Copyright Carl Janssen 2025
Preparation for numerical analysis draft 2
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.
Assuming the medium 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
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 but I believe my model has similarities to what was previously called complete Aether Drift. 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. I assume the velocity and type of flow of this medium can be measured.
In various early interferometer experiments a velocity of Aether was asserted that was different than the velocity and flow of the mixture of chemicals that light was propagating through, later the term Aether was dropped but the previously asserted velocity of the Aether which was different than the measurable and observable velocity of the mixture of chemicals light was propagating through was still used in discussions by Physicists.
For example someone can have a interferometer that is stationary on a desk and the source and receiver of light a well a the human observers can all be close to being stationary but it is asserted that it is moving because the Earth moves around the sun, although I do not deny that it might be moving relative to something it is not moving relative to the medium of propagation. My guess is that this assertion which is a superstition in my opinion traced back to the idea that it was moving relative to the Aether and that they continued to use the same speed as was previously asserted involving the Aether but simply removed the word Aether.
Fizeau
The Fizeua experiment if you believe the water was of uniform flow might hint that light actually travels closer to a partial Aether Drift model instead of in a complete Aether Drift model however I believe that it might have got different results than a complete Aether drift because narrow pipes might have made the water of laminar flow not uniform flow and when the pipes bent around corners the water was moving in a direction that was neither parallel nor anti parallel to the direction of light propagation. My model only works for uniform flow so I have no prediction based on my model as to what the Fizeau results should have been.
For some people a big deal was also made out of the idea that the Fizeau experiment used light white instead of monochromatic light and that each color of light might produce a different result.
Problem that my model is only designed for uniform flow when the atmosphere is not uniform flow
I suspect that since outer space is not a perfect vacuum what people call the cosmic microwave background might be black body radiation from outer space. I suspect that when an atomic clock is moving relative to the source of this radiation in outer space that can change how much radiation of light in a certain frequency it receives which may change the amount of time it displays as having passed to be different than if it received a different type or quality and quantity of radiation in the same amount of time. Unfortunately the calculation I use for prediction assume light is propagated through an atmosphere having uniform flow to reach it's destination, when in reality it can not be uniform flow all the way to the destination of the receiver.
Justification for model
Wikipedia has posted graphs comparing black body radiation to the cosmic microwave background radiation
Wikipedia has confirmed that outer space is not a perfect vacuum and has a measured density and or pressure listed
Wikipedia has posted a frequency related to Cesium and in regards to Cesium atomic clocks that over laps with the frequency range of cosmic microwave backgound
Use the term backdrop and explain this better - The stars tend to move around the earth from the viewpoint of someone on the earth at a certain rotational speed and this can be used for the speed of the source relative to the receiver to guess that the source of black body radiation in the imperfect vacuum of outer space is moving in a certain pattern relative to a receiver on earth based on this
The distance at which the atmosphere is a certain density or pressure or greater is longer in the straight line horizontal directions than in the straight up relative to an observer standing on the surface of the earth, where horizontal and up are defined by that observer's viewpoint. This might reduce the cosmic microwave background black body radiation a receiver receives from the horizontal directions. This means one might be able to model this my a receiver moving perpendicular and not parallel to the direction between the receiver and the source. Many of the fundamental models involved in Special Relativity and the Lorenz Aether Transformation involve a similar sort of "perpendicular movement" and so may have accidentally by coincidence for the wrong reasons in my opinion come up with similar calculations involving time and length multipliers to what I would argue is really a radiation multiplier that result in a predictable incorrect calibration of clocks that are sensitive to that type of radiation and not in a predictable dilation or constriction of space and time that results in a change of radiation rates.
Change in time displayed on clock = Reaction Rate * Change in actual time
Reaction rate for a Cesium atomic clock might be based on the number of photons of a certain frequency that hit it per time.
