“Quantum ignorance” might sound like a joke, like something a non-scientist might say to show they know nothing whatsoever about quantum mechanics. Well, here’s the punchline; “quantum ignorance” is a real thing in quantum mechanics. Even better, I’ll explain why researchers from The University of California at Davis (USA) are genuinely worried about it. Indeed, everyone should be worried about what’d going on in the field as it has consequences for every day things such as flipping a coin or winning a bet.
The discussion starts with a reminder of the uses of probability. Probability as we use it everyday is known as “classical” probability because it makes sense to us on an everyday level. There are other kinds of probability – quantum mechanics uses its own version of probability which behaves differently and is arguably the cause of all the oddness which we associate with quantum mechanics.
In classical probability, we say that when a coin is flipped, the probability that it will land on either side is equal – a “50-50 chance” in common language. When taught, this is often justified because it makes sense. An unbiased coin will by definition have no difference between the chance of a heads and the chance of a tails. This is entirely sensible on an everyday level.
The authors of the paper I’m talking about today think that we should stop thinking of this kind of thing as simply classical. By this, they mean that they think all classical probability is fundamentally rooted in the randomness of quantum mechanics. They support this argument by considering quantum mechanics in the context of the coin toss. They make a simple calculation which demonstrates that when you consider the quantum mechanics of your nerves, quantum mechanics produces exactly the same result.
The importance of this is that flipping a coin is an example of quantum mechanical probability. That’s right – the most plainly obvious example of classical probability is actually not classical at all! The authors argue that this is the case for all applications of classical probability.
However, this does make a sort-of sense to a Physicist. One of the most astounding principles of quantum mechanics is that on a large scale, the net behavior of quantum effects tends to behave like classical behavior. This is something that Physicists find again and again when considering large (i.e. “human scale”) systems. This looks like another application of the same principle.
The reason that I particularly like this paper is that they go out of their way to tell you how simple it is to prove them wrong. All you have to do is find a useful example of probability which has no relevance to quantum mechanics. However, they point out some suggestions they’ve had which seem to be true, but which have some fatal and subtle flaws. This is one of those things where I like to quote Ben Goldacre;
I think you’ll find it’s not quite as simple as that.
One more interesting thing of note is that the authors make a fascinating calculation which shows how quantum uncertainty in colliding things transforms from tiny quantum fluctuations to large-scale, obvious things. What’ amazing is that they calculate how many times different things need to bounce together before the whole situation is dominated by quantum uncertainty. The results might surprise you!
|System||Number of Collisions|
|Air in the room||-0.2|
|Water in your body||0.6|
The above table shows you how many collisions you’d need in each system for quantum uncertainty to take hold. You can see in the top two (air and water), the number of collisions is less than one and therefore the systems are quantum-uncertain all the time. This is what we know to be true. However, by simply extending the calculation to bigger things, they showed that billiards and even bumper cars (every day classical things) are governed by quantum mechanics after a point! Next time you’re playing mini-golf and considering a complicated set of ricochets, just remember that more than about eight and you might not get what you bargained for (no matter how carefully you plan it)!
So – what is the much-vaunted “quantum ignorance” that I started with? Well, quantum ignorance is the words which the researchers used to describe the way that we usually ignore quantum mechanics when flipping a coin. We use classical probability to get around our ignorance of the quantum processes – our quantum ignorance.
Andreas Albrecht, & Daniel Phillips (2012). Origin of probabilities and their application to the multiverse Arxiv arXiv: 1212.0953v1