D O C U M E N T 1 7 5 D E C E M B E R 1 9 2 3 1 7 5
oped in the 3 notes (Bull. Ac[ad]. R[oy]. Belgique 1922–1923): Interprétation phy-
sique de la Relativité Générale, which notes I had sent to you to Berlin
(University)]. Your [results] are its mathematical proof. One could, moreover, gen-
eralize your results and show that it will always be thus.
The outcome is that one must return to the older approach, i.e., that one must in-
volve directly or a priori the function
or
Two paths open up: start with the 40 potentials or with the 14 potentials
and (variational principle or generalized Hamiltonian). I hope to be able
to demonstrate that these approaches always lead to the same equations if the Ham-
iltonian function H is conveniently modified. (This result is already verified for a
particular case in your 3rd note from Berlin.)
Consequently, in accordance with that, there will be grounds for returning to the
procedure indicated, I believe, by Weyl. However, then one finds in the pure elec-
tromagnetic field (a priori without mass) an absurdity (which you had pointed out
in your old reports). To avoid this absurdity, would it not be necessary to introduce
the factor
i.e., to introduce the function
into the Hamiltonian function H. This is what I had proposed in Paris (meeting of
the Collège de France), and you had declared then that this introduction of factor
W was very important.
Since then, I have developed this point of view in supplements I, II, and V of my
“Premiers Compléments de la Gravifique einsteinienne” here in
attachment.[3]
The results do seem very encouraging. May I request your opinion concerning
this manner of describing the pure electromagnetic field?
In utmost respect, my highly esteemed colleague, yours sincerely,
T. De Donder.
Lσ σuα)Φα
α
¦(
=
α
¦iαΦα
Γαβ γ
gαβ Φα
W
β α
¦¦gαβuαuβ
≡ 1 =
Lσ.W