Károly Zsolnai-Fehér explores what randomness really means, from coin flips to quantum mechanics. Bell's theorem shows that no hidden-variable theory can match quantum predictions, proving quantum randomness is fundamental, not just ignorance of unknown causes.
Dear fellow scholars, this is two minute papers with. When using cryptography, we'd like to safely communicate over the Internet in the presence of third parties. To be able to do this and many other important applications, we need random numbers. But what does it exactly mean that something is random? Randomness is the lack of any patterns and predictability. People usually use coin flips as random events. But is a coin flip really random? If we had a really smart physicist who can model all the forces that act upon the coin, he would easily find out whether it's going to be heads or tails. Strictly speaking, a coin flip is therefore not random. What about random numbers generated with computers? Computers are a collection of processing units that run programs. If one knows the program code that generates the random numbers, they are not random anymore because it doesn't happen by chance. And, and it is possible to predict. John von Neumann famously said, anyone who considers arithmetical methods of producing random digits is of course in a state of sin. For as has been pointed out several times, there is no such thing as a random number. There are only methods to produce random numbers. And a strict arithmetic procedure, of course, is not such a method. Some websites offer high quality random numbers that are generated from atmospheric noise. Practically speaking, this. This of course sounds adequate enough. If someone wants to break the encryption of our communications, they would have to be able to model the physics and initial conditions of every single thunderbolt, which means processing millions of discharges per day. This is practically impossible. So it seems reasonable to say that random events are considered random because of our ignorance, not because they are, strictly speaking, unpredictable. You just need to be smart enough and the notion of randomness fades away in the light of your intelligence. Or so it seemed for physicists for a long time. Imagine if someone who has never heard about magnetism would see many magnets attracting each other and some added magnet powder. This person would most definitely say it's magic happening. However, if you know about magnetism, you know that things don't happen randomly. There are very simple laws that can predict all this movement. In this case, magnetic forces, we can loosely call a hidden variable. So we have a phenomenon that we cannot predict, and we are keen to say it's random. In reality, it is not. There is just a hidden variable that we don't know of that is responsible for this behavior. We have the very same phenomenon. If we look inside of an atom. Quantum level effects happen according to the physics of extremely small things, and we again find behaviors that seem completely random. We know some of the trends, just like we know which Roads in our city are expected to have a huge traffic jam every morning, but we can cannot predict where every single individual car is heading. We have it the same way with extremely small particles. We are keen to say that a behavior seems completely random because nothing that we know or measure would explain it. Other people would immediately say, wait, you don't know everything. Maybe these quantum effects are not random, as there may be hidden things, hidden variables that you don't know of, which make up for the behavior. We can't just say this or that is random. It is much, much more likely that our knowledge is insufficient to predict what is happening, as electromagnetic forces seemed magical to scientists a few hundred years ago. So is quantum mechanics completely random or does it only seem random? It is probably one of the most difficult questions ever asked. How can you find out that something you measure that seems random is really completely random and not just the act of forces that you don't know of? And hold on to your chair because this is going to blow your mind. A simple and intuitive statement of Bell's theorem states that no physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics. This means that he proved that the behavior scientists experience in quantum mechanics are really random. They cannot be explained by any theory you could possibly make up. Simple one or complicated doesn't matter. This discovery is absolutely insane. You can definitely prove that the crappy theory someone quickly made up doesn't explain a behavior. But how can you prove that it is completely impossible to build such a theory that does? No matter how hard you try, how smart you are, you can't do it. This is such a mind bogglingly awesome theorem. And please note that we definitely lose out on some details and generality because of the fact that we use intuitive words to discuss these results as opposed to the original derivation with covariances between measurements on our imaginary list of the wonders of the world. Monuments created not by the hands, but the minds of humans. This should definitely be among the best of them. Thanks for watching and for your generous support and I'll see you next time.
