Basic Quantum Physics

What is Quantum Physics?

Quantum physics is a branch of science that deals with discrete, indivisible units of energy called quanta as described by the Quantum Theory.

Schrödinger's Cat

Remember a while ago I said there was a problem with the Copenhagen interpretation? Well, you now know enough of what quantum physics is to be able to discuss what it isn't, and by far the biggest thing it isn't is complete. Sure, the math seems to be complete, but the theory includes absolutely nothing that would tie the math to any physical reality we could imagine. Furthermore, quantum physics leaves us with a rather large open question: what is reality? The Copenhagen interpretation attempts to solve this problem by saying that reality is what is measured. However, the measuring device itself is then not real until it is measured. The problem, which is known as the measurement problem, is when does the cycle stop? Remember that when we last left Schrödinger he was muttering about the "quantum jumping." He never did get used to quantum physics, but, unlike Einstein, he was able to come up with a very real demonstration of just how incomplete the physical view of our world given by quantum physics really is. Imagine a box in which there is a radioactive source, a Geiger counter (or anything that records the presence of radioactive particles), a bottle of cyanide, and a cat. The detector is turned on for just long enough that there is a fifty-fifty chance that the radioactive material will decay. If the material does decay, the Geiger counter detects the particle and crushes the bottle of cyanide, killing the cat. If the material does not decay, the cat lives. To us outside the box, the time of detection is when the box is open. At that point, the wave function collapses and the cat either dies or lives. However, until the box is opened, the cat is both dead and alive. On one hand, the cat itself could be considered the detector; it's presence is enough to collapse the wave function. But in that case, would the presence of a rat be enough? Or an ameba? Where is the line drawn? On the other hand, what if you replace the cat with a human (named "Wigner's friend" after Eugene Wigner, the physicist who developed many derivations of the Schrödinger's cat experiment). The human is certainly able to collapse the wave function, yet to us outside the box the measurement is not taken until the box is opened. If we try to develop some sort of "quantum relativity" where each individual has his own view of the world, then what is to prevent the world from getting "out of sync" between observers? While there are many different interpretations that solve the problem of Schrödinger's Cat, one of which we will discuss shortly, none of them are satisfactory enough to have convinced a majority of physicists that the consequences of these interpretation s are better then the half dead cat. Furthermore, while these interpretations do prevent a half dead cat, they do not solve the underlying measurement problem. Until a better intrepretation surfaces, we are left with the Copenhagen interpretation and it's half dead cat. We can certainly understand how Schrödinger feels when he says, "I don't like it, and I'm sorry I ever had anything to do with it." Yet the problem doesn't go away; it is just left for the great thinkers of tomorrow.

Quantum Theory

There are five main ideas represented in Quantum Theory: 1.Energy is not continuous, but comes in small but discrete units. 2.The elementary particles behave both like particles and like waves. 3.The movement of these particles is inherently random. 4.It is physically impossible to know both the position and the momentum of a particle at the same time. The more precisely one is known, the less precise the measurement of the other is. 5.The atomic world is nothing like the world we live in.

The Infinity Problem

There is one last problem that we will discuss before moving on to the alternative interpretation. Unlike the others, this problem lies primarily in the mathematics of a certain part of quantum physics called quantum electrodynamics, or QED. This branch of quantum physics explains the electromagnetic interaction in quantum terms. The problem is, when you add the interaction particles and try to solve Schrödinger's wave equation, you get an electron with infinite mass, infinite energy, and infinite charge. There is no way to get rid of the infinities using valid mathematics, so, the theorists simply divide infinity by infinity and get whatever result the guys in the lab say the mass, energy, and charge should be51. Even fudging the math, the other results of QED are so powerful that most physicists ignore the infinities and use the theory anyway. As Paul Dirac, who was one of the physicists who published quantum equations before Schrödinger, said, "Sensible mathematics involves neglecting a quantity when it turns out to be small - not neglecting it just because it is infinitely great and you do not want it!".

