Four Postulates of Quantum Mechanics Are Three

Carcassi, Gabriele; Maccone, Lorenzo; Aidala, C.

doi:10.1103/physrevlett.126.110402

Cited by 22 publications

(13 citation statements)

References 16 publications

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“…Since by (12) Σ is a constant of motion, we find that during Hamiltonian evolution the uncertainty is bounded.…”

Section: Uncertainty Principle Revisitedmentioning

confidence: 85%

“…We could go on to find other relationships and extend the ones we