Radzievskii,V.V. and Kagalnikova, I.I. Bull. Vsesoyuz. Astronomo. Geol. Obshchestva.

(Moscow) 26, 3 (1960)

Translation in U.S. Govt. tech. report FTD-TT-64-323/1+2+4 (AD-601762)

THE NATURE OF GRAVITATION

V. V. Radziyevskiy and I. I. Kagal'nikova

Introduction

The discovery of the law of universal gravitation did not

immediately attract the attention of researchers to the question

of the physical nature of gravitation. Not until the middle of

the 18th century did M. V. Lomonosov (1) and several years later,

Lesage [2, 3], make the first attempts to interpret the phenome-

non of gravitation on the basis of the hypothesis of "attraction"

of one body to another by means of "ultracosmic" corpuscles.

The hypothesis of Lomonosov and Lesage, thanks to its great

simplicity and physical clarity quickly attracted the general

attention of naturalists and during the next 150 years served as

a theme for violent polemics. It gave rise to an enormous number

of publications, among which the most interesting are the works

of Laplace [4], Secchi (5), Leray (6), V. Thomson (7), Schramm (8),

Tait (9), lsenkrahe (10), Preston (11, 12), Jarolimek (13), Waachy

(14), Rysanek (15), Lorentz (16), D. Thomson (cited in (17),

Darwin (18), H. Poincare {19, 20), Majorana (21-25), and

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Sulaiman (26, 27).

In the course of these polemics, numerous authors proposed

various modificatlons to the theory of Lomonosov and Lesage.

However, careful examination of each of these invariably led to

conclusions which were incompatible with one or another concept

of classical physics. For this reason, and also as a result of

the successful elaboration of the general theory of relativity,

interest In the Lomonosov-Lesage hypothesis declined sharply at

the beginning of the 20th century and evidently it would have

been doomed to complete oblivion, if in 1919-1922 the Italian

scientist Majorana had not published the results of his highly

interesting experiments. In a series of extremely carefully

prepared experiments, Majorana discovered the phenomenon of

gravitational absorption by massive screens placed between inter-

acting bodies, a phenomenon which is easily interpreted within

the framework of classical concepts of the mechanism of gravita-

tion, but theretofore did not have an explanation from the point

of view of the general theory of relativity.

The famous experimenter, Michelson (28), became interested

in the experiments of Majorana. However, his intention to

duplicate these experiments faded, evidently as a result of the

critical article of Russel (29), in which it was shown that if

the Majorana's gravitational absorption really did exist, then the

intensity of ocean tides on two diametrically opposite points on

the earth would differ almost 400 fold. On the basis of this

calculation of Russel, Majorana's experimental results were taken

to be groundless in spite of the fact that the experimental and

technical aspect did not arouse any concrete objections.

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In acquainting ourselves with the whole complex of pre-

relativity ideas about the nature of gravitation, we were compelled

to think of the possibility of a synthesis of the numerous classical

hypothesis, such that each of the inherent, isolated, internal con-

tradictions or disagreements with experimental data might be suc-

cessfully explained. The exposition of this "synthesis." i.e.,

unified and modernized classical hypothesis of gravitation created

primarily from the work of the authors cited above and supplemented

only to a minimum degree by our own deliberations, is the main

problem of this work. The other motive which has impelled us to

write this article is that we have discovered the above mentioned

objections of Russel against Majorana's experimental results to

be untenable; from the point of view of the classical gravitation

hypothesis no differential effect in the ocean tides need be

observed. Therefore we must again emphasize that Majorana's experi-

mental results deserve the closest attention and study. It seems

to us that duplication of Majorana's experiments and organization

of a series of other experiments which shed light on the existence

of gravitation absorption are some of the most urgent problems of

contemporary physics. Positive results of detailed experiments

could Introduce substantial corrections into even the general

theory of relativity concerning the question of gravitation absorp-

tion within the framework of this theory, while still remaining

a blank spot.

