Mauler's Layman's Guide to Quantum Mechanics
1. Very Large Particles = Newtonian Mechanics
Imagine several bullets are shot one at a time through two slits in a wall and hit another wall several feet behind the first wall. According to classical physics, any particle such as a bullet is subject to Newton’s laws of motion and therefore has mass, inertia, momentum, etc. Thus, each bullet could only travel in a straight line and would hit the second wall only in one of two very limited regions directly in line with the slits in the first wall.
2. Very Small Particles = Quantum Mechanics
When several photons are shot one at a time at a plate with two slits and hit a photosensitive screen behind the plate, the photons would land on all different parts of the screen, even those not directly in line with the slits. Measured over time, a pattern would emerge in which photons hit certain parts of the plate very often and other parts not at all, in a frequency pattern that could only be explained if the photons were acting as a wave. Somehow, even though they are shot one at a time, the photons are interfering with themselves like waves do, increasing the frequency in certain areas of the screen, and canceling it out in others. If light were a particle it would theoretically be limited by Newton’s laws and therefore produce a pattern similar to the one created by the bullets. According to classical physics, particles are incapable of diffracting and interfering to form a wave-like pattern and there is no way particles could curve around the solid sections of the slit plate to land in areas not in straight line paths from the "gun" unless an outside force acted upon them (which is not the case here). Thus, light must have wave properties.
3. Where Does This Lead Us?
If photons were true particles, no matter how many are released they should exhibit a distribution pattern similar to that of the bullets. Experiments show they do not. Rather, when many photons have been released, even just one at a time, the frequency distribution pattern measured over time is identical to the interference wave pattern. The only explanation for this phenomenon is that light somehow simultaneously acts as both a wave and a particle. Although Newton had once suggested that light was a hail of tiny particles, classical physicists became convinced (after much experimentation) that light is a wave. However, in 1905 Albert Einstein revived the particle theory of light because it was the only explanation for the photoelectric effect - the ejection of electrons from certain metals subjected to high-frequency light (even from a dim source). If light were a wave, low frequency light should also produce this same effect although it might take longer. However, only high-frequency light can cause the photoelectric effect. Einstein reasoned that light must be made be up of packets of energy (photons). Obviously, low-frequency light does not have enough energy in each packet to eject electrons, no mater how many packets there are. If this reasoning were correct, said Einstein, light must be made up of particles. This jived with Max Planck's quantum theory (1900) that radiation consists of "quanta," or individual packets of energy.
The next step in the puzzle came in 1924 when Louis de Broglie wondered, "If light can have both wave and particle properties, cannot all particles have wave properties?" De Broglie proved that all particles, even those things as large as a baseball, exhibit wave properties. His equation:
wavelength = Planck's constant / momentum
The effect of something as large as a baseball’s wave properties is negligible, however, because its mass is so great (momentum = mv), and therefore wavelength is effectively zero. Thus, thanks to De Broglie's equation, we can see that the examples of the bullets and the photons that at first appeared so different are both part of the same phenomenon!
In 1925, Erwin Schrodinger came up with an equation whose solution is known as the wave function. Schrodinger applied his wave function to the atom, theorizing that it represented the physical orbit of an electron around the nucleus. Thus, Schrodinger accounted for the energy levels of electrons in atoms (circumferences must be whole number multiples of the wavelength).
To account for the collapse of the wave function when only a single photon is launched in the two slit experiment, Max Born postulated in 1926 that the wave function was not physical as Schrodinger had contended, but rather, was a probability wave akin to a "crime wave" or mortality table that simply shows the probability of a particle being in a given location. Thus, the wave function collapses when only a single photon is launched because once the photon is detected the probability of it being located anywhere else becomes zero and the wave ceases to exist.
4. The Uncertainty Principle
Werner Heisenberg’s "Uncertainty Principle" is the idea that one can never be certain of both the momentum and the position of a particle or both the energy of a particle and the time it has that energy. The more one is certain of one element, the less one is certain of the other. This uncertainty increases the smaller the units one is trying to observe. With very large objects, uncertainty becomes negligible. The Uncertainty Principle is based upon the fact that we cannot observe anything without our observation effecting it in some way.
"Position" and "momentum" are not properties of particles. Rather, they are artificial concepts we have created to help us describe particles. Too often, we confuse words and language - abstract human creations - with actual reality. Language is not reality but only a crude (though the best we have) method for describing reality. Niels Bohr recognized this distinction. Bohr realized that physics cannot discover reality. Physics can only attempt to describe reality as closely as possible. What Bohr is saying is that one must give up the idea of an objective reality outside human experience in order to predict the outcomes of experiments. This loss of objective truth is the heavy price paid in exchange for the power of prediction.
5. Some Theories to Explain Quantum Mechanics
In Niels Bohr’s "Copenhagen Interpretation," Heisenberg's Uncertainty Principle reigns supreme. The collapse of the wave function is completely random and entirely uncertain. When the wave function collapses, the fuzzy, nebulous, ghostly world of the atom materializes into a random but concrete reality. The cause of the collapse is human observation.
Albert Einstein’s "Hidden Variables Theory" is the belief that "God does not play dice." For Einstein, concrete reality always exists, but quantum mechanics is not a good enough system to describe it outside of human observation. There are hidden factors behind the scenes: all events happen for a reason. For Einstein, the word "random" was just an easy way to explain away our own ignorance. Einstein dreamed up an experiment to support his view. Suppose, he said, a particle explodes into two fragments which are allowed to travel a long distance. Each fragment should demonstrate evidence of the other through action/reaction, Einstein believed. In the 1960s, John Bell proved the existence of a limit to the degree of cooperation between the two fragments if Einstein was correct. In experiments conducted by Alain Aspect in 1981, this limit was exceeded, proving Einstein wrong.
Hugh Everett’s "Many Worlds Theory" is the belief that for every possible outcome of an uncertain event a new universe in which that outcome occurs is created in some parallel yet utterly unreachable dimension. Thus the paradox of the ghostly simultaneous existence of contradictory outcomes until an observation is made is avoided. A good example is the paradox of Schrodinger’s Cat, in which a cat has a 50% chance of dying of cyanide poisoning. The Many Worlds Theory bypasses the unfathomable concept that the cat is in a limbo-like state of both life and death until human observation by stating that the cat either dies or does not die in our reality. If the cat dies in our reality, it lives in another reality. If it lives in our universe, it dies in another, parallel universe (Now you know where Star Trek got all its plots).
The "Mind Over Matter Theory" is the belief that the human mind is fundamental in the creation of reality: human consciousness alone is responsible for the reality we perceive around us. In 1979, John Wheeler demonstrated that a simple modification of the two slit apparatus could delay the decision of whether to measure location or momentum until after the photon has passed through the screen. Thus, humans can affect reality in the past, after it has occurred! The Mind Over Matter concept is further supported by the experiments of John von Neumann and the hypothesis of Eugene Wigner, which seem to indicate that quantum theory breaks down when it comes into contact with the human mind. If a human replaces Schrodinger’s cat, does he or she experience both life and death? No, says Wigner. However, many physicists reject Mind Over Matter because it can be used to support paranormal phenomena.