Einstein did not simply tinker with Newton’s theory; he devised a differ-
ent way of looking at the universe. Nonetheless, both Newton and Ein-
stein visualized a universe in which events could be specified by four
numbers (dimensions)—three numbers denoting spatial location, one
denoting temporal location. For Newton, however, these four numbers
were absolute; all observers would agree on how much spatial distance
there was between two events occurring at the same time, and all observ-
ers would agree on how much time had elapsed between two events oc-
curring at the same point in space. One of Einstein’s contributions was
the observation that these numbers were relative; a consequence of Ein-
stein’s theory was that moving observers would disagree as to how much
time had elapsed between two events occurring at the same point in
space. Moving rulers shorten and moving clocks run more slowly, accord-
ing to Einstein—and an experiment in which two perfectly synchronized
atomic clocks were compared, one of which stayed on the ground while
the other was f lown in a jet around the world, proved that Einstein was
right.
Nonetheless, both Newton and Einstein used four numbers to discuss
the universe; their universes are four-dimensional. There are two ques-
tions that immediately occur. The first—is our universe really four-
dimensional?—asks whether Newton, and then Einstein, got it right. The
second—are there other, non-four-dimensional universes?—is somewhat
deeper, and starts to get into the realm of philosophy (or pure mathemat-
ics).
These two questions have occupied physicists for the better part of a
century. It is the quest for the theory of everything, by which physicists
will not only explain what happens, but why it happens and whether other
things can happen (other universes exist) or they can’t (ours is the only
possible universe). Although a theory of everything will still leave many
questions unanswered, such an accomplishment would close the books
on one of the great questions of mankind.
The Geometry of the Universe
One of Newton’s most famous statements, to be found in his Principia,
was “I frame no hypotheses; for whatever is not deduced from the phe-
nomena (observational data) is to be called an hypothesis and hypothe-
ses... have no place in experimental philosophy. In this philosophy
particular propositions are inferred from the data and afterwards ren-
dered general by induction. Thus it was that... [my] laws of motion and
gravitation were... discovered.”^9
144 How Math Explains the World