ASTRONOMIS CHE NACHRICHTEN

Volume 313 1992 Number 2

Astron. Nachr. 313 (1992) 2, 65-67

Remarks on anisotropy of inertia in an anisotropic cosmos

H.-J. TREDER, Potsdam-Babelsberg, Germany

Einstein-Laboratorium

Received 1991 October 17; accepted 1992 January 15

Mach's relativity of inertia does not necessarily imply an anisotropy of inertial masses in an anisotropic universe and the Mach-Einstein doctrine is compatible with the isotropy of mass in each cosmos.

K e y words: cosmology - anisotropy of inertial masses - Mach-Einstein doctrine

A A A subject classification: 161

1. Introduction

Some years ago the question of a cosmically induced anisotropy of inertial masses m w a s in discussion with respect to the questions of the structure of the universe and to the experimental consequences and limitations (Drever 1961, Hughes 1964). These questions are connected with such fundamental problems like Mach's principle of relativity of inertia and the Mach-Einstein doctrine in General Relativity (Cocconi and Salpeter 1958, 1960, Dicke 1964, Goenner 1981, Treder 1972). In recent times we have new discussions on the astronomical and physical meaning of anisotropy of inertia. I want to remind of the earlier results with respect to the relativity of inertia and anisotropic distributions of gravitating matter in the universe.

2. Mach-Einstein doctrhe

Mach's principle together with the Mach-Einstein doctrine of the identity of the inertial and the gravitational field involves that the inertial m a s mA of a body A is a functional of all gravitational masses ,YE of the cosmos. This functional is the tensor (Treder 1972, Goenner 1981)

In eq. (1) light, Q and P are pure numbers. The bi-potential equation AAm: = 0 is valid.

is the gravitational mass of the body A, G is the Newtonian gravitational constant, c the velocity of

Approximately, the mean potential of the cosmos is (Treder 1972, 1980)

5 Astron. N x h r 313 (1992) 2

66 Astron. Nachr. 313 (1992) 2

The factor 5 gives a correspondence to the general relativistic Einstein effects (Treder et al. 1980). Then the contribution of some near "attractor", p~ = M i , to the inertial mass tensor m: is given by

The terms - bik mean the isotropic part of the inertial mass m A .

The difference between the longitudinal mass mAll and the transversal mass mAlis

2a GM2, c2 rg

A m A = mAll- m A l = P A - -

and with eq.(2) and the normalized potential

we have

-- - 2a.5 A m A

P A

According to Hughes' and Drever's experimental data (Hughes 1964, Drever 1961), we have to put 2a.5 5 5.10-23. Therefore, the limit of Q is given by Q 5 lo-''. Consequently,

we find from eq.(3) that p x 3/2. That means, /? >> a and the inertia becomes nearly isotropic. For Q = 0 the Laplace equation, Am';: = 0, is valid (Treder 1972, 1980).

The "Great Attractor" produces E x

Contrary to this, Cocconi and Salpeter (1958, 1960) supposed the ansatz

i.e., Q = 3 / 2 and p = 0. Then the difference A m A becomes

which is incompatible with the experimental data (Hughes 1964, Treder et al. 1980).

3. Inertial field

Another hypothetical ansatz (Cocconi and Salpeter 1958,1960) has no connection with the Newtonian gravitation and the Mach-Einstein doctrine. This ansatz claims a new "inertial field" in addition to the Newtonian potential field,

- G p B @ A B = - .

r A B

This "inertial field" is assumed to be independent of the bodies distances r A B . But Galileo's proportionality between gravity and inertia remains valid and the gravitational masses p~g should be the sources of the "inertial field" also,

(with some coupling constant g ) .

results In an isotropic universe with the total gravitational mass M = CB p~ and with one excentric "attractor" MT,

(10) A - - g P A ( [ M - Mi] bik + ? d ~ ~ ~ B x ~ B r ~ ~ ) .

H.-J. Treder: Remarks on anisotropy of inertia 67

According to Galileo’s equivalence of gravitating and inertial mass, the coupling constant must be taken as g = 1/M and the difference between the longitudinal inertial mass mAll and the transversal inertial mass m A l becomes

But Drever’s experiment gives

According to the astrophysical point of view, inertia induced by the cosmic masses independent of their distances implies that the masses of clusters and superclusters of galaxies in our neighbourhood give greater contributions to an anisotropy of inertia than an attractor in our galaxy. Therefore, the total mass M of the cosmos must be infinitely large.

Besides, an ansatz of the form

is impossible, because in this case excentric positions of the farthest bodies would induce the greatest anisotropy of inertia. P.e., an anisotropical ”cosmological potential” - Xg CB gives

(with a ”cosmological constant”X). influence, of course.

For n < -2 the comparatively near gravitational masses have the main

References

Cocconi, G., Salpeter, E.E.: Cocconi, G., Salpeter, E.E.: Dicke, R.H.:

Drever, R.W.: Goenner, H.F.:

Hughes, V.W.: Treder, €1.-J.: 1972, Die Relativitat der Trigheit. Berlin, Moskau 1975. Treder, H.-J., v. Borzeskowski, H.-H., van der Merwe, A., Yourgrau, W.:

1958, Nuovo Cimento 10, 646. 1960, Phys. Rev. Lett. 4, 176.

1964, The many faces of Mach. In: H.-Y. Chiu and W.F. Hoffmann (eds.): Gravitation and Relativity. New York, p. 121-141.

1961, Phil. Mag. 6 , 683. 1981, Machsches Prinzip und Theorien der Gravitation. In: Grundlagenprobleme der modernen Physik.

1964, Mach’s principle and mass anisotropy. 1. c. p. 106-120. Mannheim, p. 106-120.

1980, Fundamental Principles of General Rela- tivity. New York.

Address of the author:

Hans- Jiirgen Treder Einstein-Laboratorium Rosa-Luxemburg-Str. 17a D-0-1590 Potsdam-Babelsberg Germ any

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