2 1 0 D O C U M E N T 7 7 J U L Y 1 9 2 0

77. To Edouard Guillaume

[Berlin,] 19 July 1920

Dear Guillaume,

In the formula for the light vectors,

t means the standard clock reading at the specified location relative to the resting

coordin. system, the progression of readings of such a clock as a complete wave

passes by it (period of oscillation). Hence, both quantities are numbers that are ob-

tained as measurement results with standard clocks at rest. Both are obtained by

counting the periods by means of a standard clock.[1] I do not understand what you

conceive as a “period” in your letter; with me, it is not a number but the designation

for a cyclic process that repeats itself.

Your deduction of the relation seems to me, quite frankly, completely

crazy. In the consideration that leads to the relations [2]

, etc.,

x, y, z, t are variables, for whose total values the equations must be satisfied identi-

cally. In the second part of the consideration, x, y, z, t are the coordinates of a plane

moving with the velocity of light (x = ctl, y = ctm, z = ctn, , etc.), thus

something quite different from the first consideration. It makes absolutely no rea-

sonable sense to compare the period length with the arrival time t of that plane

moving with the velocity of light, which passes through the origin of the coordi-

nates at time t = 0.– Your relation t = invariant does not relate to all world points

but only to a three-dimensional

manifold![3]

My above remark about the meaning of and t as results of measurements taken

from standard clocks is just valid for the special theory of relativity, whereas in the

general theory of relativity only ds is defined as a measurement result. In the gen.

th. of r., dt initially has a purely conventional meaning. In the consideration about

line displacements, however, t again receives an absolute meaning in that the 4 co-

ordinates are chosen so as to have the field of an isolated mass-point become static;

thus the number of wavelengths that are traveling between the sun and the observer

cannot depend on t.–

In any case, I must emphasize that it seems absolutely senseless to establish a

relation between the quantities and t appearing in your consideration. Upon clos-

er reflection you will also find it so. If Hadamard and Levi-Cività are capable of

Asin2

------ t

lx

c

------------------------------nz+my+

–

t t =

1 l +

------------------------- =

x ct l =