Constantin,
Thank you for your objections. They illuminate where I need to express my ideas more clearly. I will attempt to give a thorough response.
You say:"It contradicts to experimental data."
The statement about smaller objects being more two-dimensional than larger objects of same shape was meant as a mathematical-not empirical-statement about the geometric properties of objects of different size. Mathematically, it seems to me hard to argue that if one takes the area-volume ratio as a parameter to compare relative dimensionalities (which I think from the context of my essay was clearly what I meant), smaller objects are indeed by this parameter more 2-dimensional than larger ones of same shape.
You say:"According to your theory, the interaction of micro-objects in a plane must be stronger than in third dimension because particles are flat and does not feel the third dimension."
I would be grateful if you could point me to any place in my essay where I mentioned anything about any kind of interactions. This essay is one of several that describe various aspects of this idea, and eventually the topic of interactions will need to be addressed as well, but I do not believe I did that here because that was outside the scope of the topic. In fact, in this paper there is not enough information to say anything specific about interactions. The idea that objects should interact more strongly in a plane than in the third dimension is yours, not mine.
You say "The existence of a three dimensional nucleus as a sphere contradicts to your theory."
Thank you for bringing up a point that evidently I did not make clear enough. When I claimed that smaller objects are more two-dimensional than larger ones of same shape, I meant that dimensionality in this specific sense (i.e. in terms of A/V) is something that takes on continuum of values, rather than 'quantized' ones (i.e. 1-D, 2-D etc.). In my example of a sphere of Bohr radius, I did not mean to say that it is two-dimensional (I would have then had to call it a 'disk') but, rather, that it *more* two-dimensional than a ball of radius 1 m by the amount indicated by the A/V parameter. Also, this argument was meant as nothing more than a motivation for axiom 1, which is really what should be attacked to destroy the idea.
You say: "Also, if nucleons were flat, they must interact in a plane stronger than in other dimensions that contradicts to experimental data."
As I was answering your objections, I just realized that a crucial concept which I did not sufficiently emphasize is bound to lead others to misunderstand this aspect of my idea. Thank you so much for bringing this to my attention!
When we actually 'measure' a nucleon (i.e. at that precise moment) its state collapses to an eigenstate. The 'collapse' is not well-understood, but I interpret this to mean that there is a brief moment where the state is not describable by a phase. One argument which may be enlisted in support of this view is that when we multiply the phase (and the rest of the wave function) by its complex conjugate to get a term proportional to its probability of occurrence, the phase disappears. Indeed, it is well known that a wavefunction uniquely specifies a state only up to a phase for this very reason. Of course, if we assume that during the measurement the phase disappears, than we must also assume that very shortly after the measurement, the phase has to reappear because the state spreads out in space again according to Schrodinger's equation. But the point is this: when we talk about the shape or dimensionality of nucleons, we talk about them usually as they are when we do a measurement on them, and when we do a measurement, if the phase presumably disappears, then the nucleon *at that moment* is not characterized by a phase, and hence not subject to the claims made in my essay. In short, at the moment it is 'measured', the nucleon exists in spacetime and, in particular, it is *not* flat (i.e. 2-dimensional), but 3-dimensional, much in agreement with your assertions. Again, I thank you for making me aware of this point which definitely needed further clarification. Please let me know if this makes things any clearer.
You say "Please read the Wikipedia_Photon: Rather, the photon seems to be a point-like particle since it is absorbed or emitted as a whole by arbitrarily small systems, systems much smaller than its wavelength, such as an atomic nucleus (10-15 m across) or even the point-like electron."
This is really another 'interaction' question, and my answer has to be again that in this paper there was not enough information provided to say anything specific about interactions. Just to be clear, I consider this a shortcoming of my argument, not a rebuttal to your objection. There is a follow-up paper (as yet not finished, unfortunately) which will hopefully provide more information on this. My original plan was to have all of the papers finished a 'go public' at the same time. Very regrettably I was not able to finish them all before the contest deadline, and taking taking advantage of this opportunity meant that it would force my hand before I was really ready. I can only request to bear with me until, hopefully very soon, the follow-up paper is finished so that there are actually specific ideas about interactions which can be evaluated.
You say: "Also, since photons must be 2-dimensional entities, they must have different properties in a plane conserning third dimension that contradicts to experimenal data."
I must admit that I'm not exactly sure what you mean. It seems to me that you are still thinking very much in terms of the classical trajectory picture. If so, please be aware that my framework makes no attempt to support such a picture for photons which is, indeed, contradicted by standard quantum theory. If I misunderstood your objection, please clarify.
Constantin, I appreciate that you took the time to evaluate the essay. My impression is that at least some of your objections arose because I presented only a part of my theory, and this incomplete picture can easily give rise to misunderstandings. Of course, it is my responsibility to present a complete picture, and I hope to have remedied this problem very soon. If you find further objections, please do not hesitate to let me know.