genesis_eqns.md

Genesis Chronofield Equations

1. Let

$$ \phi_t(\vec{r}, t) $$

be the chronal potential which affects how fast clocks tick.

2. If we define time passage (local proper time) as

$$ \frac{dt}{dx} = \sqrt{1 + \frac{2\phi_t(\vec{r}, t)}{c^2}} $$

then inspired by GR’s Schwarzschild metric:

$$ d\tau = dt \cdot \sqrt{1 - \frac{2GM}{rc^2}} \implies \sqrt{1 + \frac{2\phi_t(\vec{r}, t)}{c^2}} $$

This is another probable interpretation of time change and local proper time.

Upgrade to my proposed formula

I initially thought, that a time change (local to an observer)

$$\Delta t = \phi_t \cdot |(\vec{T} \times \vec{p})|$$

where,

$$\phi_t$$ = chronal potential, a scalar field indicating the intensity of time at a point

$$\vec{T}$$ = Chronal direction vector (direction of "temporal flow")

$$\vec{p}$$ = Momentum vector since time seems to be influenced my both mass and velocity

$$\vec{T} \times \vec{p}$$ = A vector perpendicular to both — akin to an induced "chronal torque"?

I'm trying to put forward the fact that a change in time is induced by a change in both the interaction of the body with the Time vector and its potential (a moving mass)

Here $$\phi_t$$ (chronal potential) is a relative scalar quantity that differs from material to material, I want to imply that where $$\phi_t$$ is greater, it means the mass is dense or very fast and thus time dilates and is slower with respect to it. And if there is a gradient of $$\phi_t$$, we get a chronal vector $$\vec{C} = -\nabla\phi_t$$ So then we get,

$$\Delta t = (-\nabla\phi_t) \cdot |(\vec{T} \times \vec{p})|$$

Which links directly to massive objects altering time flow and that an object parallel to the flow of time would not experience it. The required unit of chronal potential $$\phi_t$$ would be $$\frac{s}{kg \cdot m}$$

If we accept these units for the chronal potential, it means:

Chronal potential is a measure of how time flows per unit of momentum-space displacement.

It inversely scales with mass and position, implying heavier or faster-moving objects dampen the local time flow (sounds heretical to Minkowski and Schwarzschild metrics)

Let chronal field vector

$$\vec{C} = -\nabla\phi_t$$

so it becomes

$$\Delta t = \vec{C} \cdot |(\vec{T} \times \vec{p})|$$

so maybe,

This equation resembles the Lorentz force but for chronodynamics:

$$\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$$

and I'm trying to promote a similar conceptual model where time change is influenced by a potential (like electric field), and also by the interaction of motion and the time field.

Possible Experimental Setup

A Gedankenexperiment (thought experiment) or basis for simulation:

Place ultra-sensitive atomic clocks on supercooled superconducting gyroscopes that rotate in strong magnetic or gravitational fields. If a time-field exists and interacts with angular momentum, there might be a deviation in the clock rate not predicted by GR alone.

Then I will be able to compare $$\Delta t$$ not just by altitude (GR) or speed (SR), but by orientation and momentum direction in relation to a hypothesized temporal field.

Final Notes

My progress beyond this limit requires additional knowledge of advance concepts, both to proceed with mathematical proofs as well as experiments to prove where I was wrong myself. This project will be updated accordingly.