A Quantum Introduction for World Quantum Day

Happy April 14th, World Quantum Day!

The date, 4.14 represents one of the most important constants in quantum mechanics: Planck’s Constant h. The value of *h* = 4.14x10^{-15} eV*Hz (eV*Hz stands for Electron-volt Hertz, which are not considered the standard units but are helpful units for this genre of physics. In the International System of units, *h* = 6.63x10^{-34}J*Hz, or Joule Hertz). But what is quantum mechanics and what does it have to do with *h*?

Well, quantum mechanics deals with physics on a very small scale. And small here means really small. Not mouse small or even dust particle small, but electron small. Quanta, with roots in the Latin word “quantus,” meaning how much, refers to the smallest level something can break down into. (The name makes sense now, doesn’t it?) Quantum mechanics tells us how particles behave (or it tries to) and in its explanatory equations, the constant *h* keeps showing up, like a pesky younger sibling you can never shake. To help me explain what quantum is, and why it is so fun, I’ve recruited some of the major players in the field.

*"Those who are not shocked when they first come across quantum theory cannot possibly have understood it*.”- Niels Bohr

We start with a quote from our namesake here at NBLA, Niels Bohr. And in fact, he’s right. Max Planck, who discovered Planck’s Constant, came across it by mistake. He was trying to describe the behavior of radiation absorption but struggling. (The behavior Planck was studying was dubbed “The Ultraviolet Catastrophe,” which would also be a great name for a band.)

Desperate for a positive result, Planck assumed that energy could come in little packets (later called quanta) and miraculously, it worked! He published in 1900, introducing the constant *h* and the energy packet idea. Planck did not really believe his result had physical importance and that it was:

*"purely formal assumption and I really did not give it much thought except that no matter what the cost, I must bring about a positive result*” -Max Planck

This was the mathematical equivalent of the iconic Mean Girls tank top scene. Janis Ian vandalizes Regina George’s tank top in a desperate attempt at revenge but inadvertently starts a fashion revolution. However in quantum mechanics, the revolution was more subtle. Planck, and many others, did not really believe in energy packets and chalked it up to mathematical formalism.

*"My physical instincts bristle at that suggestion.*” - Albert Einstein

In full disclosure, Einstein was talking about something else related to quantum mechanics when he said that. I’m putting it here so I can talk about why this concept of energy packets is such a wild idea. In classical physics (the physics of stuff you may have learned about in high school with blocks sliding down ramps) energy is “continuous.” You can start at one level of energy and smoothly accelerate to another level of energy. If energy came in “discrete” packets, you would jump from one level to the next without the smooth acceleration. For instance, in the final scene of *When Harry Met Sally*, Harry is leisurely walking when he realizes he loves Sally and must be her New Year's kiss. He starts accelerating, jogging and first, and gradually, as the clock starts running out, he increases to an all-out sprint. If energy packets were visible in our everyday lives or in this rom-com universe, there would be no acceleration between energy levels. At one moment, he would be walking and at the next he would jump to an all-out sprint with nothing in the middle. Even Usain Bolt can’t manage this and has to humbly accelerate from standing to sprinting. It turns out that while we don’t feel these energy jumps, particles do.

At the start of the 20th century the idea of energy quanta was unimaginable. But, in 1905, Albert Einstein showed that by treating energy from light as packets, he could explain how the frequency of light was related to its energy and why atoms would only emit light at specific frequencies. Full circle moment: they’re related by a factor of Planck’s constant, *h*! This also introduced the idea of light quanta, or photons, proving light behaves both as a particle and a wave. By 1911, the quantum revolution had started.

Now that we know what quantum mechanics is, let’s talk about the fun stuff (in my opinion)!

*"Two seemingly incompatible conceptions can each represent an aspect of the truth … They may serve in turn to represent the facts without ever entering into direct conflict.*” -Louis de Broglie

De Broglie is huge in quantum mechanics. He said basically that not only does light behave as both a particle and a wave, but everything does! Yes, particles like electrons, photons, and atoms, but also you, me, and the metro car I took to work today. If everything is a wave, why don’t we see it? Wavelength is inversely proportional to momentum, so the more momentum we have (effectively the more massive we are) the smaller the wavelength. Once you get much bigger than a couple of atoms, the wavelengths are so small we don’t know it’s there.

But being both a particle and a wave isn’t what de Broglie is talking about in his quote above. He’s talking about the concept of complementarity, introduced by Niels Bohr. There are pairs of quantities in a system, like position and momentum, where both values cannot be known simultaneously. The Uncertainty Principle describes this: the more certainty you have about one value, the less you have about the other.

