Perspective of credible unitary theory

Appendix B
UNITARY FIELD THEORY AND QUANTUM GRAVITY
B.1. The process of unification in physics
B.2. Einstein's visions of geometric unitary field theory
B.3. Wheeler's geometrodynamics. Gravity and topology.
B.4. Quantum geometrodynamics
B.5. Gravitational field quantization
B.6. Unification of fundamental interactions. Supergravity. Superstrings.
B.7. General principles and perspectives of unitary field theory

B.7. General principles and perspectives of unitary field theory

From the development of unitarization of physics so far, some ideas and concepts can already be traced, which could probably play the role of basic heuristic principles in the creation of unitary field theories in the future :

a) The principle of covariance
requiring such a formulation of laws between observable quantities, that these laws do not depend on the subjective conditions of observation, eg on the chosen frame of reference (general principle of relativity) - Chapter 2.

b) Geometric bases ,
whether it is a four-dimensional space-time GTR with Riemann geometry, space-time with more general geometric properties or topological structure, or a space with a larger number of dimensions. The model here is the geometry of gravity in the general theory of relativity * ).
*) Sometimes there is the opposite view, according to which gravitational effects are negligible on subatomic scales (or do not exist) and the origin of gravity must be sought in the quantum laws of the interior of matter. The situation here would be similar to the science of elasticity: it is not the simple and elegant laws of elasticity that determine the internal structure of bodies, but on the contrary the complex electromagnetic interactions of atoms in the crystal lattice lead to the observed properties of elasticity after macroscopic averaging. If this were the case with gravity, geometric unitarization would make no sense (it would be mere fiction), just as it would be absurd to try to explain the quantum-electrodynamic laws of atomic interactions in a crystal lattice based on simple laws of macroscopic elasticity [181].

c) Quantum character .
Unitary field theory must also faithfully describe the quantum laws of the microworld *) and explain the properties of elementary particles. According to current knowledge, it cannot be expected that quantum particles could arise as a non-singular solution of classical (albeit nonlinear) field equations. On the contrary, it is probable that the theory must be built from the ground up on a quantum description, eg using state operators.
*) In the interest of objectivity, however, it is necessary to keep in mind another alternative option: that the quantum laws of the microworld we observed could have some hidden "non-quantum" origin in so far unknown mechanisms on an even deeper "floor" organization of matter at the smallest subnuclear scales ..?..

d) Symmetry and conservation laws .
These are both global symmetries (eg spacetime), from which the laws of conservation flow, and local - dynamic symmetries, which lead to the presence of other interactions. One of the basic slogans of contemporary quantum field theory is: "Interactions are dictated by symmetries" (see previous §B.6).

e ) Causality .
If the state of a physical system is known at any time, then its further behavior can be predicted from the field equations. In other words, the theory must allow the solution of the Cauchy problem (see §3.3). Such a strictly deterministic theory is, for example, Maxwell's electrodynamics. In GTR, the situation in terms of causality is more complicated, because global Cauchy hypersurfaces may not exist in some cases (§3.3, §3.5-3.9, §4.7). It is not possible to say in advance about the future unitary theory, whether it will be explicitly deterministic, but the resulting observable phenomena must correspond to experimentally verified causal relationships.

f) The principle of correspondence
reflecting the continuity of scientific knowledge: new more general laws of physics do not refute the existing experimentally verified laws, but generalize them and contain them as a special case, while there is a direct connection (correspondence) between quantities used in earlier special and newer general theory.

g) The principle of simplicity
expressing the effort to achieve the most complete description of reality with the help of as few basic independent laws as possible. This principle may seem somewhat subjective, but experience has shown that theory is convincing, only when it is logically simple and natural enough. Properly understood aesthetic criteria can be a valuable guide in the search for general unitary theories, as emphasized in particular by A.Einstein.

h) Explanation of the origin of natural constants
A complete unitary theory should explain not only the dynamics of fields and particles in the form of physical laws, but also derive from the "primary principles" also the specific values (or ratios of values) of basic natural constants - see §5.5, passage "Origin of natural constant".

The ultimate goal of unitary field theories is to create a definitive final theory or a unified theory of everything ( TOE - Theory Of Everything) - to unify the existing four types of interactions into a single interaction, described by a unitary field, whose (quantum) properties would then describe all kinds of elementary particles, their interactions. and all phenomena in nature.

Skeptical note :
Contemporary unitary field theories: Just a mathematical formalism without physical content ..?..
The current unitary field theories try to create models of fundamental particles and their interactions using complex mathematical constructions. The question is whether this is the right way..?.. Many physicists are skeptical of current unitary theories (especially superstring theories). They point to the ambiguity of its conclusions, opacity and excessive mathematical complexity, especially the difficulty of physical interpretation and the impossibility of experimental verification in the foreseeable future. Some of these theories describe exotic particles that are not observed (and probably even do not exist in nature), while common basic particles are unable to successfully modeled... These theories therefore consider them a "dead end "... It seems that maybe "everything will be different"..?..

B.6. Unification of interactions. Supergravity. Superstrings.		Conclusion, Afterword, Literature

Vojtech Ullmann