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The many-worlds interpretation isn't deducible from just the Schrödinger equation. The Schrödinger equation roughly predicts that if you put two detectors at t

The many-worlds interpretation isn't deducible from just the Schrödinger equation. The Schrödinger equation roughly predicts that if you put two detectors at the two possible positions where a light beam can go after a beam splitter, and fire a single photon at the beam splitter, both detectors will detect some "amount" of the photon*. However, what you actually see in experiments is that one of the detectors detects a single photon, and the other detects 0. However, you also notice that if you repeat the experiment many times, the probability of detection is exactly equal to the square of the modulus of the amplitude of the Schrödinger function for that state. To explain this observation, the MWI uses an extra assertion: that each "world" contains a single result, but that the number of "worlds" where the state is X corresponds to the square of the modulus of the amplitude of the Schrödinger function for that state. So, if doing simple frequentist probabilities over these "worlds", your chance as an observer to be in a "world" where the state is X is equal to that value, as the experiments observe. Note that this assumption is exactly the same assumption as the wave function collapse, known as the Born rule. * the Schrödinger equation actually predicts something more esoteric than even that: for any two complementary solutions X and Y, there is an infinity of additional solutions of the form aX + bY, with a and b real numbers with certain properties. So, in fact, it is actually impossible to use the Schrödinger equation to predict any particular state. You have to use the Schrödinger equation and a chosen basis of measurement, and only look at the solutions in that basis. The simple idea of "counting worlds" from above mostly breaks down at this stage - you need an additional third assumption of assuming a pre-existing "background" and using Decoherence to explain why only certain solutions normally manifest.

btilly 3y ago
No, it really is. Consider a sealed room with an experimenter looking at a box with Schrödinger's famous cat in it. The question we usually ask is whether the cat is alive, dead, or in a superposition before the box is opened. Schrödinger's famous equation predicts that if the cat itself can be described by quantum mechanics, then it must be in a superposition. If the experimenter can be described by quantum mechanics as well, then the experimenter must also go into a superposition upon opening the cat's box. And, thanks to thermodynamics, there is no experiment that is doable by the experimenter from which the existence of collapse can be demonstrated. Therefore the claim that there is a collapse at all is an entirely unnecessary hypotheses. All other interpretations of QM have to invent explanations for an event (collapse) that no experimental evidence exists for.
- tsimionescu 3y ago
  That's all well and good, but it then predicts that all possible outcomes have equal probability, and this is measurably false. Say you design the experiment such that the observer will see the cat is alive if 2 particles both have spin up, and dead if any particle has spin down. Say the Schrodinger equation will assign equal amplitudes to the 4 possible states (up-up, up-down, down-down, down-up), and let's ignore the composite states (e.g. 1/sqrt(2)up-up + 1/sqrt(2)up-down). So, the cat-alive (up-up) state has an amplitude which is 3* the amplitude of the cat-dead state (up-down + down-up + down-down). In a naive interpretation of MWI that only used the Schrodinger equation, there are two versions of the observer, so the probability that the observer sees one outcome versus the other is obviously 1/2: you either happen to be the version that sees the cat alive, or you happen to be the one that sees it dead. This reasoning will work if we repeat the experiment many times: since the repetitions are independent, if I repeat it 10 times, I expect that I will happen to be one of the observers who sees the cat alive about 5 times, and dead about 5 times as well. In your interpretation, the amplitude of the Schrodinger equation is irrelevant, as long as it is greater than 0: all possible events happen. If I actually do the experiment though, I will see the cat alive only about 2.5/10 times, since the total amplitude of the wavefunction for all states where the cat is alive is much lower than the total amplitude of all states where the cat is dead. So, the actual MWI says that, while there are two kinds of worlds, they are not equally likely. In the multitude of all worlds, the prevalence of worlds where the cat is alive is proportional to the wavefunction amplitude of the cat-alive state (about 1/4) and the ones where the cat is dead follows the same logic (about 3/4). So, given that I am one observer in one of the many worlds, the chance I am the observer in a world where the cat is alive is only 1/4. But this connection between the number of worlds and the amplitude of the wavefunction is an additional assumption atop the Schrodinger equation. Sure, the wavefunction doesn't collapse, but it splits according to the exact same formula as the collapse in the CI (Born's rule). And I again want to mention that even this is not enough. If |cat-alive> and |cat-dead> are solutions to the Schrodinger equation, then so is x|cat-alive>+y|cat-dead>, for an infinite number of x and y real numbers. The MWI has to explain why no observer ever actually perceives such a state (how this state would look like to to an observer is not even definable). Decoherence solves this, and it was an extremely important contribution, but it also adds an additional assumption (that CI also needs): some pre-existing classical-like background.

