For more than two centuries after Newton published his theories of space, time, and motion in 1687, most physicists were Newtonians. They believed, as Newton did, that space and time are absolute, that force causes acceleration, and that gravity is a force conveyed across a vacuum at a distance. Since Darwin there are few professional biologists who are not Darwinians, and if most psychologists no longer call themselves Freudians, few doubt that there is an unconscious or that sexuality plays a big role in it. So as we celebrate the 100th anniversary of Einstein’s great discoveries, the question arises: How many professional physicists are Einsteinians?
The superficial answer is that we all are. No professional physicist today doubts that quantum theory and relativity theory have stood up to experimental tests, but the term “Einsteinian” does not exist. I’ve never heard or read it. Nor have I ever encountered any evidence for a “school of Einstein.” There is a community of people scattered around the world who call themselves relativists, whose main scientific work centers on general relativity. But relativists make up only a tiny minority of theoretical physicists, and there is no country where they dominate the intellectual atmosphere of the field.
Strange as it may seem, Albert Einstein, the discoverer of both quantum and relativity theory, and hence clearly the preeminent physicist of the modern era, failed to leave behind an intellectual following with any appreciable influence. Why most physicists followed other leaders in directions Einstein opposed is a story that must be told if this centennial year is to be other than an empty celebration of a myth, unconnected to the reality of who Einstein was and what he believed in.
Physicists I’ve met who knew Einstein told me they found his thinking slow compared with the stars of the day. While he was competent enough with the basic mathematical tools of physics, many other physicists surrounding him in Berlin and Princeton were better at it. So what accounted for his genius? In retrospect, I believe what allowed Einstein to achieve so much was primarily a moral quality. He simply cared far more than most of his colleagues that the laws of physics should explain everything in nature coherently and consistently. As a result, he was acutely sensitive to flaws and contradictions in the logical structure of physical theories.
Einstein’s ability to see flaws and his fierce refusal to compromise had real repercussions. His professors did not support him in his search for an academic job, and he was unemployed until he found work as a patent inspector in Bern, Switzerland. The problem was not just that he skipped classes. He saw right through his elders’ complacent acceptance of Newtonian physics. The young Einstein was obsessed with logical flaws that were glaringly obvious, but only to him. While the great English physicist Lord Rayleigh said he saw “only a few clouds on the horizon” remaining to be understood, the 16-year-old Einstein wondered what would happen to his image in a mirror if he traveled at the speed of light.
From the outset, Einstein’s single goal in science was to discover what he called theories of principle. These postulate general rules that all phenomena must satisfy. If such theories are true, they must apply universally. In his study of physics he identified two existing theories of principle: the laws of motion set out by Galileo and Newton and the laws of thermodynamics. The basic principle of the first is the relativity of uniform motion, that the speed of your own unchanging motion is impossible to detect. Einstein’s discovery of special relativity came from 10 years of meditation on how to reconcile the relativity of motion with James Clerk Maxwell’s theory of electromagnetism, which describes the propagation of light.
While he mused about electromagnetism, Einstein made thermodynamics the focus of his early work. He began by following the Austrian physicist Ludwig Boltzmann, who argued that the laws of thermodynamics could be derived from applying statistics to the motion of atoms. This view was unpopular at the time because many influential professors did not believe matter was made of atoms. They instead regarded matter as continuous. Einstein’s work led to his demonstration, in 1905, that Brownian motion—the incessant, jerky movements of pollen grains or other tiny objects immersed in liquid—offered a proof of the existence of atoms.
At the same time, Einstein applied Boltzmann’s approach to thermodynamics to electrodynamics. This led to his discovery of the photon, a discrete packet of electromagnetic energy, and to the realization that such a packet must be both a wave and a particle. Although Einstein was thus the discoverer of quantum phenomena, he became in time the main opponent of quantum mechanics. By his own account, he spent far more time thinking about quantum theory than he did about relativity. But he never found a theory of quantum physics that satisfied him.
