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At the Very Bottom of Reality Is Planck's Constant

The number that divides the world into classical and quantum.
November 1, 2014, 7:25pm
Image: Jason Ralston/Flickr

What is it to be quantum? We hear the word often enough: quantum mechanics, quantum teleportation, quantum entanglement, quantum computing, quantum encryption, etc. Rarely, it seems, do we consider quantum for what the concept is at its very quantum heart. What is it to be quantized?

Our everyday experience as giant macroscopic beings occurs within the world of classical physics. As giant macroscopic beings, we experience physics as it pertains to very large organizations of matter and energy. And an organization of matter and energy can be viewed as a state in which the fundamental physics of the very small are cancelled out in favor of the clumsy ad hoc physics of the very big.


The physics of the very big would include Newton's laws of motion and classical mechanics, generally. Bodies being acted upon by forces: Work, kinetic energy, gravitation inertia, velocity, torque, and so on. What happens to a ball when it gets thrown is a question for classical or Newtonian physics. This is old physics—a physics of convenience and generality.

Classical physics breaks down at very small scales, but what is "small"? The human eye is, on average, capable of resolving (or seeing) objects down to 100 microns in diameter, which we could consider the threshold of microscopic.

In terms of atoms, a space of 100 microns could squeeze in around 500,000 atoms. The nucleus of an atom is then about 10,000 times smaller than a whole atom, while a single electron is about 2,000 smaller than a small atomic nuclei (a hydrogen isotope of one proton and one neutron). We might even just say that an electron is incomprehensibly small, but at these scales the basic notion of "size" itself starts to collapse.

Animation: Curtis Knapp

When we zoom this far in on reality, it's not just size that becomes incomprehensible. Think about light: beams, rays, lasers, flashes, pulses. Light is intuitively continuous; rather than being a material "thing," light is energy. Light is a force, purely ethereal.

That's what was assumed in physics for a very long time, anyway. In 1900, a physicist named Max Planck was stuck on a particular problem: atoms shouldn't exist. Atoms, structures consisting of electrons buzzing around nuclei of protons and neutrons, and therefore the whole of chemistry exist because atoms are stable. Those electrons will keep buzzing around so long as they don't gain or lose energy.


But electrons, as they whip around their nucleus, have acceleration and this means a changing electric field and the loss of some energy by the accelerating body. Shouldn't electrons then eventually just lose more and more energy until they spin themselves into their atom's nucleus? Only if they emit energy continuously. What Planck suggested is that they don't emit energy continuously and energy itself isn't continuous.

Instead, energy occurs in chunks or packets. There is a limit as to how far we can zoom in on a force like light or heat. We have to stop at some point and that point is the photon. There is nothing smaller and less energetic than that. We say this is where energy becomes quantized; these indivisible points are quanta of light.

These quanta have a set amount of energy. This specific quantity of energy is among the most fundamental things in the universe, if not the fundamental thing.

This is known as Planck's Constant and, even more so than our size estimations above, it is incomprehensibly small. A single photon.

The awesome thing about Planck's Constant is that it's also incomprehensibly big. Every single quantity in the universe is just a multiple of this constant. Everything. That's the implication of indivisibility. As every whole number is a multiple of 1, all of energy and matter is a multiple of Planck's Constant. The thermal energy released in a nuclear explosion will just be some integer (whole number) value—a discrete value—multiplied by this number. That's amazing.


This is where we start talking about quantum mechanics, the set of theories and principles describing how the quantized world behaves. It's quite different.

To start, we no longer talk about "things" in the quantum realm. That seems counter-intuitive: quantization is all about turning non-things into unitary things. Yes, but their existence as things is highly provisional. "Zero" doesn't exist in this world—even perfect emptiness has some energy to it. Reality here is particles, but particles described by waves. This is the fundamental duality behind the strangeness of quantum reality.

The wavefunctions behind quantum objects allow those objects to be in many places at once, with many different velocities. Their reality then is always a sum of possibilities. The universe is a poker game in which no one is ever allowed to look at their cards (and if they do, the game is over: wavefunction collapse), or a turn of roulette in which the wheel never stops spinning. You get the idea, but no one really gets it.

Finally, Planck's Constant is one of those uncomfortable "Goldilocks" coincidences. If it were different, if a photon had some different energy, things might not have worked out. For example, this number determines the efficiency of hydrogen fusion. If this efficiency were just a bit lower, hydrogen would never be able to fuse into deuterium, a crucial step toward the creation of helium.

"In this case, we'd still have stars—huge glowing balls of hydrogen," the mathematician James Stein wrote for PBS, "but no star stuff would ever form because the porridge would be too cold to create helium, the first step on the road to creating the elements necessary for life." But, if this efficiency were a bit better than it is in our universe, then, "The hydrogen in the stars would become helium so quickly that there wouldn't be much hydrogen left to form the molecule most essential for life—water."