Archive for January, 2009

why 3D+T?

January 15, 2009

I had a wonderful insight that takes the twist quantization to a marvelous level: It explains why there has to be three dimensions plus time. In my previous post I began trying to mathematically describe some of the thinking work I have done, especially in supporting the proposition of twists as a way to obtain quantization, and the unitary phase wave model to explain entanglement (entanglement and Bell’s theorem show that quantum theory cannot be local, and thus is not causal in every aspect. I proposed that if particles are a group wave Fourier composed of unitary but phase adjusted complex waves, the constraints satisfy quantum mechanics). By adding the requirement that a single quantum particle such as a photon is a twist such that the twisting material must return to the original orientation, the E=hv quantization is geometrically realizable.

I had a great insight–I was trying to think of modeling the ring approach for particles with these constraints in Mathematica. I have been working in 1D, and have been asking how an electron could absorb a sufficient energy photon such that it is destroyed into two high energy photons. In my view of how particles and photons work, there are two stable states, straight line quantized twists, and circular quantized twists (recognizing that other particle types are other geometric combinations of twists. Soo–I thought I’ll work in 2D to model particle ring behavior. But then I quickly realized, this cant work–the working view requires that rings intercept photons, which means that a third dimension has to exist. 1D allows photons, 2D allows rings, and 3D allows conversion between rings (mass) and energy (photons), with T being required for describing sequences of events. Hence in order to have energy exchanges and absorption/emission in the ring model, it is necessary to have the 3D+T. I visualized a photon capture by an electron as an arrow through the middle of a circle target, the ring.

A bit of an aside here… I read a bit of Hofstadter’s book “I am a Strange Loop”, and saw a description how physicists have abandoned the various permutations on Bohr’s atom, that is, the various forms of the semiclassical model of the atom and electron. I guess I have to be honest with you and say, yes, I’m more or less going down this rejected path, but with some important distinctions–first and foremost, I am building what looks like a semiclassical electron (a ring) but within a non-local scheme using twists to enforce quantization. Well, dear reader, if there are any of you out there–there it is–that description of my work is a truth here, and you’ll have to decide if I’m flogging a long dead horse or using the semiclassical model as a stepping stone to real truths about our existence.

OK, with that said, let’s go back to that arrow penetrating a circle. When I create a Mathematica model, the circle has its size because the twists only exist if the start of the circle matches the twist orientation of the end of the circle. The same is true for the linear version–the start of a forward moving twist must match the end, and thus enforces a quantization since any partial twist is not allowed to exist. The critical question is–so far my model uses a linear sum of waves to build particles and photons. How can a circle be a stable state? I realized, because of the same reason–there is a system of a pair of twists such that if they didnt move in a circle, the twists would not exist on their own–they would have to be HALF twists!!! It’s sort of like an energy well problem–assuming impassable walls, there are no solutions that exist that have low energy particles escaping–the lowest energy state is to stay in the well. There is no solution to the ring that provides a full twist linear particle and yet conserves momentum. But shoot a sufficient energy particle through the center, and all of a sudden, there is energy and momentum so that two full twists (photons resulting from the annihilation of the electron) can form.

The key now is to find the mathematical description of twists such that the quantization of twists can be enforced within a Schroedinger wave equation.

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Unitary Phase Wave Solution

January 7, 2009

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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