[Editor's Note:  The following extended extracts have been reprinted with the 

kind permission of the author and the original publisher,  Cambridge 

University Press.  The original and complete essay appeared in the book "Three 

hundred years of gravitation", ed. S. W. Hawking and W. Israel, Cambridge 

University Press,  pp 5-16 (1987), copyright Cambridge University Press 1987.

Any reproduction of this material must first receive the written consent of 

Cambridge University Press, 40 West 20th Street, N.Y., N.Y. 10011]



 

		Newtonianism and today's physics

                ________________________________



                        Steven Weinberg



                      University of Texas

                         Austin, Texas



             (first printed - Vol. 2, No. 7 - March, 1996)

 

	Newton was a complicated man, who lived in complicated times. It would 

take the talents of a historian to say anything new and useful about Newton 

himself. I am not a historian, and know better than to try. I am a physicist, 

and will talk here not about Newton, but Newtonianism; that is, about Newton's 

work, his achievement, as an example which over the last three hundred years 

has guided the evolution of the science in which I now work; Newton, in other 

words, to use a much over-used word, as paradigm.

 

	The central part of the Newtonian achievement I suppose is his theory 

of the solar system, which had three parts, each one of which would by itself 

guarantee his immortality. First, there is Newton's theory of gravity, which 

explains how the distribution of all the matter in the universe determines the 

gravitational force on any one particle, whether that particle is a particle 

here on earth or a particle on the sun or the moon or the stars. Second, there 

is a law of motion that describes how, given the forces acting on a particle, 

one can calculate its motion. Third, there is a method of calculation, the 

mathematical tool now known as calculus.  ...

	The first question that I as a physicist should address is: how well 

does it work? How does Newtonianism stand up after three hundred years of 

experimental testing? It stands up very well. We do now understand that there 

are small corrections to the Newtonian picture of gravity and dynamics. The 

most interesting and important corrections are those provided by Einstein's 

general theory of relativity, but they're awfully small.  ...

	However, whether the corrections are large or small doesn't seem to me 

to be the point. In 1919, when Einstein's theory began to be popular, The 

Times of London proclaimed that Einstein had disproved Newton. That's very far 

from the truth. Einstein's theory reduces to Newton's theory in the limit of 

slowly moving bodies at large distances from each other, which is certainly 

true of the outer part of the solar system ,and indeed of most of the 

universe.

	In fact, it is fair to say that, not only does Einstein's theory not 

supplant Newton's theory, it explains Newton's theory.  ...

       Newton's theory then works very well, and it now has a rationale that 

it lacked in Newton's time, provided by general relativity. We use it to 

follow the motion of objects in the solar system, some of them objects that we 

put there ourselves. I think nothing was more dramatic as an example of our 

faith in the Newtonian theory than the Apollo project. In its early stages, 

remember that astronauts were sent out in spacecraft which circled the moon, 

orbited several times, were given a little boost from a rocket motor, and then 

came back to the earth with essentially all the fuel gone; just relying on the 

validity of Newton's laws. It was somehow very appropriate that Major William 

Anders on the return from the first circumlunar voyage in December 1968, made 

the remark,'I think Isaac Newton is doing most of the driving right now.'

	So Newton's theory is not challenged as a theory of the solar system. 

What about Newton's theory as a model for physical theory in general?

                    . . .

	I would not say that either the broad picture of a deterministic 

mechanical universe, or the particular details of Newton's law of gravity, or 

Newton's equation of motion, or even the invention of the calculus constitute 

the heart of the Newtonian achievement. In preparing this, I did some soul 

searching about why Newtonianism seems to me to be such an incredible 

watershed in the history of our species. I think it is because with Newton's 

work mankind for the first time saw the glimpse of a possibility of a 

comprehensive quantitative understanding of all of nature.

	Now of course Newton was not the first person to think about nature in 

quantitative terms. The Hellenistic Greeks, such as Eratosthenes, Ptolemy, and 

Archimedes, and then in the century before Newton physicists like Huygens and 

Galileo, were masters at bringing quantitative methods to bear on physical 

reality. Also Newton was not the first person who tried to think about nature 

in comprehensive terms, who tried to make a unified theory of everything. That 

goes back even further than the Hellenistic Greeks, to Thales and Anaximenes, 

and then, closer to Newton's time, Descartes. But the two styles had never 

come together before. Those who thought comprehensively about nature from 

Thales to Descartes had never confronted the necessity of carrying their 

comprehensive world picture through to a quantitative understanding of nature 

in all its aspects. And those who thought quantitatively about nature had 

never seen the beginning of a hope of formulating laws that would describe 

everything.

