Carlos Graef argues with Albert Einstein

As related by Prof Carlos Graef Fernandez, Director of the Institute of Physics in the National University of Mexico, and formerly Professor of Relativity at Harvard, to Samuel Kaplan.

C Graef Fernández, My Tilt with Albert Einstein, American Scientist 44 (2) (1956), 204-211.

My Tilt with Albert Einstein

Einstein is dead. How that profoundly sad event carries the memory back to my unforgettable meeting with the supreme scientist of our time!

My heart beat fast as I stood before 112 Mercer Street in Princeton, N.J. I was going to defend the ideas of my dead friend Prof George D Birkhoff against those of Prof Albert Einstein. But perhaps you do not know who Birkhoff was. Know then that Birkhoff, chairman of the Department of Mathematics, Harvard University, was one of the ten greatest mathematicians of all time!

And permit me to say that Birkhoff did not minimise the importance of his extraordinary powers, as you may judge from this exchange between him and Prof Luis Enrique Erro, Director of the National Astrophysics Observatory of Mexico.

"Prof Birkhoff," said Erro, I hope that in the future the United States government will continue to send us savants of your stature."

"Prof Erro," was Birkhoff's surprising answer, "in the States I am the only one of my stature."

To which I might add the words of Dr Norbert Wiener, the present greatest American mathematician who, when making his obituary address before Birkhoff's body in Harvard University's chapel, said: "He was the first among us and he accepted the fact. He was not modest."

I first met Birkhoff when he came to Mexico in 1942 and made an impromptu talk in Spanish that gave a flashing hint of his intellectual prowess. Imagine! after teaching himself Spanish in Cambridge, and practising it for just three weeks in Mexico, he delivered this improvised talk that held us Mexican scientists spellbound by its eloquence. An amazing performance!

I was standing on Einstein's doorstep that December day in 1944 to lock horns with him about Birkhoff's New Theory of Relativity; the Theory which comes in head-on collision with Einstein's gravitational theory in his famous General Theory of Relativity.

What's so important about a gravitational theory? Let me tell you. It's a rational explanation of the motions of stars, planets, comets - of all celestial bodies. Such a theory is decidedly important when it enables us to predict the future course of the universe. Surely you will agree it is enormously important when you stop to think that it permits us to account for the future positions of all heavenly bodies and their states of motion.

Now then, bear in mind that three gravitational theories - Newton's, Einstein's, and Birkhoff's - are in use today in actual computations of physical phenomena. ... For almost three centuries Newton's Theory had been holding the fort, when something tremendously significant happened. Einstein, the great iconoclast, arrived to punch a terrific hole in it.

How? In 1905, in his majestic Special Theory of Relativity, he furnished the key that unlocks the door to a complete explanation of all phenomena bearing on light, electricity, and magnetism! It, started the greatest upheaval in the realm of science. It forced the stupefied scientists to throw overboard a mass of Newtonian notions concerning space and time: the way bodies fall, the way the planets - including the one on which lives that constructive and destructive creature MAN - move around the sun, and the way comets move.

Let me give you an example of what this means.

We will assume that an astronomer on the Earth is sweeping the skies with his telescope in 1957 and witnesses the stupendous spectacle of an exploding star. He makes computations, finds that the celestial catastrophe really took place way back in 1945 on August 6, at 8:15 a.m. This, he reminds himself, was the exact moment the atomic bomb obliterated Hiroshima.

On another planet, say Venus, another astronomer observes both star-explosion and Hiroshima bombing. According to Newton, he finds they happened simultaneously. But according to Einstein, his calculations prove one disaster happened before the other - because on Venus he is moving with respect to the Earth on which the first astronomer is located.

All very fine. But when in 1916 Einstein set up his General Theory of Relativity he laid himself wide open, and I mean wide open, to an avalanche of criticism. Why? Because it is not the logical continuation of his Theory of Special Relativity. They clash most inharmoniously.