It is not time that is being distorted but the reaction rate which is being distorted in a clock that is not calibrated correctly to handle the distortion
Incorrect Calibration of time resulting in incorrect measurements of length
If someone uses the change in time displayed on a clock instead of the change in actual time to calculate how far two objects travel away from or towards one another in a straight line at a constant speed then they may get the wrong answer. If the speed is measured correctly but the time is measured incorrectly if the time is measured to take N times as long as it actually does then the distance will be incorrectly calculated to be N times as long as it actually is.
Incorrect Calibration of time resulting in incorrect measurements of period, frequency and wavelength
If someone uses the change in time displayed on a clock instead of the change in actual time to measure the period between two signals
if the time is measured to take N times as long as it actually does then the period will be N times as long as it actually is and the frequency will be 1 / N times the quantity that it really is. If the correct velocity of the wave is used then the wavelength will incorrectly be measured to be N times longer than it actually Is.
Problem with measuring cosmic microwave background radiation
It would be desirable to test multiple things to evaluate my theory. One thing someone could do is see if the period of time between when photons of a certain frequency are emitted changes as one moves at a certain speed along a certain path. Unfortunately if one is measuring the period between photon emissions when one moves with a clock that is moving the change in the rate of radiation when moving would miscalculate the clock and throw off the measured period. The period would also be effected by the movement of the clock under Special Relativity or the Lorenz Aether Transformation only not because of a miscalibration of measured time but because they believe a different amount of time actually occurred under some interpretations of these theories.
Complete Aether Drift and wave speed independent of speed of Source and receiver.
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.
Transforming Reference Frames and Complete Aether drift
Old Reference Frame
If in a reference frame in which the medium is moving with uniform flow
The x, y and z components on the velocity of the medium are Vmx, Vmy and Vmz
The velocity components of the source of emission are Vex, Vey, Vez
The velocity components of the receiver are Vrx, Vry and Vrz
New Reference Frame
Then this can be rewritten in a reference frame in which the medium is stationary as
New Vmx = Old Vmx - Old Vmx = 0
New Vmy = Old Vmy - Old Vmy = 0
New Vmz = Old Vmz - Old Vmz = 0
New Vex = Old Vex - Old Vmx
New Vey = Old Vey - Old Vmy
New Vez = Old Vez - Old Vmz
New Vrx = Old Vrx - Old Vmx
New Vry = Old Vry - Old Vmy
New Vrz = Old Vrz - Old Vmz
Where new refers to the coordinates in the new reference frame we created in which the medium was described as stationary and old refers to the coordinates in the old reference frame in which the medium was described as moving
Assumptions for the following calculations
By speed of light I mean speed of light in that medium
1 The medium is of stationary or in other words has a speed of zero relative to the origin of the frame of reference and is not rotating in the frame of reference and the medium is of uniform flow
2 The source moves at less than the speed of light relative to the origin of the frame of reference
3 The receiver moves at less than the speed of light relative to the frame of reference
4 The receiver and source move at less than the speed of light relative to one another
5 The medium is isotropic
6 Complete Aether Drift
7 Speed of wave propagation is not dependent on speed of Source or Receiver - this might already be covered under complete Aether drift
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
Variable name prefixes and suffixes
Prefixes of R, M, L
If there are a list of three times in which a signal is emitted the first will be called the left, the second will be called the middle and the third will be called the Right. This will be indicated by a Upper Case R, M or L in front of a variable. This will also be used for other variables that are a function of the right, middle or left time variable
Prefix of S
If something resembles a symmetric limit or derivitive calculation instead of a right or left hand one then it will have an S for Symetric in front of it. This means it uses Right and Left variable labels to do calculations and does not use the middle variable label to do calculations.
Suffixes of e and r
If a variable is related to a time of Emission from the source it will end with a lowercase e after the variable. The e is shorthand for emission.
If a variable is related to a time of Reception at the receiver it will end with a lowercase r after the variable. The r is shorthand for reception.
