Peter, you said: "There are cases of both c and f, and of f and λ changing inversely to conserve the 3rd property when the media are co-moving..."
I agree this may be so, but my focus is for static media with observer at rest. What I mean can be illustrated thus:
- If a source of waves, say a plunger or finger is being dipped in water at x number of times per second, waves of this frequency, i.e. f = xHz are generated travelling out at v m/s with wavelength, λ. The relationship is v = fλ.
- Increasing the frequency of dipping, changes f. λ also changes (reduces), but v remains the same. v is characteristic of the particular medium. The relationship v = fλ still holds.
- Next, plunge or dip the finger again at x number of times per second. This time however, replace the water with a thicker fluid. Waves are still generated at xHz. However, this time the wavelength, λ is different. I assume for thicker fluid, the wavelength λ will be longer (correct me here), so v is higher. The relationship v = fλ still holds.
The importance of my analogy is that when change in wavelength of electromagnetic vibration is observed, it could be a result of change in frequency or a change in the ambient medium. If an observer, knowing the relationship v = fλ carries a 'clock' beating at certain frequency, f = v/λ and enters unknown to him a different medium, he may encounter a dilemma if he wishes to redetermine the frequency, by using wavelength. Even though there may be no change in f, i.e. the clock's beating remains the same, if v changes (e.g. if v is higher) but is unknown to the observer, who therefore goes ahead to use f = v/λ, the wavelength will appear to have become shorter. The observer, will therefore 'calculate' that the frequency is faster and say "clocks beat faster".
This maybe the state of affairs of which it is claimed that "clocks beat faster" in a higher gravitational potential, i.e. at higher altitude. An observer oblivious that c has changed and is higher in the less dense ambient medium can be excused for making this claim. This is why it would be nice to know how Steve's "cool" clocks work.
Thanks for the link to: Special edition; what is a photon? Very rich. Needs to be kept for reference.
Do I think 2020 may be optimistic? I can only be optimistic, if you give up at least two of your claims or assumptions.
First, you must give up Lorentz factor, if it means (1-v2/c2). v is meaningless in the equation. How can v have a value 30km/s, 225km/s and 371km/s simultaneously. To three experimenters looking at the same rod and the same clock in the same laboratory, with each deciding his choice whether to use earth orbital motion, solar system galactic motion or our CMB motion, which is to be used to calculate the amount of Length contraction or Time dilation to obtain a constant resultant speed of light?
Second, you may need to revisit the claim that higher density of DFM plasma has no effect on the refractive index. It is my contention that denser plasma will have higher refractive index.
Regards,
Akinbo