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How to teach quantum mechanics to kids

Does this even make sense? Doesn’t quantum mechanics involve advanced esoteric mathematics? Didn’t Richard Feynman say that nobody understands quantum mechanics, and didn’t Niels Bohr remark that those who aren’t shocked by quantum mechanics can’t possibly have understood it?

Quantum mechanics is our fundamental theory of matter. It has been confirmed to exquisite levels of accuracy and underlies much of modern technology: transistors, microchips, lasers, atomic clocks, the basic building blocks of computers, televisions, smartphones, CD players, fiber-optic telecommunications, GPS systems, MRI machines, and more. No one could say that physicists who exploit quantum mechanics to design and construct these devices fail to understand the theory.

What Feynman and Bohr meant was that quantum mechanics calls into question our commonsense classical worldview at the most fundamental level. As Einstein put it, we think of an object as having a ‘being-thus,’ a particular catalogue of definite properties. Objects are located in space and time. Our actions causally influence the properties of distant objects only via perturbations that propagate locally from neighboring region to neighboring region. The most astonishing and disturbing feature of quantum mechanics is non-locality as it occurs in the phenomenon of quantum entanglement — strangely counter-intuitive correlations between separated quantum systems that defy causal explanation. Schrodinger called entanglement ‘the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought.’ The classical worldview is fundamentally at odds with non-local entanglement.

Any educated person should be aware of major advances in science, and so should have a basic understanding of this extraordinary revolution in our conceptual framework. You might think that it’s a tall order to convey the weirdness of quantum correlations to kids, but there’s an insightful way to do this without the mathematical machinery of the theory by considering simulation games. In fact, if you don’t already understand just how quantum mechanics conflicts with our classical worldview, you will by the end of this article.

Consider an imaginary ‘superquantum’ correlation, proposed in 1994 by Sandu Popescu and Daniel Rohrlich – an extreme but possible version of the correlations that do occur in our quantum world. Popescu and Rohrlich imagine a box with two inputs, a left input and a right input, and two corresponding outputs. Inputs and outputs can each be 0 or 1, and the two possible outputs occur with equal probability for either input. The box functions in such a way that whenever both inputs are 1, the outputs are different, but for the other three combinations of inputs – both inputs 0, or left input 0 and right input 1, or left input 1 and right input 0 – the outputs are the same. Finally, Popescu and Rohrlich suppose that the two halves of the box can be separated by any distance without altering the correlation.

Jeffrey Bub compares the output of the Popescu-Rohrlich correlation box to flipping a coin. Image Credit: Coin toss by jeff_golden. CC BY-SA 2.0 via Flickr.
Jeffrey Bub compares the output of the Popescu-Rohrlich correlation box to flipping a coin. Image Credit: Coin toss by jeff_golden. CC BY-SA 2.0 via Flickr.

The Popescu-Rohrlich correlation contains all the conceptual mysteries of quantum entanglement. There’s no way you could rig a real box with some sort of mechanism to produce this correlation, but it’s quite possible for a pair of coins, say, to produce the correlation just by chance for a long run of tosses, where the inputs correspond to a coin being tossed heads up or tails up, and outputs correspond to a coin landing heads or tails, with heads and tails corresponding to 0 and 1. Of course, the longer the run, the more improbable the correlation would be, but it’s not impossible.

Suppose Alice and Bob play a game with a moderator where the goal is to simulate this correlation. Alice and Bob are allowed to discuss strategy before the start of the simulation game, but once the game begins they are separated (say in two soundproof booths) and can only communicate with the moderator. The moderator gives Alice and Bob each a 0 or a 1 chosen randomly as input at each round of the game, and they each respond with a 0 or a 1 as output. They win the round if inputs and outputs are correlated like the correlations of a Popescu-Rohrlich box.

If Alice and Bob are allowed to generate a long random list of 0’s and 1’s before the start of the game (with as many entries as there are rounds of the game) and each keeps a copy of the list to consult during the game, they can win three out of four rounds on average. For each round, the strategy is for Alice and Bob to ignore the input and respond with the 0 or 1 on the list, in order for the sequence of rounds. Then they will both respond 0 or both respond 1 with equal probability for each pair of inputs (because the lists are the same), and they will win all the rounds except the rounds for which both inputs are 1 (when they are supposed to respond differently). If the inputs are chosen randomly, they will win three out of four rounds on average. It’s not hard to prove that this is the optimal strategy if Alice and Bob are allowed only classical resources: Pencil and paper, calculators, classical computers, that sort of thing. So the optimal classical strategy is only successful for three out of four rounds on average, which is to say the probability of winning the simulation game with classical resources is at most .75.

Now here’s the punchline. If Alice and Bob are allowed quantum resources – entangled pairs of quantum systems prepared before the start of the simulation game which they share when they are separated, and measuring instruments to measure these systems – they can win the simulation game with a probability of roughly .85 if they base their responses on these measurements! So quantum systems somehow manage to produce correlations closer to a Popescu-Rohrlich correlation than classical systems. How they are able to accomplish this feat is the quantum mystery nobody understands, the mystery that requires a fundamental revision of our commonsense classical worldview.

Featured image credit: Technology by tec_estromberg. CC BY 2.0 via Flickr.

Recent Comments

  1. Alan Cooper

    Surely the clause “There’s no way you could rig a real box with some sort of mechanism to produce this correlation” needs to be modified by adding the requirement that there can be no connection or communication between the two halves of the box…?

    And doesn’t the need for Alice and Bob to have a randomly chosen shared sequence depend on the moderator trying to defeat them? (Otherwise any shared sequence with equal frequencies should work just as well.)

    These may seem like minor quibbles to one who knows what is intended, but if the intended audience is children then it may be frustrating to some of them to have definite assertions stated with key assumptions left out.

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