The quantum leap

Published : May 20, 2005 00:00 IST

Einstein was the first to realise clearly that Max Planck's introduction of energy quanta was truly revolutionary. Though Planck fired the first shot in the quantum revolution, Einstein was to lead it.

IN his house at Princeton, Albert Einstein had a few pictures and etchings. These included a drawing of Gandhi, photographs of his mother and sister Maja, besides etchings of the physicists he admired most: Isaac Newton, James Clerk Maxwell and Michael Faraday.

Newton, with his formulation of the three laws of motion and his discovery of the law of universal gravitation, laid the foundations of classical physics. He gave magisterial treatment of his system in his magnum opus Principia (1687), a true watershed in the human understanding of the physical world. Newton's world consisted of discrete mass particles, moving with time in the arena of space, under the influence of mutual forces. He also believed that light also consisted of discrete light corpuscles.

Later, the discovery of the phenomena of interference and diffraction of light led physicists to regard light as a wave. Since it was believed that waves need a medium for their propagation, a medium called `luminiferous ether' was postulated for light waves. In the 19th century, Faraday introduced the concept of continuous fields, as opposed to discrete particles, like electric and magnetic fields. Maxwell's equations for these fields (1864) unified them into a single entity called the "electro-magnetic field" generated by electric charge and currents. A windfall of this unification was the prediction of electromagnetic waves, with a constant velocity which agreed with that of light. Maxwell then proposed to identify electromagnetic waves with light, thus unifying optics with electromagnetism.

At the end of the 19th century it appeared that the classical physics of Newton, Faraday and Maxwell provided a complete description of the natural world and that the end of physics was almost in sight. It was, however, the proverbial lull before the storm.

Physics underwent two major revolutions in the first quarter of the twentieth century. The origin of one of these was in the failure to detect the motion of the earth through the ether. This problem was resolved by Einstein in the Special Theory of Relativity (1905) by the banishment of ether and a thorough revision of the Newtonian concepts of space and time. Further modifications of flat space-time to a curved one led to a change in our view of gravitation in the General Theory of Relativity of Einstein (1915). We shall not be further concerned with the Theory of Relativity but will be following the second revolution, the quantum revolution, and Einstein's contributions to it.

The origins of the quantum revolution lay in the problem of black body radiation. As is well known, all heated bodies emit radiation. They also absorb a fraction of the radiation falling on them. The precise amount of emission and absorption of radiation of a particular frequency depends on the nature and the temperature of the body. However, in 1859, Gustav Robert Kirchhoff showed that the ratio of emissivity to absorptivity of a body is independent of its nature and is thus a universal function, which is the same for all bodies. Further, this universal function was the same as the emissivity of a perfectly black body, a body that absorbs all the radiation that falls on it. He also showed that the radiation inside a cavity, kept at a fixed temperature, is the same as black body radiation.

In 1894, Wilhem Wien proposed an expression for this function, known as Wien's radiation law, which fitted the experimental data very well at higher frequencies.

Max Planck succeeded to the chair in physics occupied by Kirchoff in Berlin in 1889. He was naturally drawn to the problem of determining the universal function of Kirchhoff. Planck's idea was to assume a simple model of the cavity walls since the black body radiation is independent of the nature of the walls. He took the wall to be made of elementary oscillators, each capable of absorbing and emitting radiation only at a definite frequency. Using Maxwell's theory he found a relation between the energy density of the black body radiation and the average energy of the elementary oscillators. Shortly after this result was announced on May 18, 1899, Lord Rayleigh derived in June 1900 another radiation law (corrected by James Hopwood Jeans later in 1905) that gave a good description of the radiation at low frequencies but failed badly for higher frequencies where Wien's law was a better description. The correct law was guessed by Planck and announced on October 19, 1900. He presented a formal derivation of the law on December 14, 1900, to the German Physical Society. This can be regarded as the birth date of quantum theory.

The radical new element in Planck's work was that his elementary oscillators, with frequency f, cannot have a continuous range of energies but can only have an energy which is an integer multiple of a quantum of energy equal to hf, where h is a constant now known as Planck's constant. Planck does not seem to have realised the revolutionary nature of his proposal. He said, "This was purely a formal assumption and I really did not give it much thought except that no matter what the cost, I must bring about a positive result."

