Yanchilin V.L. The Quantum Theory of Gravitation

Contents

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.

The Outline of the Book

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.