MWI is exactly as simple mathematically as CI, so not sure what you mean by "simpler".
MWI still postulates the equivalent of wave function collapse, but instead of it happening only for the quantum system being measured, it is happening in the mind of the observer, as each "version" of that mind gets entangled with a single "version" of the outcome.
Even if you were to accept that this process is more natural (so not an "assumption") than wave-function collapse in principle, that simplicity completely falls apart when you then need to recover the relationship between the probability of observing a certain outcome and the amplitude of that outcome in the wave-function.
CI just says "when a quantum system described by a wave-function interacts with a measurement apparatus that measures in a certain basis, the wave-function gets updated to one of the values of its decomposition in that basis, with a probability equal to the modulus of the square root of its amplitude in that basis". Of course "measurement apparatus prepared in a certain basis" does a lot of work here, as we don't know how to define this in terms of a quantum system.
To make a similar quantitative prediction, MWI needs to define something like "the number of worlds", so that it can then say something like "when a quantum system interacts with a measurement apparatus prepared in a certain basis, the measurement apparatus becomes entangled with the quantum system such that for each value of that basis state there is a number of worlds proportional to the square root of the amplitude of each value of the decomposition in which the apparatus sees that particular value; if we were to compute the probability that we happen to live in a world where the apparatus is showing the value X, that probability would naturally be higher the more worlds there are where it shows this value X". So, the MWI has to actually introduce extra elements (the worlds and their number, and the observer wanting to compute a probability) to explain the actual measured results of quantum experiments.
>MWI still postulates the equivalent of wave function collapse
It's not postulated, but deduced from the Schrodinger equation. MWI is simpler in a sense that it has one fewer axiom. But Occam's razor isn't really applicable here, because it selects from otherwise equal theories, which CI isn't. There are more important criteria to use before Occam's razor.
You can't deduce the Born rule from the Schrodinger equation. MWI can say "look at every basis separately", but you still have to postulate that the probability of finding yourself asking that basis vector (seeing that measurement outcome) is proportional to the square root of the amplitude.
> you then need to recover the relationship between the probability of observing a certain outcome and the amplitude of that outcome in the wave-function.
I have never understood how that is a strong objection. We've experimentally determined that the state you are more likely to find yourself in is based on the squared amplitude. How is this different from CI but with probability of observing given state - which was also determined empirically?
> Of course "measurement apparatus prepared in a certain basis" does a lot of work here, as we don't know how to define this in terms of a quantum system.
Yes, this is where the Occam's razor bit comes in.
> So, the MWI has to actually introduce extra elements (the worlds and their number, and the observer wanting to compute a probability) to explain the actual measured results of quantum experiments.
The worlds and their number are equivalent to the states & probability of CI without having to introduce the "measurement apparatus" that is distinct from the quantum system.
> How is this different from CI but with probability of observing given state - which was also determined empirically?
It's not different, that's the point. For both interpretations, the relationship between the probability of observing a certain outcome and the amplitude of that outcome in the wave function are an extra postulate, the exact same extra postulate in fact, the Born rule.
> The worlds and their number are equivalent to the states & probability of CI without having to introduce the "measurement apparatus" that is distinct from the quantum system.
The measurement apparatus as a separate thing from the quantum system was actually partially explained by decoherence (ironically discovered by MWI proponents), which needs this separation for the same reasons as CI: we need some way to explain why quantum phenomena don't happen at our scale. Now, MWI makes this concept relative to an observer, whereas in CI it is often assumed to be absolute.
Basically, we can deduce from the Schrodinger equation alone that after the interaction of a quantum system with the environment, coherence is lost, and the different "states" of the wavefunction can no longer interfere with each other.
CI postulates that, as a result of this interaction, only one of the states will remain, with the Born rule probability. This is the most direct way of interpreting our experimental results.
MWI says that nothing changes after this interaction. It postulates though that, if we were to ask how likely we are to be in the same "state" as a particular result, we should expect that to be the Born rule probability. This explanation takes the theoretical description of the wave function to be more real in some sense than the actual observations we make.
> The measurement apparatus as a separate thing from the quantum system was actually partially explained by decoherence
I disagree that the decoherence at all partially explains a different measurement apparatus separate from the system. After observation, we still have the the system is in a superposition of multiple states. How this system "collapses" to one state in the measurement apparatus is unexplained.
