My understanding might be a bit superficial, but I thought the whole point of the MWI was to make explicit the fact that states are relative?
To me the rationale was that states are relative and if we simultaneously describe relative states and their observers we can translate the shrödinger+born-rule in a density-operator+partial-trace-rule and make the wave function collapse physical (aka unitary) through branching and decoherence, even though that’s mathematically tedious and in practice people will keep using projectors (1). States being relative means their physical reality is somewhat broken but locality is mostly saved (2), so then we postulate that they derive from a universal wave function to rehabilitate some form of physical realism (3).
As to (4), isn’t it solved if you assume that Schrödinger’s equation is actually the less fundamental formalism since it’s only valid for systems that are unrealistically isolated?
MWI claims there exists a universal quantum state, but quantum theory works perfectly well without this assumption if quantum states are taken to be fundamentally relative. Every quantum state is defined in relation to something else, which is made clear by the Wigner’s friend scenario where different observers legitimately assign different states to the same system. If states are fundamentally relative, then a “universal” quantum state makes about as much sense as a “universal velocity” in Galilean relativity.
You could arbitrarily choose a reference frame in Galilean relativity and declare it universal, but this requires an extra postulate, is unnecessary for the theory, and is completely arbitrary. Likewise, you could pick some observer’s perspective and call that the universal wavefunction, but there is no non-arbitrary reason to privilege it. That wavefunction would still be relative to that observer, just with special status assigned by fiat.
Worse, such a perspective could never truly be universal because it could not include itself. To do that you would need another external perspective, leading to infinite regress. You never obtain a quantum state that includes the entire universe. Any state you define is always relative to something within the universe, unless you define it relative to something outside of the universe, but at that point you are talking about God and not science.
The analogy to Galilean relativity actually is too kind. Galilean relativity relies on Euclidean space as a background, allowing an external viewpoint fixed to empty coordinates. Hilbert space is not a background space at all; it is always defined in terms of physical systems, what is known as a constructed space. You can transform perspectives in spacetime, but there is no transformation to a background perspective in Hilbert space because no such background exists. The closest that exists is a statistical transformation to different perspectives within Liouville space, but this only works for objects within the space; you cannot transform to the perspective of the background itself as it is not a background space.
One of the papers I linked also provides a no-go theorem as to why a universal quantum state cannot possibly exist in a way that would be consistent with relative perspectives. There are just so many conceptual and mathematical problems with a universal wavefunction. Even if you somehow resolve them all, your solution will be far more convoluted than just taking the relative states of quantum mechanics at face value. There is no need to “explain measurement” or introduce a many worlds or a universal wavefunction if you just accept the relative nature of the theory at face value and move on, rather than trying to escape it (for some reason).
But this is just one issue. The other elephant in the room is the fifth point that even if you construct a theory that is at least mathematically consistent, it still would contain no observables. MWI is a “theory” which lacks observables entirely.
The analogy to Galilean relativity actually is too kind. Galilean relativity relies on Euclidean space as a background, allowing an external viewpoint fixed to empty coordinates. Hilbert space is not a background space at all; it is always defined in terms of physical systems, what is known as a constructed space. You can transform perspectives in spacetime, but there is no transformation to a background perspective in Hilbert space because no such background exists. The closest that exists is a statistical transformation to different perspectives within Liouville space, but this only works for objects within the space; you cannot transform to the perspective of the background itself as it is not a background space.
…which is why eventually you need to switch to the grown-up version of Quantum Mechanics, Quantum Field Theory, is defined in terms of relativistic fields with a single “universal” field for each flavor of particle.
My understanding might be a bit superficial, but I thought the whole point of the MWI was to make explicit the fact that states are relative? To me the rationale was that states are relative and if we simultaneously describe relative states and their observers we can translate the shrödinger+born-rule in a density-operator+partial-trace-rule and make the wave function collapse physical (aka unitary) through branching and decoherence, even though that’s mathematically tedious and in practice people will keep using projectors (1). States being relative means their physical reality is somewhat broken but locality is mostly saved (2), so then we postulate that they derive from a universal wave function to rehabilitate some form of physical realism (3). As to (4), isn’t it solved if you assume that Schrödinger’s equation is actually the less fundamental formalism since it’s only valid for systems that are unrealistically isolated?
MWI very specifically commits to the existence of a universal wavefunction. Everett’s original paper is literally titled “The Theory of the Universal Wavefunction.” If you instead only take relative states seriously, that position is much closer to relational quantum mechanics. In fact, Carlo Rovelli explicitly describes RQM as adopting Everett’s relative-state idea while rejecting the notion of a universal quantum state.
MWI claims there exists a universal quantum state, but quantum theory works perfectly well without this assumption if quantum states are taken to be fundamentally relative. Every quantum state is defined in relation to something else, which is made clear by the Wigner’s friend scenario where different observers legitimately assign different states to the same system. If states are fundamentally relative, then a “universal” quantum state makes about as much sense as a “universal velocity” in Galilean relativity.
You could arbitrarily choose a reference frame in Galilean relativity and declare it universal, but this requires an extra postulate, is unnecessary for the theory, and is completely arbitrary. Likewise, you could pick some observer’s perspective and call that the universal wavefunction, but there is no non-arbitrary reason to privilege it. That wavefunction would still be relative to that observer, just with special status assigned by fiat.
Worse, such a perspective could never truly be universal because it could not include itself. To do that you would need another external perspective, leading to infinite regress. You never obtain a quantum state that includes the entire universe. Any state you define is always relative to something within the universe, unless you define it relative to something outside of the universe, but at that point you are talking about God and not science.
The analogy to Galilean relativity actually is too kind. Galilean relativity relies on Euclidean space as a background, allowing an external viewpoint fixed to empty coordinates. Hilbert space is not a background space at all; it is always defined in terms of physical systems, what is known as a constructed space. You can transform perspectives in spacetime, but there is no transformation to a background perspective in Hilbert space because no such background exists. The closest that exists is a statistical transformation to different perspectives within Liouville space, but this only works for objects within the space; you cannot transform to the perspective of the background itself as it is not a background space.
One of the papers I linked also provides a no-go theorem as to why a universal quantum state cannot possibly exist in a way that would be consistent with relative perspectives. There are just so many conceptual and mathematical problems with a universal wavefunction. Even if you somehow resolve them all, your solution will be far more convoluted than just taking the relative states of quantum mechanics at face value. There is no need to “explain measurement” or introduce a many worlds or a universal wavefunction if you just accept the relative nature of the theory at face value and move on, rather than trying to escape it (for some reason).
But this is just one issue. The other elephant in the room is the fifth point that even if you construct a theory that is at least mathematically consistent, it still would contain no observables. MWI is a “theory” which lacks observables entirely.
…which is why eventually you need to switch to the grown-up version of Quantum Mechanics, Quantum Field Theory, is defined in terms of relativistic fields with a single “universal” field for each flavor of particle.