This was still in my drafts even though I thought I published it, it said 2024 January 28 in the draft
I am publishing it as is and plan to look over it later
Copyright Carl Janssen 2024 January 28
I will call the object emitting the light or sound wave a source and the object receiving or being hit by the light or sound wave a receiver
If a medium is stationary from the point of view of a reference frame then
if a source is moving the frequency of light or sound waves emitted that are going parallel and in the same direction that the object is moving will increase in frequency and their period and wavelength will decrease
if a source is moving the frequency of light or sound waves emitted that are going anti-parallel and in the opposite direction that the object is moving will decrease in frequency and their period and wavelength will decrease
If from the reference frame in which the medium is stationary a object that is being hit by the light or sound wave
The energy per photon for light is equal to it's frequency times a constant. One must then ask if light was Doppler shifted would this violate conservation of energy because the
There are four answers I have read which are similar to answers I have thought of on my own prior to reading it except number 3 which I thought of as a factor to consider but did not solve it to come up with a solution as someone else has claimed to
https://duckduckgo.com/?q=doppler+shift+and+conservation+of+energy&ia=web
https://physics.stackexchange.com/questions/15279/conservation-of-energy-and-doppler-effect#15280
https://physics.stackexchange.com/questions/428810/doppler-shift-in-terms-of-energy
https://arxiv.org/abs/physics/0407077
https://physics.stackexchange.com/questions/13577/photons-in-expanding-space-how-is-energy-conserved
https://physics.stackexchange.com/questions/392147/how-to-work-out-conservation-of-energy-and-doppler-shifts
https://physics.stackexchange.com/questions/545464/doppler-shifts-appear-to-violate-conservation-of-energy
https://en.wikipedia.org/wiki/Radiation_pressure
Point number 1
Some photons gain energy but this is undone by photons going in a different direction that lose energy.
Point number 2
Energy is conserved in each non accelerating non rotating reference frame but different for different reference frames so there can be different amounts of energy in each reference frame.
Point number 3
An idea I had was that we need to think about the changing momentum of light as caused by a source or observer that is moving relative to a medium and or reference frame and how this moment of light is involved in collisions and it's relation to the frequency, period and wavelength of photons as related to things like the Compton effect, the reverse Compton effect, Thompson scattering and so on. For now I will simply post what someone else who has put more thought into it than me has said about something he called radiation pressure which is also related to the momentum of photons and his explanation of how radiation pressure solves the issue of conservation of energy and doppler shifting. I will not comment on whether or not what he said really solves the issue for now.
Point number 4
When the power of the light that is emitted by the source is increased it's duration that it hits the receiver will be decreased so that the amount of energy expended by the source is the same as the amount of energy received by the receiver. This is a oversimplified because the light might interact with other objects and transfer energy to them before it effects the receiver but each of those objects can be modeled as a receiver and the same principle would be true for energy being conserved when you consider every receiver it hits combined so this is oversimplification being solved shall not be mentioned again.
Point number 1 does not work
If the source emits two photons that would have been the same frequency before shifting in opposite directions the one photon will gain an amount of energy from the shift equal to the amount of energy the other photon would have lost so someone might argue that perhaps if photons that would have all been the same frequency are launched in a radially symmetric pattern that includes at least one photon parallel and at least one photon anti-parallel to the direction the source is moving then the energy lost by all the photons from the shift would be equal to the energy gained by all the photons from the shift and cancel out.
But it is possible to only send light in one direction or to send more photons in one direction than another direction so this is no solution to the problem, perhaps this could be accomplished simply by putting a mirror on one side of a light source but not the other side or by using a laser pointer that only shines light in one direction and does not shine light outside of itself in a radially symmetric manner or by using a flashlight that does not shine light outside of itself in a radially symmetric manner and if photons are only emitted in a source in one direction than this point number 1 would not solve this problem.
Point number 2 does not work
If you have two different reference frames that are moving relative to each other at a constant velocity with no rotation or acceleration of one relative to the other
If in one reference frames all the objects are still it will have zero kinetic energy and zero momentum but in another reference frame it will have a kinetic energy equal to the mass of all the objects added together squared then next divided by two and a momentum equal to the mass of all the objects added together then next multiplied by the velocity since they are all moving at the same velocity having a total non zero kinetic energy and a total non zero momentum. So different reference frames can have different amounts of total energy and different amounts of total momentum.
Side Note
On a side note this is why if the universe has non zero mass then all so called scientific models that do not assume the universe eternally existed and eternally had non zero mass are self contradictory because otherwise there would be a non accelerating non rotating reference frame in which the universe changes it's amount of momentum from zero momentum to a non zero amount of momentum which would violate the conservation of momentum. This is why all so called scientific models which acknowledge conservation of momentum that also claim the universe was created out of nothing many of which are supported by so called creation scientists are self contradictory. This does not disprove that the universe was created out of nothing because the universe could have been created out of nothing in violation of all scientific models that include conservation of momentum which would be called a miracle by religious people.