Decoherence explains why each state of the observer can't tell that the other states also exist.
> This is the most direct way of interpreting our experimental results.
Sure, except we have to invent an entirely new non-unitary transformation of "collapse" despite all observations and predictions of quantum mechanics showing that unitary evolution of the wavefunction continues even for large macro-scale objects.
> Decoherence explains why each state of the observer can't tell that the other states also exist.
Sure, but, again, decoherence doesn't explain (1) why the wave function is split in the classical states (position, momentum etc.) and not other states (linear combinations of position and momentum and spin etc.); and (2) doesn't explain why different states have the precise probabilities of being observed that they do. You still need to postulate these features.
> Sure, except we have to invent an entirely new non-unitary transformation of "collapse" despite all observations and predictions of quantum mechanics showing that unitary evolution of the wavefunction continues even for large macro-scale objects.
You're confusing the map for the territory. What we can see, plain as day, is that unitary evolution of the wavefunction does not continue for macro-scale objects. MWI explains this through the framework of the universal wavefunction and its mutually un-interacting "branches", CI explains it through wavefunction collapse. No one has ever successfully put a macroscopic object in superposition, so the idea that the universe itself could be in superposition remains highly theoretical at best.
Note also that movement in the classical world (and in GR) is often highly non-linear/non-unitary (such as the movement of a free pendulum, or many kinds of orbits). While far from perfect for this, the Born rule at least allows us to "sneak in" non-unitary evolution through this collapse; but, in the MWI, we predict that the movement of a free pendulum should in fact be non-chaotic. This is rarely discussed, but is an interesting observation that could be experimentally tested as we get better at creating larger and larger systems that remain coherent for longer and longer periods of time.
> Sure, but, again, decoherence doesn't explain (1) why the wave function is split in the classical states (position, momentum etc.) and not other states (linear combinations of position and momentum and spin etc.); and (2) doesn't explain why different states have the precise probabilities of being observed that they do. You still need to postulate these features.
I agree that (1) is a strong objection that I do not have an easy solution to. (2) I think is addressable in the same way that it is in CI - our theory has to explain our observed experience and the born rule (whether CI-flavored or MWI-flavored) is how we do so.
> No one has ever successfully put a macroscopic object in superposition
> (2) I think is addressable in the same way that it is in CI - our theory has to explain our observed experience and the born rule (whether CI-flavored or MWI-flavored) is how we do so.
Absolutely, but I would still say that it means we are adding an extra postulate that can't be derived directly from the Schrodinger equation even in MWI. I'm not trying to claim that the MWI is wrong: just that it is not simpler than the CI (nor it is more complex though - I'm arguing it has the same number of postulates).
> But getting larger and larger.
Sure, and I'm really hoping we'll advance closer to macroscopic objects in my lifetime, so maybe some of these questions may be elucidated.
MWI still postulates the equivalent of wave function collapse, but instead of it happening only for the quantum system being measured, it is happening in the mind of the observer, as each "version" of that mind gets entangled with a single "version" of the outcome.
Even if you were to accept that this process is more natural (so not an "assumption") than wave-function collapse in principle, that simplicity completely falls apart when you then need to recover the relationship between the probability of observing a certain outcome and the amplitude of that outcome in the wave-function.
CI just says "when a quantum system described by a wave-function interacts with a measurement apparatus that measures in a certain basis, the wave-function gets updated to one of the values of its decomposition in that basis, with a probability equal to the modulus of the square root of its amplitude in that basis". Of course "measurement apparatus prepared in a certain basis" does a lot of work here, as we don't know how to define this in terms of a quantum system.
To make a similar quantitative prediction, MWI needs to define something like "the number of worlds", so that it can then say something like "when a quantum system interacts with a measurement apparatus prepared in a certain basis, the measurement apparatus becomes entangled with the quantum system such that for each value of that basis state there is a number of worlds proportional to the square root of the amplitude of each value of the decomposition in which the apparatus sees that particular value; if we were to compute the probability that we happen to live in a world where the apparatus is showing the value X, that probability would naturally be higher the more worlds there are where it shows this value X". So, the MWI has to actually introduce extra elements (the worlds and their number, and the observer wanting to compute a probability) to explain the actual measured results of quantum experiments.