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Physics Today

The value of Einstein’s mistakes

Alfred S. Goldhaber

Published Apr 1, 2006• 2 citations
Publisher

Abstract

Steven Weinberg’s love for and knowledge of history inform his instructive sampling of Albert Einstein’s mistakes (Physics Today, November 2005, page 31). One mistake, or at least one tantalizing omission, seems worth adding to the collection. In a May 1905 letter to Conrad Habicht, Einstein wrote that he thought his revolutionary contribution was the hypothesis that light consists of particles. 1 1. A. Einstein, The Collected Papers of Albert Einstein, vol. 5, English translation, Princeton U. Press, Princeton, NJ (1995), p. 20. Consider his lifelong passion for unification, as in his resolution of the clash between Isaac Newton’s mechanics and James Clerk Maxwell’s electrodynamics (with the special theory of relativity modifying the former). It is hard to believe that Einstein did not worry about reconciling the well-established wave aspects of light with his new particle hypothesis. If he had pursued that connection, he could have developed one-photon quantum mechanics in 1905 or shortly afterward, by combining the Poynting-vector expression for the power intensity of light with his own relation between frequency and energy of a particle to obtain the photon-number intensity of a light beam. The wave equation is the Maxwell equations, and the probability interpretation pops up immediately.Many observers have said that general relativity was one advance that would have taken a very long time without Einstein, but we have no direct test for that statement. However, if you accept my argument that Einstein could have developed the first true quantum mechanics, then we can say exactly how long it took the physics community to catch up—20 years for Heisenberg’s matrix mechanics and Schrödinger’s mathematically equivalent wave mechanics. REFERENCESection:ChooseTop of pageREFERENCE <<1. A. Einstein, The Collected Papers of Albert Einstein, vol. 5, English translation, Princeton U. Press, Princeton, NJ (1995), p. 20. Google Scholar© 2006 American Institute of Physics.

