Dear Daniel,
Having looked at your essay, I see that we share the idea that gravitation can be repulsive and that space is not fundamentally continuous. Our views on what underlies all that are, however, radically different. I do not believe that space is continuous, but neither do I believe that it is discrete. In my upcoming postdoc project I intend to develop the (mathematical) notion of a semi-continuum: this is a (semi-topologiocal) space that at macroscopic space has some properties of a continuum, but the continuum structure breaks down at small scale (e.g. at Planck level).
I have some questions about your claim that your system rests on only two axioms from which everything else follows. I will focus at three things, one logics-related, one mathematics-related, and one physics-related:
1) The definition on page 1 of the notion "fundamental" is a so-called if-statement, that is, a statement of the form
[math]a \leftarrow b[/math]
This has a consequence: if an object is fundamental, then it does not follow from the definition that it is invariant.
The point is, namely, that the reasoning
[math]a \leftarrow b, \ a \ \vdash \ b[/math]
is known to be not logically valid.
On page 2 you write that "Per our definition of what is fundamental, preons(-) and preons() never change." This statement is, thus, incorrect from the point of view of formal logics: with your definition, something can be fundamental but not invariant. Did you perhaps have an if-and-only-if-statement in mind when you formulated your definition of the concept "fundamental"?
2) Furthermore, your axiom about the discreteness of space is merely about the qualitative composition of your quantum-geometrical space: apart from the fact that there is no definition of the concept "distance", by no means it follows directly from this axiom that there is a smallest possible distance, as you claim on page 1 just below the axiom. The axiom does not exclude that there are infinitely many preons(-) located at different distances from each other: there might be a positive distance between any two preons(-), but a smallest possible distance has not necessarily to exist. That is to say: isn't the statement that there is a smallest possible distance an extra assumption (axiom) in your theory?
3) In your axiom of the discreteness of space, you mention that there is a repulsive force between preons(-). Yet on page 2 you write that the preons(-) are static: they don't move. Apart from the fact that the notion "force" is not defined in your framework, the question rises: how does the repulsive force manifests itself? How can we prove that it exists at all?
I would appreciate it if you could elaborate specifically on these three topics.
With best regards, Marcoen
