Full static time frequency equation: f_total=f_∞*(1-2GM/(c^2 * r))^(1/2)*(1-(v/c)^2)^(1/2) from f^2+(v/d)^2=(f_∞)^2=(c/d)^2

Last updated on March 23, 2026

Gemini asked me why local clock rate slow when an object becomes faster when I showed it my posts yesterday, and I just figure it out in a way that complies with the static time potentinal energy equation.

Years ago, I guessed that local clock speed of an object becoming slower when object speed become faster is for the speed of object and the speed of time are like two vectors perpendicular to each other which are two legs of a right triangle, and the hypotenuse of the right triangle is a constant.

This idea is partially right, for, yes, the hypotenuse of the right triangle is a constant, but the speed of object and speed of local clock or time are not speed but shall be frequency as according to static time potential energy field theory and equation. The speed of object can be transformed to the frequency of the object traveling through the basic length of space which is Planck length d that I use below.

{PS: I was not accurate here, the two legs of the right triangle can be the speed of object and local clock/time, in whic the speed of object can be the space speed, and accordingly the local clock/time speed can be f*d, which I got later from Gemini’s transformation of my f^2+(v/d)^2=(c/d)^2 to (f*d)^2+v^2=c^2.}

For space speed/unit length = frequency of space speed, so I have equation as below:

f^2+(v/d)^2=(f_∞)^2=(c/d)^2,
f is static time field wave frequecy of a point or an object which represents the local clock/time speed of the point or the object,
v is the speed of the point or object,
d is Planck length,
c is light speed,
f_∞ is frequency of static time field wave at a point with 0 gravitational field strength.

For the flowing of static time field is perpendicular to all three space dimensions like an imaginary number, so I suppose that the frequency of static time field “f” is perpendicular to the frequency of space speed of the point or object “v/d”.

So f^2+(v/d)^2=(f_∞)^2=(c/d)^2, in which

I set f_∞=c/d, for a photon have 0 local clock/time speed, so if v=c, then f=0 which mean 0 local clock/time speed,

if v=0, then f=f_∞ which means local clock speed of the point or object with 0 space speed is maximum,

then through simple steps I got: f/f_∞=(1-(v/c)^2)^(1/2).

GROK contributes the following steps:

Then I paste my post above to Grok, and let Grok check and gave me combination of this speed factor equation and last mass factor equation under General Relativity according to the post above and my previous posts, and the Grok gave me which I copy here:

f_grav = f_∞ √(1 − 2GM/(c² r)),
f_vel = f_∞ √(1 − v²/c²),
f_total = f_∞ × √(1 − 2GM/(c² r)) × √(1 − v_local²/c²),
f_∞=c/d ≈ 1.855 × 10⁴³ Hz — it is the well-known Planck frequency.

I’d like to rewrite above below:
f_g=f_∞*(1-2GM/(c^2 * r))^(1/2),
f_v=f_∞*(1-(v/c)^2)^(1/2),
f_total=f_∞*(1-2GM/(c^2 * r))^(1/2)*(1-(v/c)^2)^(1/2).