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Unified Gravity and Electromagnetism

By M. Pajuhaan

Unified Gravity and Electromagnetism

For a century we've been "unifying" forces by adding things. Maxwell glued electricity + magnetism into one field. Einstein added time to space and made 4-D spacetime. Kaluza-Klein added a 5th dimension. Yang-Mills, the Standard Model, string theory... all stack new symmetries, new dimensions, new Lagrangian terms on top of each other and then call it a unified picture.

But in all those constructions, gravity and electromagnetism are still different objects that just happen to coexist in the same action. You write

GR term + EM term + matter term, and the "unification" is: they sit in the same integral!!

No one has really answered the microscopic question:

What is the same thing that both gravity and electromagnetism are talking about?

In the Relator framework I'm working on, I'm not adding extra fields. I'm changing the starting point.

- The wavefunction lives on a two-space C ⊕ ℝ³ -- an internal complex "generator" space C and ordinary 3-space ℝ³.

- Phase evolution everywhere obeys a single kinematic lock

- Rω = c

- Everything moves at the speed of light, but part of the motion is internal (in C) and part of it winds through physical space (in ℝ³).

From this one lock you can define a slowdown parameter D = (ω_R3 / ω)² that measures how much of the phase budget is spent on motion in space instead of internal rotation.

Here is the key:

- In weak gravity, the same D reproduces Lorentz time dilation, gravitational redshift, Shapiro delay, and the Einstein light-deflection angle δ = 4GM/(bc²) -- without ever curving spacetime, just by slowing the internal phase clock in a Newtonian potential.

- In the electromagnetic sector, the same D shows up on the matching shell of an electron and gives the shift in its internal phase rate that we usually call the g-factor correction.

Same slowdown functional, two "phenomena": GR-like gravity and QED-like self-energy.

Now add entropy to the story.

On the internal C-plane, I don't put a point particle. I put a maximum-entropy Gaussian sheet of energy dots -- the unique rotationally symmetric distribution that gives the right spin and magnetic moment when you enforce Rω = c. Its width σ is fixed as σ = R/√π by that entropy + kinematics, not by hand.

That Gaussian sheet is the source kernel.

From that one kernel, you can do two independent closures:

- A vacuum-in-volume closure in ℝ³ (a 1/R shell term versus R³ vacuum load, scaled only by the Planck length ℓᴾ) → gives you the electron mass with no fit parameters.

- A tension closure on the same locked ring in C → gives you the same mass again from a different channel (string-like tension vs EM self-reaction) and can be inverted to read off G from (mₑ, α).

And separately, the same shell geometry + lock gives you a closed, parameter-free equation for α that matches experiment at sub-ppt level, again without inserting e, ℏ, c as numerical inputs into the closure.

So:

- α is fixed by a geometric balance between a Coulomb channel and a transverse "Λ-channel" on the shell.

- mₑ is fixed by balancing 1/R terms against R³ (or R) terms built from the same Gaussian kernel and ℓᴾ.

- G can be inferred back from the same formulas instead of being fed in.

Gravity and electromagnetism are no longer two unrelated terms. They are two ways the same entropic kernel talks to the same phase clock:

- Gravity: "slow the clock because mass distorts how the internal phase can distribute itself in a potential" → time dilation, redshift, light bending arise from D in a Newtonian φ(r), not from a separate curved metric.

- Electromagnetism: "slow the clock because the charged Gaussian sheet drags its own vector field on the shell" → Coulomb law, α, g-2, and lepton structure arise from the scalar + vector channels of exactly the same geometry.

No extra dimensions. No new gauge group bolted on top. No separate "entropic gravity" ansatz that ignores charge. Just one microscopic object -- the Relator kernel on C with Rω = c -- and a single slowdown functional D that shows up in both what we call "GR effects" and what we call "QED effects."

I'm not claiming I have a finished theory of everything. I'm not "adding gravity to electromagnetism" in the usual marketing sense.

What I am saying is:

In this framework, for the first time (as far as I can see), the same microscopic source kernel and the same phase-slowdown functional generate both Coulomb and Newton behaviour with their couplings emerging, instead of being written as two separate fields with matching 1/r² powers.

If that picture is right, then "unified gravity and electromagnetism" doesn't mean writing two Lagrangians in the same PDF. It means:

Curvature, gauge fields, and charge are all shadows of one constraint Rω = c acting on a single entropic kernel in C ⊕ ℝ³.

And that's a very different kind of unification.

Sources manuscripts:

One Kernel Behind Gravity and Electromagnetism

Rω=c (Main Paper)

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