Transverse short 1

Copyright Carl Janssen 2025

Transverse short 1

Spelling corrections and spellings to remember

Lorentz Factor not lorenz factor search for Loren to find

Fizeau

Scope

I have longer explanations as to why these calculations are done if need be but I am trying to explain how the Calculation can be one in a much shorter form.

Sections with extra information not necessary to understand how to do the calculations are marked with You can skip reading until continue reading followed by continue reading where you can start reading again if you are not interested in the information

The frequency of a single individual photon is not the same as the frequency at which photons are emitted or received

A hertz is one cycle per second.

If one photon having a frequency of 5 Hertz is emitted at a frequency of once per second this is not the same as one photon having a frequency of 1 Hertz being emitted.  I am not interested in the frequency of the individual photons that are emitted but in the frequency at which the photons are emitted.  I am interested in the number of photons emitted per time not the frequency of each photon that is emitted individually.  

One might look up the standard answer for the Doppler effect but in introductory physics classes it is not necessarily explained which of these different type of frequencies is Doppler shifted and the answer that I calculate is different than the answer one would look up in a textbook or find online for the transverse Doppler shift.

Examples in modern standard physics that show my point.  You can skip this until continue reading if you already accept my point as true.

Individual single photons are said to collide against other individual single photons or other particles in physics calculations and the results of the collision are based on the frequency of a single photon.  The frequency of the single photon is said to determine it's energy and the magnitude of it's momentum, and the momentum is said to be conserved before and after the collision.  These collisions are not relevant to this except to emphasize to doubters of my claim that in modern standard model physics calculations a single photon by itself is said to have a specific frequency.  Compton scattering or the Compton effect is one of many examples of this other effects involving photon collisions have other specific names but essentially following the same principle.  The principle is that a group of particles collides then is replaced with another group of particles and the total charge and momentum of all the particles combined is the same before an after the collision.

Continue reading

Doppler Shift and conservation of energy

Assume the receiver and the medium of propagation are stationary in the chosen reference frame and the source is moving at a constant speed at a straight line toward or away from the source in one dimension until specific examples are given otherwise later.

It is very important in terms of conservation of energy if the Doppler shift applies to a shift in the frequency of individual photons or the frequency at which photons are emitted or both.  

If the Doppler shift is only in terms of the number of photons emitted per time but not in the frequency of individual photons that are emitted then there is no difficult problem in terms of conservation of energy.  If when the source is moving toward or away the receiver at a certain velocity v then period at which photons are received is multiplied by N then the difference between the time when the first photon is received and the last photon is received is also multiplied by N but the frequency at which photons are received per time is divided by N.  In this case the number of photons that are received would be the same as the number of photons that are emitted and if each photon is of the same frequency the energy would be conserved.  The power or energy per time received would be divided by N but the time in which photons were received would be multiplied by N.  In this case no matter what direction or magnitude for v you select for the source and the receiver would receive the same amount of total energy because when the power is multiplied by N the time in which the energy is received is divided by N.  This actually is a over simplification because problems involving the selection of the sampling window which I explain later combined with the idea that the energy is received in discrete packets not in a continuous manner as a function of time makes this complication much more difficult then I describe.

However if the frequency of each individual photon is doppler shifted when the source moves then for photons moving towards the receiver the source will emit more energy per photon if the source is moving toward the receiver but less energy per photon if the source is moving away from the receiver.  This would seem to imply that a flashlight powered battery if it emits the same number of photons per time regardless of what speed it is move by a third party source should run out of energy stored in a battery at a different rate if it is moving at different speed relative to a wall that it shined light on if the medium of propagation is stationary relative to that wall.  If the frequency at which photons are emitted in terms of number of photons is unchanged when the flashlight moves that does not mean that the frequency at which photons are received in terms of number of photons that hit the wall would remain unchanged.

One might argue that for every photon that is emitted in one direction costing more energy another photon is emitted in the opposite direction costing less energy and if the increase in cost in one direction is equal to the decrease in cost in the other direction then the same amount of energy will be expended whether the source is moving or stationary ignoring the energy spent to move the source which is expended by a third party source.

However using the Doppler shift frequency calculations this is not always true.

Assume the medium is stationary relative to the frame of reference

Assume photons move at a speed of c through the medium

Assume any movement is at a straight line in a constant speed

Assume the problem is one dimensional, the source(s) and receiver(s) all exist on a single straight line

https://en.wikipedia.org/wiki/Doppler_effect

If there is a stationary source emitting one photon toward a receiver moving away from the source at a speed of v an emitting one photon toward a receiver moving toward the source at a speed of v.  And if the frequency of the individual photon a receiver receives is effected by the receiver's movement relative to the source.  Then the sum of the Doppler shift multipliers of the frequencies of the two photons will be the following if the classical Doppler shift formula is used not the special relativity Doppler shift formula.

classical Doppler stationary source with receiver moving toward source ( c + v ) / c

classical Doppler stationary source with receiver moving away from source ( c - v ) / c

sum = ( c + v ) / c + ( c - v ) / c

sum = [ ( c + v ) + ( c - v ) ] / c

sum = 2 * c / c = 2

There are two photons so divide the sum by 2 to get the average energy multiplier

Energy Multiplier = sum / 2  = 2 / 2 = 1

The energy per photon equals the frequency of that photon times a constant so the total energy received in both receivers is the same regardless of what speed the receivers move in this case

If there are two stationary receivers on opposite sides of a source and the source is moving at a speed of v toward one receiver and a speed of v away from the other receiver.  Then the sum of the Doppler shift multipliers of the frequencies of the two photons will be the following if the classical Doppler shift formula is used not the special relativity Doppler shift formula.

classical Doppler stationary receiver with source moving away from receiver c / ( c + v )

classical Doppler stationary receiver with source moving toward receiver c / ( c - v )

sum = c / [ c + v ] + c / [ c - v ] 

( c + v ) * ( c - v ) = c ^ 2 - v ^ 2

multiply one by ( c + v ) / ( c + v ) and the other by ( c - v ) / ( c - v )

sum = c * ( c + v ) / ( c ^ 2 - v ^ 2 ) + c * ( c - v ) / ( c ^ 2 - v ^ 2 )

sum = ( c ^ 2 + c * v + c ^ 2 - c * v ) / ( c ^ 2 - v ^ 2 )

sum = ( 2 * c ^ 2 ) / ( c ^ 2 - v ^ 2 )

multiply by ( 1 / c ^2 ) / ( 1 / c ^ 2 )

sum = 2 / ( 1 - v ^2 / c ^ 2 )

There are two photons so divide the sum by 2 to get the energy multiplier

Energy Multiplier = sum / 2  = [ 2 / ( 1 - v ^2 / c ^ 2 ) ]

Energy Multiplier =  1 / ( 1 - v ^2 / c ^ 2 )

Energy Multiplier = Lorentz Factor Gamma Squared

https://en.wikipedia.org/wiki/Lorentz_factor

The energy per photon equals the frequency of that photon times a constant so the total energy received in both receivers combined using classical Doppler shift formulas is equal to the Lorentz Factor squared as a function of the speed and is not the same regardless of what speed the source moves in this case

Difference between frequencies from a sampled time window and frequencies gotten from taking the inverse of the period.

