Editor's note: This article appeared in the Smithsonian Annual Report for
1927, the second centenary of Newton's death. It's somewhat dense, but then,
what do you expect from the "greatest scientist who ever lived" talking about the
accomplishments of the other "greatest scientist who ever lived?"
The 200th anniversary of the death of Newton falls at this time. One's thoughts
cannot but turn to this shining spirit, who pointed out, as none before or
after him did, the path of Western thought and research and practical
construction. He was not only an inventor of genius in respect of particular
guiding methods; he also showed a unique mastery of the empirical material
known in his time, and he was marvelously inventive in special mathematical and
physical demonstrations. For all these reasons he deserves our deep veneration.
He is, however, a yet more significant figure than his own mastery makes him,
since he was placed by fate at a turning point in the world's intellectual
development. This is brought home vividly to us when we recall that before
Newton there was no comprehensive system of physical causality which could in
any way render the deeper characters of the world of concrete experience.
The great materialists of ancient Greek civilization had indeed postulated the
reference of all material phenomena to a process of atomic movements controlled
by rigid laws, without appealing to the will of living creatures as an
independent cause. Descartes, in his own fashion, had revived this ultimate
conception. But it remained a bold postulate, the problematic ideal of a school
of philosophy. In the way of actual justification of our confidence in the
existence of an entirely physical causality, virtually nothing had been
achieved before Newton.
Newton's aim
Newton's aim was to find an answer to the question: Does there exist a simple
rule by which the motion of the heavenly bodies of our planetary system can be
completely calculated, if the state of motion of all these bodies at a single
moment is known? Kepler's empirical laws of the motion of the planets, based on
Tycho Brahe's observations, were already enunciated, and demanded an
interpretation.* These laws gave a complete answer to the question of how the
planets moved round the sun (elliptical orbit, equal areas described by the
radius vector in equal periods, relation between semi-major axis and period of
revolution). But these rules do not satisfy the requirement of causality. The
three rules are logically independent of one another, and show no sign of any
interconnection. The third law cannot be extended numerically as it stands,
from the sun to another central body; there is, for instance, no relation
between a planet's period of revolution round the sun and the period of
revolution of a moon round its planet.
But the principal thing is that these laws have reference to motion as a whole,
and not to the question of how there is developed from one condition of motion of
a system that which immediately follows it in time. They are, in our
phraseology of today, integral laws and not differential laws.
It was, no doubt, especially impressive to learn that the cause of
the movements of the heavenly bodies is identical with the force of gravity so
familiar to us from everyday experience.
The differential law is the form which alone entirely satisfies the modern
physicist's requirement of causality. The clear conception of the differential
law is one of the greatest of Newton's intellectual achievements. What was
needed was not only the idea but a formal mathematical method which was,
indeed, extant in rudiment but had still to gain a systemic shape. This also
Newton found in the differential and integral calculus. It is unnecessary to
consider whether Leibniz arrived at these same mathematical methods
independently of Newton or not; in any case, their development was a necessity
for Newton, as they were required in order to give Newton the means of
expressing his thought.
From Galileo to Newton
Galileo had already made a significant first step in the recognition of the law
of motion. He discovered the law of inertia and the law of free falling in the
Earth's field of gravitation: A mass (or, more accurately, a material point)
uninfluenced by other masses moves uniformly in a straight line; the vertical
velocity of a free body increases in the field of gravity in proportion to the
time. It may seem to us today to be only a small step from Galileo's
observations to Newton's laws of motion. But it has to be observed that the two
propositions above, in the form in which they are given, relate to motion as a
whole, while Newton's law of motion gives an answer to the question: How does
the condition of motion of a point-mass change in an infinitely small period
under the influence of an external force? Only after proceeding to consider the
phenomenon during an infinitely short period (differential law) does Newton
arrive at a formula which is applicable to all motions. He takes the conception
of force from the already highly developed theory of statics. He is only able
to connect force with acceleration by introducing the new conception of mass,
which, indeed, is supported curiously enough by an apparent definition. Today
we are so accustomed to forming conceptions which correspond to differential
quotients that we can hardly realize any longer how great a capacity for
abstraction was needed to pass across a double barrier to the general
differential laws of motion, with the further need to evolve the conception of
mass.
