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| HPS 2590 |
Einstein | Fall 2015 |
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Einstein's 1905 "On the Electrodynamics of Moving Bodies" is quite possibly the most famous scientific paper ever written. It develops the special theory of relativity, which is the basis of much of the physics of the new century. Methodologically, it has one of the most important conceptual analyses of science, the analysis of simultaneity; and Einstein's operational approach was emulated for nearly a century to come.
The first derivation of the famous result was in a short paper of 1905. Over the years following, Einstein returned to rederive the result several times. The result is a little more subtle that it first seems.
These papers are a two drawn from the extraordinary papers of 1905 that make it Einstein's annus mirabilis. Those papers are described here.
The content of the special theory of relativity is already encoded within the electrodynamics of the 19th century. Lorentz and Poincaré had also discerned the basic mathematical structure and used it heavily. Einstein's contribution was to recognize that the Lorentz transformation was not merely an odd artifact of electrodynamics, but a direct reflection of the nature of space and time. The celebrated ether drift experiments contribute to special relativity indirectly through 19th century electrodynamics.
General relativity is Einstein's singular contribution to physics. While most major advances--special relativity, quantum theory--are collaborative efforts of many, general relativity is almost entirely Einstein's work alone.
This first phase of Einstein's work was driven by the "elevator" thought experiment from which Einstein built up a novel theory of static gravitational fields. It included many qualitative effects that are familiar from the later, full theory, including the gravitational slowing of clocks and bending of light.
In collaboration with his mathematician friend, Marcel Grossmann, the two wrote a sketch of a generalized theory of relativity and gravitation. It is essentially the complete theory with the extraordinary omission of the celebrated generally covariant gravitational field equations now attached to his name. Einstein and Grossmann had considered something close to them, but abandoned them in favor of equations of limited and then unknown covariance.
Einstein struggled on for two years with his misshapen theory, developing novel mathematical techniques in an effort to understand it better. His unhappiness came to a head in November 1915 when he returned to general covariance. In four rapid communications, one per week, he polished his results and arrived at the completed theory. In the third, he found that his new theory explained the anomalous motion of Mercury, possibly the moment of greatest triumph of his scientific life.
This notebook contains Einstein's private calculations from the crucial period during which the Entwurf theory is developed. It provides an unmatched window onto Einstein at work at the peak of his creativity. It has been the subject of very extensive scholarly scrutiny.
As the Entwurf theory developed, Einstein exchanged a manuscript of calculations with his friend Michele Besso in which they jointly worked on the properties of the new theory. They computed the motion of Mercury in the theory and got impossible results to which they reacted with . . .
Einstein's account of the foundations of his general theory of relativity rested on principles: the principles of equivalence, general covariance, general relativity and Mach's principle. Precisely how these principles interact and combine to ground general relativity has was then contentious; and the issue is still not fully resolved today.
Michel Janssen, "The Twins and the Bucket: How Einstein Made Gravity rather than Motion Relative in General Relativity", Studies in History and Philosophy of Modern Physics 43 (2012): 159–175.
John D. Norton, "General Covariance and the Foundations of General Relativity: Eight Decades of Dispute," Reports on Progress in Physics, 56 , pp.791-858.
After Einstein and Grossmann failed to settle on a generally covariant theory, Einstein hit upon an ingenious argument that appeared to show that a generally covariant theory would be uninteresting because it would be indeterministic (=violating the "law of causality.") This argument and its resolution took on an outsized importance in the subsequent philosophical development of general relativity. It has more recently been revived in the context of debates in modern philosophy of space and time; and has proven important in efforts to find a quantum theory of gravity.
In 1917, in an effort to enforce a properly "Machian" character on his new general theory of relativity, Einstein introduced a novel cosmology, the Einstein universe, and with it his notorious/famous cosmological constant λ.
John D. Norton, "Mach's Principle before Einstein." in J. Barbour and H. Pfister, eds., Mach's Principle: From Newton's Bucket to Quantum Gravity: Einstein Studies, Vol. 6. Boston: Birkhäuser, 1995, pp.9-57.
Einstein subsequently found himself embroiled in debates over whether his theory truly had Machian character. De Sitter introduced what we now call the de Sitter spacetime an alternative cosmological model. With Hermann Weyl's engagement, the debates devolved into some muddled treatments of coordinate singularities as real singularities.
In the mid to late 1910s, Einstein studied the linearized form of general relativity, eventually recovering quadrupole gravitational radiation. In a curious development, in 1936, working in collaboration with Nathan Rosen, Einstein convinced himself that gravitational waves do not arise in general relativity. The paper was flawed. Even the great Einstein can suffer rejection by referees (and respond in high dudgeon).
Einstein's name is tied by unbreakable bonds to relativity and also somewhat to quantum theory. However Einstein was accomplished in statistical physics and made important contributions to it.
It is easy to imagine that the Einstein of the annus mirabilis of 1905 was a novice publishing for the first time. However the reality is otherwise. Einstein had been publishing steadily in Annalen der Physik since 1901. His papers of 1902-1904 develop independently what is otherwise known as the Gibb's formalism for statistical physics. A key contribution was his fluctuations formula, which was used to great effect in his work on quantum theory.
Clayton A. Gearhart, "Einstein before 1905: The Early Papers on Statistical Mechanics," American Journal of Physics, 58 (1990):468-480.