	With Newton, for the first time one saw the possibility of a 

quantitative understanding of everything, not just the motion of the planets 

around the sun, but of all physical phenomena. Newton showed us what could be 

done.  In this sense, the most important part of Newton's opus was not his 

theory of planetary motion, but his theory of the motion of the moon, in book 

three of the Principia. There Newton observes that on earth the force of 

gravity makes objects fall with a certain acceleration, which can be described 

by saying that a body allowed to drop from rest in the first second will fall 

sixteen feet. The surface of the earth where we do our experiments is a 

certain distance from the center of the earth, and Newton knew that you could 

think of the earth as if all its mass was concentrated at the center. The moon 

is sixty times farther from the center of the earth than we are here on the 

earth's surface, so from the inverse square law the moon, if allowed to drop 

from rest, in the first second should fall not sixteen feet, but an amount 

less than that by a factor of sixty squared, or 3600. You can easily work out 

that sixteen feet divided by 3600 is about a twentieth of an inch. So if you 

let the moon drop from rest, it should fall toward the earth a twentieth of an 

inch in the first second. Now of course the moon isn't at rest, it's going 

around in a circular orbit, but it's really the same thing. If the moon were 

not attracted to the earth it would go off in a straight line, a tangent to 

wherever it was in its orbit at that moment. Instead of going in a straight 

line it curves toward the earth; that's what a circle does. And any one second 

it curves toward the earth an amount which brings it closer to the earth than 

if it had gone in a straight line in that second by an amount which is in fact 

just a twentieth of an inch. The beautiful thing about this argument is that 

Newton was not just relating celestial phenomena to each other. He was 

relating a celestial phenomenon, the moon's orbit, to something here on earth, 

an apple falling on his head in Cambridgeshire. (No, I don't know if the apple 

ever fell on his head.) Newton broke down the barrier between the celestial 

and terrestrial styles in physics, and in so doing he not only demystified the 

heavens, he opened up the possibility of an understanding which would embrace 

the heavens and the earth, all in one synthesis.

                    . . .

	But Newton of course only provided us with a glimpse of a really 

comprehensive system of nature. Newton knew there were other forces in nature 

besides gravitation, and he knew that he didn't know what they were, but he 

hoped that the same kind of mathematical reasoning, the same clarity of vision 

that had revealed the nature of the force of gravitation through its role in 

the solar system, would reveal the nature of the other forces, and their role 

governing all the phenomena of nature. In the preface to the first edition of 

the Principia, which Newton wrote at Trinity College on 8 May 1686, he said, 

'I wish we could derive the rest of the phenomena of nature by the same kind 

of reasoning for mechanical principles, for I am induced by many reasons to 

suspect that they may all depend on certain forces.' But he didn't know what 

those forces were, and it took a long time to understand what they were. There 

was the understanding in the nineteenth century by organic chemists that the 

chemicals of living things were not subject to separate chemical laws, but 

were subject to the same chemical laws as ordinary inorganic chemicals. There 

was the understanding by Darwin and Wallace that the growth of various species 

of living things on earth did not have to be accounted for by some extra 

biological laws separate from the ordinary laws of physics and chemistry, but 

could be accounted for by the operations of chance on inheritable variations 

among organisms. There was the realization by Maxwell that light was not 

something separate from the rest of nature, but was a manifestation of 

oscillating electric and magnetic fields.	

	And so on. These were all great steps in the development of a unified 

view of nature, but by the beginning of the twentieth century we were still a 

long way from understanding even the possibility of a really unified view.

                    . . .

    So it goes. Newton's hope,'I wish we could derive the rest of the 

phenomena of nature . . .', has not been fulfilled, but we are working on it, 

very much in the Newtonian tradition: the formulation of increasingly 

comprehensive quantitative laws. From this high viewpoint, all that has 

happened since 1687 is a gloss on the *Principia*.