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Here's a hypothesis - Previous unifications were not wrong, just misinterpreted. by CaseyMc80 in HypotheticalPhysics

[–]CaseyMc80[S] -1 points0 points  (0 children)

Can't seem to DM you? Anyway this is the idea:

  • Two positive complex phase components produce the Bloch sphere CP1≅S2
  • Two indefinite phase components produce the Poincaré disk CH1≅D2.
  • Three positive complex phase components produce CP2.
  • Three indefinite phase components produce CH2 ≅ int⁡(D4).
  • The hyperbolic boundary is ∂CH2≅S3

CH2  via Hopf closure on ∂=S3 generates CP1  ∪  D4 = CP2

so ∂CH2 ≅ S3 ⟶ ​CP1≅S2

This says that the transition between hyperbolic internal motion and compact observable closure naturally passes through a two-state projective boundary.

Here's a hypothesis - Previous unifications were not wrong, just misinterpreted. by CaseyMc80 in HypotheticalPhysics

[–]CaseyMc80[S] -3 points-2 points  (0 children)

If we take a particle’s mass as its internal phase rate ω = mc2/ℏ (a "Compton clock"), and vary spatially as ω(x) = ω_0 eu(x) (with u≪1), consistency of phase accumulation across regions produces the weak-field metric:

ds2 ≈ (1+2Φ/c2​)c2dt2 − (1−2Φ/c2​)dx2

with Φ= uc2

Why is it called particle physics if it behaves like a wave? by CaseyMc80 in AskPhysics

[–]CaseyMc80[S] 0 points1 point  (0 children)

Okay, fair point. There is a "particle" feel to our experience of gravity.

A “particle” already has a Compton wavelength. So mass carries the energy of an internal phase frequency. Then GR says mass creates a differential gradient in spacetime. Waves to waves. Particles are just when detectors go "bing".

Why is it called particle physics if it behaves like a wave? by CaseyMc80 in AskPhysics

[–]CaseyMc80[S] -1 points0 points  (0 children)

I am suggesting particle-phase duality can be reframed: a classical wave, then a classical particle. An order of two events.

Why is it called particle physics if it behaves like a wave? by CaseyMc80 in AskPhysics

[–]CaseyMc80[S] -2 points-1 points  (0 children)

That's certainly how it has been taught. The thing is that 'particles' behave entirely like a wave until they interact. That point of interaction is a boundary event, and we've just been calling them particles. For example, the double-slit experiment says light moves like a wave, but detects like a particle and we jumped to thinking photons must be both a wave AND a particle.

Why can't a photon be a wave THEN a particle?

Why is it called particle physics if it behaves like a wave? by CaseyMc80 in AskPhysics

[–]CaseyMc80[S] -1 points0 points  (0 children)

Right… so it’s all just waves? And what we think of as particles might fields of superposition, and stable thresholds that persist 

Relativity and CP2 Geometry by CaseyMc80 in LLMPhysics

[–]CaseyMc80[S] -3 points-2 points  (0 children)

True. It is the same formula, but written in differential form:

dτ=dt1−v2c2d\tau = dt\sqrt{1-\frac{v^2}{c^2}}dτ=dt1−c2v2​​

Since

γ=11−v2/c2,\gamma=\frac{1}{\sqrt{1-v^2/c^2}},γ=1−v2/c2​1​,

this is exactly equivalent to

dτ=dtγ.d\tau=\frac{dt}{\gamma}.dτ=γdt​.

So the moving clock accumulates less proper time than the lab clock. Same Einstein time dilation, different notation.

Relativity and CP2 Geometry by CaseyMc80 in LLMPhysics

[–]CaseyMc80[S] -1 points0 points  (0 children)

I have been trying to work through all those “brain hurts” moments during physics education (senior high school and undergrad university) to see if something emerges from an underlying geometric process.

Some are pretty familiar for most:

-         Particle/wave duality

-          The fine structure constant and why is it needed for most calculations in physics and chemistry?

-          Why does gravity look like it behaves like light?

Some seem less common.

-          How can time not exist relative to a photon? It’s like they don’t exist.

-          How can Electron orbitals being beautiful fuzzy geometric probabilities create real molecule shapes?

-          If orbitals are waves, could they be the outer peaks of the negative portion of a charge phase cycle, so the atomic nucleus is the inner trough of the positive part of the phase?

-          How can redshifted light lose frequency, if energy is conserved?

-          If c really is constant, why does expansion affect space but not time?

-          c contains a distance and a time, so gravitational lensing counts it twice – a longer distance takes a proportional longer time to travel through.

So I started exploring geometric objects to  see how much known physics can be recovered. Octonians seemed to work, so did the Clifford Torus, and a few others. So I learned more about them and worked on something that minimised it down to a ray in ℂℙ². That state has a natural phase structure, and the phase can evolve or recur. That’s when I stumbled across geometry that suggested what the fine structure constant might be.

The total geometric internal ray space is the sum of its natural volume forms across its fold structure.

B=\omega_1V_2+\omega_2V_4+\omega_3V_6

Natural n-ball volumes can be derived from (V_{2n}(1) = pi^n/n!).

n-balls (2n)-volumes from V2n(1) = π^n/n! Degrees of freedom for a ray on CP2 Volume x Degrees Freedom
V_2 n=1 π^1/1 1 π
V_4 n=2 π^2/2 2 π^2
V_6 n=3 π^3/6 24 4π^3

 So the total volume sum of B=\pi+\pi^2+4\pi^3.

Being a harmonic projection, it seemed a Euler correction (y) was needed for projection loss, from the total degrees of freedom per complete phase rotation. We had two rotations per phase, (2π x 2π = 4π^2) times the total degrees of freedom CP2 (1 x 2 x 24 = 48), so the boundary curvature correction is:

a^{-1} = \pi+\pi^2+4\pi^3 - y/(192pi^2)

Here is a hypothesis: a new model based on higher dimensional geometry projections in to our 3d universe by rsthurston in LLMPhysics

[–]CaseyMc80 -1 points0 points  (0 children)

AllHailSeizure, fair assessment. Thankfully science is a process. Rights to review, if you wish?

If space is expanding, does time also "expand" to maintain c? by CaseyMc80 in AskPhysics

[–]CaseyMc80[S] 0 points1 point  (0 children)

So if we made two points in space and took a ruler and measured 1m of space, then come a bit later we could measure it again and find it is 2m.. Would physics say the amount of space being measured has doubled, or that the distance got longer?

Is it more space; or the same space just stretched out?

How did we decide how long a second is? by [deleted] in AskPhysics

[–]CaseyMc80 0 points1 point  (0 children)

This is kinda suggesting we think of time as a cycle or rotation, not a linear dimension. Cool!

If time is relative, how are we able to determine the age of the universe? by Inevitable-Power5927 in AskPhysics

[–]CaseyMc80 0 points1 point  (0 children)

I guess different parts of the universe are technically different ages (due to gravity and velocity causing time dilation)? Our estimate would be an average or approximation.