History topic: Light through the ages: Relativity and quantum era


The study of light from ancient Greek times up to the revolutionary breakthrough by Maxwell is studied in the article Light through the ages: Ancient Greece to Maxwell. In this article we look at the more modern developments which began at the end of the 19th century but took place mainly in the 20th century.

Maxwell can be thought of as the person who completed the classical description of light, and also as the person who began the modern developments. He wrote an article for Encyclopaedia Britannica in 1878 in which he described how light is propagated as a transverse wave, and that its consists of electromagnetic radiation with specific wavelengths. He gave his famous four partial differential equations, now known as Maxwell's equations, which completely describe classical electromagnetic theory. In the article Maxwell, despite Faraday's introduction of field theory, states clearly that he believes in an aether:-

Whatever difficulties we may have in forming a consistent idea of the constitution of the aether, there can be no doubt that the interplanetary and interstellar spaces are occupied by a material substance of body.

There certainly were extreme difficulties with the idea, as Maxwell was well aware, for to carry such high frequency vibrations as light the substance needed to be incredibly rigid, yet the earth, moon and other planets passed through this rigid material as if it were not there. However, in his 1878 Encyclopaedia Britannica article Maxwell proposed an experiment to determine the velocity of the earth through the aether using light in the following way. Split a ray of light, suggested Maxwell, and send the two resulting rays at right angles to each other. Let one travel at right angles to the motion of the earth through the aether while the other travels in the direction of the motion of the earth through the aether. Reflect the two rays back after each has travelled exactly the same distance to join up again and let them interfere. Maxwell made the 'obvious' assumption that each beam would travel at the same speed through the aether so, due to the earth's motion, one should return slightly before the other and measuring the interference fringes would let the earth's speed through the aether be measured.

Maxwell did not believe that this experiment was practical when he proposed it. Albert Michelson, however, who was spending study leave in Helmholtz's laboratory in Berlin in 1881, tried to carry out Maxwell's experiment. Although he could detect no difference in the time taken by the two rays of light, this was put down to his experiment not being accurate enough or that the earth dragged the aether with it in much the same way that it drags the atmosphere. Lorentz showed in 1885, however, that the aether drag theory was not possible. Michelson now teamed up with a chemist Edward Morley who was a highly skilled experimenter. In 1887 they carried out a much more accurate version of Maxwell's experiment. This was so accurate that when it failed to show any difference in the time taken by the two rays of light, it could no longer be put down to experimental error.

Of course the result of the Michelson-Morley experiment is totally incomprehensible if one thinks in a classical way about light travelling. Think about the light travelling in the direction that the earth is moving. It gets back to the detector in the same length of time irrespective of whether the detector is moving or not. How does it know when it is on its journey whether the detector is moving or not? FitzGerald explained the failure of the Michelson-Morley experiment in 1889 by suggesting that a moving object is foreshortened in the direction of travel. The amount of this foreshortening for an object moving with velocity v was √(1 - v2/c2), where c is the velocity of light. Of course this is very close to 1 for velocities v which are small compared to that of light but it explained the results of the experiment by foreshortening the instruments while still allowing there to be an aether through which light travelled at a fixed velocity.

Lorentz, independently, made a similar suggestion to FitzGerald and worked out the full implications of it in 1904 giving transformations which would describe the way that light would look to observers moving relative to each other. Einstein published the special theory of relativity in the following year which is based on the remarkable suggestion that the speed of light remains constant for all observers independent of their relative velocities. His theory was influenced by Lorentz's work but not the Michelson-Morley experiment. However it had its origin from the time that Einstein was a boy when he tried to imagine what would happen if he were moving at the same speed as a beam of light. Of course if the notion that the speed of light is the same for all observers seems hard to understand, then so would the classical view which would suggest that if one could travel faster than light then one could set out on a journey and arrive soon enough to be able to look back and see oneself setting out!