In Special Relativity, Einstein assumes that space is undistorted. But observe that in General Relativity, to account for the curved motions of the planets, he assumes the contrary, a curved space. For years Einstein and his collaborators, working on the unified field theory, have tried to marry these rebellious theories, but haven"t yet succeeded in getting them to sleep in the same bed.

And then in 1942, with the crash of a tidal wave, came the New Gravitational Theory of my revered friend Birkhoff.

Heavens, how it rocked the scientific ship from end to end. Its brilliant logic makes understandable every single phenomenon that Newton's and Einstein's cannot; such as for instance, the motion of one star around another, a phenomenon incapable of correct explanation in either of the other theories.

You will appreciate its grandeur if you keep in mind that Birkhoff takes Einstein's Theory of Special Relativity, builds it up so that the new system explains all phenomena concerned with light, electricity, magnetism, falling bodies, moving planets and comets. In a word, it gives a single unified explanation of extremely diversified phenomena.

Birkhoff's Theory assumes that the pull the sun exerts on the Earth and all other planets travels with the velocity of light through space; that the Earth's pull on the moon has the same speed. Furthermore that the gravitational pull a body exercises on another body depends upon the velocities with which both are moving. These two are the characteristic features of Birkhoff's Theory.

What are its advantages over Einstein's? Its mathematics are far simpler. It is more consistent with common sense - it does not introduce such peculiar properties as curved space and a closed and finite universe.

At the time Birkhoff started working with Mexican scientists (he came to the National University of Mexico in 1943 as a visiting lecturer, sent by the United States State Department), his Theory still lacked a rigorous mathematical basis. My colleague, Barajas Celis, who is now Director of the School of Science, National University of Mexico, addressed himself to this task.

I will ask you to imagine yourself marooned with a scientist in space between the stars, far above the stratosphere, in a closed spaceship, without propulsion. You will notice it is pulled by the star nearest it, and moves with an accelerated motion. This it does in accordance with Einstein's Principle of Equivalence - that the stars pull each other!

With enormous satisfaction Barajas Celis proved that this Principle is equally valid in Birkhoff's Theory; thus he nailed down a sound mathematical flooring for the new scientific system.

In the meantime I was doing a bit of mathematical carpentering myself, working on another application of Birkhoff's Theory to astronomical phenomena.

On a bright summer night, when you look at our celestial neighbours with the naked eye, you may think you are seeing individual stars. You will be in error. Actually about a third of these apparently single bodies turn out to be systems of two, three, or more stars revolving around each other.

I found that in the case of a two-star system, the line joining the two bright bodies, when they are closest to each other, rotates slowly in a plane. This fascinating phenomenon is in astronomical parlance called "rotation of the apsidal line." So now with the mathematical tools supplied by Birkhoff's Theory I had the honour of solving "the two-body problem" of calculating completely the motions of two-star systems.

In Einstein's Theory, I may add, it is impossible to solve the two body problem except by making very far-fetched assumptions.

Again, using Birkhoff's Theory as a compass, I studied the motions of the galaxies of the universe.

You are an amateur star gazer, not so? To you then, those heavenly points of light may seem scattered haphazardly, as if shaken out of a cosmic tablecloth. On the contrary, they are clustered into systems of galaxies. These are by no means insignificant affairs. The galaxy to which our sun is honoured to belong - with its train of planets - contains approximately two hundred thousand million stars!

As seen from our galaxy all others are running away from us.

Light, which travels at the rate of 186,324 miles per second, takes 500,000,000 years to span the inconceivable gulf from the farthest galaxy that has been photographed, to our Earth. This galaxy, which doesn"t seem to want to be in the vicinity of a planet that enjoys a world war, and some minor ones, every few years, is streaking away from us at the respectable speed of 20,000 miles per second.

[Note by EFR. This was written in 1956. In 2023 we observe galaxies with the James Webb Space Telescope whose light has taken nearly 14,000,000,000 years to reach us. Today these galaxies will be around 35×102235 \times 10^{22} km from us.]

I wish to point out to you that Einstein's Theory cannot say without the help of observations if the galaxies are moving away from, or toward, us. But not so with Birkhoff's Theory. It flatly predicts their motion away from each other, and excludes any motion of approach.

