Dear Constantin,
We make only models of reality in our head to describe empirical reality. Some physical models are continuous and some physical models are discrete and some models are both. To say that reality is continuous or that reality is discrete is useless. We only have our models of reality. And sometimes our models can predict some properties or some phenomena. The model that complies most with what we see is the most plausible model. But we can never know the "ding an sich". Even if we have a discrete model for physical reality, we can't know if there will rise a model that is continuous but complies also in the same way with physical reality. We can't say that a theory is 'true' (yes, I am a nihilist. 'true' is a concept in our psyche, just like moral values, authority, property, responsibility, free will, gods, ghosts e.d. They are psychological illusionary projections of our brain into our psyche. Those illusionary concepts must have had survival value and therefore where produced by natural selection. Evolution wants us to think that they have absolute meaning, but they don't. That's another reason why I like the movie "The Matrix" very much).
Your model is completely discrete. And I like your model because if nature is discrete then your model is a beautiful example.
My model is continuous. I like Einsteins General Theory of Relativity which is continuous. Your argument that nature is discrete because the expanding of the universe can only be explained by discretion of nature doesn't hold, because General Relativity is a continuous theory that also complies with an expanding universe. I propose that relativistic mechanics without phase results in an continuous description of nature and that a relativistic mechanics with phase results in an relativistic quantum mechanics. I say that phase is responsible for the quantum phenomena. When we introduce phase then we get all kinds of quantum phenomena like probability waves and non-local effects like entaglement.
Can we say that quantum mechanics is pure discrete? Energy is exchanged in packets, quanta. And that was something new. There where two theories about light: one theory in which light has a wave descriptions and other theory in which light was described as composed of particles. But in both theories time and space are used as continuous physical phenomena. The fact that energy is exchanged as quanta complies with the theory of light consisting of particles. Around an atom we can have certain wavepatterns. Standing waves. And those wavepatterns are probabilities where the electron can be found around the atom. And it is not specific the electron, but it is the place of the electron or the momentum of the electron conform the uncertainty principle.
The probability wave shows interference and therefore we must conclude that the wave of an electron can pass two different holes at the same time. But does the electron also pass two holes? And the properties of an electron like place and momentum, do they exist before measurement?
"A quantum is the minimum amount of any physical entity involved in an interaction" (wiki). And 'entity' can either be a physical property or a physical object. The magnitude of a physical property can take on only certain discrete values. The property of a physical object can be quantized. But on the other hand a physical object like a particle can also be discrete. A photon is a single quantum of light. So we must understand what we are talking about: a physical property or a physical object. For example the discrete property of spin.
"Causal Dynamical Triangulation: At large scales, it re-creates the familiar 4-dimensional spacetime, but it shows spacetime to be 2-d near the Planck scale, and reveals a fractal structure on slices of constant time." (wiki) So this looks likes Ray Munroe's approach.
explanation: It is widely accepted that, at the very smallest scales, space is not static but is instead dynamically-varying. Near the Planck scale, the structure of spacetime itself is constantly changing, due to quantum fluctuations. CDT has some similarities with loop quantum gravity, especially with its spin foam formulations.
Your theory suggest that the consequence of the quantization proces is that also time and space are quantized. And you mean that there must be physical objects. Even if there is a quantization of space and time, does this exclude that space and time can also be continuous? I see nature as an octonionic manifold. I stil don't know how electromagnetic phenomena and gravitomangetic phenomena can be put into one theory. But in my essay I show a quadratic metric underlying the maxwell equations, a continuous description. I argue that phase is responsible for the quantum behaviour of nature. You say that because I use planck units I comply with a descretion of nature. But I have shown on page 7 of my essay that the planck units aren't understood well.
If nature is quantized then this must have consequences for the mathematics of hypercomplex algebras. If nature is quantized, then also the mathematical hypercomplex algebras must be quantized.
