One of the unexpected outcomes from my latest thinking (see previous post, https://wordpress.com/post/agemozphysics.com/1700) was the realization that the wavefunction probabalistic nature of quantum theory has a rational basis. Quantum behavior is all about probability amplitudes, and a good question is “why do we work with probabilities rather than the math of wave propagation”. The famous quote attributed to Einstein “God does not play dice” is referencing his denial that probability could be intrinsic to nature. I think there’s a good way to understand why it is intrinsic to us as observers.
In that previous post, I showed how thinking of elementary point source particles with constant mass and charge of particles has to mean that they complete rotations in zero time, but the background state of the rotation enforces quantization (for example, constant mass for all electrons) and rotates at the quantum wave rate of the particle, thus forming interference wave patterns in its neighborhood. As I stated in that post, there are a lot of interesting results from this line of thought, and one of them has profound implications for quantum field theory.
Quantum Field Theory, or QFT, is used to evaluate the wavefunction probability outcomes for various particle interactions. There are two best-known mathematically equivalent methodologies–the path-integral approach and the operator approach. The former is essentially a normalized multiplication of all LaGrange path computation probabilities that result from a source set of particles going to a destination set of particles. The second approach is a matrix (operator) method of calculating the probability of a given destination outcome. The path-integral approach integrates the propagator times the action (a LaGrange minimum energy path computation) for each possible path from source to destination. The terms in the action must include all possible interaction behaviors such as a source particle going straight to a destination particle, or perhaps doing a photon exchange with an adjacent particle before becoming a destination particle, or even interacting with a spontaneously form particle-antiparticle pair before becoming a destination particle.
There are generally an infinite number of these possible action terms for a given interaction, so convergence to a valid result becomes a major issue in performing the calculation. Fortunately, charged interactions act with diminishing force over distance, so the computation perturbs the results with diminishing effect for each added action term. And, a lot of paths by symmetry often cancel out, simplifying the number of significant actions. This isn’t the case for quarks where the strong force does not diminish with distance, so the approximations and assumptions are much harder to compute. In any event, analytically computing QFT outcomes is severely limited to some very basic cases. The recent muon wobble calculations are done iteratively with computed lattice methods or something similar.
But let’s back up a bit. There’s a really interesting clue for understanding elementary particles here that really starts to make a lot of sense when you look at particle interactions having a zero-time rotation rate. This idea means that the rotation rate is infinite, we can never know what the current phase is–so when a detector intercepts the particle, to us as observers, it is completely random whether it absorbs and resolves to a observable state. It’s a nice way to explain why we have to work with probability amplitudes in quantum theory rather than just mathematically time propagating an initial state wave. Entangled particles are a special case and I describe my ideas how this works in previous posts.
But let’s take a look at how we compute path integrals in QFT. One action case that is really interesting to think about is the case where a source particle goes straight to a destination particle, but a nearby particle-antiparticle pair will form and perturb the result without directly interacting via photons. It doesn’t trouble me that this happens, but what surprises me is that it doesn’t matter where the particle-antiparticle pair is! It doesn’t matter how far apart the pair is, nor does it matter how long the pair stays apart! The computation is the same, it does not vary the result. This is so interesting to me because it strongly points to what does matter. A clue is provided by the operator methodology–there will be a multiplicand which includes a creation operator followed shortly by an annihilation operator. The thing that matters is solely the creation (and annihilation), just as I found in my thinking described in the previous post.
So what does this mean? Here’s what I think: since I have worked out that elementary particles and fields must be background state twists in a 4D spacetime (R3 + T), ( see this discussed in previous posts ad nauseum, such as https://wordpress.com/post/agemozphysics.com/1580). I see where the quantization must come from, the thing that affects the QFT probability computation: the only thing that affects the probability of a particular path is whether a twist splits into two or more twists–or recombines into one twist. It doesn’t matter where this happens, it doesn’t matter how long the split is maintained–it only matters that now there is a different twist configuration than there was prior to the interaction. Once it splits, then a new set of waves is added in to the system that affects the overall path probability independent of location or time of the split.
Now, using this idea, can I work with this infinite base rotation rate with a quantized background state rotation rate (forming field waves) to come up with a scheme that gives us a basis for QFT? This post is already too long, I’ll save that for an upcoming post. where I will describe my analysis of a very specific case.
Agemoz
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