Facts So Romantic

Why Every Coin Flip May Be a Schrödinger’s Cat

Schrödinger’s Cat
Schrödinger’s Cat image: Wikipedia

During a recent conference on cosmic frontiers, University of California, Davis, professor Andreas Albrecht made a provocative statement: “Every Brownian motion is a Schrödinger’s Cat.” Technically, it was part of a broader talk on implications for a multiverse contained in various models of inflation in the early universe—based in turn on a recent technical paperBut Albrecht’s colorful phrasing prompted me to ponder more deeply the conventional wisdom about the difference between classical and quantum probabilities. Because what he’s really saying is that all classical probabilities emerge from quantum probabilities.

The connection between the microscopic quantum world and the macroscopic classical world can be seen in Brownian motion, the random jittery movements of small particles suspended in a liquid or gas. It gets its name from the 19th-century botanist Robert Brown, who noticed [pdf] that pollen grains floating in water under a microscope seemed to move randomly of their own accord. That’s because a grain of pollen is 250,000 times larger than the water molecules, which jiggle from thermal motion. Even though they can’t be seen with the naked eye, they are colliding with the much larger pollen grains constantly, from all directions. You’d think these collisions would all cancel out in the end, but because they are random, there are always tiny imbalances at any given time—slightly more molecules pushing the grain to the right than pushing to the left.

This has implications for probabilistic predictions. Classically speaking, if you flip a coin, you would say that there is a 50/50 chance it will land heads or tails, simply because you don’t have enough information about the many factors that could influence its landing position—the rate of spin, height, a slight gust of wind. In principle, you could always acquire more information to refine your prediction so that it is more accurate. The classical probability is a way of quantifying our ignorance, if you will. Furthermore, you know that one side is definitely heads, and the other is definitely tails before the coin lands. So there is zero probability that it will be both heads and tails at the same time.

Quantum physics is fundamentally different: There’s no further information to acquire beyond the stated probability. In the quantum world, things can hover in a fuzzy, nebulous cloud of probability that encompasses all potential states: heads and tails, particle and wave. Things become definite only when an observation forces them to settle on a specific outcome. Technically, the coin exists in an indeterminate state of both heads and tails until it lands.

But it would be silly to think this applies to the macroscale world of everyday life, right? That was the whole point of Schrödinger’s cat, the famous thought experiment devised by Erwin Schrödinger to illustrate the absurdity of the quantum realm. I’ll let Sheldon Cooper of The Big Bang Theory explain:

That’s why Albrecht’s declaration caught my attention: He maintains that this kind of quantum probability works at every scale, from a simple coin toss to predicting the weather. Albrecht and his UC Davis co-author, Daniel Phillips, employed a billiard ball analogy to illustrate this—or rather, molecules in a gas that collide with each other like billiard balls. They show that the uncertainty of such a system increases with every collision, and when that uncertainty becomes large enough, it’s quantum effects that become the dominant factor in the outcome—not classical mechanics.

Size matters when it comes to the number of collisions needed to hit that threshold. For an actual game of billiards, it takes just eight collisions between billiard balls for quantum uncertainty to dominate; it takes 25 if we’re talking about bumper cars. But it only takes a single collision between molecules in water or air to make the uncertainty large enough that what’s going on at the quantum level impacts the macroscale properties of the system.

It’s a kind of chaotic system, in which the tiny fluctuations at the quantum scale—the equivalent of a butterfly flapping its wings in, say, Africa—become amplified via countless molecular interactions, until they collectively manage to have an impact on the macroscale—the proverbial tornado in Kansas. Ergo, flipping a coin is the probabilistic equivalent to Schrödinger’s cat: The coin’s final state cannot be predicted until it has actually been flipped.

“It is very likely that all serious probabilities, be it a coin landing heads-up or a child being female, are manifestations of quantum chanciness,” King’s College London philosopher David Papineau told Physics World when asked about Albrecht’s and Phillips’ work. “Indeed we have devices, such as Geiger counters, that show how big results are often caused by chancy micro-events.”

So, if “all successful applications of probability to describe nature can be traced to quantum origins,” as Albrecht and Phillips maintain, that means that even when we think we’re using classical probabilities, deep down, it’s really the quantum world calling the shots. We are opening the box on Schrödinger’s cat every time we flip a coin or check the weather, and countless other times during every day.

Jennifer Ouellette is a science writer and the author of The Calculus Diaries and the forthcoming Me, Myself and Why: Searching for the Science of Self. Follow her on Twitter @JenLucPiquant.

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