Probability

Probability is a deeply weird and disturbing topic. The harder I look at it, the weirder and more disturbing it becomes. I find the many-worlds interpretation of quantum mechanics to be the least weird and disturbing way to think about it.

Let me tell you a story. In ninth grade math, we took a break from all the trigonometry to do a little section on probability. It wasn’t anything exotic, just the likelihood of pulling certain cards out of a deck, stuff like that. I had been a straight-A math student my whole life until that point, and I couldn’t wrap my head around probability at all. I could memorize the equations well enough, but I was used to intuitively understanding the rationale behind the equations, and with probability I just could not do it. When you flip a coin and it winds up tails, where does the heads outcome “go?” How does the coin “know” it’s supposed to converge on a fifty-fifty ratio of heads and tails as you flip it more and more times? I almost flunked the test on that unit, I was so baffled.

I forgot the whole thing until more recently when I started learning about quantum mechanics. That’s where the probability questions get to be way more philosophically disturbing than in coin-flipping and card-choosing.

The situation is summed up best by the famous double-slit experiment. In this experiment, you shine light through a screen with a pair of slits in it onto photographic film. You get a stripy interference pattern as the waves of light coming from each slit overlap each other, the way overlapping ripples in a pond do. In this case, what’s “waving” is the probability density of a given photon passing through a given slit and landing at a given spot on the screen. Just the thought of probability having a physical density gives me intense vertigo, but it gets worse.

If you shoot a single photon at a time through the slits onto the film, the result looks like this:

Each individual photon somehow “knows” that there are two slits, and that the probability waves emanating from each slit interfere with each other. So even when the photons come one at a time and don’t interact with each other at all, they still obey the same probability distribution as if you fired them all at once. What’s even weirder is that you can get this same result with any quantum particle, and even entire molecules like buckyballs.

You can interpret this situation to mean that the probability waves are some sort of physical entity, a “pilot” wave that tells each photon what to do, which somehow extends forwards and backwards in time. I find this idea repugnant. You could also interpret the experiment to mean that space and time are nonlocal in some way that lets the single photon go through both slits at once. I also find this idea repugnant.

The only explanation of the double-slit experiment that makes any sense to me is the many-worlds interpretation. Because the left-slit universe and the right-slit universes are so similar, they overlap and mutually interfere, and that’s what produces the stripy pattern. It took me some time to get used to many-worlds, but once I got comfortable with it, I’ve become much more relaxed when I think about probabilities. Now I just see the different possible outcomes as all happening in some universe, and the “probability density” is just the density of the different universes. If I flip a coin, there’s an equal number of universes where it lands heads or tails, plus a very small number of universes where all the particles in the coin spontaneously jump into the Andromeda galaxy.

I’m not a mathematician or a scientist. I’m just a humanities guy who likes math and science. So if you’re a professional in one of these fields and you can correct me or clarify what I’m trying to say here, please do, I want to understand this stuff more clearly.

Original post on Quora