Where Quantum Probability Comes FromFirst, let's respond to the title and the subtitle in a no-nonsense way. First, the title: Where does the quantum probability come from?
There are many different ways to think about probability. Quantum mechanics embodies them all.
Well, the fact that the probability is needed is experimentally proven by the random outcomes of experiments. The probabilities are calculated in QM through Born's rule. And the probability amplitudes are the most fundamental, elementary, irreducible objects in the theory so it's a fallacy to try to reduce them to something else!
So the quantum probability "sociologically" came from the experimenters such as those who observed the (random) radioactive decay or the interference phenomena of electrons; and among theorists, it came mainly from Max Born and others who understood it quickly. Logically, the probabilistic nature of quantum mechanics comes directly from the axioms i.e. the universal postulates of quantum mechanics. A user of this theory must understand what probabilities mean. There's no way to start from "zero" and teachers are those whose task is to explain notions such as "probability".
Now, the subtitle: Quantum mechanics embodies all ways to think about probability. (Sean Carroll wasn't capable of merging the two sentences into one.) Well, the obvious point is that every context or theory where the probabilistic description plays a role embodies all ways to think about probability. For example, in the casino, you may talk about Bayesian and frequentist probability, too.
Probability is always the same quantity and quantum mechanics doesn't bring us anything new about the definition of probability or the ways to talk about it (although John von Neumann tried to generalize logic and probability calculus). Quantum mechanics only brings us a completely new universal Ansatz for all the formulae by which the probabilities are calculated! In quantum mechanics, all the probabilities are calculated by formulae of the form\[
Prob = \sum_i |c_i|^2
\] where \(c_i\in\CC\) are some matrix elements of linear operators on a complex Hilbert space. This type of formula to calculate a probability was never used before 1925, now it's used "everywhere", and the transition to this new kind of formula may be said to be equivalent to the whole quantum revolution.
For this reason, Carroll's complaint that
Quantum mechanics as it is currently understood doesn’t really help us choose between competing conceptions of probability, as every conception has a home in some quantum formulation or other.is exactly as ludicrous as the complaint that quantum mechanics doesn't tell us whether girls at the Sussex High School should wear skirts or trousers (the feminists – self-described warriors for the equality of sexes – have banned skirts because they consider it a symbol of the inferior sex; only the superior sex's dress, pants, is allowed – try it in Scotland; clearly, feminists have come a full circle). It's just utterly ludicrous to expect quantum mechanics to settle such questions. Bayes' theorem and frequentist theorems about probability are all true, it's silly to expect that a physical theory will "choose" which one we should like.
If Sean Carroll asked a competent physicist for some help, he could have answered these questions by three simple paragraphs – whose value already wildly surpasses the value of all anti-QM books published in recent years – and readers of the Quanta Magazine could have saved the time needed to read dozens of pages of confusing, verbose nonsense.
Most of this text is some superficial, not too controversial, review of probability (including its different interpretations) and quantum mechanics for the high school students. I think that every intelligent physician or electrical engineer must understand that Carroll can't be possibly saying anything that is actually studied by good researchers as of 2019 – it's just too trivial. In the middle of the text, he gets controversial and promotes the three main types of revisionism of quantum mechanics. I won't repeat my explanations why these ideas are wrong.
Instead, let me focus on something that is more characteristic for this Quanta Magazine text:
How is probability involved [in MWI] at all? An answer is provided by the idea of “self-locating,” or “indexical,” uncertainty. [...] It doesn’t make sense to ask, “After the measurement, which world will I be on?” There will be two people [...]This "science" loves to produce completely redundant yet pompously sounding phrases such as "self-locating or indexical uncertainty". Note that one redundant phrase, "self-locating uncertainty", wouldn't be enough for Carroll so he prefers to generously share two redundant synonyms with you! When you study the actual beef of all these complicated words, you will get the same conclusion as Feynman who needed to understand the sentence "The individual member of the social community often receives his information via visual, symbolic channels."
The translation of that verbose sentence was "people read" while the whole 1-megabyte essay of Carroll's colleague said "sometimes people read, sometimes they listen to radio". It's similar in the case of Carroll except that his conclusion is wrong, instead of an innocent tautology such as "people read".
