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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 (eg with
torsion) 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 elast
and emotion 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 ofinteractions
of atoms in the crystal lattice [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 space 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, whether it will
be explicitly deterministic about the future unitary theory, 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 "primary principles" 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 - T heory O f E verything) - to unify the existing four types of interactions into a single interaction , described by a unitary field , whose (quantum) properties would then describe all types of elementary particles .
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 interactionsusing
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 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 "..?..
Gravity, black holes and space-time physics : | ||
Gravity in physics | General theory of relativity | Geometry and topology |
Black holes | Relativistic cosmology | Unitary field theory |
Anthropic principle or cosmic God | ||
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