Quantum Mechanics, the Bangles, and Another Manic Monday

by Shane L. Larson

At the opening of Harry Potter and the Deathly Hallows, Part 1 we find Professor Snape stalking up to the imposing wrought-iron gate of Malfoy Manor.  With a casual flick of his wand, he passes through the gate, unimpeded.  If you look quickly around the theatre, you can spot every physicist in the crowd because they are all nodding sagely: magic is just science, and Snape just quantum tunneled through the Malfoy Manor Gate.

Quantum tunneling. The name evokes little trills of excitement, wonder, and possibly confusion because it uses the magic “q” word from the Twentieth Century: quantum.  No aspect of fundamental physics challenged our understanding of Nature more than the ideas of quantum mechanics.  At the start of the 1900s, we were for the first time using our wits and our technology to attempt to understand Nature on scales that had been unaccessible to us since the dawn of time –– the scales of atoms.  The consequence of those explorations and discoveries is all the wonder and convenience of our modern technological society.

Every one of us encounters quantum mechanics everyday.  This morning at 6:21am my alarm clock went off, blaring the dulcet admonitions of the Bangles that this Monday, like last Monday, is just another Manic Monday.  That doleful message was enabled by quantum mechanics.   Deep down inside most devices of modern convenience is one of the great marvels of our time –– the integrated circuit. They are small and innocuous, little black squares of ceramic and rare earth metals with small metal legs splayed out, giving them the appearance of some strange robotic bug. But deep inside they are machines if wonder. They have no moving parts, but their job is to corral and gate billions of tiny electronic denizens that we have dispatched to do our bidding (in the case of your clock radio, to wake you up). The beasts of burden in the world of electronics are electrons, fundamental particles if Nature with a mass 0.000 000 000 000 000 000 000 000 000 006 times the mass of a regulation baseball. Electrons are very small!  It is only in the last 100 years that we have truly understood the laws of physics for the very small –– we call those laws “quantum mechanics.” If you want to herd electrons around a semiconductor and make them do your bidding, then you have to be a master if quantum mechanics.

So what are the laws of quantum mechanics? At its most rudimentary level it is just mechanics, that branch of physics that tells us about the motion of objects. The purpose of mechanics is to determine the location and position of objects as a function of time.  If I throw a baseball, how long does it take to cross home plate? If I slam on my brakes in an attempt to prevent my 1979 Yugo from rear-ending a Lexus that is sitting at a green light, how far do I skid?  How fast does a rocket have to go to break the bonds of Earth, heading outbound through the solar system?  These questions are the purview of mechanics. Quantum mechanics is about these same kinds of questions, but applied to the sub-atomic world.

Many of the axioms of life that you learned as a child provide equally good advice for doing science. An important one is “there is more than one way to skin a cat.”  For every problem in physics, there is more than one way to solve it. In mechanics, there are often many ways to think about problems.  One of the most common ways to think about mechanics is in terms of speed and acceleration –– how fast an object is moving and how that motion is changing. Another common way to think about mechanics is in terms of energy.  Energy has an intuitive foundation you can imagine, characterizing how much effort you had to expend to get an object moving, or the potential an object has to do something.  For instance, a Mack truck rolling down the highway at 65 mph has a lot of energy; it takes a lot of effort to get such a large object moving so fast! In a similar way, an anvil perched precariously on the edge of a cliff must have some energy stored in it, because it has the potential to do a lot of damage to someone far below (as Wile E. Coyote knows well).

Fundamentally, quantum mechanics is an approach to mechanics that thinks about energy. The “quantum” part of the name comes from a discovery of the physicist, Max Planck.  Planck stumbled on the fact that when you look at the energy of sub-atomic systems, the energy comes in discrete packets that he called quanta.  Planck argued that you could not have any energy, but you had to have a specific energy that was a discrete number of quanta added together.  These quanta are tiny, like the objects Planck was trying to describe.  For typical atoms, a quantum of energy is about a hundred billion-billion times smaller the energy of a Major League fastball.

