contact Interaction Theory, electrical field can also be interpreted as a “repercute” of the distribution of electron vectors in space.

As a result, both the gravitational and electrical fields can be derived from Particle Radiation and Contact Interaction Theory with a linear relationship to the distributions of graviton vectors and electron vectors respectively. Therefore, Particle Radiation and Contact Interaction Theory can be considered as the foundation of Quantum Field Theory, Quantum Gravity Theory and Unified Field Theory.

Edward Wu "All photons and electrons have their predetermined quantum energy states"

The quantum energy states arise in e.g. quantum harmonic oscillator. The Bell's inequality describes so-called degenerate state: superposition of two states corresponding to exactly same energy.

Also, the key proof of Bell's inequality is built on fact that there is no really certain 'predetermined' or 'pure' states in degenerate case - e.g. lineraly polarized phton can be described as superposition of 1/sqrt(2) amplitudes of left and right polarized photon or same with +-45 degree degree polarized photons. The requirement for quantum mechanics to work same way in any arbitrary basis producing different superposition is essential for Bell's proof. Basically he explicitly pointed out (using just a few pages of rather simple math) that from information point there is now way to equip each photon with an 'envelope of instructions' aka 'local hidden variables' to independently behave to satisfy quantum mechanics. Therefore we have to accept what Einstein pretty much rejected as 'a spooky action at distance'. Interesting to note - for Bell himself, a dedicated Catholic that was in a way the proof of existence of God .

Nikolay Pavlov

We both agree that all electrons shall occupy an exclusive quantum energy state (predetermined variables). The only difference between us is the entangled electrons.

According to quantum mechanics:

(1) For each entangled electron, both spin up and spin down can coexist.

(2) Upon observation, either spin up or spin down, only one will be revealed at 50% probability.

(3) Once one electron is observed, the other one is guaranteed 100% to have the opposite spin.

In contrast, according to Yangton and Yington Theory:

(1') For each entangled electron, either spin up or spin down, only one (predetermined variables) can exist.

(2') With active measurement such as magnetic polarization, subject to the quantum energy state of the electron and the polarization strength dependent on the angle of polarization, electron can be converted to the opposite spin direction.

(3') In case one entangled electron is flipped in the polarization process, the other entangled electron will also be flipped with the same polarization process and the entanglement will always be maintained.

(2') and (3') of Yangton and Yington Theory can be used nicely to explain (2) and (3) of quantum mechanics. Also, (2') meets the experiment better than (2), especially the 50% probability in (2) totally against the experimental results.

As far as Bell's Inequality, it just makes everything more complicated due to its unclear definition and doubtful presentation. To me, it is wasting time trying to understand what Bell's Inequality really means and what it intends to prove simply because the quantum energy states are different each time through the transformation process (polarization, measurement). They are no longer the same sample space as defined by Set Theory the basis of Inequality.

All photons and electrons have predetermined quantum states (Hidden Variables). During photon polarization and electron magnetic polarization processes, their quantum states (Hidden Variables) can be changed either by adding energy to electron or reducing energy from photon to become a new quantum states (Field Dependent Hidden Variables). For further transformation (polarization processes), according to Principle of Normalization, a normalized quantum energy states can be achieved (Normalized Field Dependent Hidden Variables). Since Bell Inequality based on Set Theory can only be applied on the same sample space, therefore, Bell Inequality applying on the mixed sample spaces (the actual measurement) cannot be used to prove if Hidden Variables or Field Dependent Hidden Variables exist or not. Furthermore, both entangled photons and electrons have the same Hidden Variables except in opposite spin directions. Also under the same polarization processes (measurements), they both gain or lose the same energies and pass through the same threshold energy barriers to get to the same Field Dependent Hidden Variables. Therefore, they are always entangled no matter how far the distance and how fast the time are. Field Dependent Hidden Variables raises a big challenge to Bell’s Inequality, Quantum Superposition and Quantum Entanglement.

Since Bell Inequality based on Set Theory can only be applied on the same sample space, therefore, for polarization experiments applying on the mixed sample spaces (Hidden Variables and Field Dependent Hidden Variables), Bell’s Inequality cannot be used to prove if Hidden Variables exist or not. On the other hand, for Quantum Entanglement experiments applying on the same sample space of Hidden Variables, Bell’s Inequality does obeyed which proves the existence of the Hidden Variables (see attachment). Furthermore, since both entangled photons (and entangled electrons) have the same Hidden Variables except in opposite spin directions. Under the same polarization processes (measurements), they both gain or lose the same energies and pass through the same threshold energy barriers to get to the same Field Dependent Hidden Variables in opposite directions. Therefore, they are always entangled no matter how far the distance and how fast the time are. The existence of Hidden Variables fulfills Bell’s Inequality which raises a big challenge to Quantum Superposition and Quantum Entanglement.

Both photon and electron have wave and particle properties. In Double Slit Interference experiment, particle detector can be used to influence the phase angles of particle waves such that the coherency is disturbed and the interference patterns are diminished or even totally disappeared. However, the interruption of the interference patterns cannot to be used to prove the non-existence of wave property, or even to prove that wave and particle properties cannot coexist at the same time under observation. Therefore, “Complementarity Principle” is not true. In addition, both photon and electron have predetermined quantum energy states (Hidden Variables). In electron spin measurements, energy can be added to electrons through electron polarization process. Subject to the threshold energy, electrons can move to the new quantum energy states (Field Dependent Hidden Variables) either by staying at the same spin mode or flipping of to the opposite spin mode. On the other hand, in photon polarization measurements, energy can be removed from photons through photon polarization process. Subject to the threshold energy, photons can either enter into the new quantum energy states (Field Dependent Hidden Variables) by maintaining the same spin mode or totally blocked by the energy barrier. Even more, through further transformations, both photons and electrons can be transferred to normalized quantum energy states (Normalized Field Dependent Hidden Variables). In Quantum Entanglement experiments, both entangled photons and electrons have the same Hidden Variables except in opposite spin directions. Under the same polarization transformation processes (measurements), they both gain or lose the same energies as passing through the same threshold energy barriers and have the same Field Dependent Hidden Variables except in the opposite spin directions. Therefore, they are always entangled no matter how far the distance and how fast the time are. Bell’s Inequality is based on Set Theory and can only be applied on the same sample space. Therefore, in photon polarization experiments, Bell’s Inequality applying on the mixed sample spaces cannot be used to prove if Hidden Variables exist or not. On the other hand, in Quantum Entanglement experiments, with the right experimental data, Bell’s Inequality applying on the same sample space does approve the existence of the Hidden Variables. As a result, both electron and photon do carry predetermined Hidden Variables, and Schrödinger’s Cat cannot be both alive and dead at the same time. Therefore, “Quantum Superposition” cannot be true. Also, there is no mystery, no surprise and certainly no “Spooky” behavior. Einstein is correct after all.