Evidently a strict interpretation of the Majorana phenomenon

la possible only from the position of a quantum-relativistic theory

of gravitation. However, insofar as this theory is still only

being conceived it seems appropriate, as a first approximation, to

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examine an interpretation of this problem on the basis of the

"synthetic hypothesis" presented below, especially as the last

includes the known attempts at a theory of quantum gravitation.

We shall begin with a short exposition of the history of the

question.

1. Discussion of the Lomonosov-Lesage hypothesis

According to the Lomonosov-Lesage hypothesis, outer space is

filled with "ultracosmic" particles which move with tremendous

speed and can almost freely penetrate matter. The latter only

slightly impedes the momentum of the particles In proportion to

the magnitude of the penetrating momentum, the density of the

matter, and the path length of the particle within the body.

Thanks to spatial isotropy in the distribution and motion of

ultracosmic particles, the cumulative momentum which is absorbed

by an isolated body is equal to zero and the body experiences only

a state of compression. In the presence of two bodies (A and B)

the stream of particles from body B, impinging on body A, is

attenuated by absorption within body B. Therefore, the surplus

of the flux striking body A from the outer side drives the latter

toward body B.

In connection with the Lomonosov-Lesage hypothesis, the

question of the mechanism of momentum absorption immediately

arises. Generally speaking the following variants are possible:

1. The overwhelming majority of particles pass through

matter without loss of momentum, and an insignificant part are

either completely absorbed by the matter or undergo elastic

reflection (Schramm (8)). Evidently, in the first case constant

"scooping" of ultracosmic particles by matter must take place,

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leading to secular decrease in the gravitation constant. In

addition, as it is easy to show, in this case an inadmissable

rapid increment of the body's mass must occur. If the speed of the

ultracosmic particles is close to that of light. In the second

case as Waschy (14) showed, the reflected particles must compensate

for the anisotropy in the motion of the particles, which was

created by the interacting bodies. In other words, the driving

of the bodies in this caae would be completely compensated for by

the repulsion of the reflected particles and no gravitation would

result.

2. All particles passing through matter experience something

like friction, as a result of which they lose part of their

momentum owing to a decrease in speed (Lesage (2, 3), Leray (6),

Darwin [18], and others). Evidently in this case there would also

be a gradual weakening of the gravitational interaction of the

bodies (lsenkrahe (10)).

A way out from the described difficulty was made possible by

the proposal of Thomasin (cited in (19, 17)), D. Thomson (cited in

(17)), Lorentz (15), Brush (30), Klutz (31), Poincare (19, 20),

and others, for a new modification of the Lomonosov-Lesage hypothe-

sis, according to which the ultracosmic particles are replaced by

extremely hard and penetrating electromagnetic wave radiation.

If in this case we assume that matter is capable of absorbing only

primary radiation and radiates secondary radiation, which still

posesses great penetrating power, then the Waschy effect (repulsion

of secondary radiation) may be eliminated.*

_______________________________

* However, in order that a secular decrease in the gravitation

constant does not occur It is necessary to suppose that the quanta

of secondary radiation, after being radiated, decompose to primary

radiation and, as a consequence, at some distance, depending on the

duration of their lives, the gravitational interaction between bodies

approaches zero.

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The next question which arises in connection with the Lomonosv-

Lesage hypothesis concerns the fate of the energy which is absorbed

by the body along with the momentum of the gravitational field. As

Maxwell (32) and Poincare (19, 20) have shown, if we attribute to

gravity a speed not less than the speed of light, then in order to

ensure the gravitational force observed in nature it is necessary

to accept that momentum is absorbed which is equal to an amount of

energy that can transform all material into vapor in one second.

However, these ideas lose their force when the ideas of Thomasin,

G. Thomson, and Lorentz are considered, according to which the

absorbed energy is not transformed into heat, but is reradiated as

secondary radiation according to laws which are distinct from the

laws of thermal radiation.

There was still one group of very ticklish questions connected

with the astronomical consequences of the Lomonosov-Lesage hypothe-

sis. As Laplace has shown [4], the propagation of gravitation with

a finite speed must cause gravitational aberration, giving rise to

so many significant disturbances in the motion of heavenly bodies

that it would be possible to miss them only if the propagation

velocity of gravitation exceeded the velocity of light by at least

several million times.

