D O C U M E N T 6 8 J U N E 1 9 2 0 2 0 3
As various persons have explained to me, however, it would be very fruitful if
you could substantiate your position sometime; and for me personally it has be-
come absolutely necessary that you speak up. For in a controversy in the press (in
the N[eue] S[chweizer] Z[eitung]), your friend Grossmann wrote that my “views
about relativity had been completely repudiated (?) by
you.”[4]
When I thereupon
asked Grossmann when and where you had expressed yourself in this
way,[5]
he re-
plied to me that in a letter, you had written that my “views on relativity were
nonsense.”[6]
This groundless judgment, which is apt to hurt me to the highest de-
gree, forces me to insist that either it be given a basis or retracted. That is why I
must ask you, dear Einstein, for a reply that I can
publicize.[7]
This you really can’t
refuse your old Office
colleague![8]
It will be even easier now that the experimen-
tum crucis—the spectrum-line shift—which is decisive for my interpretation, has
been established in my favor by Prof. Julius on the basis of
measurements.[9]
Briefly, my interpretation can be summarized as follows:
1. As I have proven in my last paper, time can be singly or multiparametrically
described. 2. This descriptive equivalence requires that in the quadratic forms
; ,
the quantities and are not periods but different masses of the same
timespan; dU and du have only one physical meaning: they represent “light paths.”
You can find the proof in the mentioned paper and on the enclosed printer’s
proof.[10]
This interpretation can be illustrated very nicely with the help of the Lorentz
transformation. For a light signal, you have for an infinitesimal time interval
, ;
hence, if we set
(1) ,
where is an infinitesimal quantity independent of ,
(2) .
(1) represents an elementary light sphere and (2) shows that it appears, “judged”
from , as a rotational ellipsoid with one focus at the origin.
This thoroughly simple consideration shows how the principle of relative con-
stancy of the velocity of light, which I have introduced, must be understood. For if
one puts
;
you thus obtain:
In a sphere:
ds2 dU2 dX2
–
dY2
–
dZ2
– =
ds2 g44du2
–
g11dx2
– =
dU
c0
-------
du
c0
----- -
du2 du1 dx1 – = dx1 du1
1
cos =
du2 =
2
du1
1
1
cos –
----------------------------------- - =
K1
du2 c2dt = c0dt =
K2 c2 c0 =