But this was still a long way from the causal comprehension of the phenomena of
motion. For the motion was only determined by the equation of motion if the
force was given. Newton had the idea, to which he was probably led by the laws
of the planetary motions, that the force acting on a mass is determined by the
position of all masses at a sufficiently small distance from the mass in
question. Not until this connection was realized was a completely causal
comprehension of the phenomena of motion obtained. How Newton, proceeding from
Kepler's laws of the motion of planets, solved this problem for gravitation and
so discovered the identity of the nature of gravity with the motive forces
acting on the stars is common knowledge. It is only the combination
of—
(Law of motion) + (Law of attraction)
through which is constituted that wonderful thought-structure which enables the
earlier and later conditions of a system to be calculated from the conditions
ruling at one particular time, insofar as the phenomena occur under the sole
influence of the forces of gravitation. The logical completeness of Newton's
system of ideas lay in the fact that the sole causes of the acceleration of the
masses of a system prove to be the masses themselves.
On the basis sketched Newton succeeded in explaining the motions of the
planets, moons, comets, down to fine details as well as the ebb and flow of the
tides and the precessional movement of the Earth—this last a deductive
achievement of particular brilliance. It was, no doubt, especially impressive
to learn that the cause of the movements of the heavenly bodies is identical
with the force of gravity so familiar to us from everyday experience.
Significance of Newton's achievement
The significance, however, of Newton's achievement lay not only in its
provision of a serviceable and logically satisfactory basis for mechanics
proper; up to the end of the 19th century it formed the program of all
theoretical research. All physical phenomena were to be referred to as masses
subject to Newton's law of motion. Only the law of force had to be amplified
and adapted to the type of phenomena which were being considered. Newton
himself tried to apply the program in optics, on the hypothesis that light
consisted of inert corpuscles. The optics of the undulatory theory also made
use of Newton's law of motion, the law being applied to continuously diffused
masses. The kinetic theory of heat rested solely on Newton's formulae of
motion; and this theory not only prepared people's minds for recognition of the
law of the conservation of energy, but also supplied a theory of gases
confirmed in its smallest details, and a deepened conception of the nature of
the second law of thermodynamics. The theory of electricity and magnetism also
developed down to modern times entirely under the guidance of Newton's basic
ideas (electric and magnetic substance, forces at a distance). Even Faraday and
Maxwell's revolution in electrodynamics and optics, which was the first great
advance in the fundamental principles of theoretical physics since Newton, was
still achieved entirely under the guidance of Newton's ideas. Maxwell,
Boltzmann, and Lord Kelvin never tired of trying again and again to reduce
electromagnetic fields and their dynamical reciprocal action to mechanical
processes occurring in continuously distributed hypothetical masses. But owing
to the barrenness, or at least the unfruitfulness, of these efforts there
gradually occurred, after the end of the 19th century, a revulsion in
fundamental conceptions; theoretical physics outgrew Newton's framework, which
had for nearly two centuries provided fixity and intellectual guidance for
science.
Newton’s theory of motion suffered its first shock from Maxwell’s
theory of electricity.
Newton on its limitations
Newton's basic principles were so satisfying from a logical standpoint that the
impulse to fresh departures could only come from the pressure of the facts of
experience. Before I enter into this I must emphasize that Newton himself was
better aware of the weak sides of his thought-structure than the succeeding
generations of students. This fact has always excited my reverent admiration; I
should like, therefore, to dwell a little on it.
