In the many-worlds interpretation, the cut between the observed and the observer, the quantum and the classical is removed, and it logically follows that there can be a universal wavefunction. When something is measured, the observer is in a superposition of seeing the thing that is measured in different states. However, I could not understand how the process of measurement branches the universe into multiple in the many worlds interpretation, instead of just the observer being in a superposition. How does branching from the many-worlds interpretation come from the assumption of a universal wavefunction?
Quantum Mechanics – How Does Branching in Many-Worlds Interpretation Come From Universal Wavefunction?
Measurementsquantum mechanicsquantum-interpretationswavefunction
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Binary branching is just a simplification to make it easier to explain without math. The actual math is very simple, and can handle unequal probabilities.
At the simplest level, a branching occurs when you can write the wavefunction as a sum $$|\psi \rangle = |\psi_1 \rangle + |\psi_2 \rangle$$ where $|\psi_1 \rangle$ and $|\psi_2 \rangle$ are orthogonal and decohered, i.e. that there is no reasonable physical process that can make them overlap again. In this case we colloquially describe the two terms as "worlds" or "branches", and the probability of being in each one is the norm $\langle \psi_i | \psi_i \rangle$, which can be an arbitrary number between zero and one. The same logic goes for branching into more than two "worlds" at once, and repeated branching: you just get a sum of many terms, and the probability of each one is its norm.
After some comments, I get the feeling you really want a discussion of where the probability in the many worlds interpretation "comes from". Again, this is a very subjective and debatable thing, but my favorite take on it is "self-locating uncertainty".
Suppose that somebody kidnaps you, blindfolds you, and takes you somewhere in Uzbekistan. When you come to your senses, are you closer to Samarkand than Tashkent? You don't know for sure, so you can only answer in terms of probabilities. This is self-locating uncertainty: you're certainly in a definite place, and it's not like there are many copies of you running around, but there's probability nonetheless. You can use a variety of information to help. For example, if you weight by area, about 85% of the country is closer to Samarkand. (But this doesn't mean there are $85$ copies of you near Samarkand and $15$ copies of you near Tashkent!) But if you weight by population, substantially more of the population is closer to Tashkent, because it's the capital. Of course, which weighting is the correct choice depends on how the kidnappers set things up.
Now, suppose that after the spin of a particle is measured by a device, the state is $$|\psi \rangle = \sqrt{0.85} |\text{spin up measured} \rangle + \sqrt{0.15} |\text{spin down measured} \rangle.$$ You are living in one and only one branch of the wavefunction, but until you look at what the device is reading, you don't know which. At best, you can assign probabilities. The core assumption of many worlds is that the correct choice of probability (i.e. the choice that corresponds to what you actually observe, when averaged over many measurements) is to take the coefficient of each branch and take its norm squared, i.e. to assign an 85% chance to observing spin up.
If you ask where this assumption comes from, it's a perfectly legitimate question! However, the point is, there's no principle that says the probabilities have to be equal across branches. That's like saying every day must have a 50% chance of rain because it can either be rainy or not.
Best Answer
"However, I could not understand how the process of measurement branches the universe into multiple in the many worlds interpretation, instead of just the observer being in a superposition."
You are correct. The Everett Interpretation (see Everett's thesis) does not talk about branching the universe - it only says the observer is in a superposition.
One of the popularisers of Everett's Interpretation (either Wheeler or DeWitt, I think) tried to explain it to the general public by saying that from the observer's point of view, it would look as if each outcome happened in a separate world. The superposed states are orthogonal, they don't interact, they evolve independently, so it is as if the universe had split into several parallel universes, with one possible outcome happening in each. This became more popularly known as the Many Worlds Interpretation.
The whole point of Everett's proposal was that you only needed plain unitary quantum mechanics. There was no faster-than-light wavefunction collapse. There's no classical/quantum division. The laws of physics are time-reversible, deterministic, local, realist. The problem with splitting universes is that it effectively re-introduces collapse by the back door - obvious questions like how fast the rip separating the universes propagates, what triggers a rip, what is its actual detailed mechanism, is the splitting of universes reversible, and so on reintroduce many of the problems Everett had got rid of.
'Many Worlds' is a useful analogy for imagining what it looks like to an observer from the inside, at a very introductory level. But the analogy quickly falls apart if you try to work at a deeper and more detailed level. The observer and observed enter an orthogonal superposition of joint states in each of which the observer part of the state is correlated with the state of the system observed.