I found the laws of motion of the galaxies and of the "photons". The latter are the carriers of light-energy. You realise, do you not, that the space requirements of atoms and electrons are extremely modest. Those of photons are even more so! The photons are "corpuscles" which traverse the gigantic distances separating us from other galaxies, and enable astronomers and physicists to pick up and interpret vital bits of "news" constantly streaming from the distant star systems.

So you can understand it was with the greatest of pleasure that I laid my findings before my friend Erro. This distinguished astronomer checked my conclusions against observational material gathered over many years by astronomers throughout the world. To his astonishment he found a complete accord between my theoretical judgments and the observational data. Alas, Birkhoff dying in November 1944 was denied the thrill of witnessing the confirmation of this phase of his epochal theory by Erro and myself. The repercussions of that dramatic event, which took place at the meeting of the American Astronomical Society in 1946, still reverberate around the scientific world.

A guest of the Department of Mathematics, Princeton University, in December 1944, I was tremendously pleased when Einstein invited me to come and discuss Birkhoff's Theory.

All the way to Einstein's home I kept thinking of Birkhoff. What an irreparable loss to the world, to die at sixty-two, at the zenith of his creative powers! We Mexican scientists were eternally in debt to him. He had stimulated our abilities, and won our admiration and love by freely sharing with us his vast store of original knowledge.

A maid ushered me to the library. Einstein greeted me with a smile and a piercing but friendly stare. After exchange of courtesies, Einstein genially remarked:

I think the principal difference between Birkhoff's point of view and mine lies in what we consider to be the scientific explanation of a physical system. Now what is your opinion in this matter, Graef?"

"Well, let us consider a concrete example, say the solar system," I answered. "I think a person who has a set of formulae which enables him to predict accurately the future of the solar system has completely explained that system."

By this, if you are so good as to follow me, I meant that one who fully understands the solar system can unerringly predict the positions of the Moon, Mars, Venus, Jupiter, Saturn and the other planets, at any given hour of any future date.

Einstein could not conceal his impatience. "Do you really think that what you claim is all there is to an explanation?"

"Yes. An explanation for us is nothing but an order of formulae which empowers one to predict the future."

Einstein vehemently disagreed. "The set of formulae, which for you is all there is to an explanation, has to be consistent with the philosophy of nature in order to be a true explanation. Otherwise it is only a convenient device for predicting the future of a system, but does not give a real insight into its nature."

This pronouncement made me smile. It reminded me that for over two thousand years one thinker after another had tried to fashion a system of ideas that would embody in a single harmonious doctrine all explanations of nature. Each in turn had fallen in ruins when a later scientific discovery became the midwife that delivered a brand new system.

And every one of them had been considered "the philosophy of nature" in the days of its acceptance.

At this point I almost burst out laughing at thought of "the philosophy of nature" which existed at the time of publication of Einstein's Theory of Special Relativity. It had to undergo a major surgical operation in order to conform to the new, revolutionary ideas about time and space Einstein introduced. Truly it's astonishing, I told myself, that the scientist who precipitated the greatest overhauling of "the philosophy of nature" should himself take the position that his system of ideas is something immutable, changeless, to which physical theories must conform.

Therefore it was with lively curiosity that I asked: "Prof Einstein, how exactly does this philosophy of nature rule out, in your opinion, Birkhoff's Theory of Gravitation as an explanation of the solar system?"

Said Einstein: "For Newton, the fundamental cause for the curved motions of the planets was the sun itself. The great mass of the sun, in the centre of the system, attracts celestial bodies in the vicinity toward itself. Thus the presence of a mass in space is the cause of the force that urges the planets on their courses."

"But contemporary physics," he went on, "has abandoned this point of view. Today we consider the force as primary, as more fundamental. The physicist can measure this force directly, as he does on earth. Contemporary science prefers to consider those physical entities, the planets, as fundamental; as causes which can be observed and measured directly. And it prefers to think of entities which cannot be measured or observed directly, like the sun, as derived or secondary."