Although everyone has remarked how Newton strove to represent his
thought-system as necessarily subject to the confirmation of experience, and to
introduce the minimum of conceptions not directly referable to matters of
experience, he makes use of the conceptions of absolute space and absolute
time. In our own day he has often been criticized for this. But it is in this
very point that Newton is particularly consistent. He had recognized that the
observable geometrical magnitudes (distances of material points from one
another) and their change in process of time do not completely determine
movements in a physical sense. He shows this in the famous bucket experiment.
There is, therefore, in addition to masses and their distances, varying with
time, something else, which determines what happens; this "something" he
conceives as the relation to "absolute space." He recognizes that space must
possess a sort of physical reality if his laws of motion are to have a meaning,
a reality of the same sort as the material points and their distances.
This clear recognition shows both Newton's wisdom and a weak side of his
theory. For a logical construction of the theory would certainly be more
satisfactory without this shadowy conception; only those objects (point-masses,
distances) would then come into the laws whose relation to our perceptions is
perfectly clear.
The introduction of direct instantaneously acting forces at a distance into
the exposition of the effects of gravitation does not correspond to the
character of most of the phenomena which are familiar to us in our daily
experience. Newton meets this objection by pointing out that his law of
reciprocal gravitation is not to be taken as an ultimate explanation, but as a
rule induced from experience.
Newton's theory offered no explanation of the very remarkable fact that the
weight and inertia of a body are determined by the same magnitude (the mass).
The remarkable nature of this fact struck Newton also.
None of these three points can rank as a logical objection against the theory.
They form, as it were, merely unsatisfied needs of the scientific spirit in its
effort to penetrate the processes of nature by a complete and unified set of
ideas.
The theory of the electromagnetic field
Newton's theory of motion, considered as a program for the whole field of
theoretical physics, suffered its first shock from Maxwell's theory of
electricity. It was found that the reciprocal action between bodies through
electrical and magnetic bodies does not take place through instantaneously
acting forces at a distance, but through processes which are transmitted with
finite velocity through space. Alongside the point-mass and its movements there
arose, in Faraday's conception, a new sort of physically real thing, the
"field." It was first sought to conceive this, with the aid of mechanical modes
of thought, as a mechanical condition (of movement or strain) of a hypothetical
space-filling medium (the ether). When, however, in spite of the most obstinate
efforts, this mechanical interpretation refused to work, students slowly
accustomed themselves to the conception of the "electromagnetic field" as the
ultimate irreducible foundation stone of physical reality. We owe to [Heinrich]
Hertz the deliberate liberation of the conception of the field from all the
scaffolding of the conceptions of mechanics, and to [Hendrik Antoon] Lorentz
the liberation of the conception of the field from a material bearer; according
to Lorentz the physical empty space (or ether) alone figured as bearer of the
field; in Newton's mechanics, indeed, space had not been devoid of all physical
functions. When this development had been completed, no one any longer believed
in directly acting instantaneous forces at a distance, even in connection with
gravitation, though a field theory for gravitation, for lack of sufficient
known facts, was not unmistakably indicated. The development of the theory of
the electromagnetic field also led, after Newton's hypothesis of action at a
distance had been abandoned, to the attempt to find an electromagnetic
explanation for Newton's law of motion, or to replace that law by a more
accurate law based on the field theory. These efforts were not crowned with
full success, but the mechanical basic conceptions ceased to be regarded as
foundation stones of the physical conception of the universe.
The Maxwell-Lorentz theory led inevitably to the special theory of relativity,
which, by destroying the conception of absolute simultaneity, negatived the
existence of forces at a distance. Under this theory mass is not an unalterable
magnitude, but a magnitude dependent on (and, indeed, identical with) the
amount of energy. The theory also showed that Newton's law of motion can only
be considered as a limiting law valid only for small velocities, and
substituted for it a new law of motion, in which the velocity of light in a
vacuum appears as the limiting velocity.
