III
In the seventeenth century Galileo and Descartes
adumbrated the law of inertia, which later became
Newton's first law of motion: every body continues in
its state of rest, or of uniform motion in a straight line,
unless it is compelled to change that state by forces
impressed upon it. That this had not been formulated
millennia earlier should not surprise us, for terrestrial
experience strongly suggests that bodies left to them-
selves come to rest, and that force is needed to maintain
them in motion. True, the celestial motions seemed to
continue indefinitely, but these motions were for the
most part circular, and it was natural for the Greeks
to believe that the heavens were subject to laws far
different from those that held sway on the earth.
It is hard to overestimate the importance of the first
law. Uniform motion in a straight line was now the
natural motion, needing no external cause. Bodies,
being possessed of an innate inertia, resisted change
of motion; and only change of motion demanded the
presence of external force. Because of this new view-
point Newton was able to create a conceptual system
that brought together the dynamics of the heavens and
the earth in a mighty synthesis built seemingly on just
his three laws of motion and his law of universal gravi-
tation.
But only seemingly. By themselves, Newton's laws
made no sense. Take the first law, for example. What
does the phrase “uniform motion in a straight line”
mean? Imagine a bead on a straight wire marked off
in inches. If the bead traverses equal distances along
the wire in equal times we can certainly claim that
it is moving uniformly in a straight line. But our claim
will be superficial and ill-founded. What, for instance,
if the clock with which we timed the bead had been
unreliable? Or the wire had been whirling and reeling
—say with the Keplerian earth?
Newton was acutely aware of such problems. In his
Principia, before stating his laws of motion, he carefully
prepared a conceptual setting in which they could take
on meaning. Saying disarmingly “I do not define time,
space, place, and motion [since they are] well known
to all,” he nevertheless proceeded to define their abso-
lute as distinguished from their relative aspects:
“Absolute, true, and mathematical time, of itself, and
from its own nature, flows equably without relation
to anything external....
“Absolute space, in its own nature, without relation
to anything external, remains always similar and im-
movable....”
These are basic assertions, not operational defini-
tions. For example, they provide no method of deciding
which of our clocks comes closest to ticking uniformly.
Spurred by penetrating criticisms by Berkeley and
Leibniz, Newton added a famous Scholium in a later
edition of the Principia. Here is a short excerpt: “[God]
is not eternity and infinity, but eternal and infinite;
he is not duration or space, but he... endures forever
and is everywhere present; and by existing always and
everywhere he constitutes duration and space.”
For Newton, absolute time and absolute space were
vividly present. Without them, as we have seen, his
laws would be meaningless. With them he could form
cosmic concepts of absolute rest, of absolute uniform
motion in a straight line, and of absolute deviations
from such motion.
By noting the centrifugal effects of rotation, among
them the concavity of the surface of rotating water
in his famous bucket experiment, Newton had con-
vinced himself that rotation is absolute, in powerful
agreement with his concept of absolute space. How-
ever, his laws of motion did not faithfully mirror the
absoluteness of their setting. To appreciate this, let us
begin with everyday experience. In a vehicle, we feel
no motion when the velocity is steady. We feel the
changes in motion—the accelerations or decelerations
—when the vehicle speeds up, or swerves, or jerks, or
slows down. If we look out of the window we can learn
of our relative motion, but when a sudden acceleration
throws us off balance we need no view of the scenery to
convince us that the ride has been unsteady.
Because of this, we sense that acceleration differs
significantly from velocity and from rest. But we have
been speaking in terrestrial terms. Newton's laws were
set in absolute space and absolute time, which cosmically
implied absolute rest, absolute velocity, and absolute
acceleration. Yet the laws, while making acceleration
(which term includes rotation) absolute, provided no
way of detecting absolute rest or absolute velocity. Ac-
cording to the laws, although acceleration was absolute,
both rest and velocity were, dynamically, always rela-
tive. Newton presented this as an almost immediate
consequence of his laws. His Corollary V reads “The
motions of bodies included in a given space [i.e. refer-
ence system] are the same among themselves whether
that space is at rest, or moves uniformly forward in a
straight line without any circular motion.” We shall
refer to this as the Newtonian principle of relativity,
though a better phrase might well be the Newtonian
dilemma. It troubled Newton.
Since his laws did not provide absolute location,
absolute rest, or absolute velocity, he introduced an
extraneous “Hypothesis I: That the center of the system
of the world is immovable.” This unmoving center
could not be the center of the sun, since the sun, pulled
by the planets this way and that, would be intricately
accelerated. A fortiori, no point primarily related to
the earth could fill the role of the fixed center of the
world.
The solar system did, however, have a theoretical
sort of balance point that we would now call its center
of mass; and Newton argued that according to his laws
the center of mass of the solar system would be unac-
celerated. It would thus be either at rest or in uniform
motion in a straight line—the laws could not say which.
Transcending his laws, Newton now declared that this
center of mass of the solar system, this abstract disem-
bodied point never far from the sun, was the center
of the world, and ipso facto immovable.
With the solar system pinned like a collector's but-
terfly to the immovable center of the world, absolute
location, rest, and velocity acquired human vividness.
Yet they did so only through Newton's ad hoc inter-
vention. Had Newton allowed the center of mass of
the solar system to move uniformly in a straight
line—as it had every right to do under the laws—there
would have been no dynamical effect of this motion.
A word of caution, though. In the above we have
followed Newton in ignoring the possible dynamical
effects of the distant stars.