In 1915 Einstein published the general theory of relativity which predicted the bending of rays of light passing through a gravitational field. In 1919 Eddington made an expedition to Principe Island off the west coast of Africa to observe a solar eclipse and to measure the apparent position of stars observed close to the disk of the eclipsed sun. Although his observations were hampered by the weather he was able to get one good value which confirmed the bending predicted by general relativity. In 1926 Michelson carried out his last and most accurate experiment to determine the velocity of light. Using a light path of length 35 km from the Mount Wilson observatory to the telescope on Mount San Antonio, he found the value of 299,796 km per sec.

Another important development in the understanding of light, namely the development of quantum theory, had taken place over this same period of time, roughly 1880 to 1926. Josef Stefan discovered experimentally in 1879 that the total radiation energy per unit time emitted from a blackbody, namely a body which absorbs all radiation energy falling on it, is proportional to the fourth power of the absolute temperature of the body. Ten years later Boltzmann derived Stefan's law using the second law of thermodynamics. In 1896 Wilhelm Wien described the spectrum produced by a blackbody when it radiates. He discovered that the wavelength at which the maximum energy is radiated becomes shorter as the temperature of the blackbody is increased.

Lord Rayleigh made an important contribution to light in 1899 when he explained that the sky is blue, and sunsets are red, because blue light is scattered by molecules in the earth's atmosphere. Rayleigh (and Jeans) also tried to explain Wien's blackbody result making the assumption that all possible frequency modes could radiate with equal probability. A good agreement with Wien's results were achieved at low frequencies, but increasing radiation of energy at higher frequencies led to the impossible result that the total energy radiated by the body would be infinite. Planck, in 1900, showed that the impossible result could be corrected by assuming that electromagnetic energy can only be emitted in quanta. He did not believe in the physical reality of the light quanta, there was far too much evidence that light was a transverse wave for him to change to a corpuscular theory on account of this. Planck thought of his quanta as a mathematical way round the problem of blackbody radiation, rather than thinking that light was actually composed of particles.

A second problem also led to a quantum theory of light, and this time to a belief in the physical reality of the quanta. Heinrich Hertz discovered the photoelectric effect, so called because it was caused by light rays, in 1887. He observed that when that ultraviolet light was shone onto metallic electrodes the voltage required for sparking to take place was lowered. In 1900 Philipp Lenard, a student of Hertz, showed that the photoelectric effect was caused by electrons, which had been discovered by J J Thomson three years earlier, being ejected from the surface of a metal plate when it was struck by light rays.

In 1905 Einstein explained the photoelectric effect by showing that light was composed of discrete particles, now called photons, which are essentially energy quanta. The wave theory of light, which had totally triumphed over the corpuscular theory, could not explain this effect. We should note here that Einstein's explanation of the photoelectric effect was incomplete, for the temperature of the metal surface was seen experimentally to affect the energy of the emitted electrons yet this was not covered by Einstein's model. A fuller model incorporating this feature was discovered by Fowler in 1931.

Bose published his paper Planck's Law and the Hypothesis of Light Quanta in 1924 which derived the blackbody radiation from the hypothesis that light consisted of particles obeying certain statistical laws. In the same year de Broglie put forward his particle-wave duality theory in his doctoral thesis which proposed that matter has the properties of both particles and waves. Not only could photons of light behave like waves, suggested de Broglie, but so could other particles such as the electron. In 1927 de Broglie's claim that electrons could behave like waves was experimentally verified and, in the following year, Bohr put forwards his complementarity principle which stated that photons of light (and electrons) could behave either as waves or as particles, but it is impossible to observe both the wave and particle aspects simultaneously.

Two mathematical models of quantum mechanics were presented, that of matrix mechanics, proposed by Werner Heisenberg, Max Born, and Pascual Jordan, and that of wave mechanics proposed by Erwin Schrödinger. In 1927 Heisenberg put forward his uncertainty principle which states that there is a limit to the precision with which the position and the momentum a particle of light can be known. By 1930 the interpretation of quantum theory called the Copenhagen interpretation, mainly due to Bohr and his co-workers, was essentially complete. It attempted to explain the dual wave-particle duality of light which, in the words of Baierlein [1]:-

... travels as a wave but departs and arrives as a particle.

