arXiv subjects

Zhonghao Lu

Publications and source records attributed to Zhonghao Lu.

3 recordsLinked to original sources

arXiv2026

Unbounded Operators, Physicality, and Modality in Quantum Theories

In this paper, I address the problem regarding the physicality of Hilbert space in quantum mechanics, a topic brought into focus by Carcassi et al.'s paper "The unphysicality of Hilbert spaces" recently. I argue for the physicality of the Hilbert space in quantum mechanics, and demonstrate that there are inevitable ambiguity and arbitrariness if we want to identify the set of physical states with a proper subset of it. Moreover, I distinguish the ontological and modal reading of physicality from the pragmatic and operational reading of physicality, and then develop what I call the hierarchical view of physicality. According to this view, physicality is not a monolithic concept, but a layered one that admits degrees. I show the connection between the concept of physicality and modal metaphysics, and finally explain how it can be used to address the interpretational problem of quantum field theory brought by the existence of inequivalent representations.

quant-ph↗

arXiv2026

Is the existence of unbounded operators a problem for quantum mechanics? In response to Carcassi, Calderon, and Aidala

In this paper I argue against Carcassi, Calderon, and Aidala's recent claim that the Hilbert spaces are unphysical and should be replaced with the Schwartz spaces in quantum mechanics, since Hilbert spaces include states with infinite expectation values for certain observables. I also review and discuss issues regarding unbounded operators in quantum mechanics raised by Streater and Wightman, Heathcote, and Lemos. I argue that the existence of infinite expectation values does not cause problems in quantum mechanics. On the other hand, replacing the Hilbert spaces with the Schwartz spaces would cause more issues, as it would exclude a class of meaningful Hamiltonian evolutions. I also discuss the question in literature whether reformulating quantum mechanics with essentially self-adjoint operators instead of self-adjoint operators may cause problems. I further analyse the hierarchies of the notions of "physicality" and possibility in fundamental physics, and suggest that "physicality" is a vague concept. Finally, I connect the problem raised by Carcassi, Calderon, and Aidala with the problem of the Hadamard condition in quantum field theory.

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arXiv2023

Personal Identity and Uncertainty in the Everett Interpretation of Quantum Mechanics

The deterministic nature of EQM (the Everett Interpretation of Quantum Mechanics) seems to be inconsistent to the use of probability in EQM, giving rise to what is known as the "incoherence problem". In this paper, I explore approaches to solve the incoherence problem of EQM via pre-measurement uncertainty. Previous discussions on the validity of pre-measurement uncertainty have leaned heavily on intricate aspects of the theory of semantics and reference, the embrace of either 4-dimensionalism or 3-dimensionalism of personhood, or the ontology of EQM. In this paper, I argue that, regardless of the adoption of whether 3-dimensionalism or 4-dimensionalism of personhood, the overlapping view or the divergence view of the ontology of EQM, the pre-measurement uncertainty approach to the incoherence problem of EQM can only archive success while contradicting fundamental principles of physicalism. I also use the divergence view of EQM as an example to illustrate my analyses.

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