# Quantum Mechanics

As mentioned before, our brains have trouble comprehending the very large, the very small, the very fast, and the very slow. Over millions of years, evolution has sculpted the human brain, magnificent organ that it is, to model the world around us accurately, so that we may survive. That world consists of a region, apparently flat, dozens of miles across, filled with animals ranging in size from an ant to an elephant, with speeds ranging from a turtle to a cheetah, and life spans ranging from a few hours to a few decades. Anything beyond this will be difficult to intuit.

Sometimes we can get there, with years of practice - like a pilot who is comfortable flying thousands of miles around the earth. After hundreds of flights, she has an intuitive grasp of the size of the earth, something our hunter gatherer ancestors couldn't have imagined. However, when the concepts are even more extreme, such as intergalactic distances, or a black hole, even the experts cannot develop an intuition for the subject at hand. This is the case for quantum mechanics. It is so strange, that Richard Feynman, the foremost authority in the field, said, “If you think you understand quantum mechanics, you don't.”

Quantum mechanics deals with the very small, smaller than a bacteria, smaller than most molecules. It is no wonder we have no intuition for this realm. Matter behaves quite strangely at these dimensions. Entire books have been written on the subject, some with simple explanations, and some with calculus in complex variables. I will give only three examples . I realize this doesn't do justice to the topic, but it will have to do.

## Particle Wave Duality

You are standing in front of a picket fence, with a bucket of baseballs at your side. The spaces between the boards are wide enough for a baseball to pass through. There is a vertical board, a picket, directly in front of you, 10 meters distant. I'll call it board 0. Being an excellent pitcher, like Justin Verlander, you can throw a baseball just to the right of board 0, whence it passes through the slot. You pick up another baseball, and throw it just a hair to the left, so that it passes through the slot just to the left of board 0. For the purposes of this experiment, these are the only two slots in the fence. You never throw wild; you always throw the baseball through the left slot or the right slot.

Now shrink the entire experiment down to the size of an atom. You are just a few angstroms tall, and you are throwing a particle that is the size of an electron. You can still think of it as a baseball if you wish. In this realm, you can throw your baseball through both slots at once. Indeed, you almost have to. It is difficult to direct the ball to one slot or the other. The ball leaves your hand, and becomes a wave, and passes through both slots simultaneously, like a wave of water going around a rock. The baseball is both a particle and a wave.

Your friend Alice wants to get a handle on this situation. She watches the right slot to see if the ball goes through. Perhaps she puts a detector there, a camera of sorts. Now the ball goes through one slot or the other. Half the time it passes through the left slot, and half the time it passes through the right slot. The choice of slots is random. You can no longer pitch with precision, as you could when you were two meters tall.

The ball is no longer a wave, or if you prefer, the wave collapses - simply because Alice is looking. But how does the ball know that Alice is watching? It's just a ball.

Next Alice sets up a video camera, to record the ball as it passes. She's not looking, but she might look later. Still the ball passes through one slot or the other. How does the ball know that Alice has set up a camera, and might look later? And what if Alice never looks? And what is special about Alice? Does she have to be a conscious, intelligent observer to collapse the wave nature of the ball? It is baffling!

## Entanglement

There is a pitching machine out in space, halfway between Earth and Mars. It fires two baseballs in opposite directions, one toward Earth and one toward Mars. This machine specializes in curve balls. The two balls are spinning as they leave the machine, one clockwise and one counterclockwise. In the parlance of quantum mechanics, we might call these spin up and spin down. You can think of them as clockwise and counterclockwise if you wish.

You are on Earth, and your friend Alice is on Mars. When the baseball comes to you, you measure its spin. If it is spin up, then the ball that reaches Alice is spin down. If your ball is spin down then Alice's ball is spin up. You communicate with her by radio and confirm the correlation. Indeed, your balls have opposite spins. This happens over and over again, as the machine spits out its pairs of balls. Nothing strange so far, but hang on.

The pitching machine chooses the spins at random, as it spits out these pairs of balls. This is truly random, not pseudo random like a computer might generate. It is the very essence of random, i.e. unpredictable. You have no idea what the spin will be, but as soon as you measure it, you instantly know the spin of the corresponding ball on Mars; it is the opposite of yours.

But it is stranger still. The spin isn't even determined until you measure it. The pitching machine does not impart a particular spin to the two balls, it merely guarantees that the balls will have opposite spin. When you measure the spin of your ball, that "determines" the spin of Alice's ball, 50 million miles away. This seems like communication at a distance. It seems like we are sending information faster than light. This would contradict einsteins principles of relativity. Indeed, it takes 20 minutes for Alice to tell you, by radio, the spin of her ball, whence you can confirm it is opposite to yours. How do the balls know? How does measuring the spin of one, instantly determine the spin of the other, as measured by an observer at that location? Einstein called it “spooky action at a distance”, and indeed it is.

You can't use entanglement to send information faster than light, because you cannot make the ball spin one way or the other. If you could force it to spin up for yes and down for know, then Alice would know, instantly, whether you said yes or know. But you can't do that. You can only measure it's spin and note that it is up or down, and realize, at that moment, that Alice's ball has the opposite spin.

## Tunnelling

You stand on one side of a solid fence, with no slots, and Alice stands on the other. You have a bucket of baseballs as before. You place a baseball on the ground next to the fence. It just sits there. If you want to give it to Alice, you have to lift it up with your hand, which takes energy, and pass it over the fence to Alice. She then lowers the ball, recapturing the energy you put into the ball, and places it on the ground on her side of the fence. The ball has the same energy it had before, but it is on the other side of the fence. It can't burrow through the fence, you have to lift it up over the fence.

Now shrink the entire experiment down to the size of an atom. The ball can, with a certain probability, burrow through the fence and wind up on the other side. This is because the ball is a wave, and the wave extends through the fence to the other side. If the fence is thick, the ball is less likely to tunnel through. If the fence is thin, tunnelling becomes more likely.

There is no free lunch here. The energy of the ball is the same on either side of the fence, and energy is conserved. But it didn't have to hop over the fence; it just went through.

## Applications

Strange as it may seem, All this stuff is real - it really happens, and many electronic components are designed with quantum mechanics in mind. Indeed, they would not function properly without it. Examples include light emitting diodes, flash memory, lasers, mri machines, and atomic clocks. The latter is indispensable for gps operations, and where would we be without gps? Lost!

Laboratories around the world are trying to build a quantum computer. This would solve certain problems exponentially faster than a classical computer. In oversimplified terms, a quantum computer throws a lot of baseballs through a lot of slots simultaneously. The fence is carefully constructed so that the interference of all those baseballs, acting as waves, produces the solution to the problem. Not all problems are amenable to a quantum computer, but it would be another tool in our toolbox.