The EPR Experiment

"God does not play dice" was Albert Einstein's reply to the Uncertainty Principle. Thus being his belief, he spent a good deal of his life after 1925 trying to determine both the position and the momentum of a particle. In 1935, Einstein and two other physicists, Podolski and Rosen, presented what is now known as the EPR paper in which they suggested a way to do just that. The idea is this: set up an interaction such that two particles are go off in opposite directions and do not interact with anything else. Wait until they are far apart, then measure the momentum of one and the position of the other. Because of conservation of momentum, you can determine the momentum of the particle not measured, so when you measure it's position you know both it's momentum and position. The only way quantum physics could be true is if the particles could communicate faster then the speed of light, which Einstein reasoned would be impossible because of his Theory of Relativity. In 1982, Alain Aspect, a French physicist, carried out the EPR experiment. He found that even if information needed to be communicated faster then light to prevent it, it was not possible to determine both the position and the momentum of a particle at the same time. This does not mean that it is possible to send a message faster then light, since viewing either one of the two particles gives no information about the other. It is only when both are seen that we find that quantum physics has agreed with the experiment. So does this mean relativity is wrong? No, it just means that the particles do not communicate by any means we know about. All we know is that every particle knows what every other particle it has ever interacted with is doing.

Particle/Wave Duality

Particle/wave duality is perhaps the easiest way to get aquatinted with quantum theory because it shows, in a few simple experiments, how different the atomic world is from our world.

The Wave Function

In 1926, just weeks after several other physicists had published equations describing quantum physics in terms of matrices, Erwin Schrödinger created quantum equations based on wave mathematics , a mathematical system that corresponds to the world we know much more then the matrices. After the initial shock, first Schrödinger himself then others proved that the equations were mathematically equivalent. Bohr then invited Schrödinger to Copenhagen where they found that Schrödinger's waves were in fact nothing like real waves. For one thing, each particle that was being described as a wave required three dimensions. Even worse, from Schrödinger's point of view, particles still jumped from one quantum state to another; even expressed in terms of waves space was still not continuous. Unfortunately, even today people try to imagine the atomic world as being a bunch of classical waves. As Schrödinger found out, this could not be further from the truth. The atomic world is nothing like our world, no matter how much we try to pretend it is. In many ways, the success of Schrödinger's equations has prevented people from thinking more deeply about the true nature of the atomic world.

The Uncertainty Principle

Newton figured that much out back in the early eighteenth century; just observe the position and momentum of the electron as it leaves the electron gun and we can determine exactly where it goes. How exactly are we to determine the position and the momentum of the electron? If we disturb the electrons just in seeing if they are there or not, how are we possibly going to determine both their position and momentum? Still, a clever enough person, say Albert Einstein, should be able to come up with something, right? Unfortunately not. Einstein did actually spend a good deal of his life trying to do just that and failed. Furthermore, it turns out that if it were possible to determine both the position and the momentum at the same time, Quantum Physics would collapse. Because of the latter, Werner Heisenberg proposed in 1925 that it is in fact physically impossible to do so. As he stated it in what now is called the Heisenberg Uncertainty Principle, if you determine an object's position with uncertainty x, there must be an uncertainty in momentum, p, such that xp > h/4pi, where h is Planck's constant. In other words, you can determine either the position or the momentum of an object as accurately as you like, but the act of doing so makes your measurement of the other property that much less. Human beings may someday build a device capable of transporting objects across the galaxy, but no one will ever be able to measure both the momentum and the position of an object at the same time. This applies not only to electrons but also to objects such as tennis balls and toasters, though for these objects the amount of uncertainty is so small compared to there size that it can safely be ignored under most circumstances

Many Worlds

One other interpretation, presented first by Hugh Everett III in 1957, is the many worlds or branching universe interpretation. In this theory, whenever a measurement takes place, the entire universe divides as many times as there are possible outcomes of the measurement. All universes are identical except for the outcome of that measurement. Unlike the science fiction view of "parallel universes", it is not possible for any of these worlds to interact with each other. While this creates an unthinkable number of different worlds, it does solve the problem of Schrödinger's cat. Instead of one cat, we now have two; one is dead, the other alive. However, it has still not solved the measurement problem! If the universe split every time there was more then one possibility, then we would not see the interference pattern in the electron experiment. So when does it split? No alternative interpretation has yet answered this question in a satisfactory way. And so the search continues...

