Yes they are both particles and waves, but “collapse” is also purely a mathematical trick and isn’t something that physically occurs. Quantum theory is a statistical theory and like all statistical theories, you model the evolution of the system statistically up until it gets to the point you want to make a prediction for. But state vector notation (the “wave function”) is just a mathematical convenience that works when you are dealing with a system in a pure state that is only subject to Schrodinger evolution. It doesn’t work when a system undergoes decoherence, which follows the Born rule, and that says to compute the square magnitude of the state vector. But if you compute the square magnitude of the state vector, you get a new vector that is no longer a valid state vector.
Conveniently, whenever a system is subject to decoherence/Born evolution, that happens to be a situation when you can acquire new physical information about a system, whereas whenever it is subject to Schrodinger evolution, that corresponds to a situation when you cannot. People thus do this mathematical trick where, whenever a system undergoes decoherence/Born evolution, they take pause their statistical simulation, grab the new information provided about the system, and plug it back into the state vector, which allows them to reduce one probability amplitude to 1 and the rest to 0, which gives you a valid state vector again, and then they press play on their statistical simulation and carry it on from there.
This works, yes, but you can also pause a classical statistical simulation, grab new information from real-world measurements, and plug it in as well, unpause the simulation, and you would also see a sudden “jump” in the mathematics, but this is because you went around the statistical machinery itself into the real world to collect new information to plug into the computation. It doesn’t represent anything actually physically occurring to the system.
And, again, it’s ultimately just a mathematical trick because it’s easier to model a system in a pure state because you can model it with the state vector, but the state vector (the “wave function”) is simply not fundamental in quantum mechanics and this is a mistake people often make and get confused by. You can evolve a state vector according to Schrodinger evolution only as long as it is in a pure state, the moment decoherence/Born evolution gets involved, you cannot model it with the state vector anymore, and so people use this mathematical trick to basically hop over having to compute what happens during decoherence, and then delude themselves into thinking that this “hop” was something that happened in physical reality.
If you want to evolve a state vector according to the Schrodinger equation, you just compute U(t)ψ. But if you instead represent it in density matrix form, you would evolve it according to the Schrodinger equation by computing U(t)ψψᵗU(t)ᵗ. It obviously gets a lot more complicated, so in state vector form it is simpler than density matrix form, so people want to stick to state vector form, but state vector form simply cannot model decoherence/Born evolution, and so this requires you to carry out the “collapse” trick to maintain in that notation. If you instead just model the system in density matrix form, you don’t have to leave the statistical machinery with updates about real information from the real world midway through your calculations, you can keep computing the evolution of the statistics until the very end.
What you find is that the decoherence/Born evolution is not a sudden process but a continuous and linear process computed with the Kraus operators using ΣKᵢ(t)ρKᵢ(t)ᵗ and takes time to occur, cannot be faster than the quantum speed limit.
While particles can show up anywhere in the universe in quantum mechanics, that is corrected for in quantum field theory. A particle’s probability of showing up somewhere doesn’t extend beyond its light cone when you introduce relativistic constraints.
Many Worlds is an incredibly bizarre point of view.
Quantum mechanics has two fundamental postulates, that being the Schrodinger equation and the Born rule. It’s impossible to get rid of the Born rule in quantum mechanics as shown by Gleason’s Theorem, it’s an inevitable consequence of the structure of the theory. But Schrodinger’s equation implies that systems can undergo unitary evolution in certain contexts, whereas the Born rule implies systems can undergo non-unitary evolution in other contexts.
If we just take this as true at face value, then it means the wave function is not fundamental because it can only model unitary evolution, hence why you need the measurement update hack to skip over non-unitary transformations. It is only a convenient shorthand for when you are solely dealing with unitary evolution. The density matrix is then more fundamental because it is a complete description which can model both unitary and non-unitary transformations without the need for measurement update, “collapse,” and does so continuously and linearly.
However, MWI proponents have a weird unexplained bias against the Born rule and love for unitary evolution, so they insist the Born rule must actually just be due to some error in measurement, and that everything actually evolves unitarily. This is trivially false if you just take quantum mechanics at face value. The mathematics at face value unequivocally tells you that both kinds of evolution can occur under different contexts.
MWI tries to escape this by pointing out that because it’s contextual, i.e. “perspectival,” you can imagine a kind of universal perspective where everything is unitary. For example, in the Wigner’s friend scenario, for his friend, he would describe the particle undergoing non-unitary evolution, but for Wigner, he would describe the system as still unitary from his “outside” perspective. Hence, you can imagine a cosmic, godlike perspective outside of everything, and from it, everything would always remain unitary.
The problem with this is Hilbert space isn’t a background space like Minkowski space where you can apply a perspective transformation to something independent of any physical object, which is possible with background spaces because they are defined independently of the relevant objects. Hilbert space is a constructed space which is defined dependently upon the relevant objects. Two different objects described with two different wave functions would be elements of different Hilbert spaces.
That means perspective transformations are only possible to the perspective of other objects within your defined Hilbert space, you cannot adopt a “view from nowhere” like you can with a background space, so there is just nothing in the mathematics of quantum mechanics that could ever allow you to mathematically derive this cosmic perspective of the universal wave function. You could not even define it, because, again, a Hilbert space is defined in terms of the objects it contains, and so a Hilbert space containing the whole universe would require knowing the whole universe to even define it.
The issue is that this “universal wave function” is neither mathematically definable nor derivable, so it only has to be postulated, as well as its mathematical properties postulates, as a matter of fiat. Every single paper on MWI ever just postulates it entirely by fiat and defines by fiat what its mathematical properties are. Because the Born rule is inevitable form the logical structure of quantum theory, these mathematical properties always include something basically just the same as the Born rule but in a more roundabout fashion.
None of this plays any empirical role in the real world. The only point of the universal wave function is so that whenever you perceive non-unitary evolution, you can clasp your hands together and pray, “I know from the viewpoint of the great universal wave function above that is watching over us all, it is still unitary!” If you believe this, it still doesn’t play any role in how you would carry out quantum mechanics, because you don’t have access to it, so you still have to treat it as if from your perspective it’s non-unitary.