D O C . 1 3 D I A L O G U E A B O U T R E L A T I V I T Y T H E O R Y 7 1
Instead of “real” and “non-real” we should rather distinguish more clearly
between quantities that are inherent in a physical system per se (independent of
the choice of coordinate systems) and other quantities that do depend upon the
coordinate system. The obvious demand would be that physics should use only
quantities of the first kind in its laws. History has shown that this cannot be real-
ized in practice, as already the development of classical mechanics has clearly
demonstrated. One could, for example, think of—and actually it has already been
tried—to introduce into the laws of classical mechanics only the distances
between material points instead of the coordinates; a priori one might expect this
to be the simplest way to achieve the goals of the theory of relativity. Scientific
development, however, did not confirm this expectation. Relativity theory cannot
dispense with coordinates, and thus must use coordinates as quantities that are not
the result of definable measurements. According to the general theory of relativity,
the four coordinates of the space-time continuum can even be chosen completely
arbitrarily—as parameters devoid of any independent physical meaning. Part of
this arbitrariness remains even in those quantities (field components) with whose
aid we describe physical reality. Only certain ones, usually rather complicated
expressions, composed of field components and coordinates are measurable (i.e.,
real) quantities that are independent of the system of coordinates. The components
of the gravitational field in a space-time point, for example, have no equivalent
quantity that is independent of the choice of coordinates; the gravitational field at
a certain location represents nothing “physically real,” but the gravitational field
together with other data does. Therefore, one can neither say the gravitational field
at a location is “real,” nor that it is “only fictitious.”
The main difficulty in the study of the theory of relativity seems to lie in the
fact that in it the connection between quantities in equations and measurable
quantities is far more indirect than in the customary theories of old. Your last
objection too is based upon the fact that you did not focus on this distinction.
You proclaimed the fields used in the clock experiment also as merely ficti-
tious because lines of force in real gravitational fields must necessarily be gener-
ated by masses; yet there were no field-generating masses present in the example
we discussed. There is a twofold response to this. First: It is not an a priori neces-
sary requirement that the Newtonian concept of every gravitational field being
generated by masses should be kept in the general theory of relativity. This ques-
tion again is linked to the circumstances mentioned above, that the meaning of
field components is much less directly defined than it is in the Newtonian theory.
Second: One cannot say there are no masses to which the generation of the field
could be attributed. It is true, however, that accelerated coordinate systems cannot
be employed as the real causes of the field—though a humorous critic once
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