End of side note
Different energy in different reference frames is not the issue, having different energy in different reference frames does not necessarily violate conservation of energy. The issue is the problem of the total energy in the same non accelerating non rotating reference frame changing over the passing of time or in other words being different between two different times as measured in the same reference frame that would be the violation of conservation of energy if such a thing occurred.
Imagine there is a light source like a flash light or laser pointer that is powered by a chemical battery and which is constantly on and sends a beam of light at a receiver that is completely opaque and does not let light reflect from it or pass through it and none of the light misses the targeted receiver and that 100% of the light that hits the targeted receiver becomes heat which would increase the temperature of the receiver and that none of the light interacts with the medium in such a way as to transfer energy to it before it would have reached the receiver in order to simplify things.
The Chemical concentrations of different chemicals in the battery times the efficiency indicates how much energy is spent
Switching reference frames should not change chemical concentration of the bttery
Even with switching reference frames the amount of chemical concentration in a battery transferring energy to a light source producing a beam of light hitting a receiver the temperature of the receiver and the chemical concentration and temperature of the battery and the temperature of the light source should be the same for the same event or in other words the same for the same time ( if time is measured by the order of events rather than the reading on a clock label ) for all reference frames. Someone can try to make an excuse that the light wound be at a different frequency and therefore have different energy if you are observing it in a different reference frame but this excuse is potentially problematic when you consider that the chemical concentration of the chemicals used to operate the battery should be the same for all reference frames for the same event since the chemical concentration is an indication of how much energy has been expended by the battery and since the temperature of the receiver should be the same for all reference frames for the same event since the temperature of the receiver is an indication of how much energy had been transferred from the battery in the source to the receiver hit by the source's light beam because if the amount of energy gain in the receiver indicated by the temperature change of the receiver is different than the amount of energy expended to produce the light beam by the battery which can be got from the sources efficiency and it's chemical concentration than the conservation of energy is violated in spite of arguments that it does not matter that the energy of the light that has left the source but has not yet reached the target is different in different reference frames because the emitted photons that have not yet hit their target and are still traveling toward it appear to be different frequencies in different reference frames.
I will use a simplified example with a single reference frame and no reference frame switching in which the medium is measured as stationary in that reference frame and in which the receiver is not moving relative to the medium but the light source is a chemical battery powered laser pointer that is moving relative to the receiver to examine the question at hand.
Although it is true that different reference frames can have different amounts of total energy this does not solve the problem because imagine a flashlight or laser pointer that has a chemical energy source such as a chemical battery. The concentration of chemicals in the flash light should be the same for any event that is at any moment in time not as measured by the label on a clock but as measured in terms of the order of events. As energy is transferred to create light the concentration of chemicals should change through the chemical reaction involved to provide the energy to create the light. As the receiver is hit by the light it would heat up or increase electron energy levels and so on, I will just simplify this and call it receiving a certain amount of heat when it is hit equal to the amount of energy from the light that hits it. I will over simplify and assume it is a perfectly opaque and non reflective object and that all of the light that touches it heats it up instead of reflecting or going through it and refracting like could happen for a transparent object or other ways for the energy not to transfer to the receiver. In any reference frame at the same moment in time the chemical concentration of the flashlight battery will be the same as any other reference frame in the same moment of time ( as measured by order of events ) but if the amount of energy that the receiver hit by the light from the source changes as a result of the receiver or the source moving then this violates conservation of energy. Someone might say that the amount of energy the light appears to have changes as the reference frames change but that does not solve the problem. The amount of heat the receiver receives from light and the amount of chemical concentrations in the battery and the temperature of the battery and the temperature of the receiver and the temperature of the source should be the same for the same moment in time as measured by the order of events for all reference frames and if it is not that is a violation of the conservation of energy. If the battery does not change the rate at which chemical concentrations run when the source and or receiver moves at different velocities relative to the medium then conservation of energy would be violated because the amount of heat the receiver receives might be different than the amount of energy equivalent to that which would be transferred into the light beam from the change in chemical concentrations for running the chemical reactions depending on what velocity the source and or the receiver moves at relative to the medium. If it would take the same amount of time for the battery to be depleted no matter how fast and in what direction the flash light or laser pointer moves but depending on how fast and in what direction the flash light or laser pointer moves the receiver would receive a different amount of heat then conservation of energy would be violated. There is also a issue of imperfect transfer from battery chemical energy to light directed toward the receiver some possibly producing heat but this does not change my main point.
Point Number 3
"The top answer is correct but incomplete; even within a "bystander" reference frame, it is easy to observe that photons impart more energy onto the recipient when the emission source is moving towards, as opposed to away from, said recipient. Energy is indeed gained or lost by the photons.
This occurs due to radiation pressure. The emission source loses kinetic energy to photons emitted in the direction of motion while gaining kinetic energy from photons emitted in the opposite direction. Similarly, the photons impart kinetic energy onto the recipient, causing loss of kinetic energy if the recipient is moving towards the emission source or gain of energy if the recipient is moving away from the source. As photons always move at the speed of light, the gained / lost energy is observed as a change in wavelength."
https://web.archive.org/web/20231003205320/https://physics.stackexchange.com/questions/15279/conservation-of-energy-and-doppler-effect#15280
