2 8 D O C . 2 N O T E O N P A P E R B Y S C H R Ö D I N G E R

2. “Note on E. Schrödinger’s Paper

1

‘The Energy Components of the Gravitational Field’”

[Einstein 1918b]

Received 5 February 1918

Published 15 March 1918

In: Physikalische Zeitschrift 19 (1918): 115–116.

Herr Schrödinger demonstrated by means of calculation that under a suitable

choice of the coordinate system the energy components of the gravitational

field of a sphere vanish (outside of

it).2

Understandably, Herr Schrödinger is sur-

prised by this result and I too found it rather quaint at the beginning. In particular,

he asks himself if the are really to be interpreted as the energy components. To

Herr Schrödinger’s scruples I would like to add two more:

1. While the energy components of matter form a tensor, this is not the

case for the quantities that are called the “energy components” of the

gravitational field.

2. The quantities are symmetric in their indices and ,

but the analogous are not.

H. A. Lorentz and Levi-Civita have misgivings about accepting the as the

energy components of gravitation because of the reason listed first.

While I understand their scruples, I am still convinced that a more useful

determination of the energy components of the gravitational field—other than the

one I have chosen—is not possible. I already gave the most convincing formal rea-

1

This journal 19, 4 (1918).

2

Herr G. Nordström already notified me a few months ago of the vanishing of the com-

ponents for this case.

[1]

tσ

α

[2]

[3]

t4

4

tσ

α

Tσ

α

tσ

α

[4]

Tστ

α

gατ

α

∑Tσ

= σ τ

tστ

α

gατ

α

∑tσ

=

[5]

tσ

α