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