Equivalence principle

Equivalence principle of masses. Part 1 

and also Equivalence principle, Part 2 >>

Over the history of physics, the equivalence principle of masses has been the most wonderful principle. Amazingly, this principle has continued to be refined experimentally from the late 19th century up to the present day. The equivalence principle, according to which the gravitational field in a small region of space and time is identical to the accelerated frame of reference for its manifestation, is the basis of general relativity theory and results in the equality of inertial and gravitational mass.

The equivalence principle of masses was brought forward by Newton and experimentally tested by him. This principle helped explain the question of why all bodies fall to the ground with the same acceleration. This paradoxical discovery was made by Galileo when he threw bodies of different weights from the Tower of Pisa. In order to explain this phenomenon, Newton introduced the concept of mass - a new quality of matter.

In Newton's laws, mass acts at some times as a measure of inertia and at other times as a measure of gravitational properties. Newton was the first to turn attention to the equality of inertial and gravitational masses and he proved that they differ by no more than 0.1% (in other words, they are equal accurate to 10^-3).

More recently, R. Eotvos, in a set of very accurate experiments, conducted from 1890 to 1910 and continued in 1922, showed that the equivalence principle of gravitational and inertial masses is satisfied with a level of accuracy better than one twenty millionth. Eotvos's experiments examined the behavior of plumbline under the action of Earth's gravitational forceand centrifugal force. The Earth's gravitational forcedepends on the gravitational mass, while the centrifugal force caused by rotation of the Earth depends on the inertial mass.

Eotvos's experiment testing the equivalence principle of masses

The experiment was set up in the following way. A rod with two weights on the edges (made of copper and platinum) was suspended by a thread (see fig.). The rod was oriented perpendicular to the meridian (the meridian is the straight from north to south; in the figure it is indicated as NS). The shoulders of the rod are equal. Cargoes are also equal by weight.

If these (gravitational and inertial) masses were not the same, the direction of the plumbline would depend on the material (copper, platinum, lead, iron, glass, etc.) of the ball of plumbline. However, with the help of the torsion balance, Eotvos determined that the plumbline does not change its direction, regardless of the material of which it is made. Thus, the equality of gravitational and inertial masses was determined (for more details, see http://rozman2.narod.ru/otopdf/oto02.pdf). Classical mechanics did not even attempt to explain the reason for this phenomenon. The equivalence principle introduced by Newton allowed scientists to say that we are dealing with a new entity which has gravitational and inertial properties. Thus, the equivalence principle reinforced the existence of mass.

In the times of Newton, science that dealt with electric charges and their interaction was embryotic. It was known that there are two kinds of charges and that the charges of one kind repel those of the other, and that the charges of opposite kinds are attracted to each other. In those days, they were called resin and amber electricity. Later the names of the charges changed to positive and negative. From the standpoint of the mathematical approach, attraction and collision of opposite charges ends in their mutual neutralization, and charge disappears. All cosmic and ordinary material bodies were considered in the mechanics as electrically neutral bodies. Newton, therefore, could not explain the physical meaning of the equivalence principle of masses.

After the determination of the atomic structure and composition of atomic nuclei (after the discoveries of Rutherford), it became clear that all elements and, therefore, all of matter, are composed of the same stable charged particles: electrons, protons and neutrons. Charged particles have either positive or negative charge.

Under any forceful influence, a charged particle responds with the force of inertia, the nature of which is electric (see V.J. Gankin and J.V. Gankin «How chemical bonds and chemical reactions proceed»). In physics, force is an additive concept. The total force of the inertia of a material body is composed of the inertial forces of individual charged particles. The force F_{inertial_i}  acting on each particle is proportional to acceleration а according to the electrodynamic mechanism of inertia of the charged particles. Consequently, the total force acting on the whole macroscopic body is proportional to the acceleration а, and it is the subject matter of the second Newton's law F= m^.a.

The same situation exists for the force of gravity. The total force is composed of the gravitational forces of individual particles. Each force F_{grav_i}  is proportional to the acceleration g, according to Newton's fourth law, F=m^.g.

The ratio F inert_i /a = F grav_i /g  is a constant magnitude. The equivalence principle of masses is expressed in this ratio.

The equivalence principle was repeatedly refined and tested. In 1959 to 1963, the American physicist Robert Dicke increased its accuracy of measurement to 10^-11, and in 1971 the Soviet scientists V.P. Braginsky and V.I. Panov brought the accuracy of these magnitudes up ​​to 10^-12.

The nature of the equivalence principle of masses

We have compared  substances varying in density, conductivity and other parameters. Table 1 shows  calculation of the number of nucleons in the 1 gram of the element.

The atomic weight was calculated by the formula

M=1,00732*Z+1,0087*N,                                                                            (3)

in which Z is the number of protons, N is the number of neutrons, and the coefficients 1.00732 and 1.0087 take into account intranuclear interactions. The table shows the calculations for only a few stable isotopes of elements that differ in chemical and physical properties. The number of nucleons in 1 gram of a substance is identical to the 4^th digit, with differences less than 10^-3%. That is why we believe that an equal number of charged particles determines the same inertial and gravitational properties. This occurs because of the additivity of the inertial and gravitational forces and the absence of other components in any substance.

We believe that

Why are the other properties of 1 gram of a substance so different? Because these properties are determined by chemical bonds formed by atoms or molecules of the substance.

Inertial properties attributed to the mechanical mass exist only as a fact determined by belief in figures of authority and the inertia of human reasoning.

• Equivalence principle. Part 2