Suffixes of plus and minus
For the special case that will be solved the quadratic formula will be used to solve a quadratic equation which will have to solutions involving a plus or minus sign. TrPlus is the solution where the plus sign will be used in the formula and TrMinus is the solution where the minus sign will be used in the formula. All other variables with a plus or minus suffix are calculated from a TrPlus or TrMinus variable with the same suffix
What some variables stand for
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
Xe = X coordinate of Source that Emits signal at time of emission
Xr = X coordinate of Receiver of signal at time of reception
PythDS = Pythagorean Distance between source at time of emission and receiver at time of reception squared
LDS = Light Disrance squared = The square of the difference between the time of reception and the time of emission times the speed of light in the medium of reception. By figuring out how much time it took for a light signal to travel from the source to the receiver you can know the distance light traveled from the source to the receiver based on the speed of light.
General Calculation process when the above criteria already mentioned are met
Solve for Time of reception as a function of Time of emission by setting PythDS equal to LDS
PythDS = ( Xr - Xe ) ^ 2 + ( Yr - Ye ) ^ 2 + ( Zr - Ze ) ^ 2
LDS = ( Tr - Te ) * c ^ 2
Calculate the period multiplier by using the solution you just got from the previous step
RTe = MTe + Pe
LTe = MTe - Pe
RPr = RTr - MTr
SPr = ( RTr - LTr ) / 2
RPm = RPr / Pe
SPm = SPr / Pe
LPm = LPr / Pe
Checks
Division Checks
Making sure two quantities are the same
One thing will be divided by another and should give a result of 1 if the check is passed
Subtraction Checks
Making sure two quantities are the same
One thing will be subtracted from another and should give a result of 0 if the check is passed
Checks for the special case could include
Some of this will not make sense until you read how the special case is calculated but I did not want to put this after special case calculations since it is easier to write and read the special case calculation at the end
MTr = 0 or MTr = - Ye / c
Making sure the calculated MTr matches the expected MTr of either Ye0 / c or 0 depending on if a MTe value of 0 or -Y / c value is selected. This may let you know if the plus or minus version of TR should be used if only one works to get this result.
MTr - MTe = Ye0 / c
Making sure the calculated MTr minus the assigned MTe equals Ye0 / c. This may let you know if the plus or minus version of TR should be used if only one works to get this result.
MXr = Xr0 + V*MTr = 0
Making sure Xr0 + V*Tr equals 0 when the calculated value of MTr is used. This may let you know if the plus or minus version of TR should be used if only one works to get this result.
RTr > MTr > LTr and RTe > MTe > LTe
Make sure the time right, middle and left time values are in a order that makes sense in terms of what is greater than what for both time of emission and time of reception.
RTr > RTe and MTr > MTe and LTr > LTe
MTr should be greater than MTe, RTr should be greater than RTe and LTr should be greater than LTe. Since there is both a plus and a minus version of each Te if the minus version is less than the corresponding Te and the plus version is greater than the corresponding Te that will make things simple. If both the plus and minus Tr versions are greater than the corresponding Te then greater examination should be done because there should only be one solution that works in real life if the requirements are met. If both the TR versions are less than the corresponding Te than something went very wrong.
PythDS = LDS
Calculate PythDS and LDS after Tr is calculated based on quadratic formula to make sure PythDS and LDS are the same for that Tr value. Could include six combinations from plus, minus, right, middle and left. This could be accomplished with a subtraction check and a division check resulting in six times two or twelve combinations of checks. Hopefully the plus or minus version will already be decided by the previous checks and only the checks should be done for the decided version to reduce the number of checks.
Percent Errors and Lorenz Factor Alpha
My prediction is that the right, left and symmetric period multipliers for a given velocity will be close to the Lorenz Factor Alpha for the same velocity and a percent error will be calculated. The Lorenz Factor Alpha will be calculated first.
