# Quantum Mechanics 3/9/19

By Richard E. Bleil, Ph.D.

The quantum universe has become a very popular subject among sci-fi authors. And why not? The subject has sparked the imaginations of scientists and non-scientists alike.

Physics is the study of energy, and energy makes up everything. Even Einstein’s famous equation relates energy to mass, paving the road to explain how sufficient energy can give rise to matter. Classical physics, known as “Newtonian Physics”, traces its roots back to Sir Isaac Newton, who, when an apple fell on his head, said “OW! What the…??”

Newton developed the three laws of motion. These laws provide great predictive capabilities, and are based on the concept that we can simultaneously know position and velocity exactly. When I was in high school, our physics class did a very interesting experiment where we measured the velocity of a marble on a table without allowing it to fall off of the table. Based on that velocity, the height of the table and the known acceleration constant due to gravity, we had to predict where, precisely, the marble would hit the floor. The teacher came around with a small paper cup, we placed it on the floor, and as he watched we had to let the marble run off of the table. If the marble fell into the cup, we passed. Otherwise, well, it was an unforgiving experiment.

As subatomic particles were being discovered, and their properties studied, it became clear that they didn’t follow the same rules that we, you and I, follow. For one thing, it seems they can’t even decide if they are particles or waves. DeBroglie figured this one out, showing that they are so small, and travel so fast that their wave behavior is significant.

Enter Heisenberg, who became famous for saying, “I dunno!” Heisenberg’s Uncertainty principle proved, mathematically, the limitations of Newtonian Physics. As it turns out, we cannot know both velocity and position simultaneously after all. This means that Newtonian Physics fails at the subatomic level. The physicists then did something that scientists are famous for when faced something unexpected: they gave up.

Actually, no, they didn’t. Scientists love a good mystery, and it was Schrodinger who put it together. He decided that, if, indeed, we cannot know exactly what the electrons are doing, then perhaps we can know what they are probably doing. If you think of your favorite living actor, do you know exactly where that individual is at this moment? Probably not, but if you wanted to meet that actor, where would you go where you are most likely to meet her or him? This is what Schroedinger’s equation does for us. It tells us where we are most likely to find those electrons.

But the behavior of these particles is, well, impossible. For example, Schrodinger shows us things like nodes and nodal planes. These are points or planes where the electron is never allowed to exist, but, somehow, it can exist on both sides of this plane. How is this possible? We don’t know, because we, you and I, are classical beasts. Does an individual electron simultaneously exist on both sides of that wall at once? Or does it simply cease existing at one location and begin existing at another? Either answer is impossible by our understanding of physics.

If we had a quantum friend Quanta here with us today, the reality is that our behavior would seem equally impossible to Quanta. If you drive today, you will hit your top velocity of, oh, let’s say forty miles per hour. But, we don’t just go from zero to forty. In fact, we will pass through every velocity between zero and forty, which would seem impossible to our buddy Quanta. This is because our quantum friend is restricted as to what velocities are allowed. We call these energy levels “discrete”, so Quanta can be zero, for forty, but never anything in between.

At this point, the astute reader might naturally start wondering, if the behavior of quantum particles is really so odd, how do we know that quantum theory is correct? There are a couple of strong arguments that demonstrate the validity of quantum theory. First of all, the theory has incredible predictive power.

If the theory provided no useful insights, there would, quite frankly, be no reason for it. Quantum theory can not only explain behavior that was heretofore impossible to explain, but it also predicts behavior. Everything that quantum theory has been able to predict has been tested, and, to date, has always proven not just to be correct, but absolutely exactly accurate.

For example, in benzene a very odd thing happens. There are double bonds between every other pairs of atoms, but they can be reversed as well. For example, single-double-single-double or double-single-double-single. The first thought of anybody learning of this is to think that the double bonds “flip” from one location to another. Quantum theory, however, predicts that the electrons do not flip at all, but rather smear themselves out into a kind of plate above and below the carbon ring of benzene in a process called “hybridization”. Every time a newer faster and more accurate spectrometer is developed, one of the first thing it is used for is to try to find that “flipping rate” of the double bonds moving back and forth, but, alas, to date…to no avail.

The second thing, though, is that quantum theory allows scientists to develop some really off-the-wall experiments, and these experiments work. As it turns out, there are two quantum orientations of electrons. They can be spin up, or spin down, but the meaning of spin is not as overtly simplistic as many modern science textbooks lead one to believe. Two electrons can share the same space, called “orbitals”, provided they are in opposite spin (one spin up, the other spin down). Now, if an orbital has just one electron, the obvious question is, will that electron be spin up or spin down? A corollary of quantum theory states that, even though it is impossible, the electron will actually be both spin up and spin down simultaneously until some fool tries to measure its spin. Once somebody tries to measure its spin, the electron selects a spin orientation just to mess with our minds.

Some years ago, a particularly vindictive and evil physicist decided to shoot a beryllium atom with three different highly accurately tuned lasers. In a very high vacuum, the first laser knocked one of beryllium’s for electrons off, creating a charged atom (called a “cation”) which both allowed it to be held in a magnetic field, and also leaving one of its electrons unpaired. Without measuring its orientation (meaning it will exist as both spin up and spin down), the physicist shot the electron with a second laser designed to more just the spin up orientation into a higher energy state, while leaving the spin down orientation in the lower ground energy level. The third laser pushed the higher energy configuration away from the lower energy.

This may seem convoluted, but the end result is that the beryllium atom existed in two locations at the same time. It didn’t split. It was simply the same atom, existing at the same moment in time, about ten times its diameter from each other. It’s like a happy you and a sad you standing ten feet apart looking at each other.

Indeed, the quantum work is filled with anomalies, and mind boggling behavior that sparks the imagination It’s no wonder it’s such a common theme in science fiction.

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