*Quantum Physics*

*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. There are five main ideas represented in Quantum Theory: Energy is not continuous, but comes in small but discrete units. 1 The elementary particles behave both like particles and like waves. 2 The movement of these particles is inherently random. 3 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.4 The atomic world is nothing like the world we live in. 5 While at a glance this may seem like just another strange theory, it contains many clues as to the fundamental nature of the universe and is more important then even relativity in the grand scheme of things (if any one thing at that level could be said to be more important then anything else). Furthermore, it describes the nature of the universe as being much different then the world we see. As Niels Bohr said, "Anyone who is not shocked by quantum theory has not understood it." 6Particle/Wave DualityParticle/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.First let's set up a generic situation to avoid repetition. In the center of the experiment is a wall with two slits in it. To the right we have a detector. What exactly the detector is varies from experiment to experiment, but it's purpose stays the same: detect how many of whatever we are sending through the experiment reaches each point. To the left of the wall we have the originating point of whatever it is we are going to send through the experiment. That's the experiment: send something through two slits and see what happens. For simplicity, assume that nothing bounces off of the walls in funny patterns to mess up the experiment. First try the experiment with bullets. Place a gun at the originating point and use a sandbar as the detector. First try covering one slit and see what happens. You get more bullets near the center of the slit and less as you get further away. When you cover the other slit, you see the same thing with respect to the other slit. Now open both slits. You get the sum of the result of opening each slit. 7 The most bullets are found in the middle of the two slits with less being found the further you get from the center. Well, that was fun. Let's try it on something more interesting: water waves. Place a wave generator at the originating point and detect using a wave detector that measures the height of the waves that pass. Try it with one slit closed. You see a result just like that of the bullets. With the other slit closed the result is the same. Now try it with both slits open. Instead of getting the sum of the results of each slit being open, you see a wavy pattern 8; in the center there is a wave greater then the sum of what appeared there each time only one slit was open. Next to that large wave was a wave much smaller then what appeared there during either of the two single slit runs. Then the pattern repeats; large wave, though not nearly as large as the center one, then small wave. This makes sense; in some places the waves reinforced each other creating a larger wave, in other places they canceled out. In the center there was the most overlap, and therefore the largest wave. In mathematical terms, instead of the resulting intensity being the sum of the squares of the heights of the waves, it is the square of the sum. While the result was different from the bullets, there is still nothing unusual about it; everyone has seen this effect when the waves from two stones that are dropped into a lake in different places overlap. The difference between this experiment and the previous one is easily explained by saying that while the bullets each went through only one slit, the waves each went through both slits and were thus able to interfere with themselves.Now try the experiment with electrons. Recall that electrons are negatively charged particles that make up the outer layers of the atom. Certainly they could only go through one slit at a time, so their pattern should look like that of the bullets, right? Let's find out. (NOTE: to actually perform this exact experiment would take detectors more advanced then any on earth at this time. However, the experiments have been done with neutron beams 9 and the results were the same as those presented here. A slightly different experiment was done to show that electrons would behave the same way 10. For reasons of familiarity, we speak of electrons here instead of neutrons.) Place an electron gun at the originating point and an electron detector in the detector place. First try opening only one slit, then just the other. The results are just like those of the bullets and the waves. Now open both slits. The result is just like the waves!11 There must be some explanation. After all, an electron couldn't go through both slits. Instead of a continuous stream of electrons, let's turn the electron gun down so that at any one time only one electron is in the experiment. Now the electrons won't be able to cause trouble since there is no one else to interfere with. The result should now look like the bullets. But it doesn't! 12 It would seem that the electrons do go through both slits. This is indeed a strange occurrence; we should watch them ourselves to make sure that this is indeed what is happening. So, we put a light behind the wall so that we can see a flash from the slit that the electron went through, or a flash from both slits if it went through both. Try the experiment again. As each electron passes through, there is a flash in only one of the two slits. So they do only go through one slit! But something else has happened too: the result now looks like the result of the bullets experiment!! 13 Obviously the light is causing problems. Perhaps if we turned down the intensity of the light, we would be able to see them without disturbing them. When we try this, we notice first that the flashes we see are the same size. Also, some electrons now get by without being detected. 14 This is because light is not continuous but made up of particles called photons. Turning down the intensity only lowers the number of photons given out by the light source.15 The particles that flash in one slit or the other behave like the bullets, while those that go undetected behave like waves16.Well, we are not about to be outsmarted by an electron, so instead of lowering the intensity of the light, why don't we lower the frequency. The lower the frequency the less the electron will be disturbed, so we can finally see what is actually going on. Lower the frequency slightly and try the experiment again. We see the bullet curve 17. After lowering it for a while, we finally see a curve that looks somewhat like that of the waves! There is one problem, though. Lowering the frequency of light is the same as increasing it's wavelength 18, and by the time the frequency of the light is low enough to detect the wave pattern the wavelength is longer then the distance between the slits so we can no longer see which slit the electron went through 19. So have the electrons outsmarted us? Perhaps, but they have also taught us one of the most fundamental lessons in quantum physics - an observation is only valid in the context of the experiment in which it was performed 20. If you want to say that something behaves a certain way or even exists, you must give the context of this behavior or existence since in another context it may behave differently or not exist at all. We can't just say that an electron is a particle, since we have already seen proof that this is not always the case. We can only say that when we observe the electron in the two slit experiment it behaves like a particle. To see how it would behave under different conditions, we must perform a different experiment.The Copenhagen InterpretationSo 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 measured21. 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, that is the one we will use. We will discuss one of the alternatives later.The Wave FunctionIn 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 mathematics22 , 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 23. 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 24. 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. Upon discovering this, Schrödinger remarked to Bohr that "Had I known that we were not going to get rid of this damned quantum jumping, I never would have involved myself in this business." 25Unfortunately, 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 26.The Collapse of the Wave FunctionSo 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 27. As we shall see later, the "damned 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 itself28. However, when the electron is observed, it is forced to choose one path. Bohr called this the "collapse of the wave function"29. The probability that a certain path will be chosen when the wave function collapses is, essentially, the square of the path's wave function 30.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 31.The Uncertainty PrincipleWait a minute… probability??? If we are going to destroy the wave pattern by observing the experiment, then we should at least be able to determine exactly where the electron goes. 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.Well, fine. But 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 32. 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 33. Because of the latter, Werner Heisenberg proposed in 1925 that it is in fact physically impossible to do so.*