Born rule is incompatible with many-worlds

Physicist Sean M. Carroll makes another bad attempt at explaining quantum mechanics:

One of the most profound and mysterious principles in all of physics is the Born Rule, named after Max Born. In quantum mechanics, particles don’t have classical properties like “position” or “momentum”; rather, there is a wave function that assigns a (complex) number, called the “amplitude,” to each possible measurement outcome. The Born Rule is then very simple: it says that the probability of obtaining any possible measurement outcome is equal to the square of the corresponding amplitude. (The wave function is just the set of all the amplitudes.)

This is really confused. Particles certainly do have properties like position and momentum. These are observed all the time. The whole idea of a particle accelerator is to put particles in a particular position and particular momentum. They only have these properties when they are observed that way, but then they are not even particles unless they are observed that way.

The description of a wave function is over-simplified. For a system as trivial as one election, the wave function is already more complicated, and the probability is not just the square of the probability.

More importantly, once you accept the quantum mechanics premise that observables are operators on a Hilbert space, then there is nothing mysterious about the Born rule. There is no other way to make sense out of observables being operators. It is only mysterious to many-worlds advocates like Carroll, because they do not believe in probabilities. They believe that all possibilities happen in alternate universes and that there is no way to quantify those universes.

A comment explains:

As a theory, Many Worlds is in a bad state, and this paper is an example of why.

If someone tells me that there are many quantum worlds in a single wavefunction, I expect that they can tell me exactly what part of a wavefunction is a world, and how many worlds there are in a given wavefunction.

As Sean says in his article, a naive attempt to be concrete about what a world is, and how many there are in a given wavefunction, leads to something which *disagrees* with experiment.

But rather than regard this as a point against Many Worlds, and rather than try new ways to carve up the wavefunction into definite worlds… instead we have contorted sophistical arguments about how you should *think* in a multiverse, as the explanation of the Born rule.

The intellectual decline comes when people stop regarding Born probabilities as frequencies, and stop wanting a straightforward theory in which you can “count the worlds”.

Common sense tells me that if A is observed happening twice as often as B, and if we are to believe in parallel universes, then there ought to be twice as many universes where A happens, or where A is seen to happen. But a detailed multiverse theory in which this is the case is hard to construct (Robin Hanson is one of the few to have tried).

Instead what we are getting (from Deutsch, from Wallace, now here) are these rambling arguments about decision theory, rationality, and epistemology in a multiverse. They all aim to produce a conclusion of the form, “you should think that A is twice as likely as B”, without having to exhibit a clear picture of reality in which A-worlds are twice as *common* as B-worlds.

Lumo picks Carroll apart in greater detail, and concludes:

I am really annoyed by the proliferation of this trash and I am annoyed by the fact that this trash is being repetitively pumped into the public discourse by the media and blogs run by narcissist crackpots like Sean Carroll, building upon Goebbels' claim that a lie repeated 100 times becomes the truth. At the end, the reason why I am so annoyed is that people don't have time to appreciate the clever, precious, consistent, and complete way how Nature fundamentally describes phenomena, and the people – like Heisenberg et al. – who have found those gems. These people are the true heroes of the human civilization. Instead, we're flooded by junk by Carroll-style crackpots whose writings don't make any sense and who are effectively spitting on Heisenberg et al.

He is over-the-top, as usual, but he is right that this advocacy of many-worlds is crackpot stuff.