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Dynamically stable structures



 

It is likely that the structures an initial disturbance breaks into will be somewhat analogous to attractors in chaos theory. These attractors will be dynamically stable structures that pass through similar sequences of states even if they are slightly perturbed. Such structures will be transformed to different structures or `attractors' if they are perturbed sufficiently. These structures have a form of wave-particle duality. They are extended fields that transform as structural units. It is the `structural integrity' of these `attractors' that may explain the multi-particle wave function. These structures can physically overlap. In doing so they loose their individual identities. The relationship between the observation of a particle to earlier observations of particles in a multi-particle system does not require any continuity in the existence of these particles. Particles are not indivisible structures. They are the focal point and mechanism through which the wave function interacts and reveals its presence.

It is plausible to expect such a system will continually be resolving itself into stable structures. Reversibility and absolute time symmetry put constraints on what forms of evolution are possible and what structures can maintain stability. These may be reflected in macroscopic laws like the conservation laws that predict violations of Bell's inequality. Perhaps we get the correlations because there is an enormously complex process of converging to a stable state consistent with these structural conservation laws. It is plausible that at the distances of the existing experiments the most probable way this can be accomplished is through correlations between observations of the singlet state particles.

In this model isolated particles are dynamically stable structures. Multi-particle systems involve the complex dynamics of a nonlinear wave function that at times and over limited volumes approximates the behavior of an isolated particle. Since the existing theory only describes the statistical behavior of this wave function it is of limited use in gaining insight into the detailed behavior of this physical wave function.

Consider a particle that emits two photons. In the existing model there is no event of particle emission. There is a wave function that gives the probability of detecting either photon at any distance from the source. Once one of the photons is detected the other is isolated to a comparatively small region. Prior to detecting either photon there is a large uncertainty in the position of both photons. There is even uncertainty as to whether the particle decay occurred and the photons exist. The existing model gives no idea of what is actually happening. It only allows us to compute the probability that we will make certain observations. Some will argue that nothing is happening except what we observe. In the model I am proposing there is an objective process involving the emission of two photons. There is no instant of photon emission. The photons may start to appear many times and be re-absorbed. At some point the process will become irreversible and the photons in the form of two extended wave function structures will move apart.

An observation of either photon localizes both photons in the existing theory. In my theory there are two localized structures but we do not know the location of these structures until an observation is made. For the most part localization effects do not allow discrimination between my proposal and the standard theory because of the way the existing theory models the localization of entangled particles after an observation. However in an experiment in which a single particle can diffuse over an indefinitely large volume there is a difference in the two theories that is in principle experimentally detectable. Standard quantum mechanics puts no limit on the distance over which simultaneous interference effects from a single particle may be observed. There will be an absolute fixed limit to this in the class of theories I am proposing although I cannot quantify what that limit will be.

Perhaps part of what is so confusing in quantum mechanics is that it combines classical probability where new information allows us to `collapse' our model of reality in accord with an observation and a physical wave function which determines the probability that there will be a physical nonlinear transformation with a focal point at a given location. The existing theory's failure to discriminate between these two dramatically different kinds of probability may be one reason why it seems to defy conventional notions of causality.

Whether a particular transformation can complete depends in part on the conservation laws. Unless there is enough energy to support the new structure and unless symmetry and other constraints are met a transformation may start to occur but never complete. One can expect that such incomplete transformations happen and reverse themselves far more frequently than do complete transformations. The transformations that continually start and reverse could be a physical realization of Feynman diagrams  that describe all the possible interactions in a system.

A transformation is a process of converging to stable state consistent with the conservation laws. The information that determines the outcome of this process includes not only the averaged or smoothed wave function of the existing theory but also the minute details that result from discretization. This additional hidden information is not necessarily tied to the particles involved or to their wave functions in the existing model. It can be anywhere in the light cone of the transformation process.

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