3 4 D O C . 4 F O U N D A T I O N S O F G E N E R A L R E L A T I V I T Y

energy tensor , it follows that the G-field is caused and determined by the

energy tensor of matter.

As to (a), Herr Kretschmann notes that the principle of relativity, phrased in this

manner, is not a statement about physical reality, i.e., not about the content of na-

ture’s laws, but it is rather a demand with respect to their mathematical formulation.

Because physical experience pertains only to coincidences, it must always be pos-

sible to represent the causal connections between these coincidences by generally

covariant equations. He thinks it necessary to associate a different meaning to the

demand of relativity. I consider the first argument of Herr Kretschmann as correct,

but I do not believe his suggested innovation is recommendable. While it is correct

that every empirical law can be brought into a generally covariant form, principle

(a) also carries considerable heuristic weight, which has already proven itself

splendidly in the problem of gravitation. The point is the following. Among two

theoretical systems, both compatible with experience, one will have to prefer the

one that is simpler and more transparent from the point of view of absolute differ-

ential calculus. One just should bring the mechanics of Newtonian gravitation in

the form of absolute-covariant equations (four-dimensional) and one will certainly

become convinced that principle (a) excludes this theory, not on theoretical

grounds, but on practical ones!

Principle (b) was the starting point of the entire theory, and has brought with it

the formulation of principle (a); it certainly cannot be abandoned as long as one

clings to the basic ideas of the theoretical system.

Mach’s principle (c) is a different story. The necessity to uphold it is by no means

shared by all colleagues; but I myself feel it is absolutely necessary to satisfy it.

With (c), according to the field equations of gravitation, there can be no G-field

without matter. Obviously, postulate (c) is closely connected to the space-time

structure of the world as a whole, because all masses in the universe will partake in

the generation of the G-field.

Originally, I suggested for the field equations of gravitation

, (1)

with the abbreviation

.

Tμν) (

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[p. 243]

Gμν Tμν

1

2

-- -

gμνT⎠ –

⎛ ⎞

–κ⎝ =

[14]

Gμν τν) ,

στ

∑gστ(μσ

=