Last updated on April 18, 2026
Obviously I dont have enough knowledge and more time to study deeper for static time equations, although I believe static/dynamic time and digital/analog dual layer is promising as this universe’s true time structure and underlying mechnism.
So I list the equations that I can derivate here. And it’s done for me for now, haha, in which
A=(1-2GM/(c^2*r))^(1/2),
B=(1-v^2/c^2)^(1/2),
Fixed exterior coordinate is flat, rectangular and symmetric across all this universe, with Plank length as its vitual metric unit and with one point in this universe as origin.
1) static time potential energy equations
This equation represents gravitational potential energy by frequency of local clock rate which is static time frequeny first in history, which is consisnt with GR’s math.
Supposing the gravitational field potential energy E is proportional to gravity residual frequency f_g of static time excluding object speed, so:
S*m_0*(f1-f2)=E1-E2,
S*m_0*f_g=E.
Supposing maximun gravitational field potential energy when gravity and object speed are 0 is corresponding to f_p, and for E=m_0*c^2*A, so:
S*m_0*f_p=m_0*c^2,
S=c^2/f_p.
So static time gravity residual frequency f_g is:
f_g/f_p=A or f_g=f_p*A.
So static time gravity potential energy is:
E=m_0*c^2*f_g/f_p.
2) static time frequency equations
2.1) static time gravity residual frequency
f_g/f_p=A or f_g=f_p*A.
2.2) static time speed residual frequency
Supposing the flow speed of static time is perpendicular to all 3 space dimensions like an imaginary number, and for an object at gravity=0 with speed V_0 in fixed exterior coordinate, its space speed frequency V_0/d_p, static time speed residual frequency f_v and Planck frequency complay following equation (Pythagora theorem):
f_v^2+(V_0/d_p)^2=f_p^2=(c/d_p)^2 or (f_v*d_p)^2+V_0^2=c^2.
for d_p=c/f_p, so f_v^2=f_p^2-V_0^2*f_p^2/c^2, so:
f_v=f_p*B or f_v/f_p=B.
V_0 is the object speed at gravity 0 in the fixed exterior coordinate.
2.3) static time (total residual) frequency
Supposing gravity and space speed for an object’s static time total residual frequency f_s (which is local clock rate) are independent factors to each other, so:
f_s/f_p=(f_g/f_p)*(f_v/f_p),
f_s=f_p*A*B=f_g*B=f_v*A.
3) light speed observed in fixed exterior coordinates
3.1) light speed change in fixed exterior coorinates
Combining f_v and f_g into total f_s while keeping f_v fixed is like putting an object of speed V_0 (f_v) at gravity 0 to a point of gravity f_g while keeping f_v fixed, then
f_v^2+V_0^2/d_p^2=c^2/d_p^2=f_p^2, multiply A^2 at both sides, then
f_v^2*A^2+(V_0*A)^2/d_p^2=f_p^2*A^2, then
f_s^2+(V_0*f_g/f_p)^2/d_p^2=f_g^2, then
V_s=V_0*f_g/f_p=V_0*A.
V_s is the object speed in fixed exterior coordinate after combining f_v and f_g.
from V_0*f_g/f_p we can see that to combine indepent f_v and f_g into f_s while keeping f_v and f_g fixed, the object speed in fixed exterior coordinate must slow from V_0 to V_s=V_0*f_g/f_p,
or in another word, both sides *A^2 means shrinking normal trangle’s 3 sides by same factor A, and for it’s in fixed exterior coordinates where d_p is fixed, so it must be V_s=V_0*A to shrink V_0 to V_s proportionally.
3.2) light speed observed is independent from light direction and the speeds of emitter, receiver and medium
I propose an understanding for light speed as below.
a) from V_s=V_0*f_g/f_p to V_c=c*f_g/f_p, in which V_c is light speed in fixed exterior coordinates, for this is exactly that light travels between different gravity f_g while keeping its f_v=0 fixed,
or in another way, when gravity=0, V_0^2=c^2=f_p^2*d_p^2, and when gravity is f_g=f_p*A, V_0^2*A^2=f_p^2*A^2*d_p^2, so (V_0*A)^2/d_p^2=f_g^2, which means light speed V_0=c must slow down by factor A in gravity f_g.
b) after emitting, a light wave or photon travel along all possible routes at speed V_c=c*f_g/f_p according to fixed exterior rectangular coordinate, which is independent from speed of emitter, receiver and medium along the certainized light route.
c) the route of a light after emitting is certainized or realized when it’s received by the receiver or observer.
3.3) light travel time duration observed by an observer with f_s=f_p according to local time of the observer is t_x:
t_x=sum(d_p/V_c),
t_x=sum(d_p*f_p/c*f_gr),
t_x=sum(1/f_gr),
t_x=N*mean(1/f_gr),
in which, f_gr is f_g of each space unit of Planck length d_p on the certainized light route,
N is number of space units of Planck length d_p on the certainized light route.
3.4) the light travel time observed by an observer at f_s=f_sl according to the local time of the observer is t_l:
Any local static time duration of an observer corresponds to a universal time duration of underlying dynamic time, so different local time durations of different observers in this universe can correspond to same time duration of dynamic time.
Then in a same universal time duration of dynamic time, the local time duration of an observer is proportional to its local clock rate f_s, so
t_l/t_x=f_sl/f_p
t_l=t_x*f_sl/f_p
t_l=sum(1/f_gr)*f_sl/f_p,
t_l=N*mean(1/f_gr)*(f_sl/f_p).
when the observer’s local f_sl=f_p, the travel time observed is exactly t_l=t_x=sum(1/f_gr).
The light speed V_c observed by an observer of f_s=f_sl according to fixed exterior coordinates:
V_c=sum(d_p)/t_l=N*d_p/(N*f_sl*mean(1/f_gr)/f_p)=c*mean(1/f_g)/f_sl
V_c=c*mean(1/f_gr)/f_sl, so
if f_sl=1/(mean(1/f_gr)), then V_c=c,
if f_sl<1/(mean(1/f_gr)), then V_c>c,
if f_sl>1/(mean(1/f_gr)), then V_c<c.
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