There are strong arguments against many concepts of hidden variables, mainly because of the requirement that each must exist simultaneous. The hidden variable problem may be avoided if one pictures the variables as taking on the same energy as measuring apparatus and, therefore, system under observation. Observables that don't appear to bear causal relation to phenomena of wave-particle duality will inherrently appear without explanation as to why the particle may have such properties; apart from the assumption that those properties are degenerate. Human perception is reciprocal, as may be observed via Fourier transform. The brain has the power to separate certain properties of an object, in order to give the object clear definition and by observing how it interacts with the environment. One would be more likely to define objects as having no relation to hidden variables, thus enforcing their degeneracy. The closer one looks for an observable cause, the more the cause mimics the energy of the environment. It's unlikely that a physical degeneration of hidden variables occur as the result of observation made on the particle. More likely, the brain cannot function without its means of defining a system. On that note, it is possible that hidden variables occur in nature, for which we are unable to express in detail; as is a function of the mind that does not translate into the perceptual domain via Fourier transform. The harmonic oscillator is used to describe many quantum processes. In particular, it is useful in Group Theory, also as an aid to predict levels of degeneracy for symmetry problems. A major part of Group Theory is to highlight the symmetry of systems, by which the classification of molecules may be achieved. If the integral is zero, then the magnitude has symmetry element - and therefore identity. One can easily imagine that on a deeper level of quantum, an object too small to be detected by current methods undergo degeneracy to the extent that the overall energy of the system mimics that of the classical apparatus. An analogy would be to consider the way in which one defines an object. Although one knows that the object contains properties that are not readily observable, because such properties cannot be attributed to the object at the macroscopic level, their existence may nevertheless be perceived as taking on the same value as the object that may readily be observed; for example, one would not normally look at the sea and define it as a bunch of H2o particles. Phenomena, such as position and momenta may be the result of a decreased availability of space. In Group Theory, the relation between symmetry and degeneracy is that, while degeneracy of a system may be predicted, the hamiltonian does not change in the symmetry operation; the hamiltonian remains invariant under the relavant point group. The invariance of H, combined with inverse operation R-1 R, yeilds HR 'l' i= ER 'l' i(note to reader, no cut and paste eq). Where 'l' iis the eigenfunction of the hamiltonian and E is the corresponding eigenvalue. The reason Group Theory may be used as an aid to describe the existence of hidden variables such as position and momenta is that to do so, does not violate the law of conservation of energy. The observable that yeilds the properties one wishes to describe is therefore unchanged. A full definition of such phenomenae - along those lines -- might entail a concept of which the brain may never be capable; and in any case, the identity of the system used to describe the duality would be lost. However, since position and momenta are properties of objects, Group Theory is a subtle way to highlight the posibility of hidden variables. But does this offer any explanation to degeneration of hidden variables at all, since so far this article only highlights the fact that they remain unobservable? The explanation lies within the possibility that hidden variables maintain the identity of objects a) through a decrease in the amount of space, b) in the way that they simultaneously exist (that is one can't see them), in order to conserve the identity of physical objects that an observer wishes to gain more knowledge of. This equation also represents the system by which an observer may only observe aspects of an object that are readily observable.
Do you differentiate degeneration of hidden variables from decoherence. It is an interesting article and offers some ideas in support of the idea that QM is incomplete, in that we do not yet recognize or understand some level of order where hidden action supports wave particle duality at a foundational level below the fundamental level of the standard particle model.
Only in the sense that one would gain an improved knowledge of the particle. However, an answer solely regarding the degeneracy of hidden variables would be too speculative, at least at this stage, without any kind of statistical aggregate.
This article takes a non-local approach to the subject of hidden variables with local correlations. It is also attributing to the Pilot-wave theory, or the de Broglie-Bohm theory. Local, in the sense that hidden variables have no identity until distributed in a way that the identity itself is that of the observable system. The non-local aspects are that the observable system pertains to that of the entire universe. Observation of the system causes degeneracy with regards to hidden variables. While hidden variables cause degeneracy in the opposing manner: in that they re-inforce identity of the system. Here, position and momenta exist simultaneous. But complete knowledge of their distribution in space is as difficult to ascertain as a complete knowledge of the observable system. In the combined local/non-local theory of degeneracy of hidden variables - space essentially is the determistic distribution, which has correlations to the rest of the universe. The configuration of the universe therefore sets deterministic distribution of coined terms such as position and momenta and may help to describe the process by which the universe was created - because at certain levels the variables take on a constant value, in the way that they create identity of a system. This may be translated to the macro environment, where the identity of systems is nothing less than a description for one's surroundings. However, the idea of simultaneous existing position and momenta is a concept one may not grasp. The movement of space corresponds to momenta. The interlocking of space at certain levels corresponds to position. Space, by very nature is a thing that falls into itself to the point of almost ubiquity.
Identity of objects is created (remember we have only the vastness of space), by infinitesimal interlocking that create more and more gravity.