There are by now only a small minority of physicists who think Einstein was right to reject quantum theory as the foundation of our scientific description of nature. No theory has been more successful at explaining a vast array of experimental data. It is the basis for our understanding of virtually all of physics, with the possible exception of gravity and cosmology.
Einstein was willing to concede that quantum mechanics explains the recorded behavior of the subatomic world, but he was convinced it had two flaws. First, it fails to give precise predictions for the outcomes of individual processes. Instead, it gives only statistical predictions. To check them, one must do an experiment many times and compare the resulting distributions of outcomes with the predictions. Second, quantum theory fails to give an objective picture of the world that is unconnected to our role as observers. The formulas of quantum theory correspond to our actions in preparing experiments and measuring their outcomes. Einstein objected to this because he believed strongly that physics should provide a picture of nature “as it is in itself.”
After 1930, virtually all of Einstein’s colleagues were certain that the revolution was over and that physics was nearly complete. Nearly alone in his stance, Einstein saw the quantum as only a stepping stone to the real thing, which he continued to search for all the rest of his life.
Quantum mechanics was not the only theory that bothered Einstein. Few people have appreciated how dissatisfied he was with his own theories of relativity. Special relativity grew out of Einstein’s insight that the laws of electromagnetism cannot depend on relative motion and that the speed of light therefore must always be the same, no matter how the source or the observer moves. Among the consequences of that theory are that energy and mass are equivalent (the now-legendary relationship E = mc2) and that time and distance are relative, not absolute. Special relativity was the result of 10 years of intellectual struggle, yet Einstein had convinced himself it was wrong within two years of publishing it. He rejected his own theory, even before most physicists had come to accept it, for reasons that only he cared about. For another 10 years, as others in the world of physics slowly absorbed special relativity, Einstein pursued a lonely path away from it.
Why? The main reason was that he wanted to extend relativity to include all observers, whereas his special theory postulates only an equivalence among a limited class of observers—those who aren’t accelerating. A second reason was his concern with incorporating gravity, making use of what he called the equivalence principle, which postulates that observers can never distinguish the effects of gravity from those of acceleration as long as they observe phenomena only in their neighborhood. By this principle, he linked the problem of gravity with the problem of extending relativity to all observers.
Einstein was the only one who worried about these two problems. Meanwhile, other physicists came up with ways to incorporate gravitational phenomena directly into special relativity. This was the reasonable thing to do, for they were building directly on the success of the new theory Einstein had invented. And they succeeded in making the theory consistent. Moreover, their extensions of special relativity agreed with all the experiments that had been done. So why did Einstein reject it? His reason was that his colleagues’ approach—folding descriptions of gravity into special relativity rather than crafting a whole new theory—disagreed with his equivalence principle. He understood quickly that there was a key experiment that could distinguish between the incremental approach of the other physicists and his own radical approach. This was to measure the bending of light by the sun’s gravity, an effect predicted by the equivalence principle. A reasonable person might have waited to see how the experiment came out, and indeed, an opportunity to test the theory came in 1919. By that time, Einstein had invented his second theory of relativity, which he called general relativity. The experiment appeared to confirm the new theory’s predictions. The result was announced on the front pages of the world’s newspapers, making Einstein the first scientist to be a media star.
General relativity is the most radical and challenging of Einstein’s discoveries—so much so that I believe the majority of physicists, even theoretical physicists, have yet to fully incorporate it into their thinking. The flashy stuff, like black holes, gravitational waves, the expanding universe, and the Big Bang are, it turns out, the easy parts of general relativity. The theory goes much deeper: It demands a radical change in how we think of space and time.
All previous theories said that space and time have a fixed structure and that it is this structure that gives rise to the properties of things in the world, by giving every object a place and every event a time. In the transition from Aristotle to Newton to Einstein and special relativity, that structure changed, but in each case the structure is absolute. We and everything we observe live in a set space-time, with fixed and unchanging properties. That is the stage on which we play, but nothing we do or could do affects the structure of space and time themselves.