The main idea of the Copenhagen interpretation is the collapse of the wave function, namely that observing light waves makes them collapse into particles. The clearest example of how this works is to look again at Thomas Young's experiment of passing rays of light through two parallel slits and observing the interference patterns on a screen behind (see the article Light through the ages: Ancient Greece to Maxwell). This is a classical demonstration of the wave nature of light. Suppose now that we fire photons one at a time at the slits. They depart as particles, namely single photons, they arrive as particles and are detected on the screen as individual photons. However they have travelled as waves for the pattern of individual hits on the screen builds up into interference patterns.

But how can this be? Each photon must go through one slit or the other and it cannot interfere with itself. Well the answer is that the photon travels as a wave and does somehow manage to do what seems quite impossible and go through both slits and interfere with itself. If we cover one slit then we know which one it goes through and indeed the interference patterns vanish. Even more strange is the fact that it we put a detector on one of the slits to tell us whether the photon goes through that slit or the other one then the interference pattern vanishes. The act of observing the electron makes its wave nature collapse into a particle.

The nature of light really is strange! But this behaviour is not limited to photons of light far, as de Broglie predicted, electrons behave in exactly the same way. Although the Copenhagen interpretation seems completely vindicated by this experiment, it is still philosophically difficult to accept. It now appears that we, as observers, affect the way that light behaves. Would light always be a wave if nobody was there to observe it? If a dog observes the photon will its wave function collapse? This will lead us to deep philosophical questions and eventually we will be forced to ask whether the universe only exists because there are intelligent beings to observe it. We will not pursue this fascinating line any further.

The Copenhagen interpretation is in trouble from experimental evidence too, for recent subtle experiments have managed to create a situation where photons of light behave both as waves and particles at the same time contrary to Bohr's complementarity principle. But we are getting too deeply into modern day physics and away from the history, so let us end our look at the dual wave-particle nature of light here. Perhaps we should, however, end with a much quoted comment by Feynman from 1964:-

There was a time when the newspapers said that only twelve people understood the theory of relativity. I do not believe that there ever was such a time. there might have been a time when only one person did, because he was the only guy who caught on, before he wrote his paper. But after people read the paper a lot of people understand the theory of relativity in some way or other, certainly more than twelve. On the other hand, I think I can safely say that nobody understands quantum mechanics. ... Do not keep saying to yourself, if you can possibly avoid it "But how can it be like that?" because you will go down the drain into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.

There has been one other important development in the theory of light in the 20th century which we no not want to examine in too much detail, as it also takes us too deeply into physics, but needs to be mentioned in an article on the history of light. This is the development of lasers, an acronym of "light amplification by stimulated emission of radiation". The basic concept goes back to Einstein in 1916 when he showed that if an atom is excited so that it moves to a higher energy level, then if light falls on the atom at the instant it is moving to the higher energy level, then it emits radiation that is in phase with the wave that stimulated it and so amplifies that wave. Of course absorption will occur as well as the emission so only under special circumstances will the stimulated emission predominate over absorption. It was many years after Einstein discovered the principle of stimulated emission before it became possible to built a device which would produce such a coherent beam of light.

C H Townes, J P Gordon and H J Zieger built a device at Columbia University in 1953 which used ammonia to produce a coherent beam, not of light at optical wavelengths, but of microwave radiation. In the following year they published details in Molecular microwave oscillator and new hyperfine structures in the microwave spectrum of NH3. In 1958 A L Schawlow and C H Townes described how a device might amplify light by stimulated emission and the first such device was built in 1960 at the Hughes Research Laboratories by T H Maiman using a rod of ruby. Over the next few years many types of laser were built, some using a mixture of helium and neon, others carbon dioxide or organic dyes. Lasers are today in common use in applications such as laser printers, CD and DVD players, computer storage systems, guiding military hardware, accurate astronomical measurements, surgery and other medical applications and many others.

Article by: J J O'Connor and E F Robertson


August 2002

MacTutor History of Mathematics
[http://www-history.mcs.st-andrews.ac.uk/HistTopics/Light_2.html]