Quantum Superpositions

Quantum superposition is a fundamental principle of quantum mechanics that holds that a physical system—such as an electron—exists partly in all its particular theoretically possible states (or, configuration of its properties) simultaneously; but when measured or observed, it gives a result corresponding to only one of the possible configurations.

Why is this important?

While this is a fundamental concept and its implications effect our entire universe for the purposes of this blog it plays a vital role in a number of exceedingly cool Star Trek technologies, parallel universes, the entire genre of science fiction, a well known elf on any number of shelves and more importantly, an ongoing 'discussion' with my husband involving Schrödinger and his damned cat.

So, in the last installment of this 'discussion' it became painfully apparent that I could not clearly explain what Schrödinger was attempting to illustrate with his 'cat' experiment without first talking about the notion of a 'Superposition' so here is the very, very brief and high level review....

Where Did It All Start?

Ok, it might just be me, but the mention of superpositions gets me thinking about wave theory and that's Otis Redding's queue to start singing 'Sitting on the dock of the bay' on infinite loop in my head. And so the movie starts.......

Who knows where it all really started but I had to pick some place in time so I chose Egypt ('cause I think that's cool)

• It's AD 127-145, in Alexandria. Ptolemy, ancient scholar, is busy trying to figure out the world. He's still under the impression that it is the center of the universe but he starts to think about light. He writes a book, Optics, and in it mentions refraction. It's the first documented observation that light bends as it moves from one medium into another. For some reason I picture a mischievous Egyptian boy crouching over, scorching bugs with light focused through a piece of glass - but I may be way off on that one.

• Fast forward to c. 984, Baghdad. Ibn Sahl is a Muslim, Persian, mathematician, physicist and optics engineer. He studies refraction and comes up with what will eventually be known as Snell's law: That the angle of incidence equals the angle of refraction. He uses this law to produce the first lenses, mathematically designed to focus light without aberration and documents his findings in On Burning Mirrors and Lenses (984).

• Now jump to England, 1602. Thomas Harriot is an English astronomer and mathematician. He's working on building a telescope and is only a few years away from sketching the first images of the moon using that scope. He will do this more than 4 months before Galileo will do it and snag all the credit. Harriot's notes show that he has unlocked what will become Snell's law, just as Sahl had done before him but he didn't realize the value of this and chose not to publish it.

• The Netherlands, 1621, Willebrord Snellius (a name that would fit nicely in to the Hogwarts faculty list) actually put the mathematical form together but this would remain unpublished for his lifetime. 5 years later Snellius dies. 11 years after his death René Descartes independently derives the same equation and it is finally published in his treatise, Discourse on Method.

• Now the game is on. It's mid 1600's and scientists know how waves behave as they pass through media. In short they can calculate, if you drop a pebble in a puddle, how those waves propagate.

• As all this was going on a young Dutch physicist, Christiaan Huygens, was starting to gain recognition. He took Snell's law and expanded on it. Huygens looked more closely at a wavefront. How many of us have sat on a dock or a beach and watched the waves roll in? Huygens discovered that you could take that rolling wave front, extract a single point on it, and that single point would behave as the source of a new wave. Just the the pebble in the puddle did.

• This is important, because it shows that waves can, and do, combine to form new waves. If wave-forms are in sync their amplitudes add to form a new wave pattern with a greater amplitude. If they are out of sync the new wave pattern will have an amplitude driven by the difference in both source waves. This behavior leads to an interference pattern when 2 or more waves combine.

• This brings us November 24th, 1803. Thomas Young is an established English scientist. He is about to address the Royal Society of London. He opens his speach with the following line;

"The experiments I am about to relate ... may be repeated with great ease, whenever the sun shines, and without any other apparatus than is at hand to every one."

• He then goes on to describe an experiment involving a light source (in his example the sun, in today's labs it's more typically a laser) and two pieces of dark card, 1 of the cards has 2 pinholes or slits in it.

• Young's experiment showed that when you shine a single beam of light at a card with 2 small holes in it and hold the second hard behind the first, light shines from the pinholes onto the second dark card. An interference pattern is formed on the card. Since we know that interference patterns are formed when 2 or more waves combined it proves that the light is, in fact, a wave. And just like that Young provided the first proof of the wave theory of light. Ta da!

• So the world goes on happy in the knowledge that light is a wave and we've solved that mystery until 1900 when Max Planck is attempting to explain black body radiation and he comes up with the notion that even though light behaved like a wave it was, in fact, made up of tiny little particles. He called these tiny particles quanta.

• By 1905 Albert Einstein and a host of other prominent physicists have taken Planck's proposition and ran with it, that one crazy notion evolved into what is today called Quantum Mechanics.

• Now a theory is one thing, but they've got to prove it so how do they go about proving the particle theory of light. They go back to Young's Slits. Yep, they use the exact same experiment that Thomas Young had used to prove the wave theory 100 years earlier. Only this time they've got better gadgets! Instead of using a big light source (like the sun) now they can fire tiny amounts of light at those same pinholes. They fire a single quanta of light at that first card and attempt to detect which slit it travels through before it hits the second card. They do this and find that the quanta goes through either the left or right slit and no interference pattern is formed. So, ta da! Light is described by particle theory. We're done now, right? No.

• In 1926 Schrodinger publishes his equation predicting the motion of an electron in a hydrogen like atom. It's a linear equation and basically boils down to calculating whether an electron is spinning clockwise or counterclockwise. This is a big breakthrough and he will win the Nobel Prize for this equation a few years later.

• One year later, 1927. The Copenhagen Interpretation is published by Heisenberg and Bohr. They've taken Schrodinger's equation and expanded the math, using it to show how in certain situations the electron can be calculated to spin both clockwise and counterclockwise at the same time. This situation became known as superposition. When an electron can be shown to be in all possible states at the same time.

• One of the big contributors of the Copenhagen Interpretation was Heisenberg, and he had worked on his now well known Uncertainty Principle. He proposed that, from a mathematical perspective, you could know 1 thing about a target but you couldn't know everything. That the act of measuring something changed the thing that was being measured.

• So now the task was to prove that sub-atomic systems exhibited quantum superposition. How on earth do you prove that. Well they were on a roll with Young's Slits so why not give that a whirl again? Only this time they do it a little differently. Fire a single quanta of light at the slits, attempt to detect which slit it passes through, they find it goes through the left or the right but not both so that's the particle theory proven again. But Heisenberg said measuring changes the behavior of subatomic particles so what happens if they don't measure? Fire up the experiment again only don't attempt to measure anything. Instead look at the second card and they saw an interference pattern! (Who saw that coming?) Interference patterns can only be created by at least 2 light sources so the particle had to have traveled through both slits. It had to have been in both places at once.

• This experiment has been repeated the world over and is considered proof of both Quantum Superposition and The Heisenberg Uncertainty Principle.