The following is presuming perfect sampling with no error and no variation in the period at which photons are emitted.  The following is ignoring the time it takes for the photon to get from the source of emission to the receiver that measures the time when the emission occurs and assuming you can instantly know when the photon is received at it's source.

If photons are emitted at a frequency of one photon per second or a period of one second per photon and a photon is emitted at time zero.  A photon will be emitted every integer number of seconds.

One could take a time window and count the number of photons from the start of the window to the end of the window and divide by the difference in time from the start of the time window to the end of the time window to calculate the average frequency during this time window.  But if the start and end of the time window was randomly selected one would get the wrong answer for the frequency at which the photons were emitted except when both the difference is an integer number of seconds and also the start of the time window does not fall on an integer multiple of 1 second.

One could also take a list of the time each photon was emitted.  One could pick a random time and then randomly select the next or previous closest time on the list and take the absolute value of the difference to determine the period.  If the random time was the last on the list one could take the previous time to determine the difference and if it was the first on the list one could take the next time to determine the difference and if the time was in the middle of the list one could take the previous time or the next time to determine the difference.  One could then calculate the frequency by taking the reciprocal of the period.  Because the frequency is constant and has no variation this method unlike the previous method would give you the exact answer every time but this is an ideal example that does not reflect the variation in real life data sampling.

I will use this ideal method of taking the reciprocal of the period ( calculate by differences ) to determine the frequency instead of counting the number of emissions in a time window to determine frequency in the rest of this article.

Middle, Left Hand vs Right Hand vs Symmetric Calculations

The term left and right are not meant as directions thought the rest of this article but as terms similar to how right and left are used as terminology relate to limits and derivatives in calculus.  The term symmetric shall be used in a similar manner to how the term symmetric is used regarding derivatives in Calculus.  A similar manner or terminology does not necessarily mean a 100% identical manner or terminology.

Left, and right shall also have a second meaning.  Left shall refer to the first value in a list of three items, middle shall refer to the middle value in a list of three items and right shall refer to the last value in a list of three items, where the list is sorted in order from lowest to highest value with the lowest value appearing first and the highest value appearing last.

Required Prerequisites for this kind of period calculation

1 The speed of light relative to the medium must be isotropic with regard to the medium.  It does not travel different speeds in different directions.  It is isotropic in a reference frame in which the medium is stationary.

2 The velocity of light is not effected by the velocity of the source but the position of the source as a function of time effects where the light is emitted from at that time

3 The velocity of light is not effected by the velocity of the receiver

4 The medium is stationary relative to the origin of the reference frame.  The medium is not rotating in the chosen reference frame and has a constant zero velocity of zero relative to the origin of the chosen reference frame.  The medium is of uniform flow.  If the medium is of uniform flow and constant velocity but it is not stationary relative to the origin of the reference frame a new reference frame can be selected in which the medium is stationary and the velocity of the source and receiver relative the origin of the new reference frame must be adjusted accordingly.  A medium maybe of uniform flow in one reference frame but not of uniform flow in another reference frame for example if a medium is stationary and of uniform flow it is not of uniform flow when converted to a reference frame in which it is rotating around an axis this maybe similar but not identical in appearance to stars rotating in the sky around a North Star this conceptually maybe related to the back drop mentioned in an optional reading section.

5 The source and receiver move toward or away from one another at a speed of less than the speed light propagates through the medium

6 The source moves at less than the speed of light relative to the origin of the reference frame

7 The receiver moves at less than the speed of light relative to the origin of the reference frame

8 A light signal emitted by the source at a specific time is received by the receiver at a specific time exactly one time, no more an no less.  The receiver is presume to always receive the signal after it is emitted by the source and never before it is emitted by the source.  Several of the other points were stated with this goal in mind but if they are not sufficient to achieve this goal then this method will not work.

I added this section instead of listing a ninth 9th prerequisite.  These are thought experiment calculations not real calculations with real tools, real people and real data.  I am not making adjustments in the calculations based on Lorentz Aether Transformation, Special Relativity or General Relativity.  

Indirectly this ties to several other topics involving the cosmic microwave background and what I call the back drop of outer space, as well as big bang vs steady state which each have lengthy discussions.

If you want then you can skip this section until continue reading.

Change in Time displayed on clock = Reaction Rate * Change in actual time

This is a thought experiment and not a real experiment with real clocks.  It does not take into account the effects calculated in the Lorentz Aether Transformation, Special Relativity and General Relativity which I believe make predictions for how much a clock is incorrectly calibrated by but other people believe result in am actual different amount of time passing which often leads to pop culture claims of time travel in science fiction.  

I presume if two different people met up and set their watches to 1 PM and when they met again one person's watch said 1:50 PM and the other person's watch said 2:10 PM that the same amount of time passed for both people but one or both of them had incorrectly calibrated clocks. but in some interpretations of the Lorentz Aether Transformation, Special Relativity and General Relativity the clocks were correctly calibrated and a different amount of time passed for them.

I believe a change in the period at which photons are received might be resulting in incorrect calibration of certain types of clocks which is why I am calculating what I call the Period Multiplier for Reception.  The Period Multiplier for Reception is the Period at which a signal is received at an emitter divided by the Period at which a signal is emitted at a source.

I just made up the term back drop, I do not know if that term exists or is normally used in that way.  Where the back drop is metaphorically like the drapes and scenery behind actors in a theatre.  The back drop represents vast amounts of low density matter or material people ignore by pretending outer space is a perfect vacuum between the stuff people think of as important.  The back drop is not Aether.  I assume any section of outer space with a volume greater than zero has a mass greater than zero even if it is a imperfect vacuum.

I presume that the back drop of outer space is a imperfect vacuum composed of a mixture of chemicals that when within a certain very large distance from earth or less is close enough to uniform flow except when it is near certain objects including but not limited to planets, stars, comets, meteors and asteroids.  The back drop is only of uniform flow in a reference frame where it is not rotating.  When it is near these objects the back drop is connected to their atmosphere and there is no clear distinction between where one ends and the other begins except a arbitrary but ( geographically ? ) important ( in terms of terminology if you want to know where things are ) choice made by humans.

Analogies of arbitrary but important difference that can be skipped  

This is similar to how one part of a body is connected to another and anatomists just make up names for regions and where they choose the region to be often is arbitrary and does not matter in terms of the physics and chemistry of how the body works but when someone has to do surgery and actually needs to know how to find the location of something it suddenly does matter.  A similar concept happens in mapping Y shaped intersections of nerves an blood vessels in anatomy or mapping roads for driving that have a Y shaped intersection.  Assume a Y intersection with three 120 degree angles.  All of the roads are really part of one and the same road but someone has to arbitrarily choose at least two and possibly as many as three different names instead of calling them all the same one road name or people will get lost.  If they chose two names  and not three names then they could have just as easily swapped one of the road names and have equally valid justification but if they do not arbitrarily choose one name scheme then people will get lost.  Likewise two new religious denominations or two new political parties that split could both claim to have ancient roots from a previous older denomination or older party they both split from at the same time over different stances on the same disagreement while each claiming the other to be new and their's to be the original denomination or political party and one could weight out their arguments but if you want to attend a meeting at an actual location they better call each other by different names if you want to go to a meeting of one but not the other.

End of analogy

Rate of backdrop rotation relative to a stationary earth or rate of earth rotation relative to a stationary backdrop.  Uniform Flow at small scale but not at large scale.  Transitioning from back drop to atmosphere to surface of planets and changing flow.

