At the turn of the century, scientists thought that all the basic rules like this should apply to everything in nature -- but then they began to study the world of the ultra-small. Atoms, electrons, light waves, none of these things followed the normal rules. As physicists like Niels Bohr and Albert Einstein began to study particles, they discovered new physics laws that were downright quirky. These were the laws of quantum mechanics, and they got their name from the work of Max Planck.
"An Act of Desperation"
In 1900, Max Planck was a physicist in Berlin studying something called the "ultraviolet catastrophe." The problem was the laws of physics predicted that if you heat up a box in such a way that no light can get out (known as a "black box"), it should produce an infinite amount of ultraviolet radiation. In real life no such thing happened: the box radiated different colors, red, blue, white, just as heated metal does, but there was no infinite amount of anything. It didn't make sense. These were laws of physics that perfectly described how light behaved outside of the box -- why didn't they accurately describe this black box scenario?
Planck tried a mathematical trick. He presumed that the light wasn't really a continuous wave as everyone assumed, but perhaps could exist with only specific amounts, or "quanta," of energy. Planck didn't really believe this was true about light, in fact he later referred to this math gimmick as "an act of desperation." But with this adjustment, the equations worked, accurately describing the box's radiation.
It took awhile for everyone to agree on what this meant, but eventually Albert Einstein interpreted Planck's equations to mean that light can be thought of as discrete particles, just like electrons or protons. In 1926, Berkeley physicist Gilbert Lewis named them photons.
Quanta, quanta everywhere
This idea that particles could only contain lumps of energy in certain sizes moved into other areas of physics as well. Over the next decade, Niels Bohr pulled it into his description of how an atom worked. He said that electrons traveling around a nucleus couldn't have arbitrarily small or arbitrarily large amounts of energy, they could only have multiples of a standard "quantum" of energy.
Eventually scientists realized this explained why some materials are conductors of electricity and some aren't -- since atoms with differing energy electron orbits conduct electricity differently. This understanding was crucial to building a transistor, since the crystal at its core is made by mixing materials with varying amounts of conductivity.
But They're Waves Too
Here's one of the quirky things about quantum mechanics: just because an electron or a photon can be thought of as a particle, doesn't mean they can't still be though of as a wave as well. In fact, in a lot of experiments light acts much more like a wave than like a particle.
This wave nature produces some interesting effects. For example, if an electron traveling around a nucleus behaves like a wave, then its position at any one time becomes fuzzy. Instead of being in a concrete point, the electron is smeared out in space. This smearing means that electrons don't always travel quite the way one would expect. Unlike water flowing along in one direction through a hose, electrons traveling along as electrical current can sometimes follow weird paths, especially if they're moving near the surface of a material. Moreover, electrons acting like a wave can sometimes burrow right through a barrier. Understanding this odd behavior of electrons was necessary as scientists tried to control how current flowed through the first transistors.
So which is it - a particle or a wave?
Scientists interpret quantum mechanics to mean that a tiny piece of material like a photon or electron is both a particle and a wave. It can be either, depending on how one looks at it or what kind of an experiment one is doing. In fact, it might be more accurate to say that photons and electrons are neither a particle or a wave -- they're undefined up until the very moment someone looks at them or performs an experiment, thus forcing them to be either a particle or a wave.
This comes with other side effects: namely that a number of qualities for particles aren't well-defined. For example, there is a theory by Werner Heisenberg called the Uncertainty Principle. It states that if a researcher wants to measure the speed and position of a particle, he can't do both very accurately. If he measures the speed carefully, then he can't measure the position nearly as well. This doesn't just mean he doesn't have good enough measurement tools -- it's more fundamental than that. If the speed is well-established then there simply does not exist a well-established position (the electron is smeared out like a wave) and vice versa.
Albert Einstein disliked this idea. When confronted with the notion that the laws of physics left room for such vagueness he announced: "God does not play dice with the universe." Nevertheless, most physicists today accept the laws of quantum mechanics as an accurate description of the subatomic world. And certainly it was a thorough understanding of these new laws which helped Bardeen, Brattain, and Shockley invent the transistor.
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