General relativity is not about adding to those structures. It is not even about substituting those structures for a list of possible new structures. It rejects the whole idea that space and time are fixed at all. Instead, in general relativity the properties of space and time evolve dynamically, in interaction with everything they contain. Furthermore, the essence of space and time now is just a set of relationships between events that take place in the history of the world. It is sufficient, it turns out, to speak only of two kinds of relationships: how events are related to each other causally (the order in which they unfold) and how many events are contained within a given interval of time, measured by a standard clock (how quickly they unfold relative to each other).
Thus, in general relativity there is no fixed framework, no stage on which the world plays itself out. There is only an evolving network of relationships, making up the history of space, time, and matter. All the previous theories described space and time as fixed backgrounds on which things happen. The implication of general relativity is that there is no background.
This point is subtle and elusive. I was very fortunate to know the great astrophysicist Subrahmanyan Chandrasekhar during his last years. Chandra, as we called him, demonstrated in 1930 that relativity implied that stars above a certain mass would collapse into what we now call a black hole. Much later, he wrote a beautiful book describing the different solutions of the equations of general relativity that describe black holes. As I got to know him, Chandra shocked me by speaking of a deep anger toward Einstein. Chandra was upset that Einstein, after inventing general relativity, had abandoned this masterpiece, leaving it to others to struggle through it.
I now believe that Chandra partly missed the point, and he is certainly not alone. The deepest implication of general relativity is not that the universe may expand or that there are black holes. To think this way is to believe that general relativity is just another step in the progression from Aristotle to Newton to special relativity. Chandra, in his interest in the solutions of the theory, was, I fear, acting like so many others—reaching for a beautiful flower but missing the beauty of how it is that flowers come to be.
Chandra was right that in spite of the great triumph general relativity represented, Einstein did not linger long over it. For Einstein, quantum physics was the essential mystery, and nothing could be really fundamental that was not part of the solution to that problem. Because general relativity didn’t explain quantum theory, it had to be provisional as well. It could only be a step toward Einstein’s goal, which was to find a theory of quantum phenomena that would agree with all the experiments and satisfy his demand for clarity and completeness.
Einstein imagined for a time that such a theory could come from an extension of general relativity. Thus he entered into the final period of his scientific life, his search for a unified field theory. He sought an extension of general relativity that would incorporate electromagnetism, thereby wedding the large-scale world, where gravity dominates, with the small-scale world of quantum physics. He tried a variety of means, such as adding new dimensions of space-time or loosening somewhat the mathematical structure of general relativity. The irony is that some of these gambits worked, but they still led nowhere. For it turns out that unified theories are a dime a dozen. There are many ways to generalize general relativity so as to incorporate the laws of electromagnetism. Nor is it much harder, as has been done recently, to extend the theory a bit further to incorporate the nuclear forces, and so have a unified theory of all the forces.
Indeed, the number of such unified theories keeps increasing. Recent estimates based on results from string theory indicate there are more than 10100 distinct unified field theory solutions. Thus, it is as unclear now as it was for Einstein whether pursuing a unified field theory will lead to real progress in understanding nature.
One way to understand this story is to say that theoretical physics has finally caught up to Einstein. While he was shunned in his Princeton years as he pursued the unified field theory, the Institute for Advanced Study, where he worked, is now filled with theorists who search for new variants of unified field theories. It is indeed a vindication of sorts for Einstein because much of what today’s string theorists do in practice is play with unified theories of the kinds that Einstein and his few colleagues invented.
