Tuesday, August 16, 2005

Einstein's Legacy

As almost everyone knows by now, 2005 is being celebrated as a very special year in the physics community, because it is the 100th anniversay of Einstein's "annus mirabilis". This "miraculous year", 1905, saw Einstein's publication of not just one spectacular paper, but of five. Most physicists would kill to have published even one of comparable quality in their whole career. At least four of these papers, and perhaps all five, would have merited a Nobel Prize, though only one actually did win the Prize for Einstein. And it had nothing to do with relativity.

All of these papers were written and published while Einstein was working as a patent examiner in Bern and before he had even been granted a doctor's degree. This circumstance has a lot to do with the magnitude of Einstein's subsequent professional reputation and popular celebrity. An interesting recent article, Einstein's Legacy -- Where are the "Einsteinians?" by Lee Smolin, one of the leading experts on quantum gravity, considers Einstein's legagy as a whole, and considers the implications for the status of the science of physics today.

Hundreds of articles have appeared describing Einstein's achievements of 1905. Here's a good one: Five papers that shook the world. Here is a brief summary of the topics of those papers:


  • The photoelectric effect -- why the energy of electrons ejected from a target by high-energy light depends on the frequency of the light and not on its intensity. James Clerk Maxwell's theory of electrodynamics could not explain this, but Einstein's paper, building on ideas due to Max Planck, succeeded. This insight culminated two decades later in quantum mechanics (which, ironically, Einstein never fully accepted).
  • Calculation of "Avogadro's number" and the size of molecules by studying their motion in a solution. This was a major step towards proving the atomic theory of matter, which (it is surprising to realize) was still far from universally accepted in 1905. The idea that matter comes in discrete chunks is closely akin to the idea of the previous paper that light also comes in discrete chunks. It was this paper that earned Einstein his doctorate.
  • Prediction of Brownian motion. Using the kinetic theory of liquids and classical hydrodynamics, Einstein derived an equation that described the erratic motion of sufficiently small particles in a liquid. The equation was experimentally verified three years later, providing the definitive confirmation of the existence of atoms and molecules.
  • The special theory of relativity. Einstein developed this (essentially very simple) theory by taking seriously the consequences of just two postulates: (1) that the laws of electrodynamics must be valid in all reference frames in which the laws of mechanics are valid, and (2) that the speed of light is a constant that does not depend on the motions of either the observer or the emitter of the light. This theory illustrates the primary strength of Einstein's thiking: the ability to build a theory by rigorous deduction from simple principles, however counterintuitive they may have seemed.
  • The equation E=mc2. This expression of the equivalence of mass and energy turns our to be a simple consequence of the theory of special relativity.


Given how spectacular these results were, Smolin makes the surprising observation that
Physicists I’ve met who knew Einstein told me they found his thinking slow compared to 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.


If that is the case, in spite of his spectacular achievements of 1905, then what accounts for Einstein's modern reputation as a preeminent "genius"? I think Smolin puts his finger on the answer when he remarks:
Einstein’s single goal in science was to discover what he called theories of principle. These are theories that postulate general rules that all phenomena must satisfy. If such a theory is true, it 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 thermodynamics. The basic principle of the first is the relativity of uniform motion, that the speed of your own 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.


This characteristic was foreshadowed in the deduction of special relativity from just two major principles as described above. But it is seen most strikingly in Einstein's subsequent general theory of relativity, published in 1915. Einstein deduced this theory by pure thought, with practically nothing in the way of experimental evidence as a guide. He considered rigorously the necessary consequences of a small number of basic principles that a "reasonable" theory of gravity ought to abide by. Some of the principles were plausible, while others were far from "intuitively obvious". Nevertheless, when considered together, they led to a theory of gravity which even now, 90 years later, has yet to fail even a single experimental test.

Taking, for simplicity, a few small liberties, the main principles were:

  • The laws of physics must be the same for all observers, regardless of their state of motion, and must take the same mathematical form in all coordinate systems.
  • Spacetime can be described as a 4-dimensional mathematical object known as a manifold, which is a higher dimensional analog of a (2-dimensional) curved surface.
  • A particle that is not acted on by external forces moves through spacetime along a curve of minimal length (as measured in the manifold). (Such a curve is called a "geodesic" and this kind of motion is called "inertial").
  • The presence of mass (or equivalently, energy) causes spacetime to curve in such a way that the effects of "gravitational force" due to the mass acting on a particle are indistinguishable from motion along a geodesic in the curved spacetime.
  • The laws of special relativity apply to observers moving inertially (without acceleration).


From these general principles, Einstein was able to derive an equation that embodies the whole theory of general relativity and makes such astonishing predictions as the curvature of a light ray in the presence of matter, the expansion of the universe, and the existence of black holes. Most such phenomena were not even known experimentally in 1915 (though some were, such as the precession of the perihelion of Mercury). The curvature of light by matter was verified experimentally in 1919, and the success of this prediction was so dramatic that it made headlines in newspapers around the world. Other predictions were so counterintuitive that even Einstein was reluctant to believe them. He doubted the expansion of the universe until Edwin Hubble gave convincing evidence of it in 1929, and never accepted the idea of black holes. Indeed, many physicists have had their doubts about black holes until the evidence for them has become very strong quite recently.

The history of Einstein's general theory of relativity turns certain overly simplistic ideas of "scientific method" completely on their heads. Powerful theories are not necessarily derived by "induction" from observation of accumulating experimental data. They are not necessarily even derived deductively from facts already well-verified. A far-reaching theory can, in fact, be derived logically from very general principles of what ought to be true of a useful fundamental theory.

General relativity came as such a surprise to practially all physicists because of how Einstein derived if from thought alone, with little experimental evidence. It is this, as much as the papers of 1905, which conferred upon Einstein his daunting reputation.

The passage of time has only emphasized what an astonishing accomplishment this was. The bulk of Smolin's article deals, essentially, with how the entire physics community -- including Einstein himself -- has been unable to reproduce this feat in the years since 1915.

Einstein devoted the last 30 years of his career to the search for a "unified field theory" that would encompass both gravity and electromagnetism (including quantum mechanincs). Einstein failed. So have all other physicists, either in the more limited objectives that Einstein pursued or in the most general form of a "theory of everything".

The reason, almost everyone agrees, is that no one has yet been able to guess what additional fundamental principles must be postulated.

It seems likely that there are additional principles that are needed, rather than modifications to the principles from which general relativity was derived. (Quantum mechanics is rather a different story. Though it has underlying principles, it has been constructed in a more inductive manner, adapting the mathematical rules -- the basis of which no one pretends to understand -- to fit experimental facts.)

The reason that additional principles are required is that in fact it has been possible to construct a vast number of possible "theories of everything" -- as many as 10100 distinct theories in the form of superstring theory alone. It would seem that physicists must be missing some essential fundamental principles that would narrow this rather large embarassment of theories to just one. (It is also possible that many or all of this huge number of theories may in fact be realized in a multiplicity of distinct "universes" that, perhaps, comprise the "multiverse".)

But if there is in fact a single theory of everything, nobody has yet been able to offer plausible guesses about the form that the necessary principles should take in order to make the theory unique, as Einstein did so successfully for general relativity.

This doesn't necessarily mean that humans are too stupid to understand the universe. Roughly 250 years separate Einstein's theory of gravity from Isaac Newton's. We might well need another 250 years to take the next step. In any case, it may be a cause for some satisfaction that there is still so much left to learn -- as opposed to the depressing thought that physics has reached nearly the end of the road, with little left to learn.

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