The first person to realise clearly that Planck's introduction of energy quanta was truly revolutionary was Einstein. Though Planck had fired the first shot in the quantum revolution, Einstein was to lead it now. He was 26 years of age at the time he sent his paper on "light quantum hypothesis" to the journal Annalen der Physik on March 17, 1905. It was his first paper on quantum theory. During this year, his annus mirabilis, he was also to publish epoch-making papers on Brownian motion, the special theory of relativity and E = mc{+2}, besides completing his doctoral thesis on molecular dimensions. But in a letter to his friend Conrad Habicht, written at that time, Einstein applied the adjective "revolutionary" only to the paper on the light quantum hypothesis. He first shows in this paper that the radiation law of Rayleigh and Jeans is the unambiguous prediction of classical physics. Therefore, if we have to understand the phenomenon of black body radiation, a decisive break with the concepts of classical physics is involved.

Einstein was dissatisfied with the asymmetrical treatment of matter and radiation in classical physics. Matter was regarded as made of discrete particles, while radiation was described as a continuous wave field. He felt that the failure of classical physics lay perhaps in not treating radiation too as being made up of particles. But then the wave theory of radiation had had a long and successful innings. Einstein remarked in his paper, "The wave theory, operating with continuous spatial functions, has proved to be correct in representing purely optical phenomena and will probably not be replaced by any other theory. One must, however, keep in mind that the optical observations are concerned with temporal mean values and not with instantaneous values, and it is possible, in spite of the complete experimental verification of the theory of reflection, refraction, diffraction, dispersion and so on, that the theory of light which operates with continuous spatial functions may lead to contradictions with observations if we apply it to the phenomena of the generation and transformation of light."

Using Wien's radiation law, which was in good agreement with the experimental data on black body radiation at high frequencies, where the predictions of classical physics fail, Einstein found that "monochromatic radiation of small energy density... behaves... as though it consisted of distinct independent energy quanta of magnitude hf". Einstein thus introduced the hypothesis of quanta of light. He applied it to explain Stokes' law, ionisation of gas by ultraviolet light and the photoelectric effect. As Abraham Pais, the pre-eminent scientific biographer of Einstein, remarks, this was the second coming of the quantum.

Surprisingly, when Einstein discussed the theory of photoelectric effect, all the details of the phenomenon were not yet clarified through experiment, though the experimental work had been going on since the original observation of the effect by Heinrich Hertz in 1887. But by 1915-1916 the extensive experimentation of R.A. Millikan led him to say, despite his disbelief in the hypothesis of light quanta, "Einstein's photoelectric equation... appears in every case to predict exactly the observed result." Einstein was awarded the Nobel Prize for Physics for the year 1921 for this work. The announcement was made in November 1922. The discovery of the Compton effect in October 1922 finally brought about a general acceptance of the idea of light quanta.

Einstein also pioneered the extension and application of the quantum hypothesis to problems in physics other than those involving radiation. In 1907 he applied the quantum hypothesis to the study of the specific heat of solids. The predictions of classical physics were in agreement with experiment at higher temperatures but failed to explain the measurements at low temperatures. Using the same hypothesis regarding the energy of the elementary oscillators as in the derivation of Planck's radiation law, Einstein provided, using the quantum hypothesis, the first model for the specific heat of solids that was in broad agreement with the experimental data. The model was later refined by Peter Debye (1912) and by Max Born and Theodore von Karman (1912, 1918).

In 1917, Einstein used the method of chemical kinetics to give a new derivation of Planck's law. He also used the concept of discrete energy states introduced by Niels Bohr in 1913 when he applied quantum theory to the problem of atomic structure and spectra. Einstein recognised that in order to obtain Planck's law by this method it was crucial to consider the process of the stimulated emission of light. In this process an atom undergoes a transition from a state of higher energy to one of lower energy, a transition induced by the presence of radiation.

The possibility of the stimulated emission of light, first recognised by Einstein, is the fundamental mechanism underlying the functioning of lasers.

Despite various attempts by Einstein and others, there was no derivation of Planck's radiation law, which was based solely on the hypothesis of light quanta. At some point in these derivations, one had to invoke both the wave and particle nature of light. The first derivation of Planck's law based solely on the quantum hypothesis was provided by Satyendranath Bose in 1924. Bose sent his work to Einstein for evaluation. Einstein translated it into German and had it published in Zeitschrift fur Physik. Bose's idea was to regard black body radiation as a gas of non-interacting light quanta, or photons as we now call them, by the method of statistical mechanics. The rules of classical statistical mechanics due to Maxwell and Ludwig Boltzmann would have resulted in Wien's law. Bose therefore changed the rules of statistics as applied to photons. These rules are now understood as arising from the indistinguishability of photons. Bose thus founded quantum statistics. The particular counting that he proposed is known as Bose statistics and particles obeying it are known as bosons.

