IV
Having reached this stage, we may profitably regress
awhile. With a fixed earth the problem of relativity
could hardly arise. But in retrospect, once we accept
the idea of a moving earth, the very opposition to it
argues strongly in favor of a dynamical principle of
relativity. For if one could vividly feel the earth's
motion or intuitively recognize dynamical effects of
the motion, would men have been likely to have re-
garded the earth as fixed?
Evidently the earth's velocity has no noticeable
dynamical effect, and this is implicit in the Newtonian
principle of relativity. As for the earth's acceleration,
we realize in the light of Newton's theory that it does
have dynamical effects; but in everyday life these are
either too small to be noticed or else do not present
themselves to common sense as manifestations of the
acceleration. The path to the concept of a moving
earth had not been an easy one. Following Aristotle,
Ptolemy had argued powerfully against it, saying, for
example, that objects thrown in the air would be left
behind by a moving earth. He also argued that a rota-
ting earth would fly apart, to which argument Coper-
nicus retorted that Ptolemy should have worried rather
about the survival of the far larger sphere of the stars
if that sphere and not the earth were rotating once
a day.
Among the dynamical “proofs” advanced against the
hypothesis of a moving earth was that heavy bodies
when dropped ought to fall obliquely. By way of illus-
tration it was said that if one dropped a stone from
the top of the mast of a ship at rest it would land
at the foot of the mast, but if the ship was in rapid
motion the stone would “obviously” land closer to the
stern. Against this Galileo argued that the stone would
share the impetus of the moving ship and thus
(neglecting air resistance) would land at the foot of
the mast after all. In his Dialogues on the Two World
Systems he presents the point vividly in these words
of Salviati (emphasis added):
Shut yourself up with some friend in the largest room below
decks of some large ship and there procure gnats, flies, and
such other small winged creatures. Also get a great tub full
of water and within it put certain fishes; let also a certain
bottle be hung up, which drop by drop lets forth water
into another narrow-necked bottle placed underneath.
Then, the ship lying still, observe how these small winged
animals fly with like velocities towards all parts of the room;
how the fishes swim indifferently towards all sides; and how
the distilling drops all fall into the bottle placed underneath.
And casting anything towards your friend, you need not
throw it with more force one way than another, provided
the distances be equal... [Now] make the ship move with
what velocity you please, so long as the motion is uniform.
... You shall not be able to discern the least alteration
in all the forenamed effects, nor can you gather by any
of them whether the ship moves or stands still....
Galileo then has Sagredo drive the point home by
remarking:
... I remember that being in my cabin I have wondered
a hundred times whether the ship moved or stood still; and
sometimes I have imagined that it moved one way, when
it moved the other way....
The extent to which this is an anticipation of the
Newtonian principle of relativity needs clarification.
It can be interpreted in terms of the idea of inertia,
but on this Galileo was somewhat confused, being
unable wholly to emancipate himself from the Platonic
belief in circular inertia as the basic law. Certainly
the ship argument had powerful consequences. For
example, the parabolic motion of projectiles, a major
discovery of Galileo's, could have been deduced from
it right away. For if, relative to the moving ship, the
stone fell vertically with uniform acceleration, then as
viewed from the shore the path would indeed be
parabolic, being compounded of a vertical fall and a
uniform horizontal motion.
Some twenty years before the Principia appeared,
Huygens had used this principle of relativity brilliantly
in deducing laws of perfectly elastic impact by consid-
ering simple collisions taking place on shore and asking
how they would appear when viewed from a uniformly
moving boat. Indeed, as Huygens realized, the first law
of motion could have been deduced directly from the
Newtonian principle of relativity had that principle
been taken as basic. For a free body at rest in one
frame of reference would be moving uniformly as
viewed from a frame in uniform motion relative to
the first.
But Newton relegated this principle of relativity to
the minor role of a Corollary, and did his best to thwart
it, as we have seen. His intellectual and emotional need
for absolute space was overwhelming. How else could
he have had absolute acceleration? Besides, the
Galilean argument of the ships was not wholly satis-
factory. It compared phenomena on a stationary ship
with those on a ship in uniform motion, though such
ships could hardly exist on a spinning earth in orbit
around the sun.
As we have seen, Newton had avoided this sort of
difficulty by setting his laws in absolute space and time.
It is strange, therefore, that in commenting on his
Corollary V he himself used the illustration of station-
ary and uniformly moving ships. And this becomes even
more surprising when one notes that only a few pages
earlier, in defining absolute space, he had specifically
discussed how the motion of the earth is involved in
the absolute motion of a ship.
The Galilean argument of the ships can be defended.
Newton's laws imply that the uniform part of the
motion in absolute space of a ship or other reference
frame is not detectable within the reference frame.
Therefore, whatever the effects of the nonuniform part
of the absolute motion of the “stationary” ship, they
would be duplicated in the ship moving uniformly
relative to it. Thus in retrospect we may say that
Galileo, and later Huygens, did indeed have the New-
tonian principle of relativity, though they could not
have realized its Newtonian subtleties at the time.
