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Einstein's theories of relativity were developed in a way close to Descartes' mathematical-deductive method. The special theory came from an attempt to harmonize electromagnetic theory with the principle of relativity. The general theory evolved from trying to reconcile the fact that inertial mass, the "resistance" to the force in the equation F=ma, has the same value as gravitational mass, even though the two are totally unrelated in Newtonian mechanics. Quantum physics, on the other hand, emerged from attempts to explain experimental observations. In the late 1800s a major area of research centred on the explanation of "blackbody" radiation: a black object such as a fireplace poker, when heated until it begins to glow, emits light whose intensity depends on wavelength in a way which depends largely on the temperature of the body and little on its material of construction. Because of the universal nature of this phenomenon, it was apparent that it must depend on fundamental physical principles. In 1900 Max Planck used a "lucky guess" [Jammer p.19] to obtain a mathematical equation which fitted the experimental data accurately. Three months later he derived the expression theoretically. To do this he assumed that a blackbody contained many small oscillators which emitted the light, much the way the oscillations of electrons along a transmission antenna emit radio waves. However, he had to allow these oscillators to emit energy only at certain frequencies rather than with a continuous range of frequencies, as would be expected from classical electromagnetism. Planck had no physical basis for this assumption; it was just the only way that he could fit the data. Einstein used Planck's idea in his explanation of the photoelectric effect, in which electrons are ejected from a metal when it is exposed to light whose frequency exceeds a certain value. Einstein extended Planck's ideas on the emission of light from a blackbody to the general statement that light, itself, came in packets of energy, or quanta (called "photons" from the Greek "photos" meaning "light"). Each quantum has an energy E=hf, where f is the frequency of light and h is "Planck's constant". This was a bold move, since the work of Young and Fresnel had seemed to establish beyond all doubt that light acted as a wave, and Maxwell's theory did not include any mention of a particle nature to light. However, Einstein's assumption explained the fact that even an intense light below a certain frequency could not cause the emission of electrons: if each incoming light quantum gave all its energy to an electron in the metal, the electron could not escape if this energy was less than the binding energy of the electron. This explanation dismayed Planck, who never expected his suggestion to be applied so broadly. In 1911 Ernest Rutherford fired very small particles, emitted in radioactive decay, at a thin film of gold. From the scattering pattern of the particles, he determined that the atom consisted of a small, heavy, positively charged nucleus surrounded by very light electrons. Niels Bohr used this model and the quantum ideas of Planck and Einstein in 1913 to explain why the light from gas discharges was emitted at only a few, discrete frequencies; this light formed emission "lines" of different colours when the light was passed through a slit and dispersed by a prism. Bohr suggested that the electrons in an atom were only allowed to occupy certain orbits of definite radius r around the nucleus, namely orbits whose angular momentum was given by mvr=nh/2p where m and v are the mass and velocity of the electron, and n is an integer. When an electron gained energy and was "excited" to a higher orbit during the gas discharge, it could lose this energy only by falling back to one of the lower allowed orbits, with its energy loss DE being carried off by the emission of a quantum of light of energy f=DE/h. The predicted frequencies for hydrogen matched the experimental values. Beginning with the claim that mechanical models such as Bohr's were inappropriate because they tried to use the mechanics which had been developed for macroscopic bodies in situations where it might not apply, Werner Heisenberg in 1925 derived a purely mathematical theory that incorporated directly the empirical data, such as the wavelengths of spectral lines. The same year, Louis de Broglie argued that if light could act both as a wave and as a particle (photon) with definite energy, then perhaps material particles such as electrons could as well. He suggested that such a particle should have a wavelength given by l=h/mv, where m is the particle's mass and v is its velocity. By the next year, de Broglie's hypothesis had been used by Erwin Schrödinger to explain the quantization of Bohr's orbits. Moreover, Schrödinger showed that his wave mechanics was equivalent to Heisenberg's theory. By 1927, C.J. Davisson and L.H. Germer had confirmed de Broglie's hypothesis directly by producing a diffraction pattern by scattering electrons from the ordered atoms on the surface of a nickel sample, much like the two-slit