Einstein immediately saw the importance of Bose's work and applied it to material particles. As a result the new statistics proposed is also known as Bose-Einstein statistics. A prediction of this application was a new type of quantum phase transition, known as Bose-Einstein condensation, which has been experimentally observed only recently. The Nobel Prize in Physics for 2001 was awarded to Eric A. Cornell, Carl E. Wiemann and Wolfgang Ketterle for this discovery.

The initial phase of quantum theory, which lasted from 1900 to 1924, is sometimes referred to as "old quantum theory". As we have seen, Einstein played a pivotal role here. The final formulation of quantum mechanics was achieved by Werner Heisenberg (1925), Paul Dirac (1925), and Erwin Schrodinger (1926). Heisenberg's work was inspired by Einstein's methodology of analysing the observability of space-time concepts in his paper on the Special Theory of Relativity. Heisenberg wanted to do the same for concepts in atomic physics. In view of his own work in 1909, Einstein was in a special position to appreciate the wave-particle connection. Through a triangular interaction with de Broglie and Schrodinger, Einstein played the role of godfather to the wave mechanics of Schrodinger.

Even though the mathematical formalism was in place, the problem of what quantum mechanics meant, or the problem of the interpretation of quantum mechanics as it came to be known, was wide open. From now on, Einstein's main focus was on these foundational issues of quantum mechanics rather than its applications.

At the fifth Solvay conference held in Brussels in October 1927, Einstein contrasted the two following viewpoints on the meaning of quantum mechanics in the context of the phenomenon of the diffraction of electrons through a single slit. The first was the ensemble interpretation. In this view, the quantum mechanical probability of the position of an electron gives only the probability of finding some electron in a large collection at a particular position but does not give any information about the behaviour of a single electron. This is the view to which Einstein subscribed. In contrast, the second regarded quantum mechanics as a complete theory of individual processes, according to which it is one and the same electron whose probability of being at a particular position is given by the quantum probability distribution. Needless to say, this was the view of Niels Bohr.

We thus see that the ensemble interpretation of quantum mechanics, which is in some sense the operative part of quantum mechanics, goes back to Einstein. Soon, however, Bohr's views, known as the `Copenhagen interpretation' became the dominant one. Einstein, however, in view of his deep commitment to realism, did not favour it.

Einstein's strategy in his critique of quantum mechanics was to show its incompleteness. Initially, his famous debate with Bohr, which began at the fifth Solvay conference and continued later, focussed on the possibility of circumventing or evading Heisenberg's uncertainty relations. Here Bohr was able to convince him eventually that this could not be done. Einstein, together with Boris Podolsky and Nathan Rosen, was more fruitful with his observation in 1935 that in quantum mechanics two particles could be created in a combined state, an `entangled state', that could never be separated into the sum of two single particle states. As a result, the properties of the two particles were correlated even when they were physically separated and no physical signal was transmitted from the one to the other. These `non-local' correlations are known as Einstein-Podolsky-Rosen correlations. Einstein was able to show that either the wave function description is incomplete or the "the real states of spatially separated objects are independent of each other" (the principle of Einstein locality). Einstein's predilection was to believe in the locality principle.

However, recent experiments have shown, using John Bell's (1966) re-formulation of Einstein locality, that this non-locality is an essential feature of nature. The recent upsurge of research in the new fields of quantum information, quantum computing and quantum cryptography arises out of the exploitation of precisely these Einstein-Podolsky-Rosen correlations. The `entanglement' of quantum multi-particle states, which was initially an embarrassment even to some of the votaries of quantum mechanics, is now used as a resource in these applications. Even when in disagreement with the main trends in the interpretation of the advances in quantum mechanics, Einstein unerringly focussed on one of its most significant aspects, one that has continued relevance even to this day.

Einstein's public acclaim perhaps depends mostly on the relativity theory. But Einstein's eminent contemporary Max Born once remarked, "In my opinion he would be one of the greatest theoretical physicists of all times even if he had not written a single line on relativity." Einstein's legacy in quantum mechanics is still overwhelming.

A hundred years after his annus mirabilis, it is clear that Einstein belongs in the select company of Newton, Maxwell and Faraday, whom he so greatly admired.

Virendra Singh, a theoretical physicist, is currently INSA C.V. Raman Research Professor at the Tata Institute of Fundamental Research. He was the Director of the Institute between 1987 and 1997.

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