*"In atomic physics, we can never speak about nature without, at the same time, speaking about ourselves.*” -Frijitov Capra

I just love this quote! Sometimes, physics feels impersonal, but in reality there is nothing more human than interpreting our surroundings. Alright, so what the heck is he talking about? Well, we know now that small things like electrons are both particles and waves, but we need to talk about what the waves really are. These waves are a little different than the ones that flow through water or propagate through air like sound.

You can think of the wave equation like *Ella Enchanted*’s magical book (the film iteration works best for this analogy, but for the novel fans, it should work just as well). Ella’s magical book keeps track of the world as it changes through time. Likewise, the wave function changes the probabilities of the different states of a particle through time. Ella can open the book and see the location of the mischievous fairy who cursed her. In quantum, we can measure the location of a particle. But, until a measurement is made, the wave function is in a state of superposition, where everything that is possible is occurring all at once. While the book is closed, anything that is possible is unfolding its pages, unread. Mathematically solving the wave function only reveals the probabilities of each possible state. It is akin to Ella having the book with her, but keeping it unopened. She knows there is some probability that the fairy is at a giant’s wedding or maybe getting a ticket for flying while intoxicated (that part only happens in the movie).

The notion that everything possible exists until a cursed heroine or a physicist comes along to measure is uncomfortable to many. It means that we are not passively observing quantum mechanics unfold but that we are participating in it, just by measuring it.

We cannot speak about atomic physics without speaking about ourselves!

*"Do you really believe the moon is only there when you look at it?*” -Albert Einstein to Abraham Pais

If measuring something makes it happen, Einstein mused, does it mean that if we aren’t measuring, things don’t exist? Einstein was being facetious, but… like… maybe?

*"We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.*” -Pierre Simon Laplace, A Philosophical Essay on Probabilities

This quote is about what was later dubbed “Laplace’s Demon.” He describes a demon that could know everything about the current state of the world and from that, using physics, the demon could deduce the past and predict the future. This idea is called determinism but is not possible given our current understanding of quantum mechanics and thermodynamics because it’s dictated by probabilities. Some people extrapolate this to have philosophical importance and negate or support the existence of “free will.”

*"Spooky action at a distance*” -Albert Einstein

There are a lot of cool things to fall out of quantum mechanics, but coolest in my mind (and maybe the most horrifying in Einstein’s) is entanglement. Particles can be produced to have shared, intrinsically connected features. For example, electrons have something called “spin” that describes their orientation. The thing with spin is that one electron in an entangled pair will have a “positive” spin and the other must have a “negative” spin. Always. If you were to separate two entangled particles at any distance, both particles would have their superpositions of possible orientations; they are both facing all directions independently and simultaneously. However, if you measure the orientation of one of these entangled particles along a given axis, entanglement forces the other wave function to collapse and take the exact opposite orientation on that axis. This is true if the particles are two centimeters away or two million kilometers away.

It would be like if my sister and I only wore black or white shirts but we always wore opposite-colored shirts (this is important because we look very similar and it is difficult to tell us apart otherwise). Because we like both colors equally, there is a fifty-fifty chance each day that we will wear the black or white shirts. Sure, if we were in the same room getting ready it would be easy to determine which shirt to wear. Now that we do not live together, it would not be instantaneous for her to know I’ve selected a black shirt. Yet, entangled particles can do this without texting and confirming their OOTD (outfit of the day).

This means particles must be communicating faster than the speed of light. How else will the entangled particle know what spin to have? But that’s impossible because nothing can travel faster than the speed of light! Einstein and many other physicists could not stand that possibility and in a 1935 paper, they said that there must be another explanation. Perhaps it’s a set of “hidden variables,” (stuff we don’t know about yet) that dictates the particle’s behaviors. You know, like “on Wednesdays, we wear pink.”

*"This is no kooky paper. This is something very grea*t." -Abner Shimony, on Bell’s Theorem in this Oral History Interview

In 1964, almost 30 years after Einstein & co. proposed the existence of hidden variables, John Bell published a paper that proved hidden variables weren’t possible. Bell’s Theorem (or Bell’s inequality, depending on who you ask) opened a new world by showing quantum mechanics is as mysterious and magical as some feared.

Since 1964, the field has grown tremendously. Advancements in quantum mechanics enable the technology you’re reading this blog on, a new understanding of the origins of the universe, and even the ability to determine the atmospheric composition of extrasolar planets! Explore these *Inside Science* resources to learn more about quantum mechanics and the future it may bring!

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