Monday, September 10, 2018

Where exactly does probability enter the theory?

Peter Woit writes:
A central question of the interpretation of quantum mechanics is that of “where exactly does probability enter the theory?”. The simple question that has been bothering me is that of why one can’t just take as answer the same place as in the classical theory: in one’s lack of precise knowledge about the initial state.
Lee Smolin says he is writing a book, and there are 3 options: (1) orthodox quantum mechanics, (2) many-worlds, (3) hidden variable theories, like pilot waves. All attempts at (2) have failed, so he says "My personal view is that option 3) is the only way forward for physics."

This is a pretty crazy opinion. No one has been able to makes sense out of probabilities in a many-worlds theory, and Bell test experiments have ruled out all sensible hidden variable theories.

Lubos Motl posts a rant against them, as usual:
Quantum mechanics was born 93 years ago but it's still normal for people who essentially or literally claim to be theoretical physicists to admit that they misunderstand even the most basic questions about the field. As a kid, I was shocked that people could have doubted heliocentrism and other things pretty much a century after these things were convincingly justified. But in recent years, I saw it would be totally unfair to dismiss those folks as medieval morons. The "modern morons" (or perhaps "postmodern morons") keep on overlooking and denying the basic scientific discoveries for a century, too! And this centennial delay is arguably more embarrassing today because there exist faster tools to spread the knowledge than the tools in the Middle Ages.
Lumo is mostly right, but it is possible to blame uncertainties on lack of knowledge of the initial state. It is theoretically possible that if you had perfect knowledge about a radioactive nucleus, then you would know when it would decay.

However it is also true that measurements are not going to give you that knowledge, based on what we know about quantum mechanics. This is what makes determinism more of a philosophical question than a scientific one.

I agree with Lumo that deriving the Born rule is silly. The Born rule is part of quantum theory. Deriving it from something equivalent might please some theorists, but really is just a mathematical exercise with no scientific significance.

This question about the origin of probabilities only makes sense to those who view probably as the essential thing that makes quantum mechanics different from classical mechanics. I do not have that view. Probabilities enter into all of science. It is hard to imagine any scientific theory that can be tested without some resort to a probabilistic analysis. So I don't think that the appearance of probability requires any special explanation. How else would any theory work?

It is very strange that respectable physicists can have such bizarre views about things that were settled about a century ago. I agree with Lumo about that.


  1. Roger,

    Probabilistic analysis is useful in analyzing the data, but it isn't an actual physical process/force/cause of the data.

    It is one thing to have every grade in a given size class room and calculate an average.

    It is quite another to start with the class average and pretend that it allows you to backwards calculate the initial grades that allowed you to calculate your average, or any other statistic for that matter.

    In either/any case, the average is actually NOT what is going on (an average grade isn't even the grade of an actual person, it's a mathematical fiction used to represent the class activity as a number), or how the grades came about, or why, and merely hides what is going on behind a number generated by a calculation. Given how poor the models of atomic particles are at present (electron bonding theory is hogwash, it has nothing to do with how atoms bond or combine or organize, and while good for balancing the accounting equations of chemistry formulas, do next to nothing explaining how the damn things work).

    Play with statistics all you like until you go blind, they Aren't actual causes (but a placeholder for a lack thereof), or explanations of causes, they are a mathematical abstraction pretending to be a description or cause. Particles do not somehow add themselves up and do math logic to determine their aggregate behavior, the mathematical process is NOT what the physical process is doing at all.

    If you are merely content to look at highly processed group outcomes, fine, but you are really just guessing at what produced those outcomes... you only have to look at the ever growing absurdist zoo of particle physics to see it has become lost in artifacts of reified math.

    1. Quantum mechanics is one of the least successful theories of all time.

  2. Yes, but QM is not really clear on what measurement is. You are talking about using macrostates to find microstates. This could be further clarified.