A short note on the Theory of Everything

In case there are still any readers of this blog (which I rather doubt, as most of the readers I got from Unz by posting a link and after I stopped reading Unz, those people certainly already found some better sites to follow) and in case any of them (assuming there are more than one, but I know that the number is zero) are wondering what I have been doing, I decided to write some words of what I actually have been doing (and will be doing for some 4-6 months, I am afraid). I case you wonder how I happen to know how many people read this blog, it is easy, Insights shows it, so 14 readers have read the post Break in posting, and nobody has read this post. Thus, about 10 people followed this blog at the time I wrote Break on posting, and nobody follows this anymore. Naturally there are visitors, who accidentally find this blog and some of them read many posts, but do not return. I find this state quite correct, so it should be. I also do not follow anybody’s blog on a regular basis. It is not my intention to keep such a blog. This is simply my recent writings. Were there regular readers, I should regularly write something, but I prefer to take breaks in order to write better papers that need lots of work.

            Over thirty years ago I was planning on making a Ph.D. thesis on quantum field theories, actually a Theory of Everything, which means a quantum gauge field theory which unifies gravitation, electro-magnetism, and weak and strong interactions to a single gauge theory based on SU(N) gauge groups. So far the standard model of quantum field theories unifies electro-magnetism (i.e., Quantum Eletcodynamics) with weak interactions with SU(2)xU(1) Lie group and the Higgs mechanism for spontaneous symmetry breaking, and strong interactions are explained with the quark model using the SU(3) symmetry group. Gravitation is not included, it is explained by Einstein’s General Relativity. But I did not make a dissertation on this topic but on quasiregular mappings between manifolds. I still have some ten books of physics and some ten books of mathematics which were directly relevant to the physical question. That is a very small part of my professional library, which includes some more mathematical books (algebraic and geometric topology, combinatorics, traffic theory, cryptology, control theory, algorithms, grammars and so on) and lots of technical books of communications, computer networks and programming. But anyway, on pension I thought that it is a good time to look at the Theory of Everything.

            The books I decided to reread are:

1. Dietmar Ebert, Eichentheorien, Grundlage der Elementarteilchenphysics

2. Richard D. Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem

3. Julius Wess, Jonathan Bagger, Supersymmetry and Supergravity

4. Kip. S. Thorne, Richard H. Price, Douglas A. Macdonald, Black Holes the Membrane Paradigm

5. L. Landau, E. Lifshitz, Mecȃnica quȃntica, Teoria não relativista

6. D. Bailin, A. Love, Introduction to Gauge Field Theory

7. Daniel S. Freed, Karen K. Uhlenbeck, Instatons and Four-Manifolds

8. Volker Heine, Group theory in Quantum Mechanics

9. Wilhelm Magnus et al, Combinatorial Group Theory

10. Roger W. Carter, Finite Groups of Lie Type

11. Kunihiko Koidara, Complex Manifolds and Deformations of Complex Structures

12. Ulrich Bunke, Martin Olbrich, Selberg Zeta and Theta Functions

           Those are all 30 years old books, but they are still valid: the model is still the standard model. When I studied, I had access to journals and read them, today I do not have access, and my old ideas from over 30 years ago do not depend on anything newer than what is in these books. Here you see also the reason I so unwillingly give references. Let’s say, my argument uses information from those books. Let’s assume I give you a page number to one of those books as a support of my claim. If you take the book and check the page, let’s say from Dietmar Ebert, the best and clearest book on quantum field theories I have ever read, you will not understand anything, unless you read the book up to that page. Which would take you lots of time and so you do not do it. Either you have studied the topic before and know it, and do not need references, or you will not gain anything from the reference. So it is in any harder sciences or techniques. Therefore, why to give references?

            The main idea I at that time had is as follows. Of course, this idea can be totally wrong and for sure it will not be so simple, the truth is usually not simple in field theories. But anyway: If gravitation should be included in to same theory, then it should have a symmetry group of SU(N)-type (or U(N)), but for every generator of a SU(N) group there comes a gauge boson and a Noether stream (there is only one conserved Noether charge because of couplings, it is a sum of Noether charges of each generator). Obviously the symmetry group cannot be U(1), as U(1) gives electro-magnetism (one degree of freedom). It must be still more simple and there is only one group that is more simple, that is SU(1). Notice, SU(1)=1, it has only one element 1. That is, there is no symmetry, but instead we have cancellation of a free particle Schrödinger equation with the gravitation field.

            The free-particle Schrödinger equation gives the Klein-Gordon equation (□-m²(x))φ=0, so to cancel this we need the gravitation field in a form (□-m²(x))ψ=0. Here ψ is the classical gravitation field, which is almost constant in quantum distances. In Schoedinger equation the field is the wave function (=probability amplitude). In the Klein-Gordon equation Planc’s constant is set to 1, but if we put it and the gravitation constant to correct values, we get very weak coupling of gravitation, which explains why the force is so weak.

            We can get (□-m²(x))ψ=0 as a weak field approximation from General Relativity, but it cannot be an approximation. It must be exact. We get the exact form from Nordström’s gravitation theory, which is ψ^-1□ψ-Rψ =ρψ² when the field ψ is real. Changing the field to complex gives (I omit the Ricci number) ψ^-1□ψ=ρψ*ψ, multiplying from left by ψ yields □ψ=(ρψψ*)ψ=m²(x)ψ. So, that’s about it so far. There is a theorem mentioned in Wess and Bagger that the scalar field in a renormalizable quantum field theory (with a mass gap) can only be of this form. Thus, to me it seems very clear that Nordström’s gravitation theory is the correct one and General Relativity cannot be correct: there is no symmetry that would give ten equations for the curvature tensor. In Nordström’s gravitation theory there is only one equation, as there should be if the symmetry group is SU(1), no degrees of freedom.

           Ì have many other ideas, probably not any better, but more of them, but let them remain as ideas so far. It will take a while to solve the Theory of Everything, but of course I will have to try. I hope to write posts on some easier topic at some points.