3D-Space and the preferred basis cannot uniquely emerge from the quantum structure
arXiv:2102.08620 · doi:10.4310/ATMP.2022.v26.n10.a12
Abstract
Hilbert-Space Fundamentalism (HSF) states that the only fundamental structures are the quantum state vector and the Hamiltonian, and from them everything else emerge uniquely, including the 3D-space, a preferred basis, and a preferred factorization of the Hilbert space. In this article it is shown that whenever such a structure emerges from the Hamiltonian and the state vector alone, if it is physically relevant, it is not unique. Moreover, HSF leads to strange effects like "passive" travel in time and in alternative realities, realized simply by passive transformations of the Hilbert space. The results from this article affect all theories that adhere to HSF, whether they assume branching or state vector reduction (in particular the version of Everett's Interpretation coined by Carroll and Singh "Mad-dog Everettianism"), various proposals based on decoherence, proposals that aim to describe everything by the quantum structure alone, and proposals that spacetime emerges from a purely quantum theory of gravity.
arXiv comment28 pages, 1 figure
References in corpus (29)
- Decoherence, einselection, and the quantum origins of the classical
- Spin Networks and Quantum Gravity
- Quantum tensor product structures are observable-induced
- A Short Review of Loop Quantum Gravity
- Decoherence, Einselection, and the Existential Interpretation (the Rough Guide)
- Space from Hilbert Space: Recovering Geometry from Bulk Entanglement
- Can the universe afford inflation?
- The Interpretation of Quantum Mechanics: Many Worlds or Many Words?
- Against Many-Worlds Interpretations
- Consciousness as a State of Matter
- How is quantum information localized in gravity?
- Experimental motivation and empirical consistency in minimal no-collapse quantum mechanics
- Quantum Mereology: Factorizing Hilbert Space into Subsystems with Quasi-Classical Dynamics
- Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space
- Alternative Decohering Histories in Quantum Mechanics
- Quantum-first gravity
- The clock ambiguity and the emergence of physical laws
- Replacing the Notion of Spacetime Distance by the Notion of Correlation
- Global and local aspects of causality in quantum mechanics
- Quantum Structures of a Model-Universe: An Inconsistency with Everett Interpretation of Quantum Mechanics
- A representation of the wave function on the three-dimensional space
- Pure quantum interpretations are not viable
- Standard Quantum Mechanics without observers
- The Relation between Wavefunction and 3D Space Implies Many Worlds with Local Beables and Probabilities
- Nothing happens in the Universe of the Everett Interpretation
- Background freedom leads to many-worlds with local beables and probabilities
- The prince and the pauper. A quantum paradox of Hilbert-space fundamentalism
- Does the Hamiltonian determine the tensor product structure and the 3d space?
- Are observers reducible to structures?