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I agree with that. But it still does not explain how probabilities arise. What is the physical significance of "a universe with a greater measure than another?

I agree with that. But it still does not explain how probabilities arise. What is the physical significance of "a universe with a greater measure than another?" What is the physical significance of the measure in MWI at all?

jiggawatts 6y ago
Traditional view: There is one experimenter, he picks a marble, it is either red or blue. If the experimenter repeats the measurement, he gets some red, some blue, with some percentage chance. MWI view: There are many experimenters, in fact there is a continuum of them for each "run" of the experiment. The "setup" of each run that produces the mixed state in the bowl of marbles is splitting the whole universe (at the speed of light) and also splits the experimenters. Some of them are now in the "red" universe, and some of them are now in the "blue" universe and give matching answers. The percentage of them giving each answer is the same as in the situation above, but this percentage applies to even one run of the experiment. However, the many experimenters and their percentages is not observable in a single experimental run from inside their universe. The experimenters cannot communicate, so after each run they only have 1 bit of information each (red or blue). They need to repeat the experiment to gain more than one bit of information. However, now, their states are different. Some experimenters have a different history to the others. They aren't all the same any more! There's no "reset" button. This is the core of many of the "mysteries" and "apparent superluminal communication" in QM. There's no mystery. The state -- including the experimenters -- is splitting. The classic "superluminal" communication isn't: Entangled opposite particles are simply saying that some universes have the (A,B) pair, others have the (B,A) pair. When you find out that you have the "A" particle, you instantly know that in your universe the other guy must have the "B" particle. There's no communication, instead the experiment is all about finding out one bit of information about "where you are" in the multiverse.
- millstone 6y ago
  > Some of them are now in the "red" universe, and some of them are now in the "blue" universe and give matching answers. The percentage of them giving each answer is the same as in the situation above The objection is: what fraction are in red universes, and why? Why is it 2/3rds and not, say, 3/5ths or zero? In QM we can compute these fractions using the Born rule, which says that the probability of each outcome is proportional to its measure in the wavefunction. This is natural to postulate in Copenhagen, where we interpret the wavefunction as a probability density. If the measure of spin-up is twice that of spin-down, it means that spin-up is twice as likely. But in MWI, the wavefunction is definitely NOT a probability density. Both spin-up and spin-down are physically realized. So why should it matter that spin-up has a higher measure? Where does the Born rule come from in MWI? Can it be derived from the Schrödinger equation? If so, how? If not, what additional axioms are needed?
  - jiggawatts 6y ago
    The Born rule is basically saying that the wave function and the measurements are related by a squaring relationship one way, or a square root the other way. This squaring in QM is basically saying that there are two probability distributions, not one. There isn't just the particle, there is the particle and the experimenter. Similarly, there's the particle and itself in interference experiments. Or the particle and the detector. There's always (at least) two required for an interaction. Hence a squaring. It's saying that the observed and the observer are part of the same system. We're not Gods viewing squiggly cartoons on a page, like we like to draw. We are the drawing.

jiggawatts 6y ago

Traditional view: There is one experimenter, he picks a marble, it is either red or blue. If the experimenter repeats the measurement, he gets some red, some blue, with some percentage chance. MWI view: There are many experimenters, in fact there is a continuum of them for each "run" of the experiment. The "setup" of each run that produces the mixed state in the bowl of marbles is splitting the whole universe (at the speed of light) and also splits the experimenters. Some of them are now in the "red" universe, and some of them are now in the "blue" universe and give matching answers. The percentage of them giving each answer is the same as in the situation above, but this percentage applies to even one run of the experiment. However, the many experimenters and their percentages is not observable in a single experimental run from inside their universe. The experimenters cannot communicate, so after each run they only have 1 bit of information each (red or blue). They need to repeat the experiment to gain more than one bit of information. However, now, their states are different. Some experimenters have a different history to the others. They aren't all the same any more! There's no "reset" button. This is the core of many of the "mysteries" and "apparent superluminal communication" in QM. There's no mystery. The state -- including the experimenters -- is splitting. The classic "superluminal" communication isn't: Entangled opposite particles are simply saying that some universes have the (A,B) pair, others have the (B,A) pair. When you find out that you have the "A" particle, you instantly know that in your universe the other guy must have the "B" particle. There's no communication, instead the experiment is all about finding out one bit of information about "where you are" in the multiverse.

millstone 6y ago
> Some of them are now in the "red" universe, and some of them are now in the "blue" universe and give matching answers. The percentage of them giving each answer is the same as in the situation above The objection is: what fraction are in red universes, and why? Why is it 2/3rds and not, say, 3/5ths or zero? In QM we can compute these fractions using the Born rule, which says that the probability of each outcome is proportional to its measure in the wavefunction. This is natural to postulate in Copenhagen, where we interpret the wavefunction as a probability density. If the measure of spin-up is twice that of spin-down, it means that spin-up is twice as likely. But in MWI, the wavefunction is definitely NOT a probability density. Both spin-up and spin-down are physically realized. So why should it matter that spin-up has a higher measure? Where does the Born rule come from in MWI? Can it be derived from the Schrödinger equation? If so, how? If not, what additional axioms are needed?
- jiggawatts 6y ago
  The Born rule is basically saying that the wave function and the measurements are related by a squaring relationship one way, or a square root the other way. This squaring in QM is basically saying that there are two probability distributions, not one. There isn't just the particle, there is the particle and the experimenter. Similarly, there's the particle and itself in interference experiments. Or the particle and the detector. There's always (at least) two required for an interaction. Hence a squaring. It's saying that the observed and the observer are part of the same system. We're not Gods viewing squiggly cartoons on a page, like we like to draw. We are the drawing.