Poincare (20) directed attention to the fact that the motion

of even an isolated body must experience very significant braking

as a result first of the Doppler effect (head-on gravitons become

harder and consequently have more momentum than ones which are

being overtaken) and second, the mass being absorbed sets the body

In motion and a part of the body's own motion is communicated to

the mass. So that this braking not be detected by observation, it

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is necessary to assume that the speed of gravitational radiation

exceeds the speed of light by 18 orders. This idea of Poincare

is considered to be one of the strongest arguments against the Lomonosov-Lesage hypothesis.

Not too long ago a modification to the Lomonosov-Lesage

hypothesis was suggested by the Indian academician Sulaiman.

According to this hypothesis, an isolated body A radiates

gravitons in all possible directions isotropically, experiencing

a resultant force equal to zero. The presence of a second body B

slows the process of graviton radiation by body A more strongly,

the smaller the distance between the bodies. Therefore the quanti-

ty of gravitons being radiated from the side of body A facing

body B will be less than from the opposite side. This gives rise

to a resultant force which is different from zero and tends to

bring body A and body B together.

Further, Sulaiman postulated invariability of the graviton

momentum with respect to a certain absolute frame of reference.

Here the moving body must experience not braking, but rather accel-

eration coinciding with the direction of speed and being compensated

by the braking influence of the medium.

Sulaiman's hypothesis is very interesting. Unfortunately, it

does not examine the question of decreasing mass of the radiating

bodies or the question of the fate of the radiated gravitons.

As can easily be shown by elementary calculation, so that the

impulse being radiated by the body can secure the observed force

of interaction between them, it is necessary that they lose their

mass with an unacceptably great speed. It is completely clear that

no combination of longitudinal and transverse masses can save the

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thesis. There is a well-defined relationship between the relativ-

istic expressions of the momentum and the energy (33), and it is

impossible to imagine that a body radiating energy E (i.e., mass

E/c²) could with this momentum radiate more than E/c.

If we suppose that the radiation of the mass is compensated

by the corresponding reverse process of graviton absorption, then

we return to a more natural elementary variant of the Lomonosov-

Lesage hypothesis. Graviton absorption and the screening effect

which is inescapably linked with it guarantee a gravitational

attraction force without the additional concept of anisotropic

graviton radiation by one body in the presence of another.

2. Majorana's experiment, Russel's criticism.

Majorana did not insist in his investigations on a concrete

physical interpretation of the law of gravitation. He simply

started from the supposition that if there is a material screen

between two interacting material points A and B, the force of their

attraction is weakened by gravitational absorption of this screen

[21, 22, 25). As in the Lomonosov-Lesage hypothesis, Majorana

took attenuation of the gravitational flux to be proportional to

the value of the stream itself, the true density of the substance

being penetrated by it, and the path length through the substance.

The proportionality factor h in this relationship is known as the

absorption coefficient. It is evident that with the above indi-

cated supposition the relationship of the gravitational flux value

to the path length must be expressed by an exponential law.

Let us imagine a material point which is interacting with an

extended body. Since any element of this body's mass will be

attracted to the material point with a force attenuated by screening

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of that part of the body which is situated between its given

element and the material point, on the whole the heavy mass of

this body will diminish in comparison with its true or inert mass.

In his work (21), Majorana introduced a formula for the

relationship between the heavy (apparent) mass M and the inert

(true) mass M_u of a spherical body of radius R and a constant

true density d_u

M_α = ΨM_ν = ¾(1/u – 1/2u³ + e^-2u (1//u² + 1/2 u³))M_ν. (1)

where u = hδ_νR.

