“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 |

Billiards | 8 |

Bumper cars | 25 |

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

Reblogged this on Filmologìe of monsters and little princesses.

I really like your Blog. We met on another Forum. ,-)

When it comes to quantum mechanics, i always think of this quote, which reminds me, that It’s possible to understand.

“Anyone not shocked by quantum mechanics has not yet understood it.”

Niels Bohr

I have a question perhaps you could answer.

Although quantum fluctuations are believed to be random, is it possible they are not completely random but only appear to be so?

I have two reasons for suggesting this.

One has to do with behavior of networks where very large networks using very simple rules can generate very complex patterns that appear to be random or take enormously long times to repeat. However, the actual behavior of the network would be predictable if we knew the rules of it.

Two is that I don’t see how any complex structures could develop in the universe if underlying them where quantum fluctuations that are truly random.

What I am suggesting is that quantum fluctuations may be subtly biased in some way.

Good question, reply coming soon ^_^

This is a good question, but I think I might have to disappoint you. To start, we first have to be clear on what “quantum fluctuations” are. There are two potential meanings; 1) The Casimir effect (which I suspect you do not mean), or 2) the fact that how quantum systems look are not decided until you look at them. I’ll address part 2). Quantum “fluctuations” are random sort-of by definition. Back when quantum mechanics was invented, there was a huge debate among the giants of the day (Einstein and Bohr) about whether the “fluctuations” were

actually randomor whether they were some kind of “hidden variables” that we don’t understand. The answer was eventually that there are no hidden variables, and that “fluctuations” are completely, fundamentally, random. This was such a point of contention that it is one of the most famous debates in the entire history of Physics, and since the matter was settled theoretically there have been decades of experiments demonstrating that our conclusion is correct. The argument was even settled enough that Einstein himself was persuaded in the end. He became a reluctant practitioner of the “Copenhagen interpretation” of quantum mechanics. (The Copenhagen interpretation is more or less that “fluctuations” are completely random and there is no fundamental deeper mechanism).As for your reasons for suggesting the subject; both of the examples you show are reasonably well explained without the use of quantum mechanics. Their explanations rely on something called

nonlinear dynamics, which is more popularly known as “chaos theory”. In a nutshell, is a system is sufficiently large (as in both of the examples you cited), two things are observed;1) The behaviour of the system depends extremely sensitively on the initial conditions, to the point that one result is completely unrepeatable and therefore unique,

2) The system shows “patterns” which never exactly repeat, but show a property called

self similaritywhich is most well known in fractals (but is seen in all sorts of massive and complex systems).I hope that is a satisfying explanation. =]

This is a very good explanation but I am maybe still not totally persuaded.

We have the matter/anti-matter imbalance in the universe. Something which could be explained by a sort of bias in the early universe. I think some sort of imbalance has also been detected in colliders (not sure where I saw this). I know this might be confusing symmetry with the issue.

We also have the Dmitri Krioukov simulation of the growth of the universe where large scale structures appear to have a network like distribution. This distribution make perfect sense if the underlying quantum structure behaved like a network with rules. Since all particles of the universe were close sometime shortly after the Big Bang quantum entanglement could be the basis of this connectivity.

I am somewhat familiar with the Great Debate over this, although the deep mathematics is beyond me. The act of looking at quantum systems is subject to quantum fluctuations itself. For example, the selection of the moment of measurement and the selection of what to measure. How do we know that Schrodinger’s cat is slightly more alive than dead before we measure it?

Great response and I appreciate your time spent on my question.

Do you have a place where I can follow your blog with email notifications? I only see the RSS subscriptions.

Again I feel like I’m disappointing here, but I think that there’s an important distinction to make here. Fluctucations are the random change in a system (i.e. a large set of interacting things) over time. I think that perhaps you are confusing a mechanism with a phenomenon – “quantum fluctuations” are fluctuations (the phenomenon) caused deterministically by quantum mechanical interactions (the mechanism). The effect of a “fluctuation” is essentially what happens when you observe a quantum system multiple times in succession with enough time inbetween for the wave-function to relax back into a superposition of states.

In plainer language; Schrodinger’s cat (without the actual living cat) can be measured successively to be “dead” and then “alive” and so on. If you prepare the system correctly, you can control the probability that each will be observed. The thing is, this “bias” is entirely *within* the realm of standard quantum mechanics. In other words; “bias” in the sense that you use it is fine, assuming you can find an interaction and/or set of initial conditions which *produces* that bias. This is the current problem with the matter/antimatter problem you stated – what mechanism produced it, and how can we produce the theory of the *interaction* to give the relevant resulting “bias”. In a sense, you are right, but “bias” is not something which is outside “standard” QM. This is admittedly somewhat counter-intuitive, but then that’s QM for you.

Assorted points;

– There’s no such thing as “deep maths”. It’s just maths, and it’s not particularly complicated in most of the textbook cases. Indeed, some classical (i.e. non-QM) systems are more complicated than most well-studied QM systems.

– “A network with rules” is actually exactly what the universe is. In some ways of thinking of Physics, in what is termed “matrix mechanics” (nothing to do with the movies), the problem is treated exactly like that. There’s no fundamental difference between a QM universe and a “network with rules”.

– I’ll see what I can do about email notifications. Have you tried pressing “Follow” for the WordPress reader?

– The thing you mention “observed in colliders” might be what’s called the “breaking of parity” which is a different thing, which is not easily explained without the maths. It’s a type of symmetry which isn’t related to any kind of every-day experience.

Thanks again. Yes the Follow was there. My bad.

Deep math just means over my head. Maybe when I was younger I could follow it but probably not now. I work developing software and use logical thinking all of the time but actual mathematics I do very little of and have done very little of for a few decades.

There’s no fundamental difference between a QM universe and a “network with rules”.

I guess I can take some solace from that.

” By this, they mean that they think all classical probability is fundamentally rooted in the randomness of quantum mechanics. ”

I guess I was trying to say is that maybe large scale order and complexity (including chaos theory) might be rooted in quantum mechanics too.

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