Quantum entanglement: action at a distance. Quantum entanglement is the phenomenon of a pair or group of particles that at arbitrarily large distances cannot be described independent of the other. Albert Einstein called this "spooky action at a distance." The application of Group Theory to the phenomena of hidden variables may help to avoid contradicton with the theory of relativity. In the "degeneracy of hidden variables", the observer forces a degeneracy, while hidden variables reinforce their purpose. This action preserves the speed of light. Problems arise which concern the light barrier when arbitrarily large distances are considered. Because the entangled pair make the whole system, the identity of the object cannot be reinforced and this gives the impression of "spooky action at a distance." Take the identity of molecules as an example. The fact that the system has identity, highlights the acknoldgement of a system - having been scrutinized by an observer and stubborbly resisted by the hidden variables. When one considers why action at a distance occurs, hidden variables cannot complete the task of reinforcing identity of the system; no light occurs between a coupled state at such large distance because identity of the system has not been acknowledged. That the particle properties are reflections of each other implies it is a statistical aggregate of a complete system as may be observed in a vector model. To question action at a distance is perhaps equal to question whether the moon exists in three dimensions because we only get to see one zide.
Those who believe quantum theory is complete will no doubt find evidence that a hidden variables theory is not needed through Werner Heisenberg's matrix mechanics. However, one wishing to relate Albert Einstein's relativity theory - with quantum theory will disagree. For some, the question is not merely that if one can describe reality with abstract means, then is an alternative picture needed - that a complete theory may account for? But rather, how Einstein's theory of light can be neglected in favour of quantum phenomena. Group theory teaches the importance of the ability to define systems. Those systems however, can only be accounted for with a theory of light. But if such a system was to violate that theory, then where would be the axioms to suggest an identity for the system? E=mc2 may account for the assumption that there are hidden forces at work. It accounts for how a system may be identified and may account for the reason why coupled particles at arbitrarily large distance cannot be comprehended due to light speed. On the other hand, one can combine Heisenberg and Einstein's theory if one assumes that a system may accurately be described either way, but only if a proportional change in distance is equal to a proportional change in speed.
If one considers the difference between the expansion of a ball, and two smaller objects moving in the opposite direction from the centre to stop at the radius of the ball, in the same time that it took for the ball to expand, then what is the difference between position and momentum? Likewise, if the distance of a particle is so great, then what is the difference between its position and momentum, compared to an imaginary second particle that is used to make a distance?
The degeneracy of hidden variables idea cannot logically be disproved via a measure of physical qualities. This is because the observables they describe do not propose a violation of the speed of light. Position and momenta are the fundamental of everything, it would always allow for experimental matches or mismatches. A local hidden variables theory however, may find itself open to scrutiny, if it offers no way to understand how systems in states of chaos may be ordered through the nature of light and conservation of energy. There is a limit to how one may describe an observable system and one of those being Bell's theorem. A local/non local theory of hidden variables is less likely to be intercepted by such argument, because the identity of the system is left unchanged. An argument about determinism is not relavent then; one would get deterministic results half the time and indeterministic results the other half. " There is no real difference between determinism and indeterminism if a system that is determined does not imply that the act of determining that system was done under the same rule. There is no real difference between determinism and indeterminism if neither it implies it was not order that prevented indeterminism in the first place. Most likely, the brain creates order from a preconception that there was indeed any chaos."
A less arbitrary interpretation of hidden variables puts more focus on the local aspect, while maintaining a non-local framework. Suppose the actual entanglement with regards to coupled states is with the photons; and the 'spooky action at a distance' is the result of a coincidental relation between the particles, because each particle is entangled with the same photon.Suppose we have an object and a local particle on that object has a positive relation to one photon. A particle incident on the opposite side (non-local) would have a negative relation to the same photon. So, likeness between both particles has less to do with either particle, but their individual photon entanglement. In order to fulfil the obligation of non-locality, the object must take up the whole of space. The photon must therefore be part of the object. Each particle, local and non-local, is entangled with the photon. Each particle shares some relation to each of the other particles, but do not all enter into a coupled state. The local half of the object has particles at a distance the length of the observable. Because we can see both of these particles, their distance apart is finite; and though they behave as a coupled state, we can not use them in this interpretation. They do not occupy the whole of space and therefore belong to a local theory. Here, a coupled pair consists of one particle at a local side and the other at a non-local side. Say, one local particle has a 1 relation to a photon and the incident particle -1. A coupled pair. Whereas a different non-local particle could be -100 and though still entangled with the photon and related to the local particle, does not share the coupled state. If one observes a point, then the entanglement of the point and photon are related by the angle at which the photon allows us to observe the point and the angle by which the point is seen. The validity of this interpretation can be shown thus: the use of local and non-local particles mean that we can rotate the object and perform the above task again. By not using local coupled states, I am able to show how we may view the object in 3d. Concerning degeneracy, the same principle. The difference between describing entanglement of particles, rather than entanglement of particle and photon is that one could not thus describe a local and non-local system, because photons would be classed as separate from the system, therefore the system could not take up the whole of space.
