Probability

Hey there! My question is: is randomness an illusion or can everything theoretically be predicted? Let me use the coin toss analogy. At first, a coin toss appears totally random, but as we look deeper, we find that the "randomness" is simply a result of factors that we cannot perveive at first glance (ie. tossing force, distance from ground, air resistance etc). Suddenly the coin toss isn't random anymore. So is true randomness really out there or is all randomness just an illusion?

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That's an excellent question. Here is a rough reply. Oftentimes, when we refer to some everyday phenomenon as "random", we mean that we are ignorant of the fundamental causes at work -- as in games of chance. However, according to modern physics, there are some fundamental phenomena involving the behavior of sub-atomic particles that are genuinely random. For example, if a radioactive atom existing now has a half-life of (let's say) 100 seconds, then there is a 50% chance that it will decay sometime during the next 100 seconds, and there is no feature that the atom has now (or that anything else has now) that determines whether the atom will decay or won't decay. It is an irreducibly random process. In other words, the atoms that ultimately do decay before 100 seconds have passed are no different now from the atoms that do not decay during that interval. There are no "hidden variables" to distinguish them.

I should add that the reason we have for believing that these phenomena are genuinely random is NOT that scientists have looked very hard for the hidden variables, but they have not found any, and since scientists are pretty smart and resourceful, there must be no hidden variables to find. That would not be a very powerful argument! Instead, the argument is more like this: Our most empirically accurate theory of the fundamental processes of nature (namely, the theory known as "quantum mechanics") makes various statistical predictions (such as that the given atom has a 50% chance of decaying during the next 100 seconds), these statistical predictions have turned out to be quite accurate indeed, and (here's the kicker) there is no theory that hypothesizes we--behaved "hidden variables" and that makes the same statistical predictions as quantum mechanics. It's not just that no one has ever managed to come up with such a theory. It's that there cannot exist such a theory. (I haven't given you an argument for that claim -- and it should not seem obvious! Nor have I defined just what "well-behaved" means.) So either the statistical predictions made by quantum mechanics are not really as accurate as the overwhelming evidence seems to suggest, or the world is fundamentally chancy.

By the way, these sorts of fundamental chances probably have little if anything to do with the behavior of coins, dice, and so forth. At the level of such "large" objections, those chances (given the details of how the coin was tossed, the current states of the air molecules in the room, and so forth) differ only negligibly from 0% and 100%.

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