Expanding (1) into a series, it is easy to see that when

U →0, M_α→ M_ν, and when u→¥, M_α→ πR²/h. From this

h < πR²/ M_α (2)

Applying the result of (2) in the case of the sun, which is a

body with the most reliably determined apparent weight, Majorana

obtained

h < 7,65 • 10^-12 CGS. (3)

To experimentally determine the absorption coefficient h

it is theoretically sufficient to weigh some "material point" with-

out a screen and then determine the weight of this "material screen"

after placing it in the center of a hollow sphere. If in the first

case we obtain a value m then in the second case we will register

a decreased value as a result of gravitational absorption by the

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walls of the hollow sphere

m_a = me^-hdl » m (1- hdl), (4)

where d is the density of the material from which the screening

sphere is made, and I is the thickness of its walls. Designating

ε as the weight decrease m - m_a, we easily find that

h = ε/mdl . (5)

To determine the absorption coefficient value by formula (5),

Majorana began, in 1919, a series of carefully arranged experiments,

weighing a lead sphere (with a mass of 1274 g) before and after

screening with a layer of mercury or lead (a decimeter thick).

After scrupulous consideration of all the corrections it

turned out that, as a result of screening the weight of the sphere

had decreased in the first series of experiments by 9.8 • 10^-7 g

which yields, according to (5), h = 6.7 • 10^-12. In the second

series of experiments, h = 2,8 • 10^-12 was obtained.

As already mentioned, in 1921 Russel came out with a critical

article devoted to Majorana's work.

Assuming that the interaction force between two finite bodies

is expressed by the formula:

F = Gm₁ψ₁M₂ ψ₂ /r² (6)

where, in accordance with expression (1)

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ψ = ¾(1/u – 1/2u³ + e^-2u(1/u + 1/2u³))

and assuming at first that the decrease in weight as a result of

self-screening occurs while leaving the inert masses unchanged,

Russel obtained on the basis of (6) the third law of Kepler in the

form

a³₁/ a³₂ = T³₁/ T³₂ (ψ³₁/ ψ³₂) (7)

The value of ψ, calculated by Russel with the absorption

coefficient h = 6,73 • 10^-12 found by Majorana for several bodies

of the solar system, is equal to:

Sun . . . 0.33

Jupiter . . 0.951

Saturn . . 0.978

Earth . . . 0.983

Mars . . . 0.993

Moon . . . 0.997

Eros . . . 1.000

From this it follows that the true density of the sun is not 1.41,

but 4.23 g/cm².

Using the above tabulated values of ψ and Kepler's law, Russel

showed convincingly that the corresponding imbalance between the

heavy and inert masses of the planets would lead to unacceptably

great deflections of their motions. In order that the deflection

might remain unnoticed, it would be necessary for the absorption

coefficient h to be 10⁴ times the value found by Majorana. From

this Russel came to the undoubtedly true conclusion that if as a

result of self-screening the weight decrease found by Majorana did

occur, then there would have to be a simultaneous decrease in their

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inert masses.

Russel made this conclusion the basis of the second part of

his article which was devoted mainly to investigation of the

question of the influence of gravitational absorption on the

intensity of lunar and solar tides. Following Majorana's ideas,

Russel suggested that a decrease in attraction and necessarily

also a decrease in the inert mass of each cubic centimeter of

water In relation to the sun or noon would occur only if they

were below the horizon. If this is admitted, then sharp anomalies

In the tides must be observed, viz., the tides on the side of the

earth where the attracting body is located must be less intense

(2 times for lunar tides and 370 times for solar tides) than on

the opposite side of the earth. In conclusion Russel contended

that his calculations demonstrated the absence of any substantial

gravitational absorption and that consequently Majorana's results

are in need of some other interpretation, Russel himself, however,

did not come to any conclusions in this regard.

While acknowledging the ideas presented in the first part of

Russel 's work to be unquestionably right, we must first of all

state that the self-screening effect and the weight decrease

associated with It cannot be seen as a phenomenon which is contra-

dictory to the relativistic principle of equivalence: any change

in a heavy mass must be accompanied by a corresponding change in

the inert mass of the body. But is it possible to agree with the

results of the second part of Russel's article, according to which

gravitational absorption on the scale discovered by Majorana is

contradicted by the observation data of lunar and solar tides?

