Probability Is Subjective
Naval: Does probability actually exist in the physical universe, or is it a function of our ignorance? If I’m rolling a die, I don’t know which way it’s going to land; so therefore I put in a probability. But does that mean there’s an actual probabilistic unknowable thing in the universe? Is the universe rolling a die somewhere, or is it always deterministic?
Brett: All probability is actually subjective. Uncertainty and randomness are subjective. You don’t know what the outcome’s going to be, so you roll a die. That’s because you individually do not know; it’s not because there is uncertainty there deeply in the universe. What we know about quantum theory is that all physically possible things occur.
This leads to the concept of the multiverse. Rather than refute all of the failed ways of trying to understand quantum theory, we’re going to take seriously what the equations of quantum theory say. What we’re compelled to think about quantum theory, given the experiments, is that every single possible thing that can happen does happen. This means that there is no inherent uncertainty in the universe because everything that can happen actually will happen. It’s not like some things will happen and some things won’t happen. Everything happens.
You occupy a single universe, and in that universe, when you roll the die, it comes up a two. Somewhere else in physical reality, it comes up a one, somewhere else a three, a four, a five, and a six.
Naval: If I’m rolling two dice, then the universes in which they sum up to two is less than the number of universes in which we roll a seven, because that can be a three and a four, a five and a two, and so on. So the number of universes still does correspond to what we calculate as the probability.
Brett: Yes. This leads to what Deutsch calls their decision-theoretic way of understanding probability within quantum theory. Decision-theoretic means you assume there’s proportionality between the universes’ way of splitting things up. So if you’re rolling two different dice, then the universes proportion themselves into measures. A measure is a way of talking about infinities.