Did Luboš Motl really disprove the "Many Worlds Interpretation"?

Lubos Motl's argument isn't right; it's shooting down a strawman of the MWI, not the MWI itself. To recap, the argument goes like this:

  1. Many worlds claims that after a spin measurement, there are separate 'worlds' with different measurement results. For example, there could be one world where the electron is spin up, and one where the electron is spin down.
  2. We can identify whether a quantum state is spin up or spin down, and there are no quantum states that are both at once.
  3. Therefore, the electron can't be both spin up and spin down, so many worlds is false.

The trick is that in step (3), Lubos has assumed that the state of the electron in the MWI is a standard quantum state (and that the "worlds where the electron is spin up/down" are simply a quantum superposition).

However, this isn't what the MWI says at all! Instead, it says that after measurement, the electron is entangled with the measuring apparatus, so their joint quantum state is something like $$|\text{screen says +1, electron spin up}\rangle + |\text{screen says -1, electron spin down} \rangle$$ where I'm neglecting coefficients and phases. Because the electron is entangled with something else, it doesn't have a quantum state of its own, so step (3) doesn't work.

The simplest thing we can do to extract a "state" for the electron is to ignore ('trace out') the state of the apparatus. When we do this, we find that the electron is actually described by a mixed state, i.e. something like $$\text{50% chance of } |\text{spin up} \rangle + \text{50% chance of } |\text{spin down} \rangle.$$ This is a probabilistic, not quantum, mixture of states, and the $+$ sign is not quantum superposition. In accordance with step (2) above, there are no quantum states here that are both spin up and spin down at once -- just a mixture of two that are spin up and down separately. These two possibilities are what MWI people would call the two 'worlds'.

I doubt it, because the notion that any interpretation of quantum mechanics is provably true or false by experiment seems to be fundamentally wrong. A pretty mathematical "proof that something is impossible" doesn't count, even if the math is correct.

To quote from the blog itself,

Stupid monkeys are obsessed by questions whether MWI and other things are "not even wrong", "politically correct", "obeying Occam's razor", "pretty", and all such irrational adjectives, but no one seems to care about the question whether it is scientifically false or true.

IMO what he should have written is "scientists don't waste their time arguing about whether different QM interpretations are "true" or "false" because (1) there is no way of doing any experiment to answer the question, and (2) it makes no difference to any practical use of QM (and it certainly does have a practical use - for example almost every modern electronic device uses components which can only be designed and understood using quantum mechanics.)

The blog author quotes Bohr, but doesn't seem to understand what the quote means:

As Niels Bohr used to say, Physics is not a tool to describe how the reality is. Physics is a tool to say right things about what we can see.

I think the majority of working physicists don't spend much time on "interpretations" at all - or in other words, they prefer the slogan "shut up and calculate" to "shut up and contemplate". But of course the pop-science books love this sort of thing, because it sounds cool and doesn't need any equations to describe it.