Previously I wrote a series of static time field equations before I finally realized that space/interior length stretching of GR’s classic explanation may not be physics truth but a mathematics parallel convenience.
If light stretching space length can be observed by others, space of everywhere of this universe will be stretched to infinite by electromagnetic wave. If light stretching space length can be observed by only light itself and not by others, it’s exactly shrinking and slowing of itself not stretching of space length.
So I rewrite a series of static time field equations for only reality not mathematics.And also I rename some symbols used to avoid confusing and remove some wrong equations.
Below all are in a fixed exterior rectangular grid coordinates with Plank length d_p as basie metric unit, and the fixed exterior coordinates may have any point in this universe as origin.
A=(1-2GM/(c^2*r))^(1/2), is the gravitational factor A used in this work, which is the exact expression from the Schwarzschild solution of General Relativity. This is exact for non-rotating spherical masses. For rotating black holes (Kerr metric), a more complex expression is needed, but the current form already reproduces all tested predictions with excellent accuracy.
B=(1-v^2/c^2)^(1/2), is the space speed factor B used in this work, which is derivated from static time field flow direction perpendicular to all 3 space dimensions.
<1> original static time field potential energy equation
S*m*f_g=G*M*m/r, in Newton scope.
S*m*f_g=m*c^2*A, in GR scope.
S=c^2/f_p.
in which, f_g is static time gravity residual frequency, which is the static time field frequency left or residual at a point with gravity factor A.
<2> static time frequency equations
f_g=f_p*A,
f_v=f_p*B,
f_s=f_p*A*B =f_g*B =f_tv*A =f_g*f_v/f_p,
in which, f_v is static time speed residual frequency, which is the static time frequency left or residual of an object or signal at speed v,
f_s is static time total residual frequency, which is the static time frequency of a object of speed v at a point with gravity factor A,
static time frequency represents the local clock rate or time speed of an object or at a point.
<3> static time shrinking equations
L_g=L_0*A =L_0*f_g/f_p,
L_v=L_0*B=L_0*f_v/f_p,
L_s=L_0*A*B =L_0*f_g*f_v/f_p^2=L_0*f_s/f_p,
in which L_0 is the length of an object at 0 grativity and 0 space speed,
L_g is the length of an object at gravity f_g and 0 speed,
L_v is the length of an object at speed f_v and 0 gravity,
L_s is the length of an object at speed f_v and gravity f_g.
<4> static time slowing equations
V_s=V_g=V_0*A =V_0*f_g/f_p,
in which V_0 is the speed of an object at gravity 0,
V_s and V_g is the speed of an object at gravity f_g.
Why V_s=V_g? Because:
f_v^2+V_0^2/d_p^2=c^2/d_p^2=f_p^2, 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, in which V_0*A= V_0*f_g/f_p=V_g, then
f_s^2+V_g^2/d_p^2=f_g^2,
which is full static time frequency equation including gravity and space speed, so in which V_g=V_s, then
f_s^2+V_s^2/d_p^2=f_g^2.
<5> mass (energy) equations
5.1) object total mass equations
Gemini suggested a set of mass frequency equations which represents the total mass of an object of m_0 at 0 gravity and 0 speed.
m_g=m_0*f_p/f_g =m_0/A,
m_v=m_0*f_p/f_v =m_0/B,
m_s=m_0*f_p^2/(f_g*f_v) = m_0/(A*B).
5.2) object total energy equations
the object total mass equations above equal to object total energy equations below:
E_0=m_0*c^2=S*m_0*f_p,
E_t_g=E_0/A =m_g*c^2,
E_t_v=E_0/B =m_v*c^2,
E_t_s=E_0/(A*B) =m_s*c^2.
E_0 is the total potential energy of an object of m_0 at 0 gravity and 0 speed.
E_t_ means total energy of an object.
<6> Why are there both shrinking and slowing?
Talked with Gemini and Grok to leanr that light deflectin in gravity observed must be explained by two factors together: asymmetric slowing of object/wave which incurs refraction, and asymmetric shrinking of object/wave.
I cannt derivate Length formula directly from my static time frequency equations, but Gemini and Grok suggest an explanation that object length just shrink proportional to f_s/f_p.
So be it!
<7> light speed is independent from light direction and the speeds of emitter, receiver and medium
I propose an understanding for light speed as below.
after emitting, a light wave or photon travel along all possible routes at speed v_c=c*f_s/f_p according to fixed exterior rectangular coordinate, which is independent from speed of emitter, receiver and medium along the certainized light route.
the route of a light after emitting is certainized or realized when it’s received by the receiver or observer.
a) light travel time length between emitter and receiver observed by an observer with f_s=f_p according to fixed exterior coordinates is t_x:
t_x=sum(d_p/v_c),
t_x=sum(d_p*f_p/c*f_sr),
t_x=sum(1/f_sr)=sum(t_sr),
t_x=N*mean(1/f_sr)=N*mean(t_sr),
in which, f_sr is the f_s of each space unit on the certainized light route,
t_sr is the local time unit t_s of each space unit on the certainized light route, wherein t_s=1/f_s and t_p=1/f_p,
N is number of space units on the certainized light route,
sum(1/f_sr)=N*mean(1/f_sr).
b) the light travel time observed by an observer at f_s=f_sl according to the local time of the observer is t_l:
t_l=t_x*f_sl/f_p
t_l=sum(1/f_sr)*f_sl/f_p=(sum(1/f_sr)/N)*N*f_sl/f_p=mean(1/f_sr)*N*f_sl/f_p,
t_l=N*(f_sl/f_p)*mean(1/f_sr)=N*(f_sl/f_p)*mean(t_sr),
when the observer’s local f_s=f_p, the travel time observed is exactly t_l=t_x=sum(1/f_sr).
An observor’s measured light speed v_c according to fixed exterior coordinates:
v_c=sum(d_p)/t_l=N*d_p/(N*f_sl*mean(1/f_sr)/f_p)=c*mean(1/f_sr)/f_sl
v_c=c*mean(1/f_sr)/f_sl, so
if f_sl=1/(mean(1/f_sr)), then v_c=c,
if f_sl<1/(mean(1/f_sr)), then v_c>c,
if f_sl>1/(mean(1/f_sr)), then v_c<c.
<8> GR’s geometry
the nature of GR geometry is mapping/transforming rectangular coordiates into a curve surface coordinates to represent the stretching of interior length of space unit which incurs the distortion of coordinates grid into curved surface.
<9> light deflection in gravity
Gravitational light deflection can be understood entirely through the shrinking and slowing of objects and signals in the fixed exterior rectangular grid coordinates.
There are two factors for light deflection:
a) asymmetric slowing down which incur refraction, which is same as light bending in solution water with layers of different density,
b) asymmetric shrinking, which is like a centipede shorten one side of its body to turn direction.
<10> gravity gradient factor and asymmetric exterior coordinate size shrinking factor for gravity deflection of all mass and energy wave
δθ=(2GM/c^2*b)(1+v^2/c^2) is total formula Grok give out for all mass and energy wave ( electromagnetice wave including light) in a gravitation field, which include two factor: gravity gradient and asymmetric size shrinking in exterior coordinate.
So it’s same for light or photon too, but when v of a mass is far smaller than c the deflection of mass by asymmetric size shrinking in exterior coordinate is unobservable.
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