interference pattern used by Thomas Young to prove that light behaved as a wave. This result is impossible if we consider the electron as a classical particle: it means that the electron must scatter off more than one nickel atom simultaneously or, in the two-slit analogy, go through both slits at the same time! Rather than placing the electrons in the atom in definite orbits as envisioned by Bohr, Schrödinger's wave mechanics, as interpreted by Born, treated the square of the particle's wave amplitude y as giving the probability that the electron was at a particular place in space, with the most probable positions corresponding to Bohr's orbits. From this discussion it is clear that we are treating the electron both as a particle and a wave. Consider Young's two-slit experiment again, but using electrons instead of light as the incident radiation. Suppose we position a fluorescent screen behind the two holes, and decrease the intensity of the electron beam until only one electron hits the screen at a time. Experimentally we see that each electron produces a tiny flash on the screen, as though it were struck by a particle rather than a wave. However, the number of particles arriving in a given region of the screen is greater where the diffraction pattern has its maxima. The electron acts like a particle when we demand a particle-like response, but like a wave when we demand a wave-like response. This is the conclusion come to by Bohr, in establishing his "principle of complementarity": the wave and particle descriptions of matter (or electromagnetic radiation) are complementary, in the sense that our experiments can test for one or the other, but never for both properties at the same time. In 1927 Heisenberg proved that it was impossible to determine both a particle's position and momentum with arbitrary precision; if one is known very accurately, then the uncertainty in the other becomes large. This "Uncertainty Principle" showed that there are theoretical limits on a person's ability to describe the world. The limits are not a serious consideration for large bodies, but become very important for bodies the size of an atom or smaller. The uncertainty principle also makes it clear that the presence of the experimenter always affects the results of an experiment at some level. For example, if we try to determine the position of a small particle very accurately we must, in principle, change its momentum by the very act of observing it. Quantum mechanics has now been extended to explain a wide range of phenomena at the sub-microscopic level, including the structure of the atomic nucleus. Experimentally, this structure has been determined in a manner similar in principle to Rutherford's scattering experiment, using accelerators which produce incident particles of very high energy. Philosophically, the developments of quantum mechanics were far-reaching. Like relativity, they again showed that humans could not assume that the physical laws which seem to govern a 60-kg person moving at speeds up to several hundred kilometres per hour also applied to bodies far from this regime. They also brought into question the assumption of the perfectly deterministic world proposed by Laplace. Clearly it was impossible to predict the position and velocity of every body for all future times if you could not even know these coordinates accurately at a single instant in time. This conclusion has even been used as the basis of the claim that humans have free will, that all is not predetermined as would seem to be the case in a purely mechanistic, deterministic world governed by the laws of physics. These ideas are still heavily debated today, as in a recent article by Roger Penrose in the book Quantum Implications. Indeed, Einstein himself was never able to accept fully the uncertainty implied in quantum mechanics, declaring that he did not believe that God played dice (Clark, pp.414,415). In an attempt to show that quantum theory was at variance with the real world, he helped develop the Einstein-Podolsky-Rosen (EPR) paradox, a "thought experiment" which shows that quantum mechanical theory must lead to what seems like an impossible situation: what you do to one particle can affect a second, even if they are sufficiently separated in space that a light signal could not pass from the first to the second fast enough to cause the observed effect. That is, either the knowledge of the event can travel between the particles faster than the speed of light, or the two particles really are not separate but remain interconnected in some fundamental sense. It was the latter option which was under debate. An experiment designed to test this hypothesis was carried out by D. Aspect and coworkers in 1981 [Physical Review Letters 47,460 (1981) and 49, 91 (1982)] and was shown to confirm what was predicted: the two particles really were connected over large distances by "non-local" forces acting instantaneously. That is, the EPR paradox, rather than showing a basic inconsistency in quantum theory, actually points to one more aspect of nature that contravenes common sense. |
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