btilly 3y ago

No, it really is. Consider a sealed room with an experimenter looking at a box with Schrödinger's famous cat in it. The question we usually ask is whether the cat is alive, dead, or in a superposition before the box is opened. Schrödinger's famous equation predicts that if the cat itself can be described by quantum mechanics, then it must be in a superposition. If the experimenter can be described by quantum mechanics as well, then the experimenter must also go into a superposition upon opening the cat's box. And, thanks to thermodynamics, there is no experiment that is doable by the experimenter from which the existence of collapse can be demonstrated. Therefore the claim that there is a collapse at all is an entirely unnecessary hypotheses. All other interpretations of QM have to invent explanations for an event (collapse) that no experimental evidence exists for.

tsimionescu 3y ago
That's all well and good, but it then predicts that all possible outcomes have equal probability, and this is measurably false. Say you design the experiment such that the observer will see the cat is alive if 2 particles both have spin up, and dead if any particle has spin down. Say the Schrodinger equation will assign equal amplitudes to the 4 possible states (up-up, up-down, down-down, down-up), and let's ignore the composite states (e.g. 1/sqrt(2)up-up + 1/sqrt(2)up-down). So, the cat-alive (up-up) state has an amplitude which is 3* the amplitude of the cat-dead state (up-down + down-up + down-down). In a naive interpretation of MWI that only used the Schrodinger equation, there are two versions of the observer, so the probability that the observer sees one outcome versus the other is obviously 1/2: you either happen to be the version that sees the cat alive, or you happen to be the one that sees it dead. This reasoning will work if we repeat the experiment many times: since the repetitions are independent, if I repeat it 10 times, I expect that I will happen to be one of the observers who sees the cat alive about 5 times, and dead about 5 times as well. In your interpretation, the amplitude of the Schrodinger equation is irrelevant, as long as it is greater than 0: all possible events happen. If I actually do the experiment though, I will see the cat alive only about 2.5/10 times, since the total amplitude of the wavefunction for all states where the cat is alive is much lower than the total amplitude of all states where the cat is dead. So, the actual MWI says that, while there are two kinds of worlds, they are not equally likely. In the multitude of all worlds, the prevalence of worlds where the cat is alive is proportional to the wavefunction amplitude of the cat-alive state (about 1/4) and the ones where the cat is dead follows the same logic (about 3/4). So, given that I am one observer in one of the many worlds, the chance I am the observer in a world where the cat is alive is only 1/4. But this connection between the number of worlds and the amplitude of the wavefunction is an additional assumption atop the Schrodinger equation. Sure, the wavefunction doesn't collapse, but it splits according to the exact same formula as the collapse in the CI (Born's rule). And I again want to mention that even this is not enough. If |cat-alive> and |cat-dead> are solutions to the Schrodinger equation, then so is x|cat-alive>+y|cat-dead>, for an infinite number of x and y real numbers. The MWI has to explain why no observer ever actually perceives such a state (how this state would look like to to an observer is not even definable). Decoherence solves this, and it was an extremely important contribution, but it also adds an additional assumption (that CI also needs): some pre-existing classical-like background.