DOI
10.1063/1.2207014

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Steven Weinberg’s love for and knowledge of history inform his instructive sampling of Albert Einstein’s mistakes (Physics Today, November 2005, page 31). One mistake, or at least one tantalizing omission, seems worth adding to the collection. In a May 1905 letter to Conrad Habicht, Einstein wrote that he thought his revolutionary contribution was the hypothesis that light consists of particles. 1 1. A. Einstein, The Collected Papers of Albert Einstein, vol. 5, English translation, Princeton U. Press, Princeton, NJ (1995), p. 20. Consider his lifelong passion for unification, as in his resolution of the clash between Isaac Newton’s mechanics and James Clerk Maxwell’s electrodynamics (with the special theory of relativity modifying the former). It is hard to believe that Einstein did not worry about reconciling the well-established wave aspects of light with his new particle hypothesis. If he had pursued that connection, he could have developed one-photon quantum mechanics in 1905 or shortly afterward, by combining the Poynting-vector expression for the power intensity of light with his own relation between frequency and energy of a particle to obtain the photon-number intensity of a light beam. The wave equation is the Maxwell equations, and the probability interpretation pops up immediately.Many observers have said that general relativity was one advance that would have taken a very long time without Einstein, but we have no direct test for that statement. However, if you accept my argument that Einstein could have developed the first true quantum mechanics, then we can say exactly how long it took the physics community to catch up—20 years for Heisenberg’s matrix mechanics and Schrödinger’s mathematically equivalent wave mechanics. REFERENCESection:ChooseTop of pageREFERENCE <<1. A. Einstein, The Collected Papers of Albert Einstein, vol. 5, English translation, Princeton U. Press, Princeton, NJ (1995), p. 20. Google Scholar© 2006 American Institute of Physics.
In 1905 Einstein wrote five history-making papers (on the particle nature of light, Brownian motion, special relativity, energy and inertia, and on molecular dimensions). He was 26, married to Mileva Mari, with one-year-old child Hans Albert, and employed as Technical Expert (third class) by the Bern Patent Office. His relativity theory captured the public imagination, but his quantum ideas were even more revolutionary. His light quantum (now the ‘photon’) was rejected by Planck, who is often thought of as the originator of the concept, and by Millikan, whose 1916 photoelectric data agreed beautifully with Einstein’s predictions (‘a bold, not to say reckless, hypothesis of an electromagnetic light corpuscle ... which flies in the face of thoroughly established facts of interference’). Compton’s 1923 paper on the scattering of X-rays and gamma rays uses the light quantum idea, but makes no mention of Einstein. There followed more than 20 papers on various aspects of quantum theory, substantial enough to make Einstein one of the founders of quantum mechanics, possibly the founder. This paper traces the beginnings of quantum mechanics, giving an outline of Einstein’s contributions. It begins with a sketch of his early life.
In 2005 we celebrate the hundredth anniversary of the publication of five seminal papers by Albert Einstein establishing the basis of three fundamental fields of physics: the theory of relativity, quantum theory and the theory of Brownian motion. This happened at a time when the reality of atoms and molecules was still far from certain. The microscopic view Einstein took of molecular motion led to the calculation of Avogadro's number and the size of molecules by studying the motion of small particles in liquids. Combining kinetic theory and classical thermodynamics finally led Einstein to the conclusion that the displacement of a microparticle under Brownian motion varies as the square root of time. The experimental demonstration of this law three years later was considered as the striking proof that atoms and molecules are physically real. Today single atoms are probed directly in experiments, and we are able to observe the individual paths of colliding or dissociating particles. These new techniques are described in some of the papers of this issue in a very impressive way. An even more exciting development was initiated with the demonstration of Bose–Einstein condensation of dilute gases of ultracold atoms, a phenomenon first predicted by Einstein in papers published between 1916 and 1924. The first paper of Einstein's famous series of 1905, 'On an heuristic point of view about the creation and conversion of light', was an explanation of the photoelectric effect, demonstrated in several experiments over the previous few years. The explanation was based on the quantum hypothesis introduced by Max Planck five years earlier, and was considered as an additional and important proof of Planck's hypothesis. Today quantum theory and photons are the basis for much of modern science and technology. We have learned to experiment with single photons, and we have demonstrated the advantages of information transfer by single photons. Photons permit new and incredibly precise time and frequency standards. These are not only technically important, but may also lead to even more stringent tests of relativity and other fundamental laws and concepts of physics. Examples of these applications and many other uses of modern optics are discussed in this issue. Special relativity, the third of Einstein's 1905 topics, has always been closely connected with atomic, molecular and optical physics. Today atomic physics provides some of the most stringent tests of special relativity. Furthermore, fast electron beams are used in advanced light sources such as synchrotron radiation generators and free electron lasers. Those aspects and related applications are also discussed here. We hope that this special issue will be of great interest to the reader by highlighting recent advances in atomic, molecular and optical physics. This field continues to provide one of the most fertile areas for research one hundred years after it first emerged from the work of Einstein published in 1905, his 'miraculous year'.