Application of the General Calculation Method to a Special Case
Description of position of source and receiver and medium
The medium is stationary and of uniform flow
A source is stationary and locate with an X coordinate of zero and Y coordinate of a constant Ye0
The receiver is moving with Y coordinate of zero and a X coordinate of Xr0 + V * Tr
When MTr - MTe = Y / c the source and receiver are at the closest points to one another and the receiver is moving in the direction perpendicular to the direction between the source and the receiver. This can be represented with multiple choices for the variables MTr, MTe and Xr0
but these are the two simplest options for solving the equations in my opinion because they allow for a zero
If MTr = 0 then MTe = - Ye0 / c and Xr0 = 0
If MTe = 0 then MTr = Y / c and Xr0 = -V * Ye0 / c
-V*Ye0 / c + V * Ye0 / c = 0
Solution
Xr = Xr0 + V*Tr
Xe = 0
Yr = 0
Ye = Ye0
PythDS = ( Xr - Xe ) ^2 + ( Yr - Ye ) ^ 2
PythDS = ( Xr0 + V * Tr ) ^ 2 + Ye0 ^ 2
PythDS = V ^ 2 * Tr ^ 2 + 2 * Xr0 * V * Tr + Xr0 ^ 2 + Ye0 ^ 2
LDS = c ^ 2 * ( Tr - Te ) ^ 2
LDS = c ^ 2 * ( Tr ^2 - 2 * Te * Tr + Tr ^ 2 )
PythDS = LDS
V ^ 2 * Tr ^ 2 + 2 * Xr0 * V * Tr + Xr0 ^ 2 + Ye0 ^ 2 = c ^ 2 * ( Tr ^2 - 2 * Te * Tr + Tr ^ 2 )
[ V ^ 2 * Tr ^ 2 + 2 * Xr0 * V * Tr + Xr0 ^ 2 + Ye0 ^ 2 ] - [ c ^ 2 * ( Tr ^2 - 2 * Te * Tr + Tr ^ 2 ) ] = 0
Quadractic Formula to solve for Tr
A * Tr ^ 2 + B * Tr + C = 0
A = V ^ 2 - c ^ 2
B = 2 * Xr0 * V + 2 * c ^ 2 * Te
C = Ye0 ^2 - c ^ 2 * Te ^ 2
Quadractic Formula to solve for Tr
Quadratic Formula to solve for MTr
Same as above but substitute Te with MTe
Quadratic Formula to solve for RTr
A same
B = 2 * Xr0 * V + 2 * c ^ 2 * ( MTe + Pe )
C = Ye0 ^2 - c ^ 2 * ( MTe + Pe ) ^ 2
Quadratic Formula to solve for LTr
A same
B = 2 * Xr0 * V + 2 * c ^ 2 * ( MTe - Pe )
C = Ye0 ^2 - c ^ 2 * ( MTe - Pe ) ^ 2
Calculate B ^ 2 - 4 * A * C to use in other calculations for RTr, MTr and LTr
Things to do next
Calculate Tr
Do checks and decide if plus or minus version should be used
Calculate Period Multipliers
Calculate Lorenz Factor Alpha
Calculate Percent Error for how close Period Multipliers are to Lorenz Factor Alpha using the Period Multipliers a Observed and Lorenz Factor Alpha as expected or theoretical in the formula
Values to assign to use for calculations in things to do next above
One variable shall change at a time for these constants that can be chosen and the other variables on this list shall maintain a default value
V, Ye0, Pe
Other options that can be chosen but in a different way and which are dependent on one another
Xe0, Mte, and Mtr
Units
Units will be converted to seconds and meters to various powers
Constants that can not be chosen and which are "set in stone"
c
use about 3*10^8 meters per second
Possible Default Value for V
465 meters per second to match the asserted speed of earth at the equator last time I looked online
Other values for V
Start at about 3 meters per second and multiply by powers of 10 up to one tenth the speed of light then increase in fractions of one tenth the speed of light up to 9 / 10 the speed of light
Possible Default Value Pe
Just use 1 second and see if it works well without causing calculation problems
Other values for Pe
Use 10 to positive and negative integer powers and see where the electronic device starts having calculation problems if it becomes to small or too big
Possible Default value for Ye0
100,000 meters which is 100 kilometers to match the Karman line used as a boundary for space last time I looked online
Other possible values for Ye0
Use powers of 10 and see how high or low it can go before the electronic device starts having calculation problems
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