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Electrons As Waves
It ought not be surprising should particle wave dualism work in reverse, so that phenomena ordinarily considered wavelike in nature should have particle characteristics as well. Planck and Einstein had already shown radiation to consist of quanta, which, in a fashion, are particles. In 1923, Compton, the physicist who was to demonstrate the particle nature of cosmic rays, showed that such quanta possessed some down-to-earth particle qualities. He found that x-rays, on being scattered by matter, lose energy and become longer in wavelength. This effect was just what might be expected of a radiation "particle" bouncing off a matter particle: the matter particle is pushed forward, gaining energy; and the x-ray veers off, losing energy. This Compton effect helped establish the wave-particle dualism.

The matter waves had important consequences for theory, too. For one thing, they cleared up some puzzles about the structure of the atom.

In 1913, Niels Bohr had pictured the hydrogen atom, in the light of the recently propounded quantum theory, as consisting of a central nucleus surrounded by an electron that could circle that nucleus in any one of a number of orbits. These orbits are in fixed positions; if a hydrogen electron drops from an outer orbit to an inner one, it loses energy, emitting that energy in the form of a quantum possessing a fixed wavelength. If the electron were to move from the inner electron to an outer one, it would have to absorb a quantity of energy, but only one of a fixed size wavelength just enough to move it by the proper amount. Hence, hydrogen can absorb or emit only certain wavelengths of radiation, producing characteristic lines in the spectrum. Bohr's scheme, which was made gradually more complex the next decade - notably by the German physicist Arnold Johannes Sommerfield, who introduced elliptical orbits as well - was highly successful in explaining many facts about the spectra of various elements. Bohr was awarded the Nobel Prize in physics in 1922 for this theory. The German physicists James Franck and Gustav Ludwig Hertz (the latter a nephew of Heinrich Hertz), whose studies on collisions between atoms and electrons lent an experimental foundation to Bohr's theories, shared the Nobel Prize in physics in 1925.

Bohr had no explanation of why the orbits were fixed in the positions they held. He simply chose the orbits that would give the correct results, so far as absorption and emission of the actually observed wavelength of light were concerned.

In 1926, the German physicist Erwin Schrödinger decided to take another look at the atom in the light of the de Broglie theory of the wave nature of particles. Considering the electron has always, as a wave, he decided that the electron does not circle around the nucleus as a planet circles around the sun but constitutes a wave that was all around the nucleus, so that it is in all parts of its orbit at once so to speak. It turned out that, on the basis of the wavelength predicted by de Broglie for an electron, a whole number of electron waves would exactly fit the orbits outlined by Bohr. Between the orbits, the waves would not fit in a whole number but would join up out of phase; and such orbits could not be stable.

Schrödinger worked out a mathematical description of the atom called wave mechanics or quantum mechanics, which became a more satisfactory method of looking at the atom than the Bohr system had been. Schrödinger shared the Nobel Prize in 1933 with Dirac, the author of the theory of antiparticles, who also contributed to the development of this new picture of the atom. The German physicist Max Born, who contributed further to the mathematical development of quantum mechanics, shared in the Nobel Prize in physics in 1954.

The Uncertainty Principle
By this time the electron had become a pretty vague "particle" - a vagueness soon to grow worse. Werner Heisenberg of Germany proceeded to raise a profound question that projected particles, and physics itself, almost into a realm of the unknowable.

Heisenberg had presented his own model of the atom. He had abandoned all attempts to picture the atom as composed either of particles or waves. He decided that any attempt to draw an analogy between atomic structure and the structure of the world about us is doomed to failure. Instead, he described the energy levels or orbits of electrons purely in terms of numbers, without a trace of picture. Since he used a mathematical device called a matrix to manipulate these numbers, the system was called matrix mechanics.

Heisenberg received the Nobel Prize in physics in 1932 for his contributions to quantum mechanics, but his matrix system was less popular with physicists than Schrödinger's wave mechanics, since the latter seemed just as useful as Heisenberg's abstractions, and it is difficult or even physicists to force themselves to abandon the attempt to picture what they are talking about.

By 1944, physicists seem to have done the correct thing, Former Hungarian - American mathematician John von Neumann presented a line of argument that seemed to show that matrix mechanics and wave mechanics are mathematically equivalent: everything demonstrated by one could be equally well demonstrated by the other. Why not, therefore, choose the less abstract version?

After having introduced matrix mechanics (to jump back in time again), Heisenberg went on to consider the problem of describing the position of your particle. How can one determine where a particle is? The obvious answer is: Look at it. Well, let us imagine a microscope they could make an electron visible. We must shine a light or some appropriate kind of radiation on it to see it. But an electron is so small that a single photon of light striking it would move it and change its position. In the very act of measuring its position, we would have changed that position.

