Dear Helmut,
I enjoyed the novel and original perspective on the speed of light you introduced. I believe there may be an objection that can be made to your argument:
The particle-like manifestation of light does not appear to be on the same footing as its wave-like manifestation, because the former appears exclusively the instant light is absorbed. This seems in contrast to the wave-particle duality of, say, electrons, which continue to exist even after they have been localized. If we could observe the particle-like manifestation of light without causing it to go out of existence, then your argument would fully apply, but if not, then there does not seem to be a need to consider the wave-particle duality to apply to the speed of light itself.
Actually, as I am writing this, an idea occurred to me for how your dual parameterization might already have been implemented in special relativity in an as yet unrecognized way. I will outline the idea below and would appreciate your comments.
The relevant equation from special relativity to consider is:
[math]\frac{1}{\gamma^2}+\beta^2=1[/math]
Now, multiplying both sides by the speed of light squared gives
[math]\frac{c^2}{\gamma^2}+v^2=c^2[/math]
The first term is a paremeterization with units of speeds of how fast an object is observed to progress in time since:
[math]\frac{c}{\gamma}=c\frac{d\tau}{dt}[/math]
where dtau is the proper time. This can also be thought of as a speed term independent of the dimensional units since
[math]c\frac{d\tau}{dt}=\frac{ds}{dt} \equiv{v_{\tau}}[/math]
where ds is the spacetime interval and the last term is defined as motion in proper time. Inserting this into the second equation finally gives
[math]v_{\tau}^2+v^2=c^2[/math]
The relevance to your dual parameterization would seem to be this: We know that electromagnetic radiation is energy propagating at v=c in space. In this form, it has the wave-like aspect. But if it is absorbed, that energy becomes now part of a massive object which, unlike the radiation, is associated with a rest frame. In a rest frame, v_tau=c. So, in a particle manifestation, this energy in its rest frame is also associated with a speed of light but now in time, not in space.
Incidentally, I used this conceptualization of "motion in proper time" in my essay submission to the first FQXi contest four years ago. It was about the speed of light postulate, so you might find it interesting . It is topic 329 (I also have an essay this year, topic 1431, but it is less directly related to yours).
I hope you found this comments useful and interesting,
All the best,
Armin
