5. -- GRAVITATON
Translated (1980) from Recherches critiques sur l'Ėlectrodynamique
Annales de Chimie et de Physique, Vol. 13, p. 145, 1908.
If we consider the
electromagnetic theories in their present form as a general basis for the
explanation of physical phenomena, a role that only Mechanics played until now,
it will suffice, at first, to ask ourselves if we can place gravitation in this
general scheme. Is the notion of field,
(Oeuvres 346) with its consequences, capable of being applied? The response
given by Maxwell is negative.
In introducing the force which gravitation exercises at a point xyz
in space on a unit of mass, we can well, as in electrostatics, determine this
force by the system of equations (µ = density)
And the value of the energy will be
(the unit mass being chosen properly).
Since there is attraction, the integral has the sign (-). But, says
the energy being essentially positive, for E to be positive, it will be
necessary to choose an enormous value for the constant, greater that the
greatest value that the integral could attain for all possible positions of the
bodies. The intrinsic energy of the gravitational field is constrained to decrease
wherever gravity is sensible. “Since it is impossible for me to understand how
a medium could possess such properties, I cannot pursue research, in this vein,
into the cause of gravitation."
We can again say that the
condition of stability of a continuous medium, elastic or otherwise, is always
such that the energy is minimum when the deformation is zero; here; it is
maximum for R = 0. The gravitational field would be in unstable equilibrium
at infinity and wherever R is zero.
The notion of field doesn’t
seem applicable to gravitation; it shouldn’t therefore be an issue to consider
as a general base for the explanation of physical phenomena.
On the contrary, the law of
elementary action, which results from Lorentz’s theory, if we replace the
electric charges by (Oeuvres 347) masses can, as in the similar laws of Weber,
Gauss, etc., replace the classical law of gravitation, without the new terms
and the propagation they introduce having an appreciable influence on
astronomical phenomena. These terms are in fact second order and therefore extremely small. We know that Laplace had arrived at the
result that the propagation speed of
gravitation is at least 100,000,000 times greater than that of light; but this
is related to that which, in his manner of conceiving propagation, introduces a
first order term, and that moreover, this term corresponds to a friction, which
doesn’t happen with Lorentz.
Zöllner’s explanation adopted by Lorentz is, as we know, that the
attraction of two electric charges of opposite sign, is slightly greater than
the repulsion of two charges of like sign and of the same absolute value. This explanation destroys the unity of the
electric field, and is thus is applicable only to elementary actions.