This is a phenomenon occurs in ordinary life. When we measure the air pressure in a tyre with a gauge, we let a little out of the tyre and change the pressure slightly. Likewise, when we put a thermometer in a bathtub of water to measure the temperature, the thermometers absorption of heat changes the temperature slightly. A meter measuring electric current takes away a little current for moving the pointer on the dial. And so it goes in every measurement of any kind that we make.

However, in all ordinary measurements, the change in the subject we are measuring is so small we can ignore it. The situation is quite different when we come to look at the electron. Our measuring device is now at least as large as the thing we are measuring; there is no usable measuring agent smaller than the electron. Consequently our measurements must inevitably have, not a negligible, but a decisive, effect on the object measured. We could stop the electron and so determine its position at a given instant. But in that case, we could not know its motion or velocity. On the other hand, we might record its velocity, but then we could not fix its position at any given moment.

Heisenberg showed that there is no way of devising a method of pinpointing the position of a subatomic particle unless you are willing to be quite uncertain about its exact motion. And, in reverse, there is no way of pinpointing a particles exact motion unless you are willing to be quite uncertain about its exact position. To calculate both exactly, at the same instant of time, is impossible.

If Heisenberg was right, then even at absolute zero, there cannot be complete lack of energy. In energy reaches zero and particles became completely motionless, then only position need to be determined since velocity could be taken as zero. It would be expected, therefore, that some residual zero-point energy must remain, even at absolute zero, to keep particles in motion and, so to speak, uncertain. It is this zero-point energy, which cannot be removed, that is sufficient to keep helium liquid even at absolute zero.

In 1930, Einstein showed that the uncertainty principle, which stated it is impossible to reduce the error in position without increasing the error in momentum, implied that it is also impossible to reduce the error in measurement of energy without increasing the uncertainty of time during which the measurement can take place. He thought he could use this idea as a springboard to disprove the uncertainty principle, but Bohr proceeded to show that Einstein's attempted disproof was wrong.

Indeed, Einstein's version of uncertainty proved very useful, since it meant that in subatomic processes, the law of conservation of energy can be violated for very brief periods of time, provided all is brought back to the conservational state by the end of those periods: the greater the deviation from conservation, the briefer the time interval allowed (Yukawa used this notion in working out his theory of pions). It was even possible to explain certain subatomic phenomena by assuming that particles are produced out of nothing in defiance of energy conservation, but ceased to exist before the time allotted for their detection, so that they are only virtual particles. The theory of virtual particles was worked out in the late 1940 years by three men: the American physicists Julian Schwinger and Richard Phillips Feynman, and the Japanese physicist Sin itiro Tomonaga. The three were jointly awarded the 1965 Nobel Prize in physics in consequence.

There have even been speculations, since 1976, that the universe began as a tiny, but massive, virtual particle that expanded with extreme quickness and remained in existence. The universe, in this view, formed itself out of Nothing, and we may wonder about there possibly being an infinite number of universes forming (and eventually ending) in an infinite volume of Nothing.

The uncertainty principle has profoundly affected the thinking of physicists and philosophers. It had a direct bearing on the philosophical question of causality (that is, the relationship of cause and effect). But its implications for science are not those that are commonly supposed. One often reads that the principle of indeterminacy removes all certainty for nature and shows that science after all does not and never can know what is really going on, that scientific knowledge is at the mercy of the unpredictable whims of a universe in which effect does not necessarily follow cause. Whether this interpretation is valid from the standpoint of philosophy, the principle of uncertainty has in no way shaken the attitude of scientists towards scientific investigation. If, for instance, the behaviour of the individual molecule in a gas cannot be predicted with certainty, nevertheless on the average the molecules do obey certain rules, and their behaviour can be predicted on a statistical basis, just as insurance companies can calculate reliable mortality tables even though it is impossible to predict when any particular individual will die.

In most scientific observations indeed, the indeterminacy is so small compared with the scale of measurement involved than it can be neglected for all practical purposes. One can determine simultaneously both the position on the motion of a star, of a planet, of a billiard ball, or even of a grain of sand, with complete satisfactory accuracy.

As the uncertainty among the subatomic particles themselves this does not hinder but actually helps physicists. It has been used to explain facts about radioactivity and about the absorption of subatomic particle by nuclei, as well as many other subatomic events, more reasonably than would have been possible without the uncertainty principle.

The uncertainty principle means that the universe is more complex than was thought, but not that it is irrational.

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