Unitary Phase Wave Solution

Well, back from a good holiday vacation–and now I have a new (legitimate!) copy of Mathematica 7, my favorite playground, a gift courtesy of my son who works at Wolfram! I like it already!

The foundation of a lot of my thinking in the last 6 months has been due to the logical deduction that quantum mechanics, in particular quantum entanglement, logically implies that quantum particles have a noncausal wave phase that has an integer number of twists, the cause of the quantization of energy, momentum, and so on. Since the interference effects of various quantum experiments are non-causal, but all momentum derived characteristics are causal, the implication is that Fourier construction of particles is built on a continuum of waves where the phase information is noncausal but the group wave construction of a particle is causal (limited by the speed of light). Since Fourier compositions have two degrees of freedom, phase and amplitude, the amplitude component has to be unitary in order for twists to truly cause quantization, so the logical conclusion is that the universe can be analyzed as a 3D + T sum of unitary complex valued waves, such that a change in phase affects the entire wave instantly.

In this system, all existence at any point in time is defined solely by the phase values for each frequency. Adding the quantization constraint points to an additional requirement that the quantum particle must twist such that the entry and exit along the axis are in the real plane (thus forcing a fixed energy in the twist). I further postulate that electrons and other particles of mass result from geometrical constructions of these twists.

All this has been discussed at length, but now I want to mathematically detail the implications of the unitary noncausal phase wave model.

First, I will describe some implications that can be shown just by looking at the 1D model. Let’s localize a particle as a delta function, and Fourier compose into a set of frequency components: (and I will leave off the time component for now)

Coeff(k) = Integral(e^i 2Pi (k x) * delta(x0) dx) = e^(i 2Pi (k(x0)))

This shows that each wave coefficient is a unitary complex value (our system of unitary complex waves) and that to create a particle from nothing, all we have to do is set the phase of each wave frequency to k(x0–that is, each wave will get a coefficient that is linear to k*x0. Note that any random setting for phase will not yield any particles (f(random phase) = 0), since Integral(e^(i 2Pi (x + random_phase)dx over all x = 0. But a particle will emerge if the phases linearly follow the frequency.

Now with this, can we show how laws of conservation and the speed of light might emerge for such a particle construction? Well, conservation of the particle momentum and mass will result if the phase(k) has constraints on how it can change. If we move the particle, the x0(t) value gets a delta x added to it, which translates to a multiplier e^(i 2Pi (theta t – k(delta x))). This will have the effect of rotating all of the phase components about the real axis, but does not change the relative distribution of phases.

What does it mean to add a quantity to the phase that is linear to the coefficient frequency?


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