Q&A: Ontological and Epistemological Doubt, Quantum Mechanics, and Probability
Ontological and Epistemological Doubt, Quantum Mechanics, and Probability
Question
Hello Michi, in The Science of Freedom you say that there is epistemological doubt when we do not know what reality is. And in an indeterminate reality, it is ontological doubt, because reality itself is unclear, not that we are lacking knowledge about reality. When we have epistemological doubt, we can use probability, and then we can know the odds that something was a certain way, like with a die. But when reality itself is indeterminate, then we cannot say what the probability is, because there is no probability, like the law of large numbers or in chaos; rather, it is truly random. But in quantum mechanics this is "ontological doubt," and yet we do use probability. How exactly is that possible? And doesn’t that indicate that it is epistemological rather than ontological doubt?
Answer
You are mixing together two different planes. In a state of superposition there is a combination of two states in some mixture. Here there is no probability at all. When you make a measurement, you will get one of the two pure outcomes, and the chance of that is determined by the coefficients of the mixture. Here the coefficients represent probabilities. Before the measurement this is indeterminacy, and afterward probability.
Discussion on Answer
Right. But you can know that it was there, like in the double-slit experiment.
Or there are hidden variables that we just don’t know, no?
That is a possibility that has not yet been completely ruled out.
How could it even be ruled out? But Schrödinger’s cat says exactly that there are such variables, unless you’re telling me that the measurement changes something, and I don’t know why, but it feels less plausible to me that our measurement would change something in quantum mechanics. No?
The probability is about the measurement outcomes.
I once heard that the French name for the wave function (or a similar concept from the field) uses the word densité—density (as in a density function), and in my opinion that is a wonderful way to look at superposition. As if (or not just as if) the particle is present in all places with varying density, and where it is densest—that is where it is most likely to be measured.
"Likely to be measured"—after the collapse of the wave function.
It does not mean "likely to be measured" in the sense that its location will be discovered.
So superposition is a real state, it’s just that you can’t measure it?