By the end of the nineteenth century all the important elements of classical physics were fully mature. Newton's Laws had been applied with success to everything from industrial machines to planetary orbits. Classical thermodynamics had extended energy conservation arguments into thermal processes, and scientists including J. Willard Gibbs and Ludwig Boltzmann had developed the statistical interpretation of entropy. James Clerk Maxwell had explained all electromagnetic phenomena, from AC generators/motors to light, with the four Maxwell's equations and three material-dependent constitutive relations. There was serious discussion that physics was on the verge of being “finished” – becoming a closed system of knowledge like classical geometry with only essentially routine tasks left of determining how the known laws could be applied to engineering problems. Yet by 1930 the foundations of mechanics, electromagnetics, and atomic-scale systems had been shaken to the core by the new revolutions in the Theory of Relativity, the photon picture of light, and quantum physics. We are still reaping the benefits of the application of these new scientific paradigms in our technology today, including semiconductor electronic devices, lasers, and GPS systems. But the description of reality that these theories provide is still deeply anti-intuitive and disturbing. Nevertheless, quantum physics is one of the most extensively experimentally verified theories that we know. Even when quantum theory and common sense seem to diverge, quantum theory gives the right answers when tested by experiment. In the next chapter we will develop the framework of quantum theory that has been so successful when people “shut up and calculate,” as one scientist suggested as the way through the philosophical thicket of quantum physics. But in this chapter, we will spend a brief time considering the historical development and continuing paradoxical implications of quantum theory. The photoelectric effect and photons In 1905, Albert Einstein, who was a key figure in the revolution of modern physics, was working as a clerk in the patent office in Zurich, Switzerland. Einstein had finished his studies in physics, but had not obtained a coveted position as a university professor. He was intensely interested in the latest developments in classical physics and was aware of a few of the remaining loose ends that were resisting explanation in the classical model.
Einstein’s 1905 paper on the photoelectric effect, in which he considered Planck’s idea of quanta of energy to be a universal characteristic of light, marks the beginning of quantum theory. For over ten years Einstein stood alone on the issue of energy quantization of light; and although in 1915 experimental conrmation of his photoelectric effect came from painstaking experiments performed by Millikan, acceptance of the idea that light was composed of particles was far from universal. Millikan himself wrote in 1915: “Despite … the apparent complete success of the Einstein equation, the physical theory of which it was designed to be the symbolic expression is found so untenable that Einstein himself, I believe, no longer holds to it.” Einstein did hold to it. It was only in the mid 1920s, when Heisenberg, Schrödinger, Dirac, and others developed the rst forms of quantum theory, that serious discussions concerning the particle nature of light and the meaning of the new theory began. Discussions about the meaning of quantum theory continue today.
Certainly there is no unique answer to Frank Wilczek’s question, “What Is Quantum Theory?” (Physics Today, June 2000, page 11). I was not certain that a pragmatic answer, which I proposed for a course in applied quantum mechanics, 1 1. W. A. Harrison, Applied Quantum Mechanics, World Scientific, River Edge, N.J. (2000). would be sustainable for the entire course, but it seems that it was. That answer was the assertion that everything is both a particle and a wave, and that everything else would follow from that one assertion. Planck’s constant arose when the velocity of a wave (the derivative of the frequency with respect to wavenumber) was equated to the velocity of a particle (the derivative of the energy with respect to momentum), so that energy is proportional to frequency and momentum to wavenumber, with the same proportionality constant ħ. When Hamiltonian mechanics was introduced, “everything” became anything that can be described by such mechanics, or anything that satisfies a wave equation. Quantum theory does not say what nature gives, only how to predict the behavior of what is given. If nature serves up particles with half-integral angular momentum, the wavefunction that describes them must go into its negative when they are interchanged, and they therefore obey the Pauli principle.Such principles, which historically arose as independent conjectures, now follow from the one assertion. It is a matter of seeing how this peculiar assertion can turn out to be absolutely true.The relation between quantum theory and the physical world was seen as follows: Quantum theory tells what future scenarios are consistent with some initial information, and what the relative probability of each scenario is. Quantum theory cannot tell more than that, but neither can any other theory.My pragmatic approach may not satisfy everyone’s philosophical needs. But the aim of an applied quantum course is to see how to use the theory and to introduce the many approximations that have made the theory accessible to physicists and engineers. If some basic consequences are difficult to accept, the problem must lie with the initial assertion from which the consequences follow.REFERENCESection:ChooseTop of pageREFERENCE <<1. W. A. Harrison, Applied Quantum Mechanics, World Scientific, River Edge, N.J. (2000). Google ScholarCrossref© 2001 American Institute of Physics.
While I very much enjoyed Steven Weinberg’s article “Einstein’s Mistakes,” I am puzzled by the author’s statement about quantum mechanics: “The difficulty is not that quantum mechanics is probabilistic—that is something we apparently have to live with. The real difficulty is that it is also deterministic, or more precisely, that it combines a probabilistic interpretation with deterministic dynamics.” Quantum mechanics is an acausal deterministic theory in the sense that a physical system’s state (mathematically described by a state vector) at a given initial time determines its state at a specified later time, but its state is not in one-to-one correspondence with sharp values of all its dynamical variables; that correspondence is probabilistic. Therefore events, identified by sharp values of those variables at one spacetime point, are not causally connected with other events. That is something we have to live with.Why does the combination of these two attributes—acausality and determinism—constitute a special difficulty? Weinberg asks, “So where do the probabilistic rules of the Copenhagen interpretation come from?” Why do they have to come from anywhere other than from human brains? Nature exists out there, independent of human thought, but its mathematical description surely is a human construction rather than an immutable law given to us on a stone tablet.© 2006 American Institute of Physics.