Copyright Carl Janssen 2025
Not Up to date going to start a new draft that is shorter, may contain errors I am not going to bother to correct
Use of the term Aether
I am not claiming light propagates through Aether but old names for models used the term Aether, I might not be using the correct names for the models. In my model the medium of propagation for light is assumed to be whatever mixture of chemical light is propagating through instead of aether or a perfect vacuum.
Frequency of light vs Frequency of emission of light
If a light signal of a single photon with a frequency of 5 Hertz is emitted once per second this is not the same as if light signal of a single photon with a frequency of 1 Hertz that is emitted 5 times per second.
I am not using the frequency of light in calculations but the frequency at which light signals are emitted. I am calculating the frequency of reception of light signals in other words how often light signals are received and not the frequency of a photon in each light signal that is received.
Right hand, Left Hand, and Symmetric Calculation of periods
Calculations will use period instead of frequency because period is either to use for calculations. The reciprocal of the period can be used to compare with other calculations that use frequency if necessary.
Rght and Left terminology is chosen based on the naming of right, symmetric and left derivatives and right and hand left limits and not the right and left spatial directions
Pe = Period of emision
MTe = Middle Time of emisson
RTe = Right Time of emission
LTe = Left time of emssion
MTr = Middle Time of Reception
RTr = Right time of reception
LTr = Left time of reception
RPr = Right period of reception
SPr = Symmetirc Period of reception
LPr = Left period period of reception
RPm = Right Period Multiplier
SPm = Symmetric Period Multiplier
LPm = Left Period Multiplier
Solve for Time of reception as a function of Time of emission
RTe = MTe + Pe
LTe = MTe - Pe
RPr = RTr - MTr
SPr = ( RTr - LTr ) / 2
RPm = RPr / Pe
SPm = SPr / Pe
LPm = LPr / Pe
Units
Units will be converted to seconds and meters to various powers
Assuming the medoum is isotropic with respect to light speed
From a reference frame in which the source and medium are both stationary and the medium is of uniform flow and not rotating, a light signal wave front travels in the shape of the surface of a sphere with a radius that increases at a constant speed as a function of time. A ray of light travels at the same speed in every straight line direction. Light does not travel at different speeds in different direction when the source and medium are stationary.
c will be the speed of light in that specific medium when the source and medium are stationary relative to the reference frame
Complete Aether Drift
The speed at which the source from which a signal moves relative to the medium of propagation does not effect the speed at which the signal propagates relative to the medium of propagation, but where the source is located when the signal is emitted effects where the signal starts when it is propagated
Straight Right not Rotational Right
Complete Aether Drift in one dimension
If the medium of propagation is stationary with a uniform flow from a reference frame. And the source of the signal is moving at a constant velocity of positive v to the right direction then the light signal will move at a speed of c to the right and at a speed of c to the left. This results in classical Doppler shift in one dimensional problems.
If the source is stationary from a reference frame. And the medium of propagation is moving at a velocity of positive v to the right direction with a uniform flow then the light signal will move at a speed of c + v to the right and at a speed of c - v to the left.
Too Long Don't Read until continue Reading
Partial Aether Drift with Lorenz Factor modification to light propagation velocity in one dimension
If the medium of propagation is stationary with a *uniform* flow from a reference frame. And the source of the signal is moving at a constant velocity of positive v to the right direction then the light signal will move at a speed of c + alpha * v to the right and at a speed of c - alpha * v to the left
If the source is stationary from a reference frame. And the medium of propagation is moving at a constant velocity of positive v to the right direction with a *uniform* flow then the light signal will move at a speed of c + alpha * v to the right and at a speed of c - alpha * v to the left
Where alpha equals the reciprocal of the square root of 1 - ( v^2 / c ^2 )
https://en.wikipedia.org/wiki/Lorentz_factor
In some interpretations of the Fizeau experiment they found that light seemed to move faster in the direction that water is traveling relative to the speed it would have moved if the water was stationary but the increase in speed was not as great as the speed at which the water was moving.
The mathematical relationship in the Fizzeua experiment for Partial Aether Drag was not necessarily the same as the one I presented in this model for partial Aether Drag.
* It is important to notice that in the Fizzeau experiment the medium moved in a laminar flow where as I am assuming a uniform flow. The Fizzeau experiment might not give valid predictions for mediums with uniform flow. This is a one dimensional model for partial Aether Drag where as the Fizzeau experiment involved at least 2 dimension as the pipes bent and the flow was no longer parallel or anti-parellel to the direction of light propagation near where the pipes bent around corners. *
Various calculations involving Fizzeau involved a refractive index but I am interested in propagation through air or an imperfect vacuum where the refractive index would be very close to 1.
The speed of light in a stationary medium = The refractive index * the speed of light in a imperfect vacuum of stationary air or a theoretical "perfect vacuum"
A perfect vacuum has never been found in nature or a laboratory and is assumed not to exist in my theory
https://en.wikipedia.org/wiki/Refractive_index
No Aether Drift in one dimension
If the medium of propagation is stationary with a uniform flow from a reference frame. And the source of the signal is moving at a constant velocity of positive v to the right direction then the light signal will move at a speed of c + v to the right and at a speed of c - v to the left.
