Sin(ln(c1*r)*c2) may nicely explain pretty much everything. It is compatible with the nuclear force and gravity, albeit it is difficult to make it line up perfectly without some ad-hoc adjustments. Dunno how classical the behavior ends up being; the equation doesn't exactly imply the existence of particles. Trying to find some "natural" coefficients; in particular I think c2 has a natural coefficient, just damned if I can figure out the geometries.

If my geometric understanding is correct, which I put low probability on, I think it handles the electromagnetic forces as well. Quantum behavior ends up being a weird mix of Pilot Wave and perturbation, though.

(Well, more MWI than Pilot Wave, given that it doesn't have particles.)

To get the rest of physics I have to make Lorentz Contraction cause motion rather than the other way around, though. And it becomes a sort of asymmetric wave which behaves, in certain situations, like mass, which is just the amplitude of the sin(ln(r)) equation.

I think c2 can be figured out using a combination of the definition "A negative linear dimension x- corresponding to x+ can be translated to and from x+ by x-= -1/x+", and figuring out an equivalent definition for a negative closed dimension, which I think probably takes the form of a logarithmic spiral in complex dimensions. I think c2 might be related, directly or inversely, to the constant b of that logarithmic spiral, which I think might arise naturally.

@Adirian Maybe I should read the writeup on your blog about your ideas back in May. Then I may enourage or discourage you to create more writeups, depending on how much I appreciate it...

Wow, I see you already produced a new writeup, so no need for encouragement or disencouragement anymore. Maybe I should really read them.

The basic idea has remained fairly consistent, but switching to a geometric expression has simplified things a bit

A c2 of 1/pi^3 is, for the right c1, quite consistent with gravity. I don't like that, though, the period coefficient is way too high, on the order of P(n)=P(n-1)*10^73. I want a coefficient of 10^12, maybe as high as 10^15, because values in that range are consistent with things other than gravity. Unfortunately, using simple distance, coefficients that low aren't consistent with gravity on a solar system scale.

I think gravity might work if I use relativistic distances, but I'm struggling a bit to figure out what the relativistic distances would be using that equation.

A coefficient of 10^12 results in stars being repulsive up to about 10^18m, and then attractive again up to 10^24, which (might) explain the galaxy rotation curve. Lower coefficients might also explain the Kuiper Cliff; if gravity starts falling off more rapidly beyond a certain distance, objects beyond that distance, accelerated by the nearer objects' orbital speeds, would be thrown out of the solar system.

But 10^12 (c2 of around 2/pi^2) results in far too high orbital speeds for inner planets, and far too low for outer planets. Also Earth should repel itself apart. So if such low coefficients work, they would have to work by significantly higher relativistic distances being at play.

There is an assumption here that might be missing from GR, that relativistic distance matters, but I don't think the equation is self-interfering. Which... Hrm. Imagine a point mass m1 which doubles the distance to some point P, from D to 2D; m1 still treats P as D meters away. Add a second point mass m2 to the same area, however, and it will treat P as being 2D away (and now m1 will have a different distance as well, which changes the distance for m2, and so on)

Figuring out an equation to describe that effect is... mildly mind-melting.

If you want to play with it, for c2=1/pi^3, a c1 of 4*10^-10 works pretty well; multiply all of that by the mass of the sun, then by 122417 (c3, some kind of equivalent to G), and you get a decent approximation of planetary orbital speeds.

Doesn't work great for anything but solar system orbital speeds, though.

It's more a kind of proof to myself that you could approximate an inverse square relationship

Hrm. Also, entropy might be the noise left by the pilot waves/MWI. Alternatively stated, entropy is the detritus left by the recombination of universes, and represents divergent histories.

It increases because the universe converges on stable configurations, and thus the histories compatible with a given macrostate are likewise increasing. From an anthropic perspective, anyways.

Physics worth more to EU economy than retail and financial services, says study / sciencebusiness

Putting probabilities first. How Hilbert space generates and constrains them / arxiv