If a planet is rotating or moving relative to the back drop then the transition between the back drop to the atmosphere to the surface of the planet does not have uniform flow on the large scale but small locations when looked at in isolation may appear to be close enough to uniform flow when viewed from a small scale.  

I presume there is a reference frame in which the earth is spinning at one full rotation approximately every 24 hours and the back drop is stationary and of uniform flow.  I presume this is why so many objects appear to move in the sky in certain patterns in approximately 24 hour cycles such as stars appearing to rotate around the North Star or the Sun setting or rising about once every 24 hours or the moon rising almost once every 24 hours at about 24 hours and 50 minutes each day.  One could instead choose a reference frame in which the earth is stationary and the back drop is spinning but for me that would make calculations more difficult.

"moonrise is about 50 minutes later each day"

2025 October 15

https://www.iop.org/explore-physics/moon/phases-and-orbits-moon

I presume we are in a steady state universe and that black body radiation from this back drop and not any alleged expansion of the Universe in an alleged big bang explains the cosmic microwave background.  

"The cosmic microwave background radiation is an emission of uniform black body thermal energy coming from all directions. Intensity of the CMB is expressed in kelvin (K), the SI unit of temperature. The CMB has a thermal black body spectrum at a temperature of 2.72548±0.00057 K"

2025 October 15

https://en.wikipedia.org/wiki/Cosmic_microwave_background

More details of explanation of possibility of steady state instead of big bang that can be skipped

Inverse Square Law

Imagine light shined from a source with a constant power.  The source is stationary relative to the medium of propagation and the medium of propagation is isotropic with respect to the speed of light, that is the speed of light is the same in all straight line directions in a reference frame in which the medium is stationary and of uniform flow.  Imagine a spherical shell centered at the source.  If the power of light going through the shell is the same no matter the radius of the shell then the power per surface area of the shell will be equal to a constant divided by the the radius of the shell squared.  The inverse Square law does not result in a loss of light power when the radius is increased but a loss in light power per surface area under the circumstances for which it applies.  In reality the power would decrease the larger the radius of the shell because the medium of propagation would not be a perfect vacuum and the medium of propagation would not be 100% transparent if it is a imperfect vacuum.

Imagine a light beam propagating in a straight line through water

If a source and receiver are both in water that is stationary and of uniform flow and the source and receiver are stationary relative to one another.  Imagine a beam of light is sent in a perfectly straight line from the source to the receiver such that it does not lose any power per surface area due to the inverse Square law.  The greater the distance from the source to the receiver the less power the receiver would receive.  This is because although water is somewhat transparent it is not 100% transparent.  Some of the light would transfer energy to the water before it reaches the receiver and the longer the distance between the source and the receiver the greater the percent of energy that would be transferred to the water instead of the receiver.  This transfer of energy could be accomplished in such a way that each photon received at the receiver has the same amount of energy as when it was emitted at the source but less photons reach the receiver then are admitted at the source.  A second more controversial possibility is that this transfer of energy could also potentially be accomplished if the same number of photons are received at the receiver than are transferred at the source but each photon has less energy and is of a lower frequency.  And numerous other combinations could occur involving different numbers of photons and different amounts of energy per photon so long as the sum of the energy of all the photons received is less than the sum of the energy of all the photons emitted.  I am not saying that going through a medium would reduce the energy per photon but only that going through a medium might reduce the energy per photon.

Difference between the steady state and the big bang

A red shift is a decrease in light frequency from an observed light source to the observer where as a blue shift is an increase in light frequency from an observed light source to the observer.  The observer in this context regarding to red shifting and blue shifting is someone on earth looking at object's in the night's sky that are said to be in outer space.

The big bang involves the claim that most distant objects in outer space are red shifted so all the rest of the Universe as a general trend with rare exceptions is expanding or moving away from earth.  The big bang involves extreme extrapolation, if the path of the objects is traced backwards through time it all must have come from a very small original object that expanded.  This extrapolation involves a finite amount of time.  People will not answer what happened before the finite amount of time and say they do not know the laws of physics before the start of the big bang.  Essentially in my opinion they admit whatever we think the laws of physics currently are were violated by some event before the big bang.  In my opinion the assumptions that lead to the big bang are self refuting.  We must always extrapolate back further and can not limit our extrapolation time to a short duration but now we suddenly must limit our extrapolation because we can not explain before this point without violating the laws.  If you are going to limit your extrapolation to however many billion years ago then why not limit it to millions of years ago or thousands of years ago or 5 minutes ago.  If you must have a reason to need to extrapolate further than five minutes ago then why can not this same reason be used to justify the need to extrapolate further back in time than whenever the big bang was claimed to occur.

Steady state is the idea to find a set of rules to explain the Universe that could potentially work consistently in all time both forward and backward throughout eternity in both directions.  Steady state does not mean the Universe is eternal but only to try to find a set of laws that would match a hypothetical eternal universe that also match our actual observed Universe.  With steady state we can extrapolate up to any finite amount of time backwards no matter how large without the kind of logical absurdities that the big bang presents but we are not obligated to extrapolate back a certain minimum amount of time such as billions of years ( or whatever the current fad is for when the big bang was claimed to occur ) the way we are pressured to in the big bang.  Even though we can extrapolate back a very long amount of time we are not pressured to in order to discover when some event that is supposed to explain the origins of the Universe but really fails to do so occurred because no assumption of the origins of the Universe are made in the steady state model but only a description of how the Universe works in the present.  In my opinion the shorter we extrapolate back the better the predictions are as a general trend with some exceptions and based on this trend extrapolating back billions of years is really silly.  

Even though a hypothetical steady state model would enable you to extrapolate farther back than the time of the alleged big bang without the kind of logical absurdities the big bang has when trying to do so, the predictions would become less and less accurate the farther back you go but not because of a violation of the laws of physics but simply because the predictions that the laws of physics make tend to be less accurate the further back you go with some exceptions.  So although in my opinion steady state models are superior to big bang models because you can extrapolate farther back without logical absurdities, I suggest only using the models to make guesses about what happened or what will happen in events in short periods of time in the past or the future for best results.

The idea that the back drop being a certain temperature proves the big bang as the only possibility refuted by the concept of dynamic equilibrium as an alternative explanation

I presume the back drop is cold not because of a big bang but because objects get colder as they emit black body radiation.  I presume the back drop is not at absolute zero because it receives some energy from light that is absorbed by it instead of passing through it since it is almost 100% transparent but not 100% transparent.  I presume red shifts are not due to all or almost all or most of the universe expanding away from the earth in a big bang but because some of the energy is lost before it reaches earth as it is transferred to the back drop increasing the temperature of the back drop only for the back drop to lower temperature in black body radiation achieving dynamic equilibrium at a little less than 3 degrees Kelvin.  

Objects claimed to be farther away also being claimed to have more red shift does not prove the big bang as the only possibility because of an alternative explanation in this paragraph followed by more such explanations in later paragraphs

It is easy to know the direction of far away objects but much more difficult to know their size and distance from us unless we have traveled close to them in the past to know where they are now that we are far away.  Various methods can be used but a nearby pebble can be mistaken for a far away boulder if not for other familiar objects in the background because the farther away an object is the more it appears to shrink.  