The general theory of relativity
The last step in the development of the program of the field theory was the
general theory of relativity. Quantitatively it made little modification in
Newton's theory, but qualitatively a deep-seated one. Inertia, gravitation, and
the metrical behavior of bodies and clocks were reduced to the single quality
of a field, and this field in turn was made dependent on the bodies
(generalization of Newton's law of gravitation or of the corresponding field
law, as formulated by Siméon Denis Poisson). Space and time were so divested, not of their
reality, but of their causal absoluteness (absoluteness-influencing, that is,
not -influenced), which Newton was compelled to attribute to them in order to be
able to give expression to the laws then known. The generalized law of inertia
takes over the role of Newton's law of motion. From this short characterization
it will be clear how the elements of Newton's theory passed over into the
general theory of relativity, the three defects above mentioned being at the
same time overcome. It appears that within the framework of the general theory
of relativity the law of motion can be deduced from the law of the field, which
corresponds to Newton's law of force.
“The whole development of our ideas concerning natural phenomena may
be conceived as an organic development of Newton’s thought.”
Newton's mechanics prepared the way for the theory of fields in a yet more
formal sense. The application of Newton's mechanics to continuously distributed
masses led necessarily to the discovery and application of partial differential
equations, which in turn supplied the language in which alone the laws of the
theory of fields could be expressed. In this formal connection also Newton's
conception of the differential law forms the first decisive step to the
subsequent development.
The whole development of our ideas concerning natural phenomena, which has been
described above, may be conceived as an organic development of Newton's
thought. But while the construction of the theory of fields was still actively
in progress, the facts of heat radiation, spectra, radioactivity, and so on
revealed a limit to the employment of the whole system of thought, which, in
spite of gigantic successes in detail, seems to us today completely
insurmountable. Many physicists maintain, not without weighty arguments, that
in face of these facts not only the differential law but the law of causality
itself—hitherto the ultimate basic postulate of all natural
science—fails.
The very possibility of a spatio-temporal construction which can be clearly
brought into consonance with physical experience is denied. That a mechanical
system should permanently admit only discrete values of energy or discrete
states—as experience, so to say, directly shows—seems at first
hardly deducible from a theory of fields working with differential equations.
The method of [Louis] De Broglie and [Erwin] Schrödinger, which has, in a
certain sense, the character of a theory of fields, does deduce, on the basis
of differential equations, from a sort of consideration of resonance the
existence of purely discrete states and their transition into one another in
amazing agreement with the facts of experience; but it has to dispense with a
localization of the mass-particles and with strictly causal laws. Who would be
so venturesome as to decide today the question whether causal law and
differential law, these ultimate premises of Newton's treatment of nature, must
definitely be abandoned?
*Everyone knows today what gigantic efforts were needed to discover these laws
from the empirically ascertained orbits of the planets. But few reflect on the
genius of the method by which Kepler ascertained the true orbits from the
apparent ones, i.e., their directions as observed from the Earth.
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In his eulogy to Isaac Newton written in 1927, the bicentenary of the great man's
death, Einstein called him a "shining spirit."
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The German mathematician and astronomer Johannes
Kepler, in his famous laws of planetary motion, showed how the planets are held
in their orbits, but he could not explain why. That task was left to the young
Isaac Newton.
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Galileo, seen here showing his
telescope to the Doge of Venice, set the stage for Newton's formulation of his
three laws of motion.
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Newton succeeded in describing
the movements of the planets, moons, and comets to an extraordinarily fine
degree.
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The work of Michael Faraday (left) and James Clerk Maxwell on
electrodynamics was, says Einstein, "the first great advance in the fundamental
principles of theoretical physics since Newton...."
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Eventually, says Einstein of Newton (above),
"theoretical physics outgrew Newton's framework, which had for nearly two
centuries provided fixity and intellectual guidance for science."
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Newton's
ideas about the universe held sway until Einstein introduced the theory of
general relativity. But for most of what we observe in our daily experience,
Newton's laws remain completely valid today.
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