The problem with this picture is that by the end of his life Einstein had to some extent abandoned his search for a unified field theory. He had failed to find a version of the theory that did what was most important to him, which is to explain quantum phenomena in a way that involved neither measurements nor statistics. In his last years he was moving on to something even more radical. He proposed giving up the idea that space and time are continuous. It is fair to say that while the idea that matter is made of atoms goes back at least to the Greeks, few before Einstein questioned the smoothness and continuity of space and time. To one friend, Walter Dallenbäch, he wrote, “The problem seems to me how one can formulate statements about a discontinuum without calling on a continuum as an aid; the latter should be banned from the theory as a supplementary construction not justified by the essence of the problem, which corresponds to nothing ‘real.’ ”
However, Einstein made no progress with this new direction. He complained that “we still lack the mathematical structure, unfortunately.” To another friend, H. S. Joachim, he wrote: “It would be especially difficult to derive something like a spatiotemporal quasi-order from such a schema. I cannot imagine how the axiomatic framework of such a physics would appear, and I don’t like it when one talks about it in dark apostrophes. But I hold it entirely possible that the development will lead there.”
So what is Einstein’s real legacy? Are any of us his followers? In this centennial year, there will be many who claim the mantle. That includes the community of relativists, but most of them rarely look beyond the theory. Instead they study it by finding solutions on computers or by looking for gravity waves. There are also a few physicists who follow Einstein in rejecting quantum theory and in searching for an alternative. Einstein would have been happy that some scientists agree with him, but he would most likely have been critical that much of the work in that area ignores the problem of unification.
Some string theorists will claim to be Einsteinians, and certainly Einstein would have approved of their search for a unification of physics. But here is how Brian Greene, in his most recent book, The Fabric of the Cosmos, describes the state of the field: “Even today, more than three decades after its initial articulation, most string practitioners believe we still don’t have a comprehensive answer to the rudimentary question, What is string theory? Most researchers feel that our current formulation of string theory still lacks the kind of core principle we find at the heart of other major advances.”
Einstein’s whole life was a search for a theory of principles. It is hard to imagine he would have sustained interest in a theory for which, after more than 30 years of intensive investigation, no one is able to put forward any core principles.
He may in this regard have been happier with approaches to quantum gravity that stay closer to the core principles of relativity. For example, loop quantum gravity preserves his discovery that space and time have no fixed background, and it also provides an answer to Einstein’s questions of how to go beyond the continuum. But Einstein would have found unacceptable all approaches to quantum gravity, including string theory and loop quantum gravity, that take quantum mechanics as fundamental. Einstein never wavered in his rejection of quantum mechanics. His motive for making a unified field theory was not to extend the domain of quantum mechanics; it was rather to find an alternative to quantum mechanics. No research program that accepts quantum mechanics as a given can count itself to be within Einstein’s legacy.
I think a sober assessment is that up till now, almost all of us who work in theoretical physics have failed to live up to Einstein’s legacy. His demand for a coherent theory of principle was uncompromising. It has not been reached—not by quantum theory, not by special or general relativity, not by anything invented since. Einstein’s moral clarity, his insistence that we should accept nothing less than a theory that gives a completely coherent account of individual phenomena, cannot be followed unless we reject almost all contemporary theoretical physics as insufficient.
So is it possible to follow the path of Einstein? To do so, you cannot be a crank; you must be a well-trained physicist, literate in current theories and aware of their limitations. And you must insist on absolute clarity in your own work, rather than follow any fad or popular direction. Given the pressures of competition for academic positions, to follow Einstein’s path is to risk the price that he paid: unemployment in spite of abundant talent and skill at the craft of theoretical physics.
In my whole career as a theoretical physicist, I have known only a handful of colleagues who truly can be said to follow Einstein’s path. They are driven, as Einstein was, by a moral need for clear understanding. In everything they do, these few strive continually to invent a new theory of principle that could satisfy the strictest demands of coherence and consistency, without regard to fashion or the professional consequences. Most have paid for their independence, in a harder career path than equally talented scientists who follow the research agendas of the big professors.
Let us be frank and admit that most of us have neither the courage nor the patience to emulate Einstein. We should instead honor Einstein by asking whether we can do anything to ensure that in the future those few who do follow Einstein’s path, who approach science as uncompromisingly as he did, have less risk of unemployment, the sort he suffered at the beginning of his career, and less risk of the marginalization he endured at the end. If we can do this, if we can make the path easier for those few who do follow him, we may make possible a revolution in science that even Einstein failed to achieve.
