Monday, April 25, 2016
How weird is quantum mechanics, really?
by Daniel Ranard
Nearly anyone who tells you about quantum mechanics is quick to tell you how weird it is. And perhaps any science that ventures outside the realm of the visible or the human is bound to be strange. Our universe is a strange place, filled with exotic objects whose undeniable strangeness is blunted only by familiarity: the double helix, rippling force fields, supernovae. But physicists will tell you that quantum mechanics is even stranger. They explain that distant photons may be intimately entangled, or that an electron may exist in a superposition of two places at once. They describe a world not only strange in its particulars but strange in its way of being. According to quantum theory, particles may lack definite properties until measured, and the outcomes of quantum experiments are fundamentally uncertain.
What should we make of these claims? Perhaps we should be deeply impressed. After all, quantum mechanics is not some niche of modern physics; physicists expect that the rules of quantum theory underlie all physical phenomena. And if taken seriously, these claims about quantum weirdness are claims about the nature of knowledge or existence itself. Philosophers and thinkers should take note.
But even though we might be impressed, we should also be suspicious. No definite properties, fundamental uncertainty… what could it all mean? It's hard to imagine how scientific experiments (or any line of investigation, really) might yield such bold claims. You worry that the physicists have taken their equations and their metaphors too seriously. Here it's helpful to borrow a perspective from operationalism, a school of thought in the philosophy of science. A staunch operationalist might say the real content of a physical theory lies only in the list of experimental predictions it makes: "If you build an experiment in this way, you will see result X; if you build an experiment in that way, you will see that result Y," and so on. Any talk about invisible particles or fields then serves only to package and describe these predictions. Most philosophers agree this view is too simple, but it contains a point of truth: the language and concepts we use to describe our predictions are often a matter of taste and historical contingency. In fact, we expect that our most fundamental physical theories will be revealed as only useful approximations, undergirded by new theories with new descriptions.
Before we take claims of quantum weirdness seriously, we must ask whether the weirdness is a property of nature itself or only of our current description. This question is rarely broached in popular explanations of physics, or even in most physics classes. But the question stands: how do we know quantum theory will never be rephrased or replaced, that quantum weirdness is not just a figment of our odd descriptions?
It seems impossible to convince the skeptic. Imagine the conversation—
Physicist: "Electrons may exist in a ‘quantum superposition' of two places at once. Well, the electron isn't quite in two places, but it lacks a definite location until you measure it. Instead, it has a smeared out ‘wavefunction,' a diffuse blob representing many possible locations. Quantum reality is weird!"
Skeptic: "You really want me to alter my notion of reality? Maybe you're just confused about where the electron is, and in 100 years physicists will discover there's no such thing as true ‘superposition.'"
Physicist: "But we're sure the wavefunction spreads out. You see, when we send a photon through a double slit, we observe a wavy pattern, and if you know Schrodinger's equation, that means…"
Skeptic: "Sure, you saw some pattern on a screen. But did you actually see a superposition, whatever that would mean? Was anything actually weird, besides your wacky interpretation? What if wavefunctions and superpositions are just clunky concepts, soon to be reimagined and replaced?"
Popular physics writing abounds in overstated and conceptually ill-conceived claims, and the skeptic is right to be skeptical. But in this case, physicists possess an answer immune to the skeptic's well-reasoned objections, a demonstration that the world is truly weird. The trick is that even if we cannot prove quantum theory right, we can still prove other theories wrong. So to demonstrate the world is weird, we simply need an experiment that rules out any "ordinary" theory. That way, even if quantum theory were ultimately wrong, we would know any true theory is still weird.
The first of these ingenious experiments designed to rule out all ordinary theories was conceived by John Bell in the 1960s. (Bell was partly inspired by questions that Einstein had raised decades earlier.) By now, these "Bell tests" have been repeated several times. The verdict? The world is definitely weird. And because we claimed that we could rule out ordinary theories without relying on quantum theory being true, we should be able to describe the surprising results of Bell's experiment using only ordinary concepts. What luck: with a few minutes hard thought, we can actually understand what I believe to be one of the greatest scientific discoveries of all time.
It's easiest to conceive of the experiment as a game of chance. The game has two players, who almost always go by Alice and Bob (named after ‘A' and ‘B'). They cooperate to win against the game designer. It will turn out that in a world governed by any ordinary theory, Alice and Bob could not, under any circumstances, win the game more than three quarters of the time. Thus if Alice and Bob reliably average more than 75% success, we can rule out ordinary theories. In an actual experiment, machines play the roles Alice and Bob, and here's the extraordinary fact: quantum physicists can design these machines to "win" around 85% of the time.
Of course, the whole demonstration hinges on what we mean by ordinary or weird. What exactly is the class of ordinary theories we claim to rule out, and do the alternatives really deserve to be called weird? A lot may be said in the abstract. But for your first exposure, it's best to learn about the game and then decide for yourself.
