*Several readers objected to Taner Edis’s discussion of randomness in his “An Accidental World” (FI, Science *and* Religion, Fall 2002). Quantum randomness may be counterintuitive, but it isn’t just a good idea, it’s the law. We invited Edis to expound further on the admittedly quizzical quantum randomness.*

*—eds.*

Physics can get weird, so everyone who teaches physics develops a set of stories and analogies to help students imagine the unfamiliar in terms of what they already know. A colleague calls them “little lies”––we know that the physics we’re trying to explain doesn’t exactly work that way. But it’s close, and with some luck, our students learn enough to help them get started.

For example, when speaking of heat transfer between hot and cold, I may describe it as similar to the way a drop of ink spreads to color a glass of water. In fact, the equations for heat flow and diffusion are identical. However, the analogy breaks down. I have to make sure my students realize that heat is not a fluid, that we are talking about energy, and that energy itself is an abstract concept different than what we mean when we talk about “feeling energetic.” I warn them that when a New Ager speaks of “energy” it is gobbledygook to a physicist.

When I introduce an audience to the randomness in quantum mechanics, I have to play a similar game. There, my standard illustration is a coin flip––quantum events, I often say, are random like the result of a coin flip, unpredictable in advance.

There is, of course, a catch. When I speak of flipping a fair coin, I really mean an abstract, idealized mathematical model of a coin. This model is extremely simple: each individual coin flip is independent of any other and totally unpredictable. If we continued flipping the coin, we would get a series of heads and tails with no pattern connecting the result of each toss with any other. This model does not allow us to learn more about the coin-flipping process in hopes of improving our ability to guess whether heads or tails will turn up. Doing that would take us beyond the idealized model––even if we ended up with a haphazard series of heads and tails, we will have located the source of the randomness somewhere other than the coin flip.

The simple, idealized model is a decent first approximation to coin flips in real life. However, as with heat flow and ink diffusion, the analogy breaks down if we push it too far. A real coin is a complicated object, much better described by a Newtonian model. In this more realistic picture, we can identify many variables that, if we measured them, could help us predict how a coin would land. If we got a handle on the exact forces exerted on the coin as it is flipped, the mass distribution of the coin, the local strength of gravity, even the density variations in the air it spins through, we could do better than 50 percent in guessing whether it turns up heads or tails.

In fact, there is no limit to what we can predict about a Newtonian coin. It is always possible, if we just exert ourselves a bit more, to acquire more information about the coin flip and get closer to 100 percent predictability. With a couple of million dollars to fund an Institute for Coin Flip Studies, physicists could promise better than 95 percent accuracy in guessing how an actual coin would land.

In other words, a real coin flip is not random. The simple, idealized random coin flip is just an approximation we use when we know too little about the values of the many relevant variables we need to describe a Newtonian coin.

However, it turns out that modern physics is full of truly random events––events for which the appropriate model is just like the simple, idealized coin flip. We run into this true randomness in our fundamental theories, particularly in quantum mechanics. To obtain a “quantum coin,” I should more properly talk about “a quantum two-state system like a spin-1/2 particle,” but at this point jargon takes over. What is more important is that, as far as we can tell, such a quantum coin behaves exactly like our mathematical ideal and not like a Newtonian coin. A quantum coin is simple: if we flip it, we get a result that is equally likely to be heads or tails. Knowing the results of previous flips will not help us guess better. Neither are there any variables we can measure to improve our predictive ability. There is nothing more to learn about the flipping process — nothing resembling identifiable forces which, if only we knew them, would enable us to predict what would take place. Instead of always being able to increase our precision, we cannot even begin to do so.

The physics community has been acting as an Institute for Coin Flip Studies for many years, flipping quantum coins, and we can still do no better than 50 percent and cannot see how to improve.

Note that saying the result of a quantum coin flip is random is not the same as saying we just don’t know. I have to make sure my students don’t confuse randomness with mere lack of information. “Random” is not the same as “unknown,” nor does it mean that we cannot say anything about random occurrences. If a coin flip is random, we know that, in the long run, the frequency of heads and tails will be about equal. We know, again in the long run, that the sequence of results will have no pattern––that it won’t, for example, alternate like “HTHTHTHTHTHT. . . .”

Randomness means that each individual coin toss is completely unpredictable, but this unpredictability immediately implies that we know exactly what sort of sequence we will get, in terms of its statistical properties.

Everyone has to have a hobbyhorse, and, when I’m riding mine, I insist that we should take this randomness seriously. Randomness is real, it’s fundamental, and it’s not merely a manifestation of the capricious choices of Millicent, the goddess of quantum small change. Quantum coins are but one example; events like radioactive decays happen spontaneously, at random, without any cause. We should change our views of the world, including how we understand something as basic as cause and effect.

Defending my perspective takes a lot more than a brief clarification of quantum coins. So I will now use another science teachers’ trick. When I see deep waters ahead, I tell my students that, if they want a fuller picture, they should do the reading I then assign. In this case, I will shamelessly plug my own book, The Ghost in the Universe: God in Light of Modern Science. In it, I do a lot more exploring of randomness in physics and its implications for a naturalistic view of our world. It’s sold a couple of thousand copies so far; if this number gets into the millions, I can retire to a desert island and flip coins for the rest of my life. On the other hand, I suspect my chances are better if I buy a lottery ticket.

*Taner Edis is *assistant* professor of physics at Truman State University and author of The Ghost in the Universe: God in Light of Modern Science (Prometheus, 2002).*