Physics & Math / Einstein

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.

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