If the source is stationary from a reference frame. And the medium of propagation is moving at a constant velocity of positive v to the right direction with a uniform flow then the light signal will move at a speed of c + v to the right and at a speed of c - v to the left.
Question should this result in there being no Doppler shift?
Because the velocity of the source makes 0% difference to the speed of light propagation with complete Aether drift and makes partial difference with partial Aether Drift, I assumed with the terminology no Aether Drift that means it makes 100% difference. I made up this terminology.
Continue Reading
Equations for all calculations
RTe = MTe + Pe
LTe = MTe - Pe
RPr = RTr - MTr
SPr = ( RTr - LTr ) / 2
RPm = RPr / Pe
SPm = SPr / Pe
LPm = LPr / Pe
One dimensional calculation for period of reception of signal for Complete Aether Drag
The distance between the source at the time of emission and the receiver at the time of reception is equal to the amount of time it took for light to travel from the source to the receiver times the speed of light
( Tr - Te ) * c = Xr - Xe
Xr = Xr0 + Vr * Tr
Xe = Xe0 + Ve * Te
( Tr - Te ) * c = Xr0 + Vr * Tr - Xe0 - Ve * Te
Tr * c - Tr * Vr = Xr0 - Xe0 + Te * c - Te * Ve
( c - Vr ) * Tr = Xr0 - Xe0 + ( c - Ve ) * Te
Tr = [ Xr0 - Xe0 + ( c - Ve ) * Te ] / [ c - Vr ]
MTr = [ Xr0 - Xe0 + ( c - Ve ) * MTe ] / [ c - Vr ]
RTr = [ Xr0 - Xe0 + ( c - Ve ) * ( MTe + Pe ) ] / [ c - Vr ]
LTr = [ Xr0 - Xe0 + ( c - Ve ) * ( MTe - Pe ) ] / [ c - Vr ]
RPr = [ Xr0 - Xe0 + ( c - Ve ) * ( MTe + Pe ) ] / [ c - Vr ] - [ Xr0 - Xe0 + ( c - Ve ) * MTe ] / [ c - Vr ]
RPr = Pe * ( c - Ve ) / ( c -Vr )
LPr = [ Xr0 - Xe0 + ( c - Ve ) * MTe ] / [ c - Vr ] - [ Xr0 - Xe0 + ( c - Ve ) * MTe ] / [ c - Vr ]
LPr = Pe * ( c - Ve ) / ( c -Vr )
SPr = 2 * Pe * ( c - Ve ) / [ 2 * ( c -Vr ) ]
RPm = Lpm = SPm = ( c - Ve ) / ( c - Vr )
Reciprocal of period multiplier matches one of the solutions to one dimenionsonal classical doppler multiplier when calculated this way. Note that I am using Ve instead of V with the subscript s and c instead of v with the subscript m. Compared with equation at time archived
https://en.wikipedia.org/wiki/Doppler_effect
https://web.archive.org/web/20250829183124/https://en.wikipedia.org/wiki/Doppler_effect
Too Long Do Not Read Until Continue Reading
One dimensional calculation for period of reception of signal for Partial Aether Drag with wave velocity adjusted by Lorenz Factor
This math might not be correct and I do not care at this stage unless I decide to use it later
Stationary Medium
Moving Source
Stationary Receiver
Xe = Xe0 + Ve * Te
Xr = Xr0
When Xr0 > Xe0 and Xr > Xe and Ve > 0
The distance between the source at the time of emission and the receiver at the time of reception is equal to the speed that the light moves from this reference frame relative to the origin of the reference frame in the direction it travels from the source to the receiver but the light travels in this direction at the speed of c + Ve * alpha and not at the speed of c
( Tr - Te ) * ( c + Ve * alpha ) = Xr - Xe
( Tr - Te ) * ( c + Ve * alpha ) = Xr0 - ( Xe0 + Ve * Te )
Tr * ( c + Ve * alpha ) = Xr0 - ( Xe0 + Ve * Te ) + Te * ( c + Ve * alpha )
Tr * ( c + Ve * alpha ) = Xr0 - Xe0 - Te * Ve + Te * c + Te *Ve * alpha
Tr * ( c + Ve * alpha ) = Xr0 - Xe0 + Te * ( c - Ve + Ve * alpha )
Tr = [ Xr0 - Xe0 + Te * ( c - Ve + Ve * alpha ) ] / ( c + Ve * alpha )