Here's the game. Alice and Bob are led to remote locations, and at each location the staff there flip a coin, heads or tails. Based on the toss, the staff ask the player there a single question, either Question 1 or Question 2. For instance, the staff in charge of Bob might flip heads and therefore ask him Question 1, while the staff in charge of Alice might flip tails and therefore ask her Question 2. The point to remember is that there's a 25% chance of each of the four scenarios: (a) Alice receives Question 1 and Bob receives Question 2, (b) Bob receives Question 2 and Alice receives Question 1, (c) both receive Question 1, or (d) both receive Question 2.
Neither Alice nor Bob knows which question the other is asked, and both must answer a simple "yes" or "no." They win or lose according to their yes/no answers: if both are asked Question 1, they need different answers to win, and in all other cases, they need the same answers to win. Alice and Bob play this game again and again, and before every round the staff at each location flip a coin to determine which question to ask.
Alice and Bob meet to plan a strategy before playing, but once separated they are not allowed to communicate. Of course, if they could communicate, they could tell each other which questions they were asked and arrange their answers to win every time. So to prevent cheating, the staff at each location ask the questions simultaneously, and the players are forced to answer before they have a chance to conspire. In fact, Alice and Bob are forced to answer before light has time to travel between their locations. That way, there's no hope of Alice knowing Bob's question or vice versa, not even with a secret phone call.
How well can Alice and Bob expect to do? Say they simply answer "yes" every time. Then they lose whenever both are asked Question 1, because in that case they need different answers to win. But they win in all other cases, because those cases require the same answers. They therefore win 75% of the time on average, because only a quarter of the time are they both asked Question 1.
What if Bob decides to answer "no" for Question 1 but "yes" for Question 2, while Alice sticks to "yes" for both questions? Now they lose whenever Alice is asked Question 2 and Bob is asked Question 1, and otherwise they win. With this new strategy, Alice and Bob still win only 75% of the time.
Take a minute to convince yourself that whatever their strategy, Alice and Bob can never hope to average higher than 75%. (You might try listing all possible strategies; there are only a few.) If Alice and Bob use two robot supercomputers to answer for them, the same logic applies – even a computer can't beat this game of chance. And if Alice and Bob have cell phones or, say, a fiber optic communication line, they will fare no better. The staff will always demand an answer before light has time to traverse the line, and then even two supercomputers in direct communication will be stuck with a 75% success rate at best.
You already know the punchline. In numerous Bell tests, physicists have designed machines representing Alice and Bob that consistently win around 85% of rounds. Well, that's a small lie: the exact setup of the "game" varies minutely with each experiment. But in each case, the machines win more often than simple chance allows. (If you really wanted to build an experiment that corresponded exactly to the game described here, you could.)
With seemingly ordinary reason, we just argued that Alice and Bob can only average 75% wins. But to face reality, we must admit at least one of our implicit assumptions is false. Whatever these assumptions are, they underpin the "ordinary" physical theories that the Bell test proves wrong. To identify the assumptions, it's best to imagine ourselves as the dumbfounded game designers. How can Alice and Bob win so often? Maybe they managed to communicate after hearing the question but before they were forced to answer. This would contradict one of our implicit assumptions: people and machines cannot communicate faster than the speed of light, or rather no causal influence whatsoever travels faster than light. Could this be our mistaken assumption? It may seem like the least spooky resolution, but most physicists balk, for good reason. Einstein's well-tested theory of relativity suggests that even if we caught Alice calling Bob on her faster-than-light telephone, a high-speed passerby would observe Bob answer the phone before Alice made the call, ruining our notion of causality.
How else could Alice and Bob be winning? You might think they're just lucky. Then again, it turns out they beat the 75% figure so consistently that the odds of good luck are virtually zero. Could they be somehow manipulating the staff's coin tosses? Or maybe the staff in both locations are somehow prone to flipping heads, which would help Alice and Bob if they used the right strategy. In actual experiments though, the physicists have worked diligently to eliminate all possible loopholes.
If we reject faster-than-light communication and unlikely statistical errors, it's difficult to imagine how else the "Alice" and "Bob" machines might work. The machines must be choosing their answers in a way that violates our implicit assumptions. Where does our reasoning break down? Is there really no ordinary theory that explains these results? The distinction between ordinary and weird is somewhat a matter of taste, but I would say the results here are definitively weird.
At this point, you may be wondering how the "Alice" and "Bob" machines actually do pull off their stunt. To understand the technology would require quantum theory, but an inexact summary is still instructive. The key is to produce a pair of entangled particles, such as two electrons or protons. "Entangled" roughly means "correlated with each other, in a quantum way." When Alice and Bob meet to plan their strategy, they each stow away one particle from the entangled pair. (Or rather, the two particles are distributed to the separate Alice and Bob machines.) When Alice receives her question, she makes a certain measurement of her particle that depends on the question. Bob does the same. Then they answer "yes" or "no" depending on the outcomes of their measurements.
This description does not exactly shed light on the mystery. The weirdness of the Alice and Bob machines has merely been isolated as the weirdness of entangled particle behavior. How should we understand entangled particles? The next step for anyone interested in the philosophical implications of quantum physics is certainly to learn a bit of quantum physics. But remember that even our best descriptions of quantum phenomena are liable to change. And when they do, you can always return to the surprising results of this simple game.
Posted by Daniel Ranard at 12:55 AM | Permalink