Three problems of fundamental physics |

The outline of the book |

Chapter 1. | Gravitation and Modern Physics |

| 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 |

| 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 |

| 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 |

| 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 |

| 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 |

| 5.1 | History of Quantum Mechanics |

| 5.2 | The Wave Psi-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 |

Chapter 6. | The New Interpretation of Quantum Mechanics |

| 6.1 | Chaos is the Border of Space and Time |

| 6.2 | The Discrete Motion |

| 6.3 | The Heisenberg Uncertainty Principle |

| 6.4 | The Model of the Electron |

| 6.5 | The Collapse of the Wave Psi-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 |

| 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 Equation 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 |

| 8.1 | The Space-Time Scale |

| 8.2 | 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 |

| 9.1 | Measurement of Distances |

| 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 |

| 10.1 | The Evolution of the Universe |

| 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 |

Chaos and Time |

References |

Three Problems of Fundamental Physics

To understand better the subject of this book look through the
following three interesting and unsolved problems of fundamental
physics.

### Problem 1. The Mach Principle

It is known that there exist two kinds of motion: relative motion
and absolute motion. Newton was the first who paid his attention to
this fact. Straight-line motion is relative and rotational is absolute. We
can say nothing about a value of a travel velocity (for example,
a value of travel velocity of the Earth) if we do not point to another
body, relative to which we can describe the motion. However, we will
always calculate an angular velocity (for example, the angular velocity
of the Earth). It is possible because of centrifugal force acting in
a rotating body. This force deforms the body. Knowing a value of
a centrifugal force or deformation, which is the result of action of this
force, we can calculate a value of a rotational velocity of the body.

In this connection the following question arises: what is an
object, relative to which a body can rotate?

At the end of the nineteenth century the Austrian physicist Ernst
Mach had put forward an interesting hypothesis (which was called
later the Mach principle): a body rotates relative to the fixed stars.
A centrifugal force is the result of a vague connection between the huge
mass of all the stars and the rotating body.

How can we verify this assumption?

Famous American physicist Richard Feynman wrote about this:
"we have no way, at the present time, of telling whether there would
have been centrifugal force if there were no stars and nebulae around.
We have not been able to do the experiment of removing all nebulae
and then measuring our rotation, so we simply do not
know" [13, ch.l6.1].

In the year 1979 an International scientific conference dedicated
to centenary of Albert Einstein had taken place in Berlin. The most
fundamental problems of modern physics were discussed at that
conference. Scientists also discussed the Mach principle and the
general theory of relativity. Here are some phrases from the summary
on this subject: "It is known that Einstein not only took this
unorthodox principle and admired it, but also hoped to introduce the
system of Mach's ideas in his theory. Therefore he modified the first
classical formulation of the general theory of relativity. Even now
there are performed attempts -- tirelessly, sometimes with
discouraging results, often by help of witty manipulations -- to attain
the object, for which Einstein strove" [26].

Nevertheless, a problem connected with the Mach principle
may be solved! To do this, the following steps are necessary:

First, reveal a *physical* sense of the Mach principle, which is not
clear yet.

Second, create a new physical theory that would include the
Mach principle and also well-known physical laws.

Third, calculate, i.e. predict, fundamentally *new consequences* which follow from the new theory and which may be verified in
terrestrial conditions (without taking away the fixed stars). As a result
we will determine whether the Mach principle is correct or not.

### Problem 2. The Wave-Corpuscle Dualism

In physics there exist such concepts as a particle and wave.
These concepts are antagonists. Properties of a particle and properties
of a wave are mutually exclusive each other. However, quantum
objects behave sometimes as waves, sometimes as particles. For
example, an electron, in certain experimental conditions, is a particle.
Moreover, it is an indivisible particle. Nobody observes half of an
electron or other amount of its part. However, in other experimental
conditions, the electron can simply pass through two and more holes
at the same time!

If you do not know this phenomenon you will probably find it
hard to believe. It is not surprising! Formerly such a remarkable
physicist as Albert Einstein (who did very much for creating quantum
mechanics, by the way) did not accept quantum mechanics. He held
that a physical theory should not contradict common sense so much.

At present, the wave nature of an electron is an established
experimental fact. You can read about this in Feynman lectures on
physics, v.l, ch.37: "Quantum behavior" [13].

It should be noted that quantum mechanics describes "strange"
behavior of quantum objects perfectly. However, to describe is not to
explain. It is not clear yet where in the micro-world the uncertainty
comes from and how an indivisible electron contrives to pass through
two holes at the same time. Here is what Richard Feynman wrote
about "strange" behavior of quantum objects: "I think I can safely say
that nobody understands quantum mechanics" [15, p.129].

### Problem 3. Gravitation and Quantum Mechanics

All in the world attract each other. On the other hand, all in the
world obey the laws of quantum mechanics, the base of which is the
uncertainty principle. Thanks to this principle, any particle possesses
the wave properties. However, the modern theory of gravitation -- Einstein
's theory of gravitation (also as the Newtonian theory of
gravitation) -- does not take into account this fundamental principle,
i.e. does not take into account that particles possess the wave
properties. So the following question arises naturally. Is it possible to
unify the theory of gravitation and quantum mechanics so that in
description of gravitational interaction the wave properties of particles
would be taken into account?

It will be clear later that all these three problems are connected
with each other. We will understand the physical sense of the Mach
principle. From that, we will understand the origin of the uncertainty
in the micro-world. Understanding, in turn, the source of the
uncertainty in the micro-world, we will understand why bodies attract
each other. This book presents a solution to these problems.

Running ahead, we may say that uncertainty principle underlies
gravitational interaction. That is, gravitation is a pure quantum effect!

I express my gratitude to Andrei Sherstyuk for the great work
on correction of the English text.

In section 2.6, the first new equation (New Law) is introduced,
which defines the foundation of the further construction of the new
theory. In chapter 3, the main principles of the new theory are
discussed in details. In sections 4.7--4.10, we derive the equation of
propagation of light in a gravitational field on the base of those
principles. In these sections, we also determine the deflection angle
and a value of the gravitational shift of spectral lines.

In chapter 7, we formulate the quantum theory of gravitation,
building upon the new theory. We reveal the meaning of the notion of
"curved space-time": in a gravitational field, the uncertainty in motion
of particles decreases, in consequence of which atomic sizes change
(radii of electrons' shells decrease). That, in turn, causes changes in
the energy of transition of electrons from one level to another. As the
result, the radiation frequencies and wavelengths of spectral lines
change.

Precisely all that is the reason that in a gravitational field, the
scale of time and the scale of length change, which creates the
curvature of space-time near a large mass.

In section 7.5, we derive the equation of motion of a particle in
a gravitational field, proceeding from the fact that the particle
possesses wave properties. In section 7.8, we show the fundamental
difference between the quantum theory of gravitation and the general
theory of relativity. In section 8.3, we propose a simple experiment,
the result of which will help us choose either the quantum theory of
gravitation or the general theory of relativity. In section 8.7, we show
the fundamental contradiction between the general theory of relativity
and quantum mechanics.

Chapter 1 is introductory. In chapter 5, we discuss the
paradoxes of quantum mechanics. In chapter 6, we give the visual
explanation of these paradoxes from the new point of view. In
chapter 9, we discuss some problems of modern cosmology and in
chapter 10 we propose their solutions from the standpoint of the
quantum theory of gravitation.