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 34 (which we will discuss shortly). 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.The EPR Experiment"God does not play dice" was Albert Einstein's reply to the Uncertainty Principle. 35 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 36. 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 37. 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 38. 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 other39. 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.The Quantum and Planck's ConstantSo what is that h that was so important in the Uncertainty Principle? Well, technically speaking, it's 6.63 X 10-34 joule-seconds 40. 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 frequency41. 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 42. 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 43. 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 44. 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". Schrödinger's CatRemember 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 "damned 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 45.On one hand, the cat itself could be considered the detector; it's presence is enough to collapse the wave function 46. But in that case, would the presence of a rat be enough? Or an ameba? Where is the line drawn 47? 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 48. 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."49 Yet the problem doesn't go away; it is just left for the great thinkers of tomorrow.The Infinity ProblemThere 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 charge50. 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 52. 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!". 53Many WorldsOne other interpretation, presented first by Hugh Everett III in 1957, is the many worlds or branching universe interpretation54. 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 55. Unlike the science fiction view of "parallel universes", it is not possible for any of these worlds to interact with each other 56.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 57! 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…Further ReadingIf you are interested in learning more about quantum physics, here are some books that you could try (check the bibliography for more specific information on the books you are interested in):Richard Feynman's Lectures on Physics deals with the math associated with quantum physics. If you can understand basic calculus, then this book is for you. Otherwise, while Lectures still provides some valuable information, you may find yourself lost before you get too far.John Gribbin's In Search of Schrödinger's Cat is an excellent non-mathematical treatment of quantum physics. If you've been watching the footnotes you've seen that much of the data for this paper came from this book. It includes a good history of quantum physics. Be advised that the sections on supergravity and supersymmetry at the end are outdated.Alastair Rae's Quantum Physics: Illusion or Reality presents the basics of quantum physics in terms of the polarization of light. It's 118 pages, half of which are devoted to a discussion of the alternate interpretations of quantum physics, can easily be read in an afternoon. It spends more time on alternate interpretations then Gribbin's book, but is less detailed in almost every other respect. I suggest reading Gribbin's book first then this book.