Now I am not saying it is impossible to know the size and distance of far away objects on earth but just not as easy as some people might think.  I think it is reasonable to assume that humans guess distances or sizes of objects wrong more often when they simply look at something far away with the human eye while in an unfamiliar location, but can guess better in a familiar location.  I find it doubtful that humans having never traveled beyond the moon would be able to accurately measure the distance of stars much farther away then the moon on the basis of lack of familiarity reducing accuracy and precision of measurements.

When someone surveys the height of a building even if they have never been in a city before they are surrounded with other buildings and familiar backgrounds that give them contextual clues. but the contextual clues are comparatively lacking for stars in outer space.  I find the claim that we can actually know the distance of many objects we see in the sky highly doubtful other than that we can know they are too far away too touch but I will pretend we can know the distance anyway.

People will claim that objects farther away from earth tend to have a greater red shift and so in general must tend to be moving away from earth faster than objects nearby the earth and that this proves the big bang.  I presume the farther away objects are from earth the more light will tend to be red shifted because there is more distance between the earth and the object in which the energy from the light can be transferred to to the back drop by reducing energy per photon and or by reducing the number of photons.  Since an explanation for a greater red shift for a object at a greater distance from earth is presented that does not have to involve the object moving away from earth at all let alone at a greater speed is presented this refutes this argument for the big bang being the only option.  I will have further arguments for other reasons that farther away visible objects to be red shifted more later that strengthen this point in the section about the bright sky argument or in my opinion the bright sky fallacy.

Allegations of potential heat death or cold death of universe do not disprove steady state

I presume any section of the universe of finite volume has finite mass but that the universe is without limit in volume and mass and thus that there is no heat death nor cold death of the universe in which all of the universe gets so hot or cold that no life can continue to live anywhere.  Things simply cool down and emit light when they are hot and the emitted light heats up another location in the universe that later can cool down and emit light.  There is no cold death of the Universe because emitted light due to the cooling of objects in black body radiation can not leave passed the border of the universe if the universe has unlimited volume and has no border.  Since emitted light can not move passed the border of the Universe, the Universe can not lose all it's heat because the light will eventually heat something instead of leaving the border of the Universe.  There is no heat death of the Universe because hot sections of the Universe cool down as they emit light.  So claims about a heat death or cold death that would happen do not disprove a steady state universe.  There is also no death of all life due to blandness in which everything is all the same average temperature without enough variation in Temperature for life because living things have the ability to change around the distribution of temperature in different locations by converting light to an energy source that is used to do work, and that work can be used to prevent some sort of blandness or lack of regional Temperature variation in which life can not continue to function.

Gravity Crunch

A Universe of unlimited mass would crunch up into a tiny ball because unlimited mass means unlimited gravity.  Gravitational pull in one direction can be countered by gravitational pull in another direction or by an electromagnetic push or pull so this simply is not true at least in a universe of unlimited volume.

Bright sky objection to steady state refuted

I presume we do not have a sky of unlimited brightness even with a universe of unlimited size because objects farther away tend to be less bright due to the inverse square law and because all objects are partly opaque or to put it another way all objects have less than 100% transparency.  I presume that although stars emit light they are also partly opaque and block light from other stars, I also presume that planets, comets, meteors and asteroids are at least partly opaque and block light from stars.  I presume any section of the universe with a volume greater than zero has a mass greater than zero and is not 100% transparent.  I presume that the back drop is not 100% transparent but partly opaque.

I presume that objects have to emit a greater power of light or to be more precise they require a greater minimum frequency of individual light photons ( because of red shifting due to energy being transferred to the partly opaque back drop ) and also be brighter ( emit more photons ) due to the inverse square law and the partly opaque back drop in order to be seen from farther away.  I presume that in order to have more light power these farther away objects have to tend to need more mass.  I presume if you have a chemical or nuclear reaction or a source of black body radiation and other factors are the same you need more mass to emit more photons per time from the reaction.  The additional required mass to see objects that are farther away might result in more gravitational red shifting.  This might mean visible objects that are farther away have more red shifting not because they are faster as they get father away from earth as a result of a big bang but because they need more mass in order to be seen resulting in more red shifting.  This also would be another reason the sky is not of unlimited brightness because this gravitational red shifting reduces the light power of far away objects.

Religious objections to steady state refuted

Some object to the steady state saying the Universe is not eternal because it was created by a deity or deities or an intelligent designer or designers a finite amount of time ago.  I will simply say that although a steady state universe would have a set of physical laws that would allow it to exist eternally both forward and backward in time that does not mean that a Universe that follows steady state physics laws could not have been created a finite amount of time ago.  Just because a steady state universe could be eternally old does not mean that a steady state universe could not have a finite age.  I will also respond with if a creator could create a Universe that can exist eternally forward in time, why would a creator be unable to create a Universe that could exist eternally backwards in time unless that creator is not all powerful, whatever all powerful means.  By saying whatever all powerful means, I mean many clergy like to throw around the term all powerful without being very clear about what they mean.  

A steady state universe could potentially be created by a creator or could potentially exist without any creator.  If a creator could exist eternally without being created then a Universe could exist eternally without being created.  If a Universe could not exist eternally without a creator then a creator could not exist eternally without a creator of the creator.  Just because a Universe hypothetically could exist without being created does not mean that a Universe was not created.

Some claim that life has never been observed coming from materials that are not alive without a living thing to convert the materials to something that is alive so life must have been created by a creator deity or a group of creator deities.  But if a Universe is eternal life could have always come from previous living things without being created by a creator deity or a group of creator deities and without spontaneously forming from things that are not alive.  But that does not mean that life was not created by a creator deity or a group of creator deities.

Universal Gravitational Constant

I have assumed a gravitational red shift and blue shift model similar to in the General Theory of Relativity in terms of predictions even though I do not personally know the predictions it makes works correctly.  The idea is that when light travels from a object with high gravity to a object with lower gravity it is red shifted and when light travels from an object with lower gravity to an object with higher gravity it is blue shifted.  One can believe that these predictions are accurate without believing all the claims or all the interpretations of claims made in General Relativity.  One could believe the predictions are accurate for different reasons than the reasons involved with some interpretations of General Relativity.

It is easy to measure the local gravitational constant in a local lab on a low budget with a camera a ruler and a falling object.  The measurement of the Universal Gravitational Constant is not so easily available to the public because many of the low budget experiments are of extremely poor and questionable quality, they often involve ignoring the mass of high mass objects like chairs, desks, people, walls, and entire buildings while paying minute attention to lower mass objects, they often involve ignoring much larger electromagnetic forces or even possibly larger forces from a draft of air in the room, while paying attention to much smaller gravitational forces not from the earth but from tiny objects or at least tiny in terms of the amount of gravitational force they would produce.  They involve ignoring differences in results which small changes in temperature and possibly too many other factors to list might make which might be larger than the very small changes in results expected from the Universal Gravitational Constant.

End of explanation of steady state vs big bang

Back Drop, Period Multiplier, Clock Calibration, Clock Calibration influencing measurements of period multiplier, Cesium Frequency, Cosmic Microwave Backhground Frequency

I presume moving relative to this back drop effects the rate at which photons from this back drop are received by clocks on earth which effects their calibration and that moving relative to this back drop also effects clock calibration through a B field involving one charged particle moving relative to another charged particle.  I presume gravity may also effect clock calibration.  These factors may potentially effect different types of clocks in different ways and may potentially only effect the calibration of some kinds of clocks.  A cesium atomic clock maybe effected differently by these factors than a grandfather clock for example.

