Quantum Mechanics 100
What is quantum mechanics, why is it important, and why is it so weird?
Everything is quantum (mechanics)! This is definitely true on one level, and many believe it is true on a second level. In this post I’ll provide a basic overview of quantum mechanics (QM) — a two-dollar tour (except that it’s free and worth every penny).
It is definitely true, at the most fundamental level, that all of reality is quantum mechanics. Life as we know it — the classical world — is many levels of emergence above that quantum fundament and famously lacks any quantum behaviors. But reality at that lowest level is undoubtedly quantum mechanical.
Our experience, though, is that quantum characteristics fade away at higher levels of organization. Individual particles act quantum, as do atoms and even molecules. But as size increases, quantum behavior vanishes, and classical behavior takes over. Many believe this is due only to the environment, and that large systems would show quantum behavior if totally isolated from that environment (say in deep space).
Not me. I agree with the Objective Reduction (OR) notion that large objects comprise their own environment and quantum behavior vanishes regardless of the environment simply because the object has enough mass — enough gravity — to interact with itself.
But this gets ahead of the story. Let’s go back to the beginning.
It starts with wondering why our stoves and furnaces don’t turn into red-hot molten puddles of metal. They demonstrably don’t, but science at the time said they should. Because energy should spread out into an infinite number of “buckets” (frequencies) in any heated object (such as a stove). That infinite capacity should absorb an endless amount of energy (heat), so the metal should get so hot it melts.
Yet we never see that happen, and experimental results always trump theory, so back to the blackboard. Why don’t stoves melt?
Quantum Pennies
In 1900, Max Planck come up with the idea that energy is quantized — it comes in minimum size packets. It’s like money. The penny is a minimum granularity for any normal money transaction. It’s the smallest amount of change possible in a money value. For example, from $4.98 to $4.99 is the smallest increase we can make for the first amount.
Planck thought he’d invented a mathematical trick to explain why stoves don’t melt. He imagined that there were “buckets” (quanta) energy had to fill, and these have a minimum size. And as with tables in Las Vegas, the minimum size varies. It might be $1 or $2 or $5 or even $10. Very special tables might have $100 or $1000 (or higher) minimum bets. At a Vegas table, without the minimum amount, there is no bet. With particles, unless there is enough energy to fill the bucket, none goes into that bucket.
It turned out Planck was righter than he thought. The Planck Constant — the energy equivalent of a penny — was named after him and is a core element of QM. It appears that energy and matter (same thing, in a way) really do come in minimum-sized chunks, quantum pennies.
Quantum Atoms
Reality defined theory again when it came to atoms. We had figured out that atoms consist of a tiny positively charged nucleus surrounded by a number of negatively charged electrons whizzing around at (very) high speed. But such charged particles moving in curved orbits should emit energy (which we don’t see), and the electrons should thus lose that energy and spiral down into the nucleus (which they don’t).
The answer again: quanta. Electrons have a minimum energy — they can’t have zero — so they don’t spiral in. This minimum is their ground state. They also have a set of specific higher energy levels — excited states — and these vary by atom. These energy levels account for a great deal of chemistry.
We’ve been mucking about with chemistry since ancient times, so, difficulty of actually learning it aside, it seems somewhat quotidian. Kids can have chemistry sets and study it in school. But chemistry — which takes place at the tiny level of atoms and molecules — is almost entirely quantum.
Einstein’s Prize
Albert Einstein won the Nobel Prize for his 1905 paper on the photoelectric effect, which again showed us that the world — at least energy and matter — are quantized.
For a long time, it was debated whether light was a wave or a particle — it clearly has both properties. Science at the time had largely settled on light being a wave — the shadow fringe effect being one demonstration. But the photoelectric effect proves light acts like a particle, too.
In 1924, Louis de Broglie (“deh-broy”) suggested that matter is both wave-like and particle-like. This was confirmed in later experiments. Reality has a wave-particle duality.
The modern view, embodied by Quantum Field Theory (QFT), is that there is no such thing as a “particle”, there is only a minimum-sized disturbance — a “waveicle” — in a particle field. As I see it, what we perceive (with our instruments) as particles are only highly localized, i.e. point-like, interactions between waves in their respective fields.
Explaining Reality
The physical world offered other puzzles that pushed the development of quantum mechanics, a mathematical theory that explains atomic (and sub-atomic) behavior amazingly well. It grew into one of the most accurate scientific theories we have. It is currently over 100 years old and has withstood every challenge.
But that rascal Einstein gave us the theory of relativity, our other most accurate scientific theory. Relativity is about our experience of motion, time, acceleration, and gravity. And this theory doesn’t agree with quantum theory. At all.
Quantum is linear; relativity is nonlinear. Quantum assumes a background; relativity defines (is!) the background. Quantum is chunky; relativity is smooth. Quantum doesn’t include gravity; relativity is all about gravity. Quantum forces are comparatively strong; gravity is comparatively weak (a small magnet holding up a paperclip is stronger than the gravity of the entire Earth).
Trying to resolve these two great theories — with a theory of quantum gravity — is one of the biggest unsolved mysteries of modern physics.
But Why Is It So Weird?
No one truly understands quantum mechanics, we just have a really good mathematical theory for it. There are many interpretations of what the math means, but none of them have conclusively won out, so the ontology of QM remains a mystery.
An easier question is, “What is so weird?” and that has a number of answers. Three in particular stand out:
Superposition: Popularly referred to as “being in two places at once” it’s the quantum ability for a system to be in a juxtaposition of possible states, just one example of which is two possible locations. But the electron of an atom can be anywhere near that atom, so rather than two places, infinite places.
And superposition can apply to other properties. A photon can be in a superposition of horizontal and vertical polarization. A moving particle can have a superposition of different possible momentums.
Superposition is a basic quantum property not seen in the classical world where things have definite values, not a “cloud” of possible values.
Entanglement: The ability of two quantum systems separated in space (by any distance!) to be linked such that they act as if they were a single system. Which means a change to part of the system (one of the particles) is instantly reflected by the whole system (the other particle).
This appears to violate the speed of light restriction but doesn’t because it cannot be used for sending information. The “receiving” end perceives only what appears random information. It’s only when both ends meet and compare results that the correlation appears.
Interference: The reason for the bands of light in the famous two-slit experiment. Quantum systems can interfere because of their wave-like nature, and any system of waves can interact to re-enforce or cancel each other. Exactly what’s “waving” in the quantum world is an unsolved mystery, but the key equations in QM are wave equations.
As an aside, the math of interference in quantum mechanics comes from the math of complex numbers — sometimes called “imaginary” numbers. While such numbers are used in classical physics as a calculation convenience, they appear to be necessary in quantum mechanics. Which is just one more mystery. Why does reality, at its most fundamental level, require “imaginary” numbers?
Quantum Math
Unfortunately, for now, all we have is a mathematical theory. Worse, what that math tells us is impossible to visualize. We can’t even create meaningful metaphors. No popular account truly communicates the quantum world. The only accurate picture is the math, but that math has no physical correlation we understand.
This in contrast to every other area of science where the math corresponds directly to some physical situation, be it thrown baseball, launched rocket, moving tectonic plate, or whatever. We know what the math means.
But quantum math, despite so far being unassailably effective, has no meaning we fathom. That our cell phones work shows how effective our quantum grasp is, but we have not yet reached understanding.