EIGHTH LECTURE.
General Dynamics.    Principle of Relativity.

In the lecture of yesterday we saw, by means of examples,
that all continuous reversible processes of nature may be repre¬
sented as consequences of the principle of least action, and
that the whole course of such a process is uniquely determined
as soon as we know, besides the actions which are exerted upon
the system from without, the kinetic potential // as a function
of the generalized coordinates and their differential coefficients
with respect to time. The determination of this function
remains then as a special problem, and we recognize here a
rich field for further theories and hypotheses. It is my purpose
to discuss with you today an hypothesis which represents a mag¬
nificent attempt to establish quite generally the dependency of
the kinetic potential // upon the velocities, and which is commonly
designated as the principle of relativity. The gist of this prin¬
ciple is: it is in no wise possible to detect the motion of a
body relative to empty space; in fact, there is absolutely
no physical sense in speaking of such a motion. If, therefore,
two observers move with uniform but different velocities, then
each of the two with exactly the same right may assert that with
respect to empty space he is at rest, and there are no physical
methods of measurement enabling us to decide in favor of the one
or the other. The principle of relativity in its generalized form
is a very recent development. The preparatory steps were taken
by H. A. Lorentz, it was first generally formulated by A. Einstein,
and was developed into a finished mathematical system by
H. Minkowski. However, traces of it extend quite far back
into the past, and therefore it seems desirable first to say some¬
thing concerning the history of its development.

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