Dear En,
I saw your post at Ken Wharton and would like to answer your questions, but because they had nothing to do with his essay I will post the answers here.
"I wonder whether you would be willing to pose your question in an FQXi blog accessible to a larger audience"
Thank you for considering this issue sufficiently important to suggest this, but I am not sure the audience that I would potentially reach in this format is the audience I want to reach. For better or for worse, I have the impression that most of the people who frequent them are not professional physicists, but it is they who have to consider this argument. At any rate, I am working on this problem both from the relativity and from the quantum theory side, and the puzzle is by no means yet complete. Perhaps when I have more pieces together people will start paying attention.
"You are right, any inconsistencies in accepted theories must be investigated (if uncovered by qualified people)."
Well, just to be clear, I am not claiming that this issue is an inconsistency but that it is an apparent wrong prediction of the theory: A reasonable interpretation of the extrapolation of the theory to objects characterized by v=c should have led us to predict that there are no such objects, but in fact there are.
The claim that it is only "apparently" wrong, however, is based on my own ideas on how to resolve the problem, and definitely non-standard. But I don't want to force my own ideas on anyone: Anyone who wishes to do so, can try to resolve it on their own, but before this happens people first have to see that there is a problem. The bottom line, however, is that I do not take this to be grounds for rejecting special relativity. It is important for me to emphasize this because the argument could be co-opted by those who deny relativity, and I do not wish to be lumped together with the anti-relativity crowd.
"...such inconsistencies need to be looked at again regularly and not just "papered over."
Well, correcting again for the fact that this is not an inconsistency but an apparently wrong prediction, you saw Ken's response, which is a typical denialist one, as seen by the following:
a) He said "1) I think in terms of fields, not particles, *especially* when it comes to light,..." implying that my argument applies only to particles, not fields. Well, go back and check, I did not use the word "particle" even once, the argument is general enough to encompass both particles and fields, so that implication is false.
b) Even though I expressly said that my aim was only to convince him that there was a problem, and not to convince him of my ideas, he said nothing about whether he thought there was a problem or not (i.e. ignoring in his response the central issue I was talking about) but only "I'm the last person to tell anyone that a crazy idea isn't worth exploring, if you think that a promising topic has been unfairly neglected..."
So yes, this is disappointing but not unexpected. I think to a great extent this is because the problem is being pointed out by an unknown person. If it had been, say, Hawking or Witten, who pointed this out, then people would pay attention, as evidenced by the fact that theoretical physicists are willing to seriously consider ideas like 6 extra dimensions and/or a multiverse, even though there is absolutely zero evidence either in nature or in our established theories which implies this. The problem I am pointing out, on the other hand, is straightforwardly implied by what many physicists consider one of our best established theories of science.
"Just for my own curiosity, what is the evidence that such objects exist (v=c), and what is the duration of their existence, and how is that measured?"
Well, there are at least two kinds of objects associated with v=c, photons, the force carriers of the electromagnetic force in Quantum Electrodynamics, and gluons, the force carriers of the strong force in quantum chromodynamics. The indirect evidence that these exist is that they play an essential role in these theories, and these theories have very successfully withstood experimental challenge.
The direct evidence can be obtained by setting up an experiment in which a photon source is aimed at a detector a distance r away, emits photons at time t=0 and the detector indicates a detection at time t=r/c later. At a microscopic level, the emission event at the source and the absorption event at the detector are due electrons going from a higher energy level to a lower one, and vice versa, respectively. This is all well understood.
The "duration of existence" is a little tricky in relativity, because there are two time parameters, coordinate time and proper time. Proper time is the time measured in a clock at rest relative to the object you are observing. Coordinate time is the amount of time you assign based on a clock at rest relative to the observer. If the observer is at rest with respect to the thing that is being observed, the two are the same, otherwise they are related to each other by
[math]\tau=\frac{t}{\gamma}=t {\sqrt{1-v^2/c^2}[/math]
where tau is the proper time and t is the coordinate time, and gamma is the Lorentz factor. You can see that if v=c, you get tau=0, so a hypothetical clock in the rest frame of the object would stand still from the moment the object comes into existence until it goes out of existence, even if t could be billions of years (for example, light coming from galaxies billions of light years away). All this is also well understood and not controversial. However, as I mentioned in Ken Wharton's blog, it does imply a problem that is currently not recognized by physicists because, again, if we did not already know that such objects exists, this would have surely have led us to believe that a prediction of the theory is that they don't exist.
Finally, I did look over your short paper. It is rather informal. Although I tend to sympathize with what I perceive to be your main point, that the essential thing that distinguishes math from physics is that the latter uses numbers to express relationships between things characterized by physical qualities, let me just mention that one could mount a counterargument: In mathematics, there is a mathematical object called a measure, and the measure can represent any physical quality you want: Length, time, mass, apples, oranges, even probabilities. While often measures are used without dimensional units, they are used with dimensional units even in some areas of mathematics, for example length measures in geometry.
Hope you found my comments useful.
Best,
Armin