MTr = [ Xr0 - Xe0 + MTe * ( c - Ve + Ve * alpha ) ] / ( c + Ve * alpha )
RTr = [ Xr0 - Xe0 + ( MTe + Pe ) * ( c - Ve + Ve * alpha ) ] / ( c + Ve * alpha )
LTr = [ Xr0 - Xe0 + ( MTe - Pe ) * ( c - Ve + Ve * alpha ) ] / ( c + Ve * alpha )
RPr = LPr = SPr = Pe * ( c - Ve + Ve * alpha ) / ( c + Ve * alpha )
RPm = Lpm = SPm = ( c - Ve + Ve * alpha ) / ( c + Ve * alpha )
RPm = Lpm = SPm = 1 - Ve / ( c + Ve * alpha )
1 / SPm = ( c + Ve * alpha ) / ( c - Ve + Ve * alpha )
1 / SPm = 1 / [ 1 - Ve / ( c + Ve * alpha ) ]
When Xr0 > Xe0 and Xr > Xe and Ve < 0
| blank | = absolute value of blank
( Tr - Te ) * ( c - | Ve | * alpha ) = Xr - Xe
- | Ve | = + Ve when Ve < 0 if Ve is a real number
( Tr - Te ) * ( c + Ve * alpha ) = Xr - Xe
So everything ends up looking like the same solution as when Ve > 0 but keep in mind that even though it looks the same on paper Ve is negative instead of positive
No Aether Drift in one dimension
This math might not be correct and I do not care at this stage unless I decide to use it later
Xe = Xe0 + Ve * Te
Xr = Xr0 + Vr * Tr
When Xr0 > Xe0 and Xr > Xe
The distance between the source at the time of emission and the receiver at the time of reception is equal to the speed that the light moves from this reference frame relative to the origin of the reference frame in the direction it travels from the source to the receiver but the light travels in this direction at the speed of c + Ve and not at the speed of c
( Tr - Te ) * ( c + Ve ) = Xr - Xe
( Tr - Te ) * ( c + Ve ) = Xr0 + Vr * Tr - ( Xe0 + Ve * Te )
Tr * ( c + Ve - Vr ) = Xr0 - Xe0 - Ve * Te
Tr = ( Xr0 - Xe0 - Ve * Te ) / ( c + Ve - Vr )
MTr = ( Xr0 - Xe0 - Ve * MTe ) / ( c + Ve - Vr )
RTr = ( Xr0 - Xe0 - Ve * [ MTe + Pe ] ) / ( c + Ve - Vr )
LTr = ( Xr0 - Xe0 - Ve * [ MTe - Pe ] ) / ( c + Ve - Vr )
RPr = LPr = SPr = ( - Ve * Pe ) / ( c + Ve - Vr )
RPm = LPm = SPm = - Ve / ( c + Ve - Vr )
1 / SPm = - ( c + Ve - Vr ) / Ve
I would have suspected that this would result in no Doppler shift and would wonder if this is wrong
Continue Reading
Complete Aether Drift in three dimensions
RTe = MTe + Pe
LTe = MTe - Pe
RPr = RTr - MTr
SPr = ( RTr - LTr ) / 2
RPm = RPr / Pe
SPm = SPr / Pe
LPm = LPr / Pe
The distance between the source at the time of emission and the receiver at the time of reception is equal to the amount of time it took for light to travel from the source to the receiver times the speed of light
( Tr - Te ) ^ 2 * c ^2 shall be called light distance squared or LDS
( Xr - Xe ) ^ 2 + ( Yr - Ye ) ^ 2 + ( Zr - Ze ) ^ 2 shall be called Pythagorean distance or PythDS
LDS = PythDS
( Tr - Te ) ^ 2 * c ^2 = ( Xr - Xe ) ^ 2 + ( Yr - Ye ) ^ 2 + ( Zr - Ze ) ^ 2
Special Case Receiver moving perpendicular to direction between source and receiver at time MTr
Yr = 0
Ye = Ye0
Xr = Xr0 + Vr * Tr
Xe = 0
Ve =0
( Tr - Te ) ^ 2 * c ^ 2 = Xr ^ 2 + Ye0 ^ 2
( Tr - Te ) ^ 2 * c ^ 2 = ( Xr0 + Vr*Tr ) ^ 2 + Ye0 ^ 2
( c^2 ) * ( Tr^2 - 2 *Tr * Te + Te^2 ) = Xr0 ^ 2 + 2 *Xr0 * Vr * Tr + Vr ^ 2 * Tr ^ 2 + Ye0 ^ 2
0 = [ Vr ^2 - c ^2 ) * Tr ^2 + ( 2 * Xr0 * Vr0 - 2 * c ^ 2 * Te ) * Tr + Ye0 ^ 2 + Xr0 ^ 2
Quadratic Equation
A = Vr ^2 - c ^2
B = 2 * Xr0 * Vr0 - 2 * c ^ 2 * Te
C = Ye0 ^ 2 + Xr0 ^ 2
MTr - MTe = Ye0 / c
If MTe = 0 when Xe = 0 then MTr = Ye0 / c and Xr0 = -Vr*Ye0 / c
If MTr = 0 when Xe = 0 then MTe = - Ye / c and Xr0 = 0
Quadratic Equation when Xr0 = 0 and
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