^ added to quotation in place of superscript for powers

x multiplication symbol replace with * multiplication symbol in quotation

"Cosmic background radiation; primal glow The background of radiation mostly in the frequency range 3 * 10 ^ 8 to 3 * 10 ^ 11 Hz"

2025 October 15 date link accessed

https://hypertextbook.com/facts/2004/HeatherFriedberg.shtml

https://web.archive.org/web/20251015060323/https://hypertextbook.com/facts/2004/HeatherFriedberg.shtml

the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s−1

https://en.wikipedia.org/wiki/Caesium_standard

3 * 10 ^ 8 < 9 192 631 770 = about 9 * 10 ^ 9 < 3 * 10 ^ 11

The cesium frequency is in the range of the cosmic microwave background frequency but are these the same types of frequencies?  Are these the frequencies at which photons are emitted or the frequency of each photon that is emitted or a different kind of frequency?  Am I looking up the right cesium frequency or should I be comparing it with a different kind of frequency for Cesium in terms of the atomic clocks?

If one collected real data to try to calculate the Period Multiplier for Reception experimentally or empirically instead of only in a thought experiment then one would have to take into account the fact that the clock that is used to calculate the Period itself is not correctly calibrated.  I am not taking this incorrect calibration into account in these calculations.  

If N seconds passed on the time displayed on the clock for every 1 second of actual time then the period between signals one calculated using the clock would be multiplied by N.  If one had the correct velocity of either a wave or a moving object this would result in the calculated distance objects traveled being multiplied by N giving the wrong distance traveled and this would also result in the calculated wavelengths being multiplied by N and in the calculated frequency of signals being divided by N all giving incorrect answers ( in my opinion ) but incorrect answers that were correctly predicted by the Lorentz Aether Theory, Special Relativity and General Relativity presuming these theories make correct predictions.

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Terminology Abbreviations

SQRT ( blank ) = sqrt ( blank ) = square root of blank

blank ^ N = blank to the N power

blank ^ 0.5 = blank to the half power = square root of blank

blank * N = blank times N

blank / N = blank divided by N

L prefix = Left

M prefix = Middle

R prefix = Right

r suffix = reception

e suffix = emission

S prefix = Symmetric

Plus suffix = as calculate using the plus solution with the quadratic formula

Minus suffix = as calculated using the minus solution with the quadratic formula

Do not confuse lower case c with upper case C or with left parenthesis (

c = speed of light in medium

A = A coefficient for solving for Tr with quadratic formula

B = B coefficient for solving for Tr with quadratic formula

C = C coefficient for solving for Tr with quadratic formula

M A = A coefficient for solving for MTr with quadratic formula

Te = Time of Emission of signal from source

MTe = Middle Time of Emission

Tr = Time of Reception of signal at receiver

MTr = Middle time of Reception

Pe = Period of Emission

LPe = Left handed Period of Emission ( only applies to one example )

SPe = Symmetric Period of Emission ( only applies to one example )

Pr = Period of reception

LPr = Left handed Period of Reception

SPr = Symmetric Period of Reception

Pm = Period Multiplier

LPm = Left Period Multiplier

SPm = Symmetric Period Multiplier

Xr = X coordinate of Receiver at time of Reception

MXr = X coordinate of Receiver at middle time signal is Received

Ye = Y coordinate of Source at time signal is Emitted

Xr0 = Xr knot = initial X coordinate of Receiver at time 0

Ye0 = Ye knot = initial Y coordinate of source of Emission

PythDS = Pythagorean Distance Squared between source at time of emission and receiver at time of recepetion

MPythDS = PythDS for values with Middle prefix

LDS = Light Distance Squared.  Square of Amount of time it took light to travel from source to receiver times the speed of light

MLDS = LDS for values with Middle prefix

VRx = Constant scalar Velocity of Receiver in positive X direction

Units

meters squared PythDS and LDS

seconds per signal Pe an Pr

seconds Te and Tr, quadratic coefficient 

meters Xr, Ye, Xr0, Ye0

Unitless Pm

meters per second VRx

meters squared per second squared quadratic coefficient A

meters square per second quadratic coefficient B

meters squared quadratic coefficient C

Quadratic Formula Unit Check m is for meters and s is for seconds

- B / 2 A

( m^2*s^-1 ) / ( m^ 2*s ^ -2 ) = s ^ 1 matches units for Tr

B^2 - 4*A*C

(m^4*s^-2 ) - ( m ^ 2 * s ^ - 2 ) * m ^ 2 = m ^ 4 * s ^ -2 

square root of B^2 - 4*A*C

m ^ 2 * s ^ -1

[ sqrt ( B^2 - 4*A*C ) ] / [ 2 * A ]

( m ^ 2 * s ^ -1 ) / ( m ^ 2 * s ^ - 2 ) = s ^ 1 matches units for Tr

Calculations when Pe is not constant.  Used in only one example.

RPe = RTe - MTe

LPe = MTe - LTe

SPe = ( RTe - LTe ) / 2

SPe = ( RPe + LPe ) / 2

RPr = RTr - MTr 

LPr = MTr - LTr

SPr = ( RTr - LTr ) / 2

SPr = ( RPr + LPr ) / 2

RPm = RTr / RTe

LPm = LTr / LTe

SPm = ( RTr - LTr ) / ( RTe - LTe )

SPm = SPr / SPe

SPm = ( RPr + LPr ) / ( RPe + LPe )

General Calculations when Pe is constant

RTe = MTe + Pe

LTe = MTe - Pe

RPr = RTr - MTr

LPr = MTr - LTr

SPr = ( RTr - LTr ) / 2

SPr = ( RPr + LPr ) / 2

RPm = RPr / Pe

LPm = LPr / Pe

SPm = SPr / Pe

SPm = ( RTr - LTr ) / ( 2 * Pe )

SPm = ( RPr + LPr ) / ( 2 * Pe )

Mathematical Tools - ( not sure tools is the correct term )

Tools - Extra equations to help solve the problem

The time it takes light to travel from the source to the receiver should be equal to the distance between the position the receiver was at the time the signal was emitted and the position the source was at at the time the signal was received

Tools that maybe necessary to do General Calculations in some two and three dimensional cases

PythDS = ( Xr - Xe ) ^ 2 + ( Yr - Ye ) ^ 2 + ( Zr - Ze ) ^ 2

LDS = ( c ^ 2 ) * ( Tr - Te ) ^ 2

PythDS = LDS

Solve for Tr as a function of Te using PythDS = LDS and other conditions of problem including initial conditions

Solve for Te as a function of Tr using PythDS = LDS and other conditions of problem including initial conditions

The Square of the pythagorean distance is used because it is easier than using the original pythagorean distance formula with the square root as such the Light Distance must also be squared

Tools that maybe necessary to do General calculations in some one dimensional cases

CD = Coordinate Distance = Xr - Xe

LD = Light Distance = c * ( Tr - Te )

Coordinate Distance = Light Distance

Solve for Tr as a function of Te using CD = LD & other conditions of problem including initial conditions

Solve for Te as a function of Tr using CD = LD & other conditions of problem including initial conditions

In this case there is no need for a square or square root because the Pythagorean theorem is not needed

Two examples with fake data which are designed to make understanding calculations easy

This data is not data that I would expect from an actual experiment nor is it data designed to match what I would ideally expect in my model.  I simply am going to make up numbers to show how to do the Calculations with an easy problem that would not exist in real life before showing how the method works in my model which is more complicated.