Einstein's two major works in statistical physics of 1905 were his doctoral dissertation on dilute sugar solutions and his paper on Brownian motion, which can be seen to develop from the doctoral dissertation. The Brownian motion paper provided the first observable, thermal phenomenon that could not be handled by an atom-agnostic phenomenological thermodynamics.
Einstein made an early contribution to critical phenomena, which manifest as an opalescence in fluids near their critical point. The work also explains in passing why the sky is blue.
In 1905, Einstein made the only contribution to physics that he called "very revolutionary." That was his proposal of the light quantum. It remained controversial until the 1920s.
It is a now familiar result of the quantum theory that matter sometimes manifests particle and sometimes wave properties. In 1909, in an ingenious argument involving fluctuations, Einstein showed that light manifests both at the same time.
In the mid 1910s, the old quantum theory was developing rapidly through the work of Bohr, Sommerfeld and others on atomic spectra and their accommodation by the quantized Bohr atom. In 1917, Einstein gave a new derivation of the Planck energy distribution for black body radiation that was essentially stochastic in character, using transition probabilities labeled by "A" and "B" coefficients. It would prove of foundational importance in the newly developing quantum theory and, at the same time, introduced the stimulated emission that is the basis of lasers.
When the new quantum mechanics of Heisenberg, Born, Jordan, Schroedinger, Dirac and others stabilized in the mid to late 1920s, Einstein found himself unable to accept it as a fundamental theory. His debates with Bohr are legendary. Just what was Einstein's concern and just what was his view of the fundamental difficulty in quantum theory: indeterminism? non-locality? non-separability?
This paper is the epicenter of Einstein's objections to quantum theory, although Einstein almost immediately complained that Podolsky's writing of it had buried the key idea. It was and perhaps still is the most cited paper in Physical Review.
Einstein was convinced that unification was the right guide for making progress in physics. General relativity had unified gravity, inertia and spacetime and, he believed, a continuation of this program would accommodate electromagnetism and with it quantum effects. These efforts to extend general relativity began in the late 1910s and continued until his death in 1955. Einstein tried many approaches, including five dimensional Kaluza theories, affine theories, semi-vectors and non-symmetric connections.
Tilman Sauer, "Einstein's Unified Field Theory Program," in Cambridge Companion to Einstein.
Jeroen van Dongen, Einstein’s Unification. Cambridge: Cambridge University Press, 2010.
Abraham Pais, Ch. 17 "Unified Field Theory" in Subtle is the Lord. Oxford: Clarendon Press, 1982.
Dennis Lehmkuhl, "Why Einstein did not believe that general relativity geometrizes gravity," Studies in History and Philosophy of Modern Physics, 46, (2014), Pp. 316–326.
Einstein was a physicist. However he has important philosophical connections. He read philosophy and took it seriously, using it to guide his scientific work. He also became something of a philosophical oracle to philosophers of science in the early 20th century. His scientific work and methodological remarks were quite influential.
Don Howard, "Einstein's Philosophy of Science", The Stanford Encyclopedia of Philosophy.
John D. Norton, “Philosophy in Einstein’s Science," To appear in Alternatives to Materialist Philosophies of Science, Philip MacEwen, ed., The Mellen Press. Draft.
Einstein's view of the nature of theories formed as a reaction to the simple inductivism of the 19th century. There is no logical pathway from experience to theories, he insisted in response. Theories are "free creations of the human spirit." Don Howard has identified Einstein as Duhemian holist.
In the context of his work on the special theory of relativity, Einstein distinguished these two types of theories. Constructive theories build a full account of the system of interest from a knowledge of its composition, such as does the kinetic theory for gases. Principle theories leave the constitution of the system largely unknown but constrained in important ways by high level generalizations, such as the laws of thermodynamics.
Later in life, Einstein became a mathematical Platonist. "Nature is the realization of the simplest conceivable mathematical ideas," he wrote. This idea was learned, he said, from his experience with general relativity and it became the guide for his work on a unified field theory.
Jeroen van Dongen, Einstein’s Unification. Cambridge: Cambridge University Press, 2010.
John D. Norton, “'Nature is the Realisation of the Simplest Conceivable Mathematical Ideas': Einstein and the Canon of Mathematical Simplicity.” Studies in History and Philosophy of Modern Physics 31 (2000), pp. 135–170.
Einstein reported that his work on special relativity was decisively furthered by the reading of Hume and Mach. Just what did he learn from them? It might not be quite what you expected.
John D. Norton, "How Hume and Mach Helped Einstein Find Special Relativity," pp. 359-386 in M. Dickson and M. Domski, eds., Discourse on a New Method: Reinvigorating the Marriage of History and Philosophy of Science. Chicago and La Salle, IL: Open Court, 2010.
Einstein used thought experiments to very great effect in his work. What are we as philosophers to make of them? Can clever armchair imaginings replace the trouble and expense of a real experiment?
John D. Norton, "Thought Experiments in Einstein's Work," in Thought Experiments In Science and Philosophy, eds. T. Horowitz, G. J. Massey, Savage, MD: Rowman and Littlefield, 1991.
Popper credited Einstein's willingness to open his theories to severe test as a major inspiration for Popper's falsificationism. However was the inspiration even more direct? A 1919 popular article by Einstein gives more than a merely useful example. And did Einstein's own treatment of the predictions of this theories, such as for Mercury's motion, really conform with falsificationist demands?
Albert Einstein, "Induktion und Deduktion in der Physik," Berliner Tageblatt. December 25, 1919, p. 2