The Science of the Really Small

Quantum Mechanics

Energy is quantized

Wave-particle duality

The Heisenburg Uncertainty Principle

What is Quantum Mechanics? The theory of quantum mechanics was introduced when physicists found that the classical theories could not describe the behavior of particles on the atomic scale. Newtonian physics was inadequate and its predictions incorrect when concerning certain phenomena, such the photoelectric effect. This disparity between prediction and reality led Max Plank to formulate the foundations of quantum theory. Others such as Einstien, Bohr, Schrödinger, de Broglie,Heisenberg, Born, and Dirac further refined it. Quantum mechanics describes several areas that classical physics cannot. Here are some key points of quantum theory: Energy is quantized It is made of fundamental units, indivisible packets of energy. This theory was first proposed by Plank to explain the photoelectric effect. For instance, humans are quantized. You can have 1 human, 2 humans, 3 humans, or 100 humans, but you can’t have ½ a human. On the other hand, the number line is not quantized. It is continuous. It doesn’t matter which two numbers you pick, there’s always another number between them. You can divide it into an infinite number of pieces. So something that is quantized is like a staircase—it must jump up by steps. But a continuous thing is like a ramp—you can take it in any increments you like. Spin is quantized. All particles have "spin", or intrinsic angular momentum. The properties of this "spin" are just like those of a spinning, charged object. But you can’t really visualize particles spinning like a top, because to have the amount of angular momentum that they have, they would have to be spinning faster than light. So "spin" is an innate property of matter. It is quantized, and comes only in increments of 1 and ½. So you can have ½ spin, 1 spin, or 1½ spin, but never ¼ spin. Particles with spins that are increments of whole numbers (1, 2, 3…) are called bosons. Particles with increments of ½ are called fermions. All particles have spin, and thus all are either bosons or fermions. The most commonly known quanta are photons, discrete units of light energy. Return to top. Wave-particle duality In the beginning, there was light. And some said the light was made of particles, while others said the light was made of waves. Neither theory managed to encompass the full nature of light or the seemingly contradictory results of experiments. In some experiments, light would diffract (see Diffraction Grating, indicating a wave nature. In others, it would appear to be a particle, as the photoelectric effect indicated. Finally, Louis de Broglie resolved the conflict by proposing that matter and light have a dual nature. They can behave as both waves and particles. The wave nature of matter can be thought of as the probability wave of where the particle could be. So…if waves can act as particles, then can particles act as waves? Absolutely. Electrons have been shown to diffract like waves under the proper conditions. All particles, including you and I, have wavelengths. But you’ll never find a person (or even your pet rat) being diffracted, because as particles get larger, their wavelengths get smaller. For particles on a macroscopic scale, the wavelengths are so small we can’t make slits small enough to diffract them. Return to top. The Heisenburg Uncertainty Principle, This states that it is impossible to perfectly measure a particle’s position and velocity at the same time. The more accurately you measure a particle’s position, the more inaccurate your measure of its velocity, and vice versa. The reason is that to measure something, we must affect it. So by measuring, we disturb the "true nature" of that something, and therefore cannot with perfect accuracy find out its position and momentum. Imagine you are in a dark room, blindfolded. There is a large elephant walking across the room (it’s a really big room), and the only way that you can find out its location is by throwing ping pong balls at it. You can find out pretty accurately where it is, where it is going, and how fast it is going if you throw lots of ping pong balls at it. Now, imagine that same situation, but this time you want to find out information about a paper airplane that someone threw across the room. You can throw lots of ping pong balls at it, but when they hit the paper airplane they are going to move it. So you are faced with a problem. If you throw lots of ping pong balls you will know almost exactly where it is, but very little about how fast and in what direction it was originally going. If you throw just a few ping pong balls at it, you can figure out its speed and direction fairly accurately, but not its location. You can’t find out measure both things perfectly at the same time. The same sort of thing occurs on the quantum level. At a macroscopic level, the effects of the uncertainty principle are not obvious—a few photons bouncing off your couch aren’t going to move it perceptibly. But on the quantum level, when the thing you’re looking at isn’t a whole lot bigger than a photon, you really see the uncertainty principle at work. For instance, if you want to find out where an electron is, you have to bounce a photon off it. When you do so, you are going to move the electron from its original location. The more photons you bounce off the electron, the more precisely you’ll know where it was at the moment that the photon bounced off of it. But because all those photons are going to affect the motion of the electron, you will have very little idea what its original velocity (speed and direction) was. Or, you can shoot very few photons at the electron and get a very good idea of how fast it is moving and in what direction. But you will not know with much precision where the electron actually is. So it is impossible to perfectly measure a particle’s position and velocity at the same time. The Heisenburg Uncertainty Principle helps explain why some experimenters showed light behaving as a wave while others showed it behaving as a particle. The more accurately an experiment tries to measure the wave characteristics of light, the less accurately it will measure light’s particle characteristics. The opposite is also true. The clearer the particle characteristics of light are shown, the less clear the wave characteristics of light are seen. Return to top.   “Spin and Polarization.” Dixon, G. Harrison, D. Serway, R. A., & Faughn, J. S. Stedl, T. Thomas, D. “Spin.” Thomas, D. “Blackbody Radiation."