Hi Jeff,
Thanks for reading my essay and commenting on it.
Figure 2 in my essay is an illustration (as opposed to an exact representation) of the concept of stepwise motion that I have developed. The balls depict particlelike states, but it is wrong to think of these as classical "particles"; in addition, the intermediate wavelike states have nothing to do with quantum-mechanical wave functions. The universe, in which this stepwise motion takes place, could not be described with the physical language of classical mechanics, nor with that of quantum mechanics - it required the development of a new ontological repertoire. The basic concept is a 'phase quantum', but I have omitted any talk about it to render my essay accessible to a broad audience. If you are interested I can only refer to my two papers in Annalen der Physik which are mentioned in the essay; there is no other, more easy introduction to the material.
I agree with the quote in your essay: "nothing short of a revolution in our understanding of fundamental physics will be required to achieve a full understanding of the cosmic acceleration." In addition, I do not believe that such a revolution can originate at any of the so-called top universities.
Now about your essay. I have two issues with it.
1) In ยง2 on page 2, you mention that when integrating over a specific interval [a, b] two different integrands (functions) can yield the same integral. Of course this is so, e.g. the function f(x) = 2x and the constant function g(x) = 1 yield the same integral over the interval [0,1]. But then you seem to go off on a tangent. You define f1 = C - f2 and then you show that both f1 and C - f2 yield the same integral over the interval [x1, x2]. But how is that an example of two different functions yielding the same integral? The functions "f1" and "C - f2" are, namely, identical by your own definition. And as a side note, the term "C" in this defintion of yours is a constant function, not a constant of integration (which is a number) as you seem to imply in figure 2. So why this example?
2) In General Relativity (GR), the index-free form of the Einstein field equation (EFE) is
[math] G + \Lambda g = kT[/math]
I understand that you want to replace this EFE by this equation:
[math] g \Omega - L = kT[/math]
But why is that an improvement? With the EFE, one can calculate the metric tensor (or the metric tensor and the cosmological constant) given the stress-energy tensor T. But what is the physical interpretation of the tensor L in your equation? You might be able to calculate it, but what is it? You refer to figure 3 as an illustration, but what are the two scalar fields in the bottom picture physically? What is their physical source? What is the corresponding theory of gravitation (what is gravitation according to you)? It seems to me that your idea requires some further development.
All in all, the parallell between our essays is that we both question GR. But there are nuances. I believe that GR is correct in its area of application, but emergent instead of fundamental. You, on the other hand, seem to believe that GR isn't even correct in its area of application, as you suggest another field equation - I take it that you propose these as an improvement of the EFE even at macroscopic scale. Am I correct?
Good luck with the contest.
Best regards, Marcoen
@Steve: hail all hail to the revolution (Jon English).