Let us remember that Russel came to this conclusion starting from

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the freshly formed Majorana hypothesis of gravitational absorption

only under the condition that the attracting bodies are on dif-

ferent sides of the screen. Meanwhile, application of the Lomonosov-

Lesage hypothesis which painted a physical picture of gravitational

absorption leads, as we will show in the following section, to

conclusions which are completely compatible with Majorana's experi-

mental results and with the concepts set forth in the first part

of Russel's article, but at the same time, all of the conclusions

about tide anomalies lack any kind of basis. Skipping ahead some-

what let us say in short that according to the Lomonosov-Lesage

hypothesis, the weakening of attraction between two bodies must

occur when a screen intersects the straight line joining them,

regardless of whether there are gravitational bodies on various

sides or on one side of this screen.

3. The "Synthetic" Hypothesis

Let us suppose that outer space is filled with an isotropic

uniform gravitational field which we can liken to an electro-

magnetic field of extremely high frequency. Let us designate ρ

as the material density of the field, keeping in mind with this

concept the value of the inert mass contained in a unit volume of

space. Evidently the density of that part of the field which is

moving in a chosen direction within the solid angle dω is ρdω/4π

Under these conditions a mass of

dμ = dScρdω/4π (8)

carrying a momentum

dp = dSc²ρdω/4π (9)

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will pass through any area element dS in its normal direction with-

in the solid angle dω in unit time.

The mass flux (8) will fill an elementary cone, one cross

section of which serves as the area element dS. At any distance

from this area element, let us draw two planes parallel to it

which cut off an elementary frustrum of height dl, and let us

imagine that the frustrum is filled with material of density d.

It is evident that the portion of the flux (8) absorbed by this

material will be

d(dμ) = dμ hd dl (10)

or

d(dμ) = hρc (dω/4π) dm

where dm = d dSdl is the mass of the elementary frustrum.

Let us imagine a "material point" of mass m in the form of a

spherical body of density d and of sufficiently small dimensions

so that it is possible to neglect the progressive character of

the absorption within it and to consider that the absorption

proceeds in conformity with formula (11). Let us divide the sec-

tion of this spherical body into a number of area elements and

construct on each of them an elementary cone with an apex angle dω,

Applying formula (11) to these cones, and integrating with respect

to the whole mass of the material point, we obtain

Δ(dμ) = hρc (dω/4π) dm (12)

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Fig. 1. Diagram for calculation

of mass absorption of the flux

of a material field.

Formula (12) determines the value of the absorbed portion of

the field mass which has passed in unit time through a cone with

an apex angle dω, which Is circumscribed around a sufficiently

small spherical body of mass m.

To obtain the total rate of increment in the mass of the point,

it is necessary to take into consideration absorption of the field

impinging on it from all possible directions, which is equivalent

to integration (12) over the whole solid angle ω. This gives

dm/dt = hρcm. (12’)

Returning to formula (10), Imagine that the field flux inside

the cone circumscribed around material point m, penetrates the

material throughout the finite section of the path AB = L (fig. 1)

Integrating (10) from B to A, we obtain an expression which

determines the total absorption within the cone AB when δ = const

(dμ)₁ = dμe^-hδL (13)

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Let dμ be the mass of the field striking cone AB from side B,

and (d μ)_i be the mass of the field exiting this cone and impinging

on body m. The decrease in the mass of the flux because of

absorption in AB is equivalent to the decrease in its density up

to the value

ρ₁ = ρe^-hδL. (14)

Thus from the left flux of density ρ (its absorbed portion is

expressed by formula (12)) strikes material point m and from the

right, a flux of density ρ₁. The portion which is absorbed will be

Δ(dμ)₁ = hρe^-hδL (dω/4π) m. (15)

Calculating (15) and (12) and multiplying the result by c we

obtain a vector sum of the momentum absorbed by point m in unit

time equal to the value of force dF, from which point m is "attrac-

fed" to cone

dF = hρc²(dω/4π) ( 1 -