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The prince and the pauper. A quantum paradox of Hilbert-space fundamentalism
Quantum Physics · Submitted 23 Oct 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim These results show that even if a tensor product structure is assumed along with the unit vector and the Hamiltonian, concrete physically distinct worlds can be described by the same structures.
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
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The abstract, sentence by sentence
The quantum world is described by a unit vector in the Hilbert space and the Hamiltonian. Do these abstract basis-independent objects give a complete description of the physical world, or should we include observables like positions and momenta and the decomposition into subsystems? According to "Hilbert-space fundamentalism" they give a complete description, and all other features of the physical world emerge from them (Carroll, arXiv:2103.09780). Here I will give a concrete refutation of this thesis based on the symmetries of the theory of quantum measurements. These results show that even if a tensor product structure is assumed along with the unit vector and the Hamiltonian, concrete physically distinct worlds can be described by the same structures.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The quantum world is described by a unit vector in the Hilbert space and the Hamiltonian. | background 1.00 | 0.05 | 0.02 | asserted 1.00 |
| s1 | Do these abstract basis-independent objects give a complete description of the physical world, or should we include observables like positions and momenta and the decomposition into subsystems? | background 0.88 | 0.05 | 0.03 | unclear 0.92 |
| s2 | According to "Hilbert-space fundamentalism" they give a complete description, and all other features of the physical world emerge from them (Carroll, arXiv:2103.09780). | background 1.00 | 0.03 | 0.05 | asserted 1.00 |
| s3 | Here I will give a concrete refutation of this thesis based on the symmetries of the theory of quantum measurements. | contribution 0.88 | 0.81 | 0.11 | asserted 0.93 |
| s4 | These results show that even if a tensor product structure is assumed along with the unit vector and the Hamiltonian, concrete physically distinct worlds can be described by the same structures. | result 0.91 | 0.88 | 0.83 | asserted 0.99 |
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The paper
Original abstract
The quantum world is described by a unit vector in the Hilbert space and the Hamiltonian. Do these abstract basis-independent objects give a complete description of the physical world, or should we include observables like positions and momenta and the decomposition into subsystems? According to "Hilbert-space fundamentalism" they give a complete description, and all other features of the physical world emerge from them (Carroll, arXiv:2103.09780). Here I will give a concrete refutation of this thesis based on the symmetries of the theory of quantum measurements. These results show that even if a tensor product structure is assumed along with the unit vector and the Hamiltonian, concrete physically distinct worlds can be described by the same structures.
Human review
How the literature uses it
5 arXiv papers cite this in 13 sentences
Papers citing it · 6 sentences without a confident label
Uses its method or tool 1 paper
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Therefore, we can apply Lemma 1 from [ref] to any observable $Â$.
Sentient observers and the ontology of spacetime · The ambiguity of Structural Realism · 0.80
Cites it as support 4 papers
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And even if we assume a tensor product structure as given, the description of the world is maximally ambiguous [ref] .
Sentient observers and the ontology of spacetime · Do these lessons extend to the quantum world? · 1.00
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And, as shown by the examples provided in [ref] , we obtain infinitely many possible solutions that are completely distinct from a physical point of view, and they correspond to physically distinct structures like space and decomposition into subsystems.
What makes you an observer? · Puzzle: the ambiguity of the physical meaning · 1.00
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Even including a preferred TPS along with $H$ and $|ψ⟩$ is insufficient to recover a complete description of the world [ref] .
Comment on "On the emergence of preferred structures in quantum theory" by Soulas, Franzmann, and Di Biagio · So what's this comment all about? · 0.98
What it cites · 4 sentences without a confident label
Contests 3 papers
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In addition, a specific proof refuting the claim that the tensor product structure emerges uniquely from the Hamiltonian's spectrum [ref] was given in [ref] , and numerous other counterexamples to were given in [ref] .
Empirical adequacy of the time operator canonically conjugate to a Hamiltonian generating translations · Discussion · contest 0.79
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In addition, a specific proof refuting the claim that the tensor product structure emerges uniquely from the Hamiltonian's spectrum [ref] was given in [ref] , and numerous other counterexamples to were given in [ref] .
Quantum Mereology: Factorizing Hilbert Space into Subsystems with Quasi-Classical Dynamics · Discussion · contest 0.79
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In addition, a specific proof refuting the claim that the tensor product structure emerges uniquely from the Hamiltonian's spectrum [ref] was given in [ref] , and numerous other counterexamples to were given in [ref] .
Does the Hamiltonian determine the tensor product structure and the 3d space? · Discussion · contest 0.79
Cites as support 3 papers
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In [ref] it was shown that whenever any of these structures emerges from the state vector and the Hamiltonian, it is not unique.
3D-Space and the preferred basis cannot uniquely emerge from the quantum structure · Discussion · 1.00
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A proof that the tensor product structure doesn't emerge uniquely from the Hamiltonian was given in [ref] .
Does the Hamiltonian determine the tensor product structure and the 3d space? · Introduction · 0.99
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Also numerous counterexamples can be found in [ref] .
Empirical adequacy of the time operator canonically conjugate to a Hamiltonian generating translations · Introduction · 0.96
Cites as background 3 papers
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This thesis, coined “” in [ref] , is assumed in various research programs, in some approaches based on decoherence where along with the pointer state the physical meaning is supposed to emerge [ref] , claims that the tensor product structure is uniquely determined by the Hamiltonian's spectrum under conditions like the locality of the interactions [ref] , proposals that space itself emerges from these abstract structures alone [ref] , and other Quantum Gravity programs in which spacetime is supposed to emerge from the quantum structure [ref] .
3D-Space and the preferred basis cannot uniquely emerge from the quantum structure · Introduction · 0.84
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This thesis, coined “” in [ref] , is assumed in various research programs, in some approaches based on decoherence where along with the pointer state the physical meaning is supposed to emerge [ref] , claims that the tensor product structure is uniquely determined by the Hamiltonian's spectrum under conditions like the locality of the interactions [ref] , proposals that space itself emerges from these abstract structures alone [ref] , and other Quantum Gravity programs in which spacetime is supposed to emerge from the quantum structure [ref] .
Quantum Mereology: Factorizing Hilbert Space into Subsystems with Quasi-Classical Dynamics · Introduction · 0.84
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This thesis, coined “” in [ref] , is assumed in various research programs, in some approaches based on decoherence where along with the pointer state the physical meaning is supposed to emerge [ref] , claims that the tensor product structure is uniquely determined by the Hamiltonian's spectrum under conditions like the locality of the interactions [ref] , proposals that space itself emerges from these abstract structures alone [ref] , and other Quantum Gravity programs in which spacetime is supposed to emerge from the quantum structure [ref] .
Decoherence, einselection, and the quantum origins of the classical · Introduction · 0.84
Discussion
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