Energy-Momentum Distortion and Rest-Mass Closure

What connects special relativity, Schwarzschild gravity, rest mass, and the quantum phase of matter?

This paper proposes a mechanism-level answer: spacetime distortion is determined by energy-momentum, and the orientation of that distortion is determined by the orientation of the energy-momentum.

In the static spherical case, rest energy appears through its scalar monopole projection and produces radial Schwarzschild distortion.

In the local moving case, directed momentum-energy produces Lorentz distortion.

Free fall from rest at infinity gives the exact bridge between them:

χGR(r) = √(1 − rs/r)

χSR(v) = √(1 − v²/c²)

v(r)²/c² = rs/r

therefore:

χSR(v(r)) = χGR(r)

The paper then asks the next natural question: if directed energy-momentum produces directed distortion, how does rest energy mc² appear externally as an all-direction radial field?

The proposed answer is that rest mass is a closed internal Schrödinger-Compton phase mode. The rest-energy mode has the stationary quantum phase:

ψC(τ) = ψ0 exp(−iωCτ)

with

ωC = mc²/ℏ

Using the reduced Compton wavelength:

λ̄C = ℏ/(mc)

one obtains:

ωC = c/λ̄C

and therefore:

E0 = ℏωC = mc²

The closed internal phase mode carries local internal momentum, but its closed-path average cancels net external linear momentum. What remains externally is scalar rest mass and a radial gravitational source.

The paper also connects this rest-mass closure to the Planck scale. With:

rg = Gm/c²

and

λ̄C = ℏ/(mc)

their ratio is

rg/λ̄C = (m/mP)²

Thus the Planck mass is the exact scale where gravitational radius and reduced Compton wavelength meet.

Ordinary observed masses are interpreted as Compton refresh-rate fractions of that closure scale:

m = mP · ωC(m)/ωP

Finally, the paper formulates a phenomenological moving-source test ansatz.

A moving source carries both its radial rest-energy field and an additional directed momentum-energy contribution, producing a radial-plus-directed anisotropic geometry.

This gives a possible observational arena in moving lenses, matter-current lensing, gravitomagnetic systems, relativistic jets, compact binaries, and waveform corrections.