Dear Terry (if I may),
There seems to be a slight mix-up in that you replied to Silviu's response to your comment by name, yet indicated something in your last paragraph which suggests that you may have thought that you were addressing me. Indeed, I am coming a little late to this conversation, but let me thank you right away for taking the time to read my essay and making some thoughtful comments. Also, I am flattered by your appellation, but I am not a professor, just a researcher. I would like to respond to some of your comments in detail.
First, your essay contestant pledge. What a wonderful idea! I have participated in this essay contest every single time except the last, and I have expressed my distaste for the author rating system both to the moderators and even to Max Tegmark himself. I understand why he does it, but unfortunately it comes at great costs, including that ratings are invariably bound to be influenced by factors other than the rater's best judgement of the essay's quality. With your permission, I would like to forward the pledge to Max, and suggest that either it or something similar be made a requirement for participation in future contests. It won't deter the determined colluders and cheaters, but it will help make the whole thing less farcical, I believe.
Second, some thoughts on your feedback on the essay itself:
"In terms of physics, I think your observation that there is a unbreakable dimensionality barrier between sub-light (massive) and light speed (massless) particles is a nice alternative way of saying massive versus massless."
It is actually more subtle than that, as I will try to show In the second part of the 2-part series of which my essay entry was the first part. The second part will, after developing an analogous reconceptualization of time dilation, apply these ideas to quantum mechanics and derive some novel distinctions, including one involving mass.
"I don't see a new invariant in this. I've read your dimensional abatement several times, and every time I get back to the same conclusion: This is still one-dimensional Lorentz contraction, just with more dimensions added."
I understand your point of view and agree that by itself, dimensional abatement does not contribute anything not already contained in Lorentz contraction.. However, in the second paper I will combine it with its analog for time dilation to derive certain insights that could not be derived using just the concepts of length contraction and time dilation and use these as a starting point exploring for my real target: quantum foundations.
"I don't immediately see the advantage of defining the photon as 2D, even though I find that an intriguing idea."
Thank you, at this stage I agree that the value is more philosophical, but I am glad that you are open-minded enough to consider that this really is an implication of special relativity which has gone unrecognized so far.
Photons are... odd, and complex, and can push the limits of quantum theory even now if you dig deep into them. (I have a great little book on that that I seem to have lost, hmm...I)
I agree and I would love to find out which book you have in mind, if you remember.
"For example, if you imagine a photon as a 3D sphere (technically a 2-sphere for purists) with a point orbiting around its equator, you can model all possible polarizations, from linear through elliptical to circular, as nothing more than different orientations of the sphere that is then projected (made 2D) along the axis of propagation. The cohesive value in that model of treating the photon as a 3D sphere before making the final 3D to 2D projective reduction in its dimensionality says to me that one should not simply discard the 3D view as irrelevant even for a particle traveling at c."
I was unaware of this model and it sounds very interesting. As you know, while the photon is according to SR completely length contracted, it does have a wavelength and period in the direction of motion, and this can result in 3D-behavior associated with photons, of which certain polarization states like circular polarization are an excellent example. So I agree with you: My claim that photons are dimensionally reduced was not meant to make any 3D conceptualizations of photons irrelevant. Rather, it was meant to elucidate what I believe to be an overlooked implication of special relativity.
For example, if you imagine a photon as a 3D sphere (technically a 2-sphere for purists) with a point orbiting around its equator, you can model all possible polarizations, from linear through elliptical to circular, as nothing more than different orientations of the sphere that is then projected (made 2D) along the axis of propagation. The cohesive value in that model of treating the photon as a 3D sphere before making the final 3D to 2D projective reduction in its dimensionality says to me that one should not simply discard the 3D view as irrelevant even for a particle traveling at c.
"Here's my biggest problem, and it's one that affects many of the large number of submissions this year: You did not answer the question that FQXi asked, which was to explain what makes a theory "more fundamental". "
My answer to the essay question is at the top of page 2:
"And this gives us a clue for identifying the most fundamental things of a theory within any given paradigm: it has to be those things which point to, or at least hint at, the next paradigm."
I structured my essay so that the theory I presented was an illustration of that answer. Now, if you had criticized my answer by saying that I did not sufficiently elaborate on it, or that I shoe-horned my own theory into the paper, I might have agreed with you, but to me, it seems a little unfair to say that I did not answer it at all. Be it as it may, my objective in this essay contest is not to win but to reach physicists, mathematicians and philosophers of physics who have a strong interest in foundational physics with some ideas which I believe are going to lead us to the next paradigm.
Actually, from your comments on another essay I saw, it appears that you do have an interest in the foundations of quantum theory, and so you are exactly part of the core of the target audience I am trying to reach. My essay entry was just meant as an advertisement for the second paper, which uses the ideas of the essay entry and a multitude of novel ideas to provide an ontology for the textbook interpretation of quantum mechanics. My hope is that my essay entry intrigues people enough so that they are willing to invest spending time and thought on the second essay, which is conceptually far more challenging than the first.
Thank you again for your well-considered comments.
All the best,
Armin