Solo: Looking Quantum Mechanics in the Eyeball | Mindscape 355

The Copenhagen interpretation, though widely adopted, defines 'measurement' and 'wave function collapse' in a 'hilariously ill-defined' manner, lacking a precise scientific definition for when and how these events occur. Its philosophical implication, denying reality until a measurement outcome, is a 'very, very philosophically radical view to take' that most physicists who subscribe to it likely haven't fully considered.

Carroll states that the survey definition of Copenhagen (wave function collapses when measured) is problematic because it doesn't define 'measured.' He suggests most physicists haven't thought it through carefully enough to realize its radical implications.

The Everettian (Many-Worlds) interpretation is 'austere' and 'simple' in its postulates, relying only on the Schrödinger equation without ad hoc collapse rules. However, this simplicity shifts the burden to 'philosophical heavy lifting' to connect the abstract wave function to our perceived reality, particularly in identifying the observer within the universe's wave function and understanding how 'worlds' emerge.

Carroll explains that Everett's formalism just uses wave functions obeying the Schrödinger equation, with 'no extra postulates.' He notes that 'that interpretation of who you are in the wave function is a highly non-trivial thing that requires a little bit of work.'

In quantum mechanics, the wave function contains all information, and expressing it in terms of position or momentum is merely choosing different 'coordinate axes' on the underlying Hilbert space. This implies that position and momentum are not fundamental aspects of reality but rather 'projections' or 'choices of questions to ask' about the quantum state.

Carroll states, 'You just need psi of x or psi of p. You don't need psi of x and p. You don't need to know both at once. That's the origin of the uncertainty principle.' He later clarifies, 'what you call position and what you call momentum are choices of what questions to ask.'

The fundamental reality is the quantum state, represented as a vector in Hilbert space. Our familiar three-dimensional space, and the 'locations' of objects within it, are not fundamental but are emergent properties. This challenges the deep-seated intuition, even held by Einstein, that things must have locations in space.

Carroll argues, 'Position is not fundamental. Locations in space are not part of the fundamental description of reality.' He adds, 'The world is not something else, but it is represented mathematically as a vector in Hilbert space.'

The 'problem of structure' in Everettian quantum mechanics asks how the 'manifest image' of the world—stuff arranged in space—emerges from the bare, austere quantum state. 'Quantum meology' is the proposed solution: defining 'subsystems' within Hilbert space by 'carving Hilbert space at its joints' based on criteria that yield useful, self-contained emergent descriptions, much like how fluid mechanics emerges from atomic physics.

Carroll defines the problem: 'in each branch, why do things look like stuff arranged in space?' and introduces 'quantum meology' as 'the relationship between a whole thing and its parts into which you divide it up into.'

The principle of locality, stating that interactions are restricted to nearest neighbors in space, is not a fundamental axiom but an emergent property. Research suggests that among the infinite ways to divide Hilbert space, only a 'delicately chosen' few lead to local interactions, and this local subdivision is 'essentially unique.'

Referring to the Cutler, Pennington, and Renard paper, Carroll explains that 'most Hamiltonians... have no local way of talking about them.' He states that 'locality is very, very special' and that when a local way of subdividing Hilbert space exists, 'it's essentially unique.'

A significant obstacle to deriving emergent structure from quantum mechanics is the 'problem of time' in quantum gravity. The Wheeler-DeWitt equation, derived from quantizing general relativity, contains no time parameter, implying a static universe. If time evolution (dynamics) is necessary to define emergent structures and locality, a static quantum state would prevent this emergence, posing a 'real problem.'

Carroll notes that in the Wheeler-DeWitt equation, 'the Hamiltonian says the wave function does not evolve with time. There's no time in the Wheeler-DeWitt equation.' He adds, 'all of the ways that we were getting structure in our Hilbert space at the emerging level depended on the dynamics of the quantum state.'