First Example with variable rate of emission where Period of Emission is not Constant

Given

The first signal is emitted from a source at 5 seconds and received at the receiver at 100 seconds.

The second signal is emitted from a source at 20 seconds and received at the receiver at 110 seconds

The third signal is emitted from a source at 50 seconds and received at the receiver at 200 seconds

Conclude

LTe = 5 seconds

MTe = 20 seconds

RTe = 50 seconds

RPe = RTe - MTe = 50 seconds - 20 seconds = 30 seconds per signal

LPe = MTe - LTe = 20 seconds minus 5 seconds = 15 seconds per signal

SPe = ( RTe - LTe ) / 2 = ( 50 seconds - 5 seconds ) / 2 = 22.5 seconds per signal

SPe = ( RPe + LPe / 2 ) = ( 30 seconds + 15 seconds ) / 2 = 22.5 seconds per signal

LTr = 100 seconds

MTr = 110 seconds

RTr = 200 seconds

LPr = MTr - LTr = 110 seconds - 100 seconds = 10 seconds per signal

RPr = RTr - MTr = 200 seconds - 110 seconds = 90 seconds per signal

SPr = ( RTr - LTr ) / 2 = ( 200 seconds - 100 seconds ) / 2 = 50 seconds per signal

SPr = ( RPr + LPr ) / 2 = ( 10 seconds per signal + 90 seconds per signal ) / 2 = 50 seconds per signal

RPm = RPr / RPe = 90 seconds per signal / 30 seconds per signal = 3

LPm = LPr / LPe = 10 seconds per signal / 15 seconds per signal = 10 / 15

SPm = SPr / SPe = 50 seconds per signal / 22.5 seconds per signal = 50 / 22.5

SPm = ( RTr - LTr ) / ( RTe - LTe ) = ( 200 seconds - 100 seconds ) / ( 50 seconds - 5 seconds ) = 50 / 22.5

SPm = (RPr + LPr ) / ( RPe + LPe ) = ( 90 + 10 ) / ( 30 + 15 ) = 50 / 22,5

LLDS = ( LTr - LTe ) ^ 2 * c ^ 2 =( 100 seconds - 5 seconds ) ^ 2 * c ^ 2

MLDS = ( MTr - MTe ) ^ 2 * c ^ 2 =( 110 seconds - 20 seconds ) ^ 2 * c ^ 2

RLDS = ( RTr - RTe ) ^ 2 * c ^ 2 = ( 200 seconds - 50 seconds ) ^ 2 * c ^ 2

Second Example where Period of Emission is Constant

Given

One signal is emitted every 5 seconds

The middle signal is emitted at 15 seconds

The first signal is received at 100 seconds

The second signal is received at 150 seconds

The third signal is received at 250 seconds

Conclude

Pe = 5 seconds per signal

MTe = 15 seconds

LTe = MTe - Pe = 15 seconds - 5 seconds = 10 seconds

RTe = MTe + Pe = 15 seconds + 5 seconds = 20 seconds

LTr = 100 seconds

MTr = 150 seconds

RTr = 250 seconds

RPr = RTr - MTr = 250 seconds - 150 seconds = 100 seconds per signal

LPr = MTr - LTr = 150 seconds - 100 seconds = 50 seconds per signal

SPr = ( RTr - LTr ) / 2 = ( 250 seconds - 100 seconds ) / 2 = 75 seconds per signal

SPr = ( RPr + LPr ) / 2 = ( 100 + 50 ) seconds per signal  / 2 = 75 seconds per signal

RPm = RPr / Pe = 100 seconds per signal / 5 seconds per signal = 20

LPm = LPr / Pe = 50 seconds per signal / 5 seconds per signal = 10

SPm = SPr / Pe = 75 seconds per signal / 5 seconds per signal = 15

LLD = c * ( LTr - LTe ) = c * ( 100 seconds - 10 seconds ) = c * 90 seconds

RLD = RTr - RTe = c * ( 250 seconds - 20 seconds ) = c * 230 seconds

MLD = MTr - MTe = c * ( 150 seconds - 15 seconds ) = c * 135 seconds

Example with general one dimensional Doppler shift

Given

Xe = Xe0 + Ve * Te

Xr = Xr0 + Vr * Tr

Pe = constant

Conclude

CD = Xr - Xe

CD = Xr0 + Vr * Tr - ( Xe0 + Ve * Te )

LD = c * ( Tr - Te )

CD = LD

Xr0 + Vr * Tr - ( Xe0 + Ve * Te ) = c * ( Tr - Te )

( c - Vr ) * Tr = Xr0 - Xe0 - Ve * Te + c * Te

Tr = ( Xr0 - Xe0 + [ c - Ve ] * Te ) / ( c - Vr )

Replacing Te with MTe to solve for MTr using equation for TR

MTr = ( Xr0 - Xe0 + [ c - Ve ] * MTe ) / ( c - Vr )

Replacing Te with RTe to solve for RTr using equation for TR

RTe = MTe + Pe

RTr = ( Xr0 - Xe0 + [ c - Ve ] * [ MTe + Pe ] ) / ( c - Vr )

Replacing Te with LTe to solve for LTr using equation for TR

LTe = MTe - Pe

LTr = ( Xr0 - Xe0 + [ c - Ve ] * [ MTe - Pe ] ) / ( c - Vr )

Solving for periods of reception

RPr = RTr - MTr = Pe * [ c - Ve ] / ( c - Vr )

- ( -1 ) = + 1

LPr = MTr - LTr = Pe * [ c - Ve ] / ( c - Vr )

SPr = ( RTr - LTr ) / 2 =  Pe * [ c - Ve ] / ( c - Vr )

RPr = LPr = SPr in this case

Period Multiplier = Period of Reception / Period of Emission

Pr / Pe = [ Pe * ( c - Ve ) / ( c - Vr ) ] / Pe = ( c - Ve ) / ( c - Vr )

Frequency Multiplier = 1 / Period Multiplier

Frequency Multiplier = ( c - Vr ) / ( c - Ve )

This is same as classical one dimensional Doppler shift on wikipedia only I use different naming conventions for the variables and the signs are plus or minus in wikipedia.  The formula I present only works if you choose certain signs and so it might give the wrong answer sometimes which would have been correct if the signs were flipped when plugging in inputs

c is like Vm on wikipedia

Ve is like Vs on wikipedia

Vr is like Vr on wikipedia

2025 October 19 wikipedia

https://en.wikipedia.org/wiki/Doppler_effect

2025 October 10 Archive

https://web.archive.org/web/20251010003120/https://en.wikipedia.org/wiki/Doppler_effect

Two dimensional special transverse case with straight line movement and no acceleration and moving receiver with stationary source and reference frame

Given

A signal is released from the source at a constant rate of a period of Pe

Medium is stationary relative to the reference frame

Source is stationary 

Source has a X coordinate of zero

Source has a Y coordinate of Ye0

Receiver has a Y coordinate of zero

Receiver is moving in a straight line with no acceleration

During time MTr receiver is moving perpendicular to the direction between the source and receiver

