Example 10 Gravitational RedShift (Gravitational Time Dilatation) between an atomic clock at a Ground-Station and an Atomic Clock at the ESA satellite in a Gallileo Orbit at an heigth of 23 222 [m] and at the EUCLID satellite at an distance from Earth of of 1.5 [m] . The differences in the Calculated Gravitational RedShift with “General Relativity” and “Quantum Light Theory” are smaller than an amount of 16 digits beyond the decimal point related to a ground station and the ESA satellite in a Gallileo Orbit and smaller than an amount of 15 digits beyond the decimal point related to a ground station and the EUCLID satellite.
3
10
9
10
References:
46,Equation(73)
ExampleofaSphericalBeamofLight ,propagatingintheradial-direction(r-direction)
withthespeedoflightc=.
1
ϵ0μ0
TheinputfortheElectricFieldIntensity{E(x,y,z,)=ev}andtheMagneticFieldIntensity{H(x,y,z,)=
mv}havebeensubstitutedintheFieldEquationfortheElectromagneticFieldwithinaconstant
Whichcanbewrittenas:
term1=-(InertiaofLight)
1
2
c
∂×
¯
E
¯
Η
∂t
term2=(∇. )(CoulombInteraction)
ε
0
¯
E
¯
E
term3=−×(∇×)(LorentzInteraction)
ε
0
¯
E
¯
E
term4=∇. (CoulombInteraction)
μ
0
¯
Η
¯
Η
term5=−×∇×(LorentzInteraction)
μ
0
¯
Η
¯
Η
term6=-μ( . )ε( . )(ElectromagneticGravitationalInteraction)
1
2
2
ε
¯
E
¯
E
+
2
μ
¯
H
¯
H
¯
g
Equationequals:
term1+term2+term3+term4+term5+term6=0
In[]:=
ϵ0=.
In[]:=
μ0=.
In[]:=
x=.
In[]:=
y=.
In[]:=
z=.
In[]:=
t=.
In[]:=
Get["VectorAnalysis`"]
In[]:=
Get["Calculus`DSolve`"]
Out[]=
$Failed
In[]:=
InverseFunctions->True
Out[]=
InverseFunctionsTrue
In[]:=
Needs["DifferentialEquations`NDSolveProblems`"]
In[]:=
Needs["DifferentialEquations`NDSolveUtilities`"]
In[]:=
Needs["DifferentialEquations`InterpolatingFunctionAnatomy`"]
In[]:=
Get["Calculus`DSolveIntegrals`"]
Out[]=
$Failed
In[]:=
SetCoordinates[Cartesian[x,y,z]]
Out[]=
Cartesian[x,y,z]