Einstein paused to let his words sink in, then: "Thus you see, Graef, a theory built to explain the solar system has to start with the field of forces, the planets. The mass of the sun itself is a derived quantity because, as I have already remarked, it cannot be observed or measured directly. The primary quantities, the planets, are the forces which all point toward a centre. We consider that at that point, the centre, there is a singular something which we call "mass of the sun."

"This mass, you understand, Graef, is obtained by calculating it from the planets - the measured forces."

"But in Birkhoff's Theory," Einstein shook his head, "the fundamental cause for gravitation is a liquid. His point of view is a step backward. He goes back to an unobservable and unmeasurable quantity for the cause of gravitation." Again he shook his leonine head in disapproval, then, with a smile, added : "Whereas in my theory the mass of the sun is derived and calculated from the observed and measurable motion of the planets."

I should tell you that he was referring to Birkhoff's assumption that all matter is built from an elementary fluid called "Birkhoff's perfect fluid."

I looked at Einstein and thought indignantly, what! Birkhoff's setup a step backward? Controlling my emotion, I answered:

"Prof Einstein, I do not think one can always dismiss the going back to old ideas by stating - that is a step backward. Consider the theory of light. For Newton, a bright body sends out particles which are the carriers of light energy, and which cause the sensation of light when impinging on the human eye."

I was alluding, you understand, to Newton's theory that light consists of tremendously fast moving little bodies - the corpuscles already mentioned - which are emitted by the light-source.

I continued: "This theory was followed by Huygens' wave theory: that a bright body sends out waves which cause the sensation of light when they strike the human eye. The wave-theory, I need not tell you, Prof Einstein, completely defeated the corpuscular theory during Newton's lifetime and held its own up to our century."

With rising emotion I pressed on: "Now I bring up a question of the first importance. Who is chiefly responsible for our going back to corpuscles as carriers of light-energy?" I paused, looked Einstein straight in the eye. Raising my forefinger I pointed it accusingly. "You, Prof Einstein, are the man! Yet nobody can object now to the use of the photon in physics."

The photon, permit me to repeat, is a corpuscle. Einstein discovered the effect caused by photons when they impinge on metals. This, called "the photo electric effect" is the principal reason for accepting the existence of photons in modern science.

Eagerly I followed up with: "The step backward which you made has in reality been a great step forward in physics. But, Prof Einstein, if you had applied the argument of "the philosophy of nature," then current, which you now use against Birkhoff's Theory, you would never have made it."

"Ah, Graef," he said, "the photon, though a corpuscle, is not like a pebble which you can throw out of the window. There is a big difference between my photons and Newton's particles."

Instantly I retorted: "Prof Einstein, Birkhoff's fluid, though a liquid, cannot be drunk like a Coca-Cola. There is an enormous difference between Birkhoff's perfect fluid and actual liquid." ... At this moment I realised that our points of view were irreconcilable.

Einstein rose and good-naturedly patted me on the shoulder. "Graef," he said amiably, "you are a born rebel. I wish you great luck. Good-bye." And we shook hands heartily.

And now that incomparable mind is hushed for eternity. ... Ah, my friend, when will the world witness its equal again?

Editor's Note:
We have ascertained that only a minority of physicists uphold Birkhoff's views as opposed to Einstein's. However, we thought that many readers would be interested in this human story of the late Professor Einstein as it illustrates among other things his urbanity in dealing with scientific controversy. The following remarks by Professor Peter G Bergmann, Department of Physics, Syracuse University, should serve to place the subject matter of this article in the proper scientific perspective:-
Professor Graef Fernandez relates in this charming account one of the innumerable discussions that Professor Albert Einstein has had with scientists and laymen alike concerning the ultimate aims and the most fundamental notions of scientific research. He has never taken Birkhoff's theory very seriously, because it fails to provide what he would have considered a logically and aesthetically satisfactory unified theory of gravitation and electrodynamics. He formed this opinion in personal conversations with Birkhoff and, as we see, with defenders of Birkhoff's ideas.

Last Updated June 2023