N E W Y O R K C I T Y C O L L E G E L E C T U R E S 5 0 9
great German mathematician Minkowski. Professor Einstein brought laughter from his au-
dience by his amusing references to the wide-spread mis-impression that the theory of rel-
ativity had discovered a fourth dimension of space. He went on to explain that the adherents
of the theory of relativity realized perfectly that time could be measured only by clocks and
space by yardsticks, and that the two could therefore, not be identical. But since the theory
of relativity shows that the rate at which clocks measure time depends upon their special
[spatial] motion, there is great advantage in treating time and space measurements together.
In this way the world of physical events can be viewed as a four-dimensional manifold. That
means that it is necessary to make four measurements, three space measurements and one
time determination, to locate the position of an event. If we understand this we can under-
stand how the Lorentz equations can denote the same mathematical properties that would
result from a rotation of our axes of reference in a four-dimensional space.
Before the lecture, Professor Einstein invited questions and comments from his audi-
ence. A number of question were asked which he answered with great patience. In answer
to one question he pointed out that the shortening of lengths and the slowing up of clocks
were true only on the principle of the constancy of the velocity of light, and that these short-
enings held true only if we take our center of measurement in some system with reference
to which we are moving. In answer to one inquirer who wished to press him to give the rela-
tion of his philosophy to that of Vaihinger’s Die Philosophie des Als Ob, Professor Einstein
replied that he thought all true philosophical systems could be harmonized with true natural
science. To another inquirer he pointed out that while a velocity greater than that of light is
conceivable it is not physically possible since it would demand infinite energy.
III. T
HE
GENERAL THEORY
OF
RELATIVITY
AND
GRAVITATION.
For his third lecture, Professor Einstein took as his subject the generalized theory of Rel-
ativity. He began with some preliminary remarks about his advanced mathematical meth-
ods. But thereafter he stuck rather close to plain prose interspersed with a few geometrical
illustrations on the blackboard. The general principle of Relativity means that detecting
motion or describing its laws it ought to be immaterial from what reference body we start
our measurement. But if this is so we may well ask why stop at the special theory of Rela-
tivity which asserts that the laws of nature are the same in all systems moving uniformly
with reference to each other. Why should we not go to say that the laws of nature must be
the same no matter what are the relative motions of the different observers? The usual
objection to this is found in Newtonian mechanics which asserts that a body not acted upon
by external forces moves uniformly in a straight line, but if acted on by forces it will move
with accelerated motion. Now, if two observers are moving relative to each other with non-
uniform velocity, the same body which seems to one observer to move in a straight line will
seem to the other to move in a curved line, which involves accelerated motion. It would
seem, then, that the two observers could not find the same laws of nature governing the
motion of the body which they are observing. This objection Professor Einstein showed