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Contents
(The Quantum Theory of Gravitation)
Three Problems of Fundamental Physics
Problem 1. The Mach Principle
Problem 2. The WaveCorpuscle Dualism
Problem 3. Gravitation and Quantum Mechanics
The Outline of the Book
Chapter 1. Gravitation and Modern Physics
It is the introductory chapter, where main ideas of modern
physics are presented. Unsolved problems are given a particular
attention.
1.1 Gravitation
1.2 The Gravitational Potential of the Universe
1.3 Homogeneity of the Gravitational Potential
1.4 The Features of Gravitation
1.5 The Law of Inertia
1.6 The Mach Principle
1.7 The Special Theory of Relativity
1.8 Mass and Energy
1.9 The General Theory of Relativity
1.10 Quantum Mechanics
1.11 The Fundamental Constants
1.12 The Problems of Modern Physics
Chapter 2. The Construction of the New Theory
To solve the problem connected with the Mach principle, it is
necessary to construct a theory on the base of this principle and
then consider its consequences. An experimental verification of
these consequences will allow us to understand whether the
Mach principle is correct or not.
2.1 The Statement of the Problem
2.2 The Experiment Outside of the Universe
2.3 The Virtual Brick
2.4 The Draft of the New Picture of the World
2.5 The Necessary Remark
2.6 The New Law of Physics
2.7 The Constancy of the Speed of Light
2.8 Experimental Verification of the New Law
2.9 The Fine Structure Constant
2.10 Planck’s Constant in the Gravitational Field
Chapter 3. The Bases of the New Theory
In this chapter we will consider the main suggestions
underlying the new theory. We will also consider the most
important consequences following from the theory.
3.1 The New Model of Space-Time
3.2 Inertia and Gravitation
3.3 Einstein’s Formula
3.4 Mass in a Gravitational Field
3.5 What is the Potential Energy Equal to?
3.6 Mass of an Elementary Particle
3.7 Modern Physics and the Mach Principle
3.8 Summary
Chapter 4. The New Interpretation of the General Theory of Relativity
It is suggested in the general theory of relativity, which is the generally
accepted theory of gravitation, that space-time is curved in a gravitational
field. That is, the space-time scale changes from one point to another. What
does this mean? What kind of physical difference exists between different
points in a gravitational field? Within the limits of the new theory we can give
the following answer to this questions. In a gravitational field, the speed of
light and Planck’s constant change with transition from one point in space to
another. In the first approximation (i.e. when ћ « ћ, с « с), this effect can be
regarded as curvature of space-time.
4.1 The Foundation of the General Theory of Relativity
4.2 The Curvature of the Space-Time
4.3 Distance and Time
4.4 The Relativistic Gravitational Effects
1. The Motion of the Mercury Perihelion
2. The Gravitational Shift of Spectral Lines
3. The Deflection of Light Beams that Pass near the Sun
4. The Shapiro Effect
5. Deceleration of time
4.5 The Limits of Applicability of the General Theory of Relativity
4.6 The Equivalence Principle
4.7 Deflection of Light Beams
4.8 The Propagation of Electromagnetic Waves
4.9 The Refractive Index
4.10 Shift of Spectral Lines
4.11 The Black Holes
4.12 The Radar Signal Lag
4.13 The Principle of the General Relativity
4.14 When One Says That the General Theory of Relativity is Corroborated Experimentally, then
what does One Mean?
Chapter 5. The Paradoxes of Quantum Mechanics
“I am going to tell you what nature behaves like. If you will
simply admit that maybe she does behave like this, you will
find her a delightful, entrancing thing. Do not keep saying to
yourself, if you can possibly avoid it, ‘But how can it be like
that?’ because you will get ‘down the drain’, into a blind alley
from which nobody has yet escaped. Nobody knows how it
can be like that.”
Richard Feynman [15,p.129]
This chapter will be all about paradoxes of quantum
mechanics and analysis of main ideas underlying this branch
of physics. The aim of this chapter is to show the principal
difference between the micro world and macro world.
5.1 History of Quantum Mechanics
5.2 The Wave Function
5.3 Two Interpretations of Quantum Mechanics
5.4 The Electron Interference
5.5 The Discussion between Einstein and Bohr
5.6 Virtual Photons
5.7 Quantum Mechanics and Common Sense
1 Regularity and Chance: the Probable Character of the Quantum-Mechanical Laws
2 Certainty and Uncertainty
3 The Wave-Corpuscle Dualism
4 Non-locality of Quantum Mechanics
Chapter 6. The New Interpretation of Quantum Mechanics
The suggestion of existence of Chaos outside of the gravitational field of the Universe
underlies the new theory. From this point of view, the uncertainty observed in the
micro world is the remainder of chaotic motion limited by the stars’ influence. In this
chapter, a new physical idea of discrete (chaotic) motion is introduced. Using this idea
we can visually explain all the processes in micro-world.
