The energy of what? First we were talking about a photon being reflected off a mirror on the HST, then we were talking about a photon that's being slowed down for some reason. Don't blame me for your confusion if you keep changing the subject.
If the *energy* of a photon is also decreasing as its speed nears 0, then there's no need for its momentum to increase.
But let's go back to the reflected photon. You stated that this photon's energy does not decrease as it is reflected. You also stated that both its speed and its wavelength increases. If you keep energy constant, but increase velocity, you must also decrease momentum. It makes no sense to say that two particles of the same mass (in this case zero) but different speeds can nonetheless have the same momentum.
And you can't ditch the invariance of c and still keep E/c as the momentum of a photon.. Either they're both right or both wrong. The momentum/energy relationship from which that formula is derived entails (not just assumes as I might have suggested earlier) that not only photons, but any and all massless particles that might exist in an inertial frame, always move at c in that frame.
In my model, photons have energy and distance. All other properties can be calculated from them when required, but the model doesn't need them to work.
https://mikehelland.github.io/hubbles-law/index.htm#photon-treatment
This model represents light at the individual photon level. It's not a quantum theory, nor is it a relativistic theory, but it's also not completely classical. To illustrate, the photon was defined as having a distance from its source.
Where is this photon? It doesn't have an (x,y,z) coordinate. Instead, it occupies every point around its source at the specified distance. It's not a classical particle or wave in this form.
Later, we added velocity, frequency, and wavelength to the photon.
Code:
photon = {
distance: 0,
velocity: 1,
frequency: 6e5,
wavelength: 499.65
}
For the purposes of this model, the photon actually only needs distance and energy.
Code:
photon = {
distance: 0,
energy: 2.48,
}
We know from classical mechanics that the speed of a wave is its frequency × wavelength. In quantum mechanics the energy of a photon is frequency × Planck's constant (h). And hypothesis 1 says the speed of a photon is c - H × D. Given these formulas:
Code:
speed of a photon v = c - H × D
speed of wave v = f × w
energy of a photon E = h × f
the photon's velocity, frequency, and wavelength can be determined at any time from its distance and initial energy.
However, those values don't need to be there at all times, and since the photon is a quantum particle, they probably shouldn't be there until we need them.
What we know about a photon we determine from its interaction with a measurement apparatus, not because we can observe it in-flight.
We know that a red-shifted photon will deliver less energy than it started out with. Assuming the ratio of energy observed to energy emitted is the same ratio as the photon's velocity to c, we can calculate the observed energy of a photon using just the photon's original energy and the distance from its source:
Code:
E_observed = E_emitted × v/c
= E_emitted × (c - H × D)/c
And if we put that over Planck's constant (h) we get the new red-shifted frequency of the photon:
Code:
frequency_observed = (E_emitted × (c - H × D)/c) / h
The photon's distance from where it was emitted is crucial to keep in mind at all times. Consider light that has traveled billions of years to reach your telescope. The light enters the lens, gets focused to the eyepiece, and then into your eyeball.
Seems pretty straightforward. But at some level, some type of interaction with the light and the lens must be focusing the light. At the quantum level, the photon will have been absorbed by atoms in the lens. Then it is re-emitted (or an entirely new photon is emitted), and focused to your telescope's eyepiece.
The photon may have traveled great distances from its source before it encountered your telescope, but the light inside the telescope will be very close to its source: the lens that focused it. The distance to the source of the photons in the telescope will be less than a meter, not millions of light years.
In that case the refreshed photon will be traveling at c, which now results in an elongated wavelength when calculated.
