Dear Yuri, I read your essay with attention.
My thought of physics is based on maintaining a balance between theory and empirical facts.
On this basis, there are points of your essay in which I fully agree:
4D space is not continuous, if not discrete, quantized. But a space quantization inevitably leads to a minimum quantization time lapse. Heisenberg uncertainty principle, the absence of infinite oscillators, which invalidated the approximate mathematical method, not with physical reality, the infinite sum of Feynman paths, since the lack of an infinite amount of energy, forced to invent the method of renormalization. Method that bases its predictive success, a mathematical equivalence between the quantization of spacetime-mass and the renormalization Riemann zeta function.
I disagree, with all due respect to his work: gravitation is quite possibly the most fundamental force.
But you, makes observations on a general two-dimensional holography, which I find quite agree with the actual physical facts.
I mean the dimension two, or surfaces have the property to contain any information of higher dimensions, since for a d dimensional sphere is satisfied:
[math]x_{1}^{2}+x_{2}^{2}+...-x_{d+1}^{2}=0[/math]
There are theoretical indications (string theory) and experimental very strong, which seem to show this basic and fundamental holography in two-dimensional surfaces.
Some theoretical and experimental indicators:
-The dimensionless factor of the entropy of a black hole
[math]\frac{A}{4l_{p}^{2}}=\frac{4\pi r^{2}}{4l_{p}^{2}}\:;\: r=l_{p}
[/math]
Casimir force:
[math]\left(\frac{S_{BH}(r=l_{p})}{k}\right)^{2}\frac{\hbar c}{K(8d)a^{4}}=F_{casimir}
[/math]
The graviton, must necessarily exist. Experimentally the energy loss of high speed orbital systems, pulsars, indicating a loss of energy consistent with the predictions of general relativity, and due to the emission of gravitational waves.
Moreover, the so-called, big crunch, is purely an idea, without any experimental minimal support, direct or indirect.
By contrast, the inflaction, yes, is based on a theoretical and experimental basis
More specifically: if space-time dimensions and mass are completely equivalent, then it can be shown that the so-called Hubble constant, is actually the inverse of the twice frequency of the cosmological vacuum energy.
The scaling law in this case inflaction factor, must meet two basic requirements:
1) This factor must be a direct function of the value twice of the cosmological vacuum energy, with respect to the change of scale with reference to the maximum mass scale: the Planck mass
2) This same factor will always be at least equal to the fine structure constant, alpha, for zero momentum. This last fact ensures the separation point of the matter-coupling electromagnetic radiation (microwave background of the universe), in early universe.
The Hubble constant, or frequency of "negative" energy, repulsive, the cosmological vacuum, obeys a simple second order differential equation, which in turn directly implies a twice scaling factor volume of a sphere in four dimensions, his beloved 4d sphere, dear Yuri.
This dimensionless factor has a product factor, which is the length Planckian associated due to the fine structure constant, zero momentum
In short, an equation can be worth a thousand words:
[math]l_{\gamma}=\sqrt{\frac{\alpha^{-1}}{4\pi}}=3.3022686622801
[/math]
[math]H_{0}=l_{\gamma}\cdot t_{p}\cdot\exp(\exp(\pi^{2}/2))
[/math]
[math]Planck\: time=t_{p}=l_{p}/c=5.391238134E-44\: s
[/math]
[math]H_{0}=2.3054E-18\: s^{-1}
[/math]
[math]
vacuum\: energy=(1/2)\cdot m_{Planck}c^{2}\cdot\exp-\{[\exp(\pi^{2}/2)+\ln(l_{\gamma})]/2\}
[/math]
[math](1/2)\cdot m_{Planck}c^{2}\cdot\exp-\{[\exp(\pi^{2}/2)+\ln(l_{\gamma})]/2\}\rightarrow2.1521E-3\: ev
[/math]
I was very pleasantly surprised, its discovery, the pattern of pseudo scalar mesons, that having zero spin, this pattern must have a clear relationship with the vacuum Higss, among other things
Always be learning new things, thankfully
In general, your essay seems interesting and worthwhile
Thank you very much, Yuri¡¡