During time MTr receiver has an X coordinate of zero

From a reference frame in which the source and medium are stationary and the receiver is moving the receiver receives the middle signal out of three signals when the source and receiver are at their closest points

Ye = Ye0

Xe = 0

Yr = 0

Xr = Xr0 + Vr * Tr

Choices on initial conditions

MTr - MTe = Ye0 / c

0 = Xr0 + Vr * MTr

These two equations above result in the following equations to find the other two variables initial conditions if a value for one variable is selected as an initial condition

Xr0 = -Vr * MTr

MTe = MTr - Ye0 / c

MTr = Ye0 / c + MTe

Xr0 = -Vr * ( Ye0 / c + MTe )

I assume it is easiest to choose a zero value for one of the variables for an initial condition

If MTr = 0 then MTe = - Ye0 / c and Xe0 = 0

If MTe = 0 then MTr = Ye0 / c and Xe0 = - Vr * Ye0 / c

Conclude

PythDS = ( Xr - Xe ) ^ 2 + ( Yr - Ye ) ^ 2

PythDS = ( Xr0 + Vr * Tr ) ^ 2 + Ye0 ^ 2

PythDS = Vr ^ 2 * Tr ^ 2 + 2 * Xr0 * Vr * Tr + Ye0 ^ 2

LDS = ( Tr - Te ) ^ 2 * c ^ 2

LDS = c ^ 2 * [ Tr ^ 2 - 2 * Te * Tr + Te ^ 2 ] 

PythDS = LDS

PythDS - LDS = 0

( Vr ^ 2 - c ^ 2 ) * Tr ^ 2 + ( 2 * Xr0 * Vr +  2 * c ^ 2 * Te ) * Tr + Ye0 ^ 2 - c  ^ 2 * Te ^ 2 = 0

Quadratic Formula to solve for Tr

A = Vr ^ 2 - c ^ 2

B = 2 * Xr0 * Vr + 2 * c ^ 2 * Te

C = Ye0 ^ 2 - c  ^ 2 * Te ^ 2 

Plug in MTe based on initial conditions to find if the correct solution for Tr is plus or minus.  The correct solution will make the calculated MTr the same as the MTr in the initial condition choices and will make MXr equal to 0 when the calculated MTr is plugged into the equation for Xr.

Quadratic Formula to solve for MTr

MA = Vr ^ 2 - c ^ 2

MB = 2 * Xr0 * Vr +  2 * c ^ 2 * MTe

MC = Ye0 ^ 2 - c  ^ 2 * MTe ^ 2

 

Quadratic Formula to solve for RTr

RTe = MTe + Pe

Can just have computer calculate RTe and plug in RTe

LA = Vr ^ 2 - c ^ 2

LB = 2 * Xr0 * Vr +  2 * c ^ 2 * ( MTe + Pe )

LC = Ye0 ^ 2 - c  ^ 2 * ( MTe + Pe ) ^ 2

Quadratic Formula to solve for LTr

LTe = MTe - Pe

Can just have computer calculate LTe and plug in LTe

LA = Vr ^ 2 - c ^ 2

LB = 2 * Xr0 * Vr + 2 * c ^ 2 * ( MTe - Pe )

LC = Ye0 ^ 2 - c  ^ 2 * ( MTe - Pe ) ^ 2

Check that LPythDS = LLDS and RPythDS = RLDS and MPythDS = MLDS

RPr = RTr - MTr

LPr = MTr - LTr

SPr = ( RTr - LTr ) / 2

SPr = ( RPr + LPr ) / 2

RPm = RPr / Pe

LPm = LPr / Pe

Symmetric Period Multipler

SPm = SPr / Pe

compare RPm, LPm and SPm with different function of Lorentz Factor gamma and alpha such as gamma or alpha to different powers

I did this twice using Google spreadsheets to simulate Microsoft excel and both times I found that the symmetric period multiplier was closer to gamma squared for certain values of Pe and Ye0 when an Xr0 of zero was chosen.  The solutions which used the minus sign instead of the plus sign for the quadratic equations were used because the plus sign did not give the correct result for sanity testing.  When an Xr0 was chosen that was not zero Microsoft excel seemed to have more problems with sanity testing.  Sanity testing involved seeing if one could get a similar value for the calculated MTr and the chosen or expected MTr based on the chosen initial conditions.  Sanity testing also involved seeing if PythDS was equal to LDS.  Sanity tests were not passed perfectly for Microsoft excel regarding PythDS and LDS but some sanity tests failed by a smaller amount than others.  The Middle values for PythDS and LDS should have also been equal to Ye0 squared when using the calculated MTr if the calculated MTr was equal to the chosen or expected MTr based on initial conditions.

A symmetric period multiplier of gamma squared is equivalent to a symmetric frequency multiplier of alpha squared

The frequency multiplier for a moving receiver with a stationary source and stationary medium with transverse movement in which the receiver moves in a straight line at a constant speed perpendicular to the direction between the source and receiver during reception of the middle signal should be closer to 1 than the frequency multiplier for parallel one dimensional Doppler with constant speed in which the source is stationary and the receiver is moving away from the source.  In both cases the symmetric period should be increase but the symmetric period should be increased more with transverse movement than with parallel movement at the same speed because the receiver is moving away from the source faster with parallel movement than it is when it is moving away from the source in the right handed period calculation for transverse movement.

Transverse 

Lorentz Factor Alpha ^ 2 = 1 - v ^ 2 / c ^ 2

Parallel

( c - v ) / c = 1 - v / c

Passes criteria of being closer to 1 for values of v greater than 0 and less than c

0 < 1 - v / c < 1 - v ^ 2 / c ^ 2 < 1

Example if v / c = 0.8

0 < 1 - 0.8 = 0.2 < 1 - 0.8 ^ 2 = 1 - 0.64 = 0.36 < 1

Calculating Period multiplier for transverse movement when the source is moving and the receiver is stationary instead of the other way around as previously done in the previous problem

There is a delay for light traveling to source from receiver so that for the same signal if it is emitted when the source is in one position it will be received when the source is in another position. 

Wikipedia describes some of these position variations with the following paragraph headings

Variation 1 - Source and receiver are at their points of closest approach

Variation 2 - Receiver sees the source as being at its closest point

Numbers 1, 2 could be switched this is just a list not an official academic title

Accessed link 2025 October 24

https://en.wikipedia.org/wiki/Relativistic_Doppler_effect

https://web.archive.org/web/20250923144348/https://en.wikipedia.org/wiki/Relativistic_Doppler_effect

My variation in the previous problem - In the previous problem I choose a variation in which from a reference frame in which the source and medium are stationary and the receiver is moving the receiver receives the middle signal out of three signals when the source and receiver are at their closest points.  But in this example for this new problem the source is moving and the receiver and the medium are stationary in the chosen reference frame.  These two examples are not equivalent to one another only just described in different reference frames when one takes into account the velocity of the medium.  

Since the source is moving and the receiver is stationary if the source emits the signal when the source and receiver are at their closest point then the receiver will receive a signal when the source is actually farther away from the receiver than at the closest point.

