Crackpot Physics: Things I Expect are the Same
There are some things my interpretations of physics lead me to believe are the same; in some cases, they’re things I figured out must exist before I learned that they already had a name.
If matter is interpreted as a waveform, and velocity and acceleration are also waveforms, then Rindler Coordinates should be identical to the waveform for acceleration. That is, if you apply a transformation to the waveform of matter to accelerate it, this waveform will be identical to the Rindler Coordinates arising from the acceleration of that matter.
Given this, the Abraham-Lorentz-Dirac-Langevin equation should be isomorphic to a Kaluza-Klein interpretation of Rindler Coordinates. The “retroactive” / “pathological” cases of the equation, in this interpretation, arise naturally as a result of the non-discrete nature of jerk.
The waveform of acceleration should likewise be identical to a waveform description of spacetime curvature itself. That is, if we treat spacetime curvature as a wave, then, considering a planet and an object falling into that planet, then the acceleration of the particle falling into the planet is equivalent to the transformation of the falling object’s spacetime curvature (its waveform) when the spacetime curvature of the planet (its waveform) is “applied”. Likewise, the falling object is accelerating the planet - and in a certain sense this acceleration is relative, once we imagine how the waveforms interact on an individual particle basis.
That last bit may be unintuitive. So, let us consider waveforms in terms of their wavelength. Gravitational curvature shortens wavelength - imagine a “planet” composed of five particles. The falling object’s wave shortens the wave of all five particles - but when we then apply each particle’s wave to each other particle’s wave, they shorten each other further. I expect acceleration to be more relative than it is currently interpreted to be. (However, I do expect a difference in jerk!)
I believe I have previously commented that I expect that the stress-energy distribution (which I sometimes call the mass-energy distribution for reasons) to be equivalent to the probability distribution. What's possibly more interesting there is that, if this is the case, particles are interacting long before we observe the interaction - I expect some of the more counterintuitive results in quantum physics may flow out of this. This behavior arises because the particles don’t have a meaningful location - they occupy the entire universe, what we think of as their location is merely the area where their waveform is most dense.
So, if we think of an accelerating particle, I think it’s worth noticing that the acceleration isn’t uniform. Most of the time, this is fine - and sometimes the waveform is so strongly divided as to become, in effect, two distinct waveforms. There aren’t too many things that can split a wave in spacetime itself, but a singularity could do it; thus, at the root of all non-composite particles (leptons, probably gluons) are singularities.
If we consider temperature, it is scale-relative; it is the degree to which the scales below the scale under consideration are not fully stable / fully (locally) entropic. Temperature is a measurement of the amount of change occurring at scales below the scale under consideration. Entropy, then, is also scale-relative, and the smaller the scale, the more rapidly it approaches completion. An Einstein-Bose condensate is, then, I expect, identical to the state of sufficiently small particles, whose local entropy approached maximum in the first few seconds of the universe. These sufficiently small particles, SSPs for short, then, like macroscopic matter, only exhibit quantum mechanical behavior, as we understand it, when their local temperature is sufficiently low; introduce enough energy, say, through a particle accelerator, and I expect quantum mechanics to break down at their scale. (The actual timescale involved is so small I somewhat doubt we can actually observe this, however.)
It perhaps goes without saying that I think all forces are identical, given that I expect them to all be described by an equation similar to sin(ln(x))/x.
One thing I -don’t- expect to be identical: I don’t expect “gravity gravitates” to be identical to negative mass binding. In a 1/x^2 gravity regime, this mostly doesn’t matter; it matters a lot to a unified field theory, like sin(ln(x))/x, where the behavior of the field varies with distance. Curvature means that gravity wells are “bigger on the inside” - a bowl has more surface area than a plate. Compare a plate with a six inch radius, to a plate with a bowlike depression in the center with a six inch radius; measuring three inches from the center across the surface of these two objects, and, for the flat plate, the three inches reaches halfway from the center to the radius; it does not reach as far with the bowllike depression.
This means that, if we suppose the unified field theory switches from an attractive to a repulsive phase at 10^6 meters in flat space, a sufficiently massive object can reduce this to 10^5 meters, because the other 90% of the distance is crossing curvature. (If the logarithmic period of the unified field theory is ~10^6, as opposed to the ~10^12 I personally expect, this has some explanatory power re:the surface temperature of the sun. Gravity is super-weak there.)
This also implies, with a little bit of math, that hydrogen atoms might around a meter across, measured from the inside. How close this is to equating the mass of a hydrogen atom to the vacuum energy of empty space is a somewhat fascinating question, and one I think, with a full accounting, might be quite illuminating.
(If all mass and energy in the universe is spacetime curvature - that is, geometry - then it is not, at the core of principles, either mass or energy that is conserved, it is spacetime itself.)
Also mentioned before: The interior and exterior of a singularity. If you handle curvature as rotation, I think this becomes more intuitive.
Likewise, I expect “forward” and “backward” in time, as time is conceptualized in relativity, are functionally identical in terms of how we humans conceptualize time (but have some ramifications in terms of physics - like rotating one direction versus rotating in another). Distance and time are more straightforwardly identical.
Electrical charge and matter/antimatter. It is possibly contentious to argue that, if we take protons to be matter, then electrons are antimatter - but really, why?
There are some other things which I think I’ve covered or at least hinted at, such as that gravitic waves are identical to electromagnetic waves, possibly with the exception of shape/orientation. But that’s probably enough of this nonsense for now.