6.1 Chaos is the Border of Space-Time
6.2 The Discrete Motion
1 The Chaotic Motion
2 The Continuous Motion
6.3 The Heisenberg Uncertainty Principle
6.4 The Model of the Electron
6.5 The Collapse of the Wave Function
6.6 Splitting of the Wave Packet
6.7 Non-Locality of Quantum Mechanics
6.8 The EinsteinPodolskyRozen Paradox
6.9 Why is Time Irreversible?
6.10 The Wave  Corpuscle Dualism
Chapter 7. The Quantum Theory of Gravitation
In chapter 2, using the Mach principle we had concluded that near a
large mass the uncertainty in a particle’s motion decreases. From that,
it follows that near a large mass a particle’s trajectory is curved.
Therefore, within the limits of the new theory, the gravitational
interaction can be considered as a purely quantum effect. Such
approach to gravitation will be elaborated in this chapter.
7.1 The Main Shortcoming of the General Theory of Relativity from a Standpoint of Quantum
Mechanics
7.2 What does “the Quantum Theory of Gravitation” Mean?
7.3 The Mechanism of Gravitation
7.4 The Principle of Least Action
7.5 The Equations of Motion in the Quantum Theory of Gravitation
7.6 Newton’s Law of Gravitation
7.7 Einstein’s Theory of Gravitation
7.8 The Difference between the Quantum Theory of Gravitation and the General Theory of
Relativity
7.9 The Gravitational Anomalies
7.10 The Atom in a Gravitational Field
7.11 The Atom and the General Theory of Relativity
7.12 The Advantages of the Quantum Theory of Gravitation
Chapter 8. Time and Gravitation
In the case of a weak gravitational field, the only but radical difference between
the quantum theory of gravitation and the general theory of gravitation is the
following. From a standpoint of the general theory of relativity, time “slows
down” near a large mass, whereas from a standpoint of the quantum theory of
gravitation, it “is accelerated”. In this chapter, we will study this subject in detail
and will consider arguments in favour of the first or the second points of view.
8.1 The Space-Time Scale8.2 Non-Uniformity of Time
8.3 The Experiment on Verification of the Quantum Theory of Gravitation
8.4 The Experiments on Verification of the General Theory of Relativity
8.5 The Photons in a Gravitational Field
8.6 Time and the General Theory of Relativity
8.7 Particle in a Gravitational Field
8.8 The Physical Sense of an Interval
8.9 How Should One Arrange the Limits of Integration in the Equation of Motion?
8.10 Two Interpretations of the Red Shift
8.11 The New Interpretation of the Red Shift
8.12 The Rate of Time
Chapter 9. The Problems of Modern Cosmology
In this chapter, we will consider the most interesting problems of
modern cosmology, which are unsolvable within the limits of the
standard model of the expanding Universe based on the equations
of the general theory of relativity.
9.1 Measurement of Distances
1. The Trigonometric Parallax
2. The Method of a Moving Cluster
3. Cepheides
4. Hubble’s Law
5. Supernovas
9.2 The Universe Expansion
9.3 The Cosmological Constant
9.4 Dark Matter
9.5 The Universe Age
9.6 The Baryon Asymmetry of the Universe
9.7 The Quasars
9.8 The Acceleration of Galaxies
9.9 Inflation
Chapter 10. Cosmology and the Quantum Theory of Gravitation
In this chapter, we will consider the evolution of the Universe from the
standpoint of the quantum theory of gravitation taking into account the influence
of the distribution of the Universe matter on physical processes. While doing
this, we will show how many cosmological puzzles may be solved.
10.1 The Evolution of the Universe
1. The Speed of Light and Planck’s Constant
2. The Mass of the Universe
3. The Energy of the Universe
4. The Closed Universe
5. Elementary Particles
6. Matter and Radiation
10.2 Where did antimatter go?
10.3 The Energy Source of Quasars
10.4 The Origin of Radioactive Elements
10.5 The Density of Matter in the Universe
10.6 The Cosmological Red Shift
10.7 The Hubble Constant
10.8 The Physical Vacuum
10.9 The Mass and the Size of the Universe
10.10 The Experiment to Measure the Rate of the Expansion of the Universe
10.11 The Experimental Astrophysics
1. The Rate of the Universe Expansion
2. A Search for Black Holes
3. The Density of Matter in the Universe
Chaos and Time
Reference