> You’re wrong about MWI in that it’s a more elegant interpretation because it adds nothing extra to the wave equation and treats the universe as fundamentally quantum with no arbitrary dividing lines for classically scaled objects.
That's how it's often presented, but this is wrong. In fact, it does add something to the theory, and that's a measure of how many "worlds" there are after a quantum measurement, which helps translate the wave function values into testable probabilities (the Born rule).
In the CI, after a measurement, the wave function collapses into a single value, leaving the single world in a single classical state, with some probability that's equal to the modulus of the wave function amplitude of that state (or is there some squaring involved as well?).
In the MWI, after a measurement, different versions of the observer observe different states, and the number of versions of the observer observing each state corresponds to the modulus of the wave function amplitude of that state. Then, via simple probability, we can say this count corresponds to the actual probability that any one version of the observer will notice one particular state, even though in the actual multiverse all of the states actually happen.
As you can see, the two interpretations require the same amount of extra postulates above and beyond the wave function itself. Also, the MWI has to somehow define a formal notion of an observer/a classical world, which runs into questions of scale just as much as the measurement postulate of CI.
> and that's a measure of how many "worlds" there are after a quantum measurement, which helps translate the wave function values into testable probabilities (the Born rule).
All interpretations need to induce a measure over observations (not "worlds") to produce meaningful results. Without that all you have is an abstract mathematical object.
> As you can see, the two interpretations require the same amount of extra postulates above and beyond the wave function itself.
CI isn't really a single thing. Some people use it to mean "shut up and calculate", which requires no postulates by virtue of making no meaningful claims. Some people use it to mean various sorts of subjective probability anti-realism, which is similarly not really competing for the same territory as MWI. And some people use it to mean objective collapse, which requires actual modifications to the formalism.
> All interpretations need to induce a measure over observations (not "worlds") to produce meaningful results. Without that all you have is an abstract mathematical object.
Agreed, but the MWI in particular does so by applying frequentist probabilities over all versions of an observer, the so-called worlds. The argument goes that there is an apparent non-deterministic process from the point of view of every individual observer, and that we can compute its probability based on how many observers would see a particular state versus the total number of observers.
For some reason, many MWI adherents want to claim that this is not an additional postulate, that MWI only needs the Shrodinger equation, but it clearly is a postulate in addition to that equation, just as much as the collapse idea in other interpretations.
You are right about the CI though, it's not really a useful term.
> For some reason, many MWI adherents want to claim that this is not an additional postulate, that MWI only needs the Shrodinger equation, but it clearly is a postulate in addition to that equation, just as much as the collapse idea in other interpretations.
I think you're misinterpreting them (us). The claim is that MWI requires one additional postulate, whereas collapse interpretations need at least two: they both need a way to make distributions into probability distributions over observations, but collapse additionally requires some way of dodging Wigner's Friend type scenarios: an objective classical transition, extra state beyond the wavefunction, outright antirealism, etc.
It's not really anymore than tables and chairs not being part of fundamental physics means they're additional postulates to physics. Because table and chairs emerge from the underlying physics. Same thing with measurement, observers and probability in MWI. Or to put it another way, the baggage of classical physics being quantized misleads us into thinking measurement and probability need to be fundamental postulates.
> That's how it's often presented, but this is wrong. In fact, it does add something to the theory, and that's a measure of how many "worlds" there are after a quantum measurement, which helps translate the wave function values into testable probabilities (the Born rule).
The distribution of worlds/branches is determined by the wave function. A more likely outcome means there are many more worlds with that outcome. You can calculate the percentage of worlds that have that outcome.
> Also, the MWI has to somehow define a formal notion of an observer/a classical world, which runs into questions of scale just as much as the measurement postulate of CI.
Measurement, observer and classical shouldn't be part of a physical theory. The answer as to why things appear that way to us is decoherence.
> A more likely outcome means there are many more worlds with that outcome. You can calculate the percentage of worlds that have that outcome.
First of all, this is a new postulate of QM, you can't derive it from the Schrodinger equation. It is perfectly equivalent with the measurement postulate.
> Measurement, observer and classical shouldn't be part of a physical theory. The answer as to why things appear that way to us is decoherence.
This contradicts the other part, where you were talking about a notion of worlds that can be counted. If they can be counted, they have to be defined as classical worlds. Decoherence only explains why worlds can't interact with each other, it doesn't help define what they are without appealing to measurements. Even the notion of "the environment" is somewhat ill defined if we go down to the philosophical level.
Measurements are interactions that result in entanglement. Atoms radioactively decaying in your body are interactions. The environment is the entire universe as it becomes entangled with a quantum event.
Entanglement is not enough to give you the properties of measurements. While it is often presented as "when a spin-0 particle decays into two particles, one must have spin +1 and the other spin -1", that is not what the math actually says.
What the math actually says is that the spin of each particle is a linear combination of |+1> and |-1>, and that their sum must be 0. For example, one of the entangled particles could have state 1/3|+1> + 2/3|-1>, and the other would have 2/3|+1> + 1/3|-1> (or something similar, I'm a bit fuzzy on the exact math). There is nothing that says that particles must be in pure states from their own perspective. And yet, we only ever observe pure states (with some probability) in our own perspectives. So, there must be some additional law that favors these states.
Decoherence from entanglement with the environment interferes with the coherence of the supposition, so we only see the pure state as I understand Sean Carol's argument. At this point in the video below he goes over the spin states.
> the MWI has to somehow define a formal notion of an observer/a classical world
Yes: in MWI, those things don't exist. The world is quantum all the way up and all the way down, observers are simply (other) quantum system that get to interact with the quantum system under the consideration. An observation, then, is simply an interaction between two quantum systems and follows all the usual rules so instead of the wave-function collapse leaving you with the observed system in pure state X and the observer is in pure state Y, you get a huge superposition of "the observed system in pure state Xi, the observer is in pure state Yi" states in the end. Those substates, in a sense, are multiple worlds.
You're missing the point I was highlighting. Quantum mechanics makes very specific, very precise predictions about the probabilities of an observer seeing any of those states, which we have confirmed are correct to extraordinary precision.
The problem is explaining what is the relationship between these observed probabilities and the wave function amplitudes. If we say that all possible quantum states are realized in the universal wave function, we the need to explain why different states have different probabilities to an observer. The only way to do that in the deterministic world of MWI is to add a new postulate: one that says that for any state Xi, there are N observers in state Yi, where N = |psi(Xi)|, so that we can compute regular frequentist probabilities of an observer seeing a particular state over the amount of observers.
This is perfectly reasonable, but it is just as much an extra postulate as the measurement postulate.
That's how it's often presented, but this is wrong. In fact, it does add something to the theory, and that's a measure of how many "worlds" there are after a quantum measurement, which helps translate the wave function values into testable probabilities (the Born rule).
In the CI, after a measurement, the wave function collapses into a single value, leaving the single world in a single classical state, with some probability that's equal to the modulus of the wave function amplitude of that state (or is there some squaring involved as well?).
In the MWI, after a measurement, different versions of the observer observe different states, and the number of versions of the observer observing each state corresponds to the modulus of the wave function amplitude of that state. Then, via simple probability, we can say this count corresponds to the actual probability that any one version of the observer will notice one particular state, even though in the actual multiverse all of the states actually happen.
As you can see, the two interpretations require the same amount of extra postulates above and beyond the wave function itself. Also, the MWI has to somehow define a formal notion of an observer/a classical world, which runs into questions of scale just as much as the measurement postulate of CI.