This is a followup to my post on real probability.
My brother Brian and I, when we lived together in Bozeman, read a lot of interesting books and talked about a lot of interesting topics. A couple of books that I remember being the most interesting covered such diverse topics as chaos theory, time, and quantum mechanics.
Something I remember reading about was called quantum tunneling. What that is, in simple terms that most people (like me) still won’t understand, is basically the phenomemon of electrons showing up in energy states that they shouldn’t be in. There is a certain small probability that the electron will “break through” an energy barrier and end up in a state that it normally shouldn’t be in.
Because of my lack of understanding and reading too much into some of the analogies that were given to explain the concept I had this idea that actual atoms could tunnel through physical barriers, instead of electrons through an energy barrier. Brian and I immediately expounded on the idea.
Okay, if one particle can get through an object, why can’t two? At the exact same time? The probability would just be the probability of it happening to one squared. With the incredibly tiny numbers involved, we understood that the chances of this happening were infinitesimal. And we kept going with it: why couldn’t a bunch of particles tunnel together? Why couldn’t billions or trillions of particles (your body) tunnel through something? We knew we were getting ridiculous, but it was fun.
We started calling out the probabilities in units of time, kind of like MTBF, which is mean time between failures. How much time can you expect to pass before a system fails, which is usually given in a number of hours. It isn’t a guarantee that something will or will not happen, it’s basically just a guess or measurement of past performance. We said that one can expect one particle to quantum tunnel every millenium, or every million years, or whatever we came up with. So that means (using 1,000 years) that you could “expect” two particles to tunnel together once every million years. And you would have to wait one trillion years for four particles to tunnel. A trillion years, that’s longer than some scientists say that the universe has been around and longer than it will be around.
We needed a new numbering system. The probabilities were going to start getting really ridiculous pretty soon. A new measure was born: “lifetimes of the universe”. An indeterminate amount of astromically long time. Now things were expected to happen on the scale of millions and billions of lifetimes of the universe.
Yep, we’re big nerds, not to mention the fact that we were just plain wrong, but we had a great time thinking about it.
