Q&A: Randomness and Lawfulness
Randomness and Lawfulness
Question
From your books I learned that even if we assume there are random systems in nature, intervening in them is still a miracle. In other words, even randomness is a certain kind of lawfulness, since it distributes 50:50 according to the law of large numbers. I would be happy if you could sharpen this for me a bit more: can one not argue that such a system is not under any law at all? That is, not that there is a law of randomness, but that there really are places where no physical law determines cause and effect. And if so, intervention in such a place is not a miracle, since a miracle means intervention in the laws of nature, not in a place where nature has nothing to say.
Thank you in advance
Answer
But in the laws of quantum mechanics, the laws do have something to say. They determine the distribution. In principle one can imagine a system with no law at all, but as a matter of fact we do not know of such a system in our nature. a0
Discussion on Answer
Not at all. The distribution is determined by physics. Think about a fair die. The distribution of outcomes is uniform (a 1/6 chance for each result). Who determined that distribution? The structure of the die, meaning the physics.
That is true for a six-sided die, but in a random system where there can only be two outcomes, could it also be that after a million trials there would not be a 50:50 distribution, assuming there is no law there at all?
Maybe I’ll explain the question a bit more: if I understand correctly, in a random system there are only two possibilities: particle or wave. The other possibilities are not taken into account, since they are “bound” by rigid laws. But of these two possibilities, let us assume there is no law in the world at all acting on them. Now suppose we checked, and after a million trials the distribution was 50 percent wave and 50 percent particle. Seemingly the reason for this is that when there are only two possibilities, they will always split half and half—even if no necessity operated on them.
By contrast, with a die, the very fact that it is divided into six and not five or seven proves that there is some basic system of physical data according to which the die operates.
Every distribution is a result of the circumstances, including a uniform distribution (like half and half). I think we’ve exhausted this.
Thank you for the answer, but seemingly the distribution is determined by the laws of statistics, not by the laws of physics.