Wave Equation

One question that has come to me–if the twist is such a great solution, surely a zillion people before me would have followed this path–why haven’t they? It’s either because it doesn’t work, or because no one has seen it yet as a valid solution. Unfortunately, the odds are rather good that lots of people a whole lot smarter than me have already looked at it and said it doesn’t work. If that’s true, then I’m wasting my time, and anyone’s time who is reading this. But I actually think there’s a small possibility that a field twist as a quantum solution hasn’t been followed through enough. I’ve already posted a lot that shows why it maybe should be taken seriously, but am finding it taxes my abilities and IQ to prove that it is the correct solution to things like photons and electrons. The most important reason that I think it has validity is the clean way it provides a geometric basis for quantization. All particles, whether force-exchange particles like photons or stable particles like electrons, must be quantized as E=hv. And all fields must consist of quantized exchange particles (see QFT). So–this says that the energy of the quantized entity comes in integer multiples, and fields have to be built out of these. The only geometrical transform for this is a modulo function, which can be modeled as, and only as, a rotation that returns to a starting point. In other words, a twist.

So why hasn’t this popped out of all the math of quantum field theory? Why hasn’t there been studies of twists as a logical outcome of the experimental evidence. It’s a relatively simple construct, there’s absolutely no question that every physics researcher and mathematician would have thought of this as a quantum solution. Why do they abandon it? Well, one possibility is that it just plain doesn’t work, and they find it trivial to see why. Science history spends no time or documentation of failed theories.

But I think there’s a possibility there’s another reason why. The history of science is full of cases where the right solution was not seen for a long time because a conceptual bias about the problem blinded researchers to the actual solution. In the case of quantum mechanics, the math is elegant when working with waves. Everything works well, and any solutions that aren’t geometrically obvious from compositions of waves can be derived because linear combinations of waves (Fourier) can produce any analytical, and hence physical, solution. The problem is that many physical solutions require an infinite number of waves to produce, and both quantized particles and twists fall into that category. Waves are infinitely repeating cycles, but quantized particles and twists are localized. A delta function is one of the closest analogs and requires an infinite Fourier composition to produce. Twists are significantly worse–I wouldn’t be surprised if analytical solutions based on waves provide a significant barrier to understanding their value as a solution. But look at the Schroedinger wave equation and Klein-Gordon! Differential equations don’t readily lend themselves to non wave-based solutions, and thus other valid solutions can be extremely difficult to find. Sure, second order equations such as 3D Schroedinger can yield provably limited base vector sets of solutions–but it doesn’t restrict any combination of waves, so all we can say is that whatever solution results must be analytic–a rather large subset in solution space!

All I’m saying here is, I think quantized field twists are an “out of the box (waves) possibility” and deserve a lot of study. There’s a lot of potential for using them to form a basis for the field and particle behavior we see in reality, and the math of QFT is ill suited to working with them.



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