Dear Fellow Scholars, this is Two Minute Papers with Károly Zsolnai-Fehér.
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 coinflips as random events. But is a coinflip 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 coinflip 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 it is possible to predict.
John von Neumann famously said: "Any one 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, 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're 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 cannot predict where
every single individual car is heading. We have it the same way with extremely small particles.
We're keen to say that a behavior seems completely random, because
nothing that we know or measure would explain it. Other people will 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 a 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 them.
Thanks for watching and for your generous support, and I'll see you next time!