The Copenhagen Interpretation

So sometimes a particle acts like a particle and other times it acts like a wave. So which is it? According to Niels Bohr, who worked in Copenhagen when he presented what is now known as the Copenhagen interpretation of quantum theory, the particle is what you measure it to be. When it looks like a particle, it is a particle. When it looks like a wave, it is a wave. Furthermore, it is meaningless to ascribe any properties or even existence to anything that has not been measured. Bohr is basically saying that nothing is real unless it is observed. While there are many other interpretations of quantum physics, all based on the Copenhagen interpretation, the Copenhagen interpretation is by far the most widely used because it provides a "generic" interpretation that does not try to say any more then can be proven. Even so, the Copenhagen interpretation does have a flaw that we will discuss later. Still, since after 70 years no one has been able to come up with an interpretation that works better then the Copenhagen interpretation.

The Quantum and Planck's Constant

So what is that h that was so important in the Uncertainty Principle? Well, technically speaking, it's 6.63 X 10^-34 joule-seconds. It's call Planck's constant after Max Planck who, in 1900, introduced it in the equation E=hv where E is the energy of each quantum of radiation and v is it's frequency. What this says is that energy is not continuous as everyone had assumed but only comes in certain finite sizes based on Planck's constant. At first physicists thought that this was just a neat mathematical trick Planck used to explain experimental results that did not agree with classical physics. Then, in 1904, Einstein used this idea to explain certain properties of light--he said that light was in fact a particle with energy E=hv. After that the idea that energy isn't continuous was taken as a fact of nature - and with amazing results. There was now a reason why electrons were only found in certain energy levels around the nucleus of an atom. Ironically, Einstein gave quantum theory the push it needed to become the valid theory it is today, though he would spend the rest of his lift trying to prove that it was not a true description of nature. Also, by combining Planck's constant, the constant of gravity, and the speed of light, it is possible to create a quantum of length (about 10^-35 meter) and a quantum of time (about 10^-43 sec), called, respectively, Planck's length and Planck's time. While saying that energy is not continuous might not be too startling to the average person, since what we commonly think of as energy is not all that well defined anyway, it is startling to say that there are quantities of space and time that cannot be broken up into smaller pieces. Yet it is exactly this that gives nature a finite number of routes to take when an electron interferes with itself. Although it may seem like the idea that energy is quantized is a minor part of quantum physics when compared with ghost electrons and the uncertainty principle, it really is a fundamental statement about nature that caused everything else we've talked about to be discovered. And it is always true. In the strange world of the atom, anything that can be taken for granted is a major step towards an "atomic world view".

The Collapse of the Wave Function

So why bring up the wave function at all if it hampers full appreciation of the atomic world? For one thing, the equations are much more familiar to physicists, so Schrödinger's equations are used much more often then the others. Also, it turns out that Bohr liked the idea and used it in his Copenhagen interpretation. Remember our experiment with electrons? Each possible route that the electron could take, called a ghost, could be described by a wave function. As we shall see later, the "quantum jumping" insures that there are only a finite, though large, number of possible routes. When no one is watching, the electron take every possible route and therefore interferes with itself. However, when the electron is observed, it is forced to choose one path. Bohr called this the "collapse of the wave function". The probability that a certain path will be chosen when the wave function collapses is, essentially, the square of the path's wave function . Bohr reasoned that nature likes to keep it possibilities open, and therefore follows every possible path. Only when observed is nature forced to choose only one path, so only then is just one path taken .