Since the source is moving and the receiver is stationary if the source emits the signal at a certain time before the source and the receiver are at the closest point then the receiver will receive a signal when the source and the receiver are at their closest point

These variations make my chosen initial conditions more difficult for me to be certain if I chose correctly in this problem than the previous problem

Given

Medium is stationary relative to the reference frame

Receiver is stationary 

Receiver has a X coordinate of zero

Receiver has a Y coordinate of Yr0

Source has a Y coordinate of zero

Source is moving in a straight line with no acceleration

A signal is released from the source at a constant rate of a period of Pe

Yr = Yr0

Xr = 0

Ye = 0

Xe = Xe0 + Ve * Te

 Conclude

PythDS = ( Xe0 + Ve * Te ) ^ 2 + Yr0 ^ 2

LDS = c ^ 2 * ( Tr - Te ) ^ 2

PythDS = LDS

( Xe0 + Ve * Te ) ^ 2 + Yr0 ^ 2 = c ^ 2 * ( Tr - Te ) ^ 2

PythDS - LDS = 0

( Xe0 + Ve * Te ) ^ 2 + Yr0 ^ 2 - c ^ 2 * ( Tr - Te ) ^ 2 = 0

- c^2*Tr + 2 * c * Tr * Te + ( Ve^2 - c^2 ) * Te ^ 2 + 2 * Xe0 * Ve * Te + Xe0 ^ 2 + Yr0 ^ 2 = 0

Quadratic Formula to solve for Tr

A = - c ^ 2

B = 2 * c ^ 2 * Te

C = 2*Xe0 * Ve * Te + Xe0 ^ 2 + Yr0 ^ 2 + ( Ve ^ 2 - c ^2 ) * Te ^ 2

If Xe0 = 0 then C = Yr0 ^ 2 + ( Ve ^ 2 - c ^2 ) * Te ^ 2

If initial conditions are selected such that Xe0 = 0 then

- B / ( 2 * A ) = ( - 1 ) * ( 2 * c ^ 2 * Te ) / [ 2 * ( - c ^ 2 ) ]

- 2 / - 2 = + 1

- B / ( 2 * A ) = Te

B ^ 2 = 4 * c ^ 4 * Te ^ 2

- 4 * A * C = ( - 4 ) * ( - c ^ 2 )  * [ Yr0 ^ 2 + ( Ve ^ 2 - c ^2 ) * Te ^ 2 ]

- 4 * A * C = 4 * c ^ 2 * [ Yr0 ^ 2 + ( Ve ^ 2 - c ^2 ) * Te ^ 2 ]

4 * c ^ 4 * Te ^ 2 -  c ^ 2 * c ^2 * Te ^ 2 = 0

B ^ 2 - 4 * A * C = 4 * c ^2 * [ Yr0 ^ 2 + Ve0 ^ 2 * Te ^ 2 ]

I am not sure these initial conditions would be correct based on the given conditions.  If it is possible to let MTe = 0 and Xe = 0 for initial conditions without mathematical errors or contradictions compared to the given conditions then the following would result.  

MTe = 0

RTe = Pe

LTe = - Pe

Quadratic Formula for MTr

- B / ( 2 * A ) = MTe = 0

B ^ 2 - 4 * A * C = 4 * c ^2 * [ Yr0 ^ 2 + Ve0 ^ 2 * ( 0 ) ^ 2 ]

B ^ 2 - 4 * A * C = 4 * c ^2 * Yr0 ^ 2

sqrt ( B ^ 2 - 4 * A * C ) = 2 * c * Yr0

MA = - c ^ 2

MB = 2 * c ^ 2 * 0 = 0

MC = Yr0 ^ 2 + ( Ve ^ 2 - c ^2 ) * 0 ^ 2 = Yr0 ^ 2

-4 * A * C =  ( -4) * - c ^ 2 * Yr0 ^ 2 = 4 * c ^2 * Yr0 ^ 2

Quaratic Formula for LTr

- B / ( 2 * A ) = LTe = - Pe

B ^ 2 - 4 * A * C = 4 * c ^2 * [ Yr0 ^ 2 + Ve0 ^ 2 * ( - Pe ) ^ 2 ]

LA = - c ^ 2

LB = 2 * c ^ 2 * ( - Pe )

LC = Yr0 ^ 2 + ( Ve ^ 2 - c ^2 ) * ( - Pe ) ^ 2

Quadratic Formula for RTr

- B / ( 2 * A ) = RTe = Pe

B ^ 2 - 4 * A * C = 4 * c ^2 * [ Yr0 ^ 2 + Ve0 ^ 2 * ( + Pe ) ^ 2 ]

RA = - c ^ 2

RB = 2 * c ^ 2 * Pe

RC = Yr0 ^ 2 + ( Ve ^ 2 - c ^2 ) * ( Pe ) ^ 2

Cancelling out sqrt ( B ^ 2 - 4 * A * C ) when calculating RTr - LTr

4 * c ^2 * [ Yr0 ^ 2 + Ve0 ^ 2 * ( - Pe ) ^ 2 ] = 4 * c ^2 * [ Yr0 ^ 2 + Ve0 ^ 2 * ( + Pe ) ^ 2 ]

if Q = P then sqrt(Q) = sqrt(P) when the sign is the same for the solution

RTr - LTr = Pe + Blank - ( - Pe +Blank )

RTr - LTr = Pe - - Pe = 2 * Pe

Calculating Symmetric Period Multiplier

SPm = ( RTr - LTr ) / ( 2 * Pe )

SPm = 1

This is the traditional answer for transverse Doppler shift but it is a different answer then the previous answer for a transverse Doppler shift under other circumstances

Right and Left Period Multipliers could be calculated numerically because they are more difficult to calculate than the Symmetric Period Multiplier

Atmospheric Thickness

T is the vertical distance away from a spot on the surface of a spherical planet in which the atmosphere is a certain density

R is the radius of the spherical planet

H is the horizontal straight line distance away from the same spot on the surface of a spherical planet in which the atmosphere is the same density

To be that density or greater you must be at less than a distance of R + T from the center of the planet

Assume the air density is a function of distance away from the center of the planet and decreases as you get farther away.  Assume at the same distance from the center no matter the direction the air density is always the same for distances greater than R.  This is an ideal over simplification to make the math easy and it does not work this way in real life.

Outer circle Radius R + T

Inner circle Radius R

Distance from ( 0, 0 ) to ( H, R ) equals distance from ( 0 , 0 ) to ( 0 , R + T ) 

H ^ 2 + R ^ 2 = ( R + T ) ^ 2

H ^ 2 + R ^ 2 = R ^ 2 + 2 * R * T + T ^ 2

H ^ 2 = 2 * R * T + T ^ 2

H = sqrt ( 2 * R * T + T ^ 2 )

You can skip this until continue reading

Implication of atmospheric fitness

Because the atmosphere is a certain density or greater in a straight horizontal line from a receiver on the surface of the earth than vertically from the same receiver.  Radiation from the part of the back drop above the receiver which the receiver is moving "perpendicular" to related to the 2 dimensional period multiplier calculations maybe of more importance than of radiation from the part of the back drop located horizontally from the receiver in the direction or the opposite direction of how the receiver is moving in the 1 dimensional calculation of 2 signals hitting the same receiver from two sources in opposite directions.  This also maybe related to why you do not get sunburn horizontally near sunrise and sunset but get sunburn vertically during noon and possibly also related to why sunrise and moon rise are red shifted compared to the sun at noon or the moon at a 90 degree angle of altitude or directly over head.

continue reading

end unless more material added after this