This simple prediction, borne out to high precision in laboratory experiments, has famously non-intuitive consequences for the world.  Perhaps the most renowned is the Heisenberg Uncertainty Principle, which tells us that precision knowledge of all the physical properties of a quantum mechanical system is not possible.  Suppose I wanted to look at the electrons in my alarm clock, scurrying around their integrated circuits in their quest to insure the Bangles get me out of bed at the right time. If the electrons were little cars on highways (like in the Tron movies), I might be tempted to ask “where is each electron and how fast is it moving?”  But the Heisenberg Uncertainty Principle tells me this is not possible; if I want to I can measure where the electron is or how fast it is moving, but I can’t know both accurately.  The more well known the position is, the more uncertain the speed is, and vice versa.

This is disturbing to say the least because it sounds completely counter-intuitive to our everyday experience.  But more importantly to scientists, it suggests a deadly conundrum for our deepest held passions about how the world should work: we believe that there should be a consistent set of physical laws that apply to everything, whether they are baseballs or electrons!  As hundreds of thousands of Major League Baseball replays have shown, we can know where a baseball is (over the outside corner of the plate) and the speed at the same time (it’s printed right there on the screen!).  But Heisenberg says this is not possible.  How is this conundrum resolved?

One way to ask the question is to apply quantum mechanics to a system that is not small.  One could ask “Is a cow a quantum mechanical system?”  When you are first exposed to quantum mechanics, this is the obvious question to ask.  Neils Bohr, one of the early architects of quantum mechanics, pondered the same question.  How could it be that quantum mechanics governs how electrons move around in a semiconductor, but not how a cow walks around a corral?  The resolution to this is that the classical world, on the scale of meatballs and Boeing passenger jets and wallabies, is a gigantic quantum system operating on scales much different than those of an individual atom.  The physical properties of a cow, say its energy or its angular momentum (how fast it is spinning –– imagine a cow on ice skates, if that helps), are 1030 larger than those of a hydrogen atom.  When we look at the quantum world, what we observe are changes in quantum states.  We give each state a name to keep track of a quantity called the principle quantum number, n.  For a hydrogen atom, the n values typically have very small numbers: n = 1, n = 2.  A cow has very large quantum numbers, like 1030.  The quantum nature of a cow is very hard to detect because the difference between two quantum states, say ncow = 1000000000000000000000000000000 and ncow = 1000000000000000000000000000002 is much harder to detect than the quantum states of a hydrogen atom, say nhydrogen = 2 and nhydrogen = 4.

“But wait!” says the Hermione Granger in the back of the room.  “Both of those are still just different by a factor of 2!” Yes, that’s true.  But identifying the quantum state is about counting the values and then noting the differences.  If I lay 5 Oreos on the table, and you sneak one when you think I’m not looking, I’ll probably notice.  If I lay even a moderately large number of Oreos on the table, say 50 (let alone 1030), it is far less likely I’ll notice that you snarfed one.  The same is true of measuring the quantum nature of everyday objects –– it’s hard to notice the small, quantum mechanical changes.

And so it seems physics is saved –– we could use quantum mechanics to describe a cow because in the macroscopic world, the more convenient physical laws we use to describe the mechanics of cows, passed down to us from Galileo and Newton, are derived from quantum mechanics itself; we just don’t notice the small, quantum mechanical changes in the state of the system.  We call this the classical or the continuum limit.  This is the great lesson of science –– our knowledge of the world is continuously changing, and when it does change, our goal is to understand how our old knowledge fits in the new framework.  Sometimes it requires us to discard long held passions and beliefs, and other times it requires us to bend and stretch our minds to encompass a larger world view than we had before.  Either way, the process is confusing, exhilarating, painful, but ultimately rewarding.  It’s what gets a scientist out of bed after a long weekend –– the promise that your job is going to be just another Manic Monday.


One response to “Quantum Mechanics, the Bangles, and Another Manic Monday

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