If you're incapable of critical rational thinking, just try to imagine or pretend for a minute that you have this capability. If you had it, what you would think about Carroll's recommended thesis defining his preferred new foundations of physics? The thesis is:
It doesn’t make sense to ask, “After the measurement, which world will I be on?”Let's pick the most famous example (but it is completely irrelevant which example we pick): a cat is either killed or not by an apparatus that depends on a random event (radioactive decay). Now, let's accept Carroll's description in terms of the "splitting worlds" and translate Carroll's pompous verbose prose into the language of the rational people. The question "After..." really says, in our example:
After the measurement, which world will I be on, the world with the dead cat or the world with the alive cat?Now, let's translate this sentence into English by throwing away all the "symbolic channels" redundant garbage by which the speaker pretends intelligence that he doesn't actually possess. What does the question actually mean when it's stripped of all the nonsense? Well, it's just the mandatory decoration of the equivalent question
Will the cat survive?All the many words describing the many worlds are present just in order to make very simple things sound unusually contrived. So what Carroll is actually saying includes the sentence about our example
It doesn't make sense to ask, "Will the cat survive?"Oh, really? How it could not make sense? Say it to the kids who owned the cat. "Your cat's survival is meaningless, bastards." It's a typical example of the questions that actually make perfect sense. All questions about the future are of this form. They actually ask about an event that can have various outcomes but only one of them will be real and we want to know which one.
Because the experiment with the cat was just an example – but the comments equally apply to every single meaningful question about the future in the real world, it is clear that using the pompous language, Carroll is saying nothing else than:
It doesn't make sense to ask any question about the future that is actually meaningful.It doesn't make sense to ask whether the cat will survive, whether AfD, AOC, or Trump will win the next elections, whether the spin will be measured to be up, whether most of the people of Hiroshima survive the nuclear blast ... anything.
How much stupidity does someone need to make a statement like that? A statement that the category of all questions about the future that we actually meaningfully ask is meaningless? Indeed, the required amount of stupidity is absolutely flabbergasting. And it is exactly what he is saying – he is just using some pompous cumbersome language. Everything that is meaningful is meaningless according to Carroll – and vice versa.
It doesn’t make sense to ask, "After the measurement, will the cat survive?" There will be two cats, one on each branch, both descended from a single cat; neither has a better claim to being “really the cat” than the other.Great. Except that all actual meaningful experiments will agree that there's only one cat after the measurement. This is either a direct, sharp contradiction between Carroll's MWI statements and the experiments; or, if we're very generous, a proof that Carroll's MWI ideas have zero capability to say anything about the questions that experiments are actually built to answer – about all meaningful questions about the real world.
Carroll wants his stupid readers to parrot nonsense about the existence of two cats – the number of cats would surely be infinite in a hypothetical "real MWI" but he doesn't have any rules how to make a list or calculate which kind of infinity etc. and how to calculate each of the terms in the hypothetical "natural split of the wave function" – and no one can find any natural rules of this sort because they can't exist for mathematical reasons. But this nonsense may be seen as either directly incompatible with the basic observations; or guaranteed to be just a sentence that can't ever be connected with any observations. His verbose ideology is 100% disjoint with the things that a scientist (or any person who hasn't lost contact with the real world) wants to understand or know.
But even if both people know the wave function of the universe, there is now something they don’t know: which branch of the wave function they are on.It's completely upside down, too. After the measurement, the people know "which world they live in" – whether a world with an alive cat or a dead cat – because they have simply observed the cat and saw whether it was alive or dead. What they cannot know is the "wave function of the Universe" that would contain both terms – simply because the wave function can never include the "wrong term" after the measurement. If they know that the cat has survived, they also know that the amplitude of the "dead cat" states is zero. The previous sentence is a simple tautology – the wave function is just a reflection of what the observer knows from observations. If you separate this tight connection that is really a definition of the wave function, then you cut all links between the wave function and the observations – and the "universal MWI wave function", whatever it is, will have nothing to do with empirical science or any real-world facts whatsoever.
If the mathematical objects in "your theory" don't actually respond to the observations, then they "don't know" what is going on and they can't be expected to produce valid predictions based on the empirical science. Is this trivial kindergarten point so hard to understand?
The rest of the text gets even worse. He conflates decoherence with the observation of a single answer among many possibilities – these are two completely different processes (decoherence makes the density matrix diagonal but it doesn't turn the density matrix to the \((0,0,0,1,0,0)\) form corresponding to a particular outcome) – and falsely claims that he has derived Born's rule out of nothing – which is clearly impossible and all proofs with this conclusion, if they're not completely invalid, are circular.
Well, thousands of people read this utter garbage in the New York Times, the Quanta Magazine, and elsewhere, and some of them smack their lips. Only two things are infinite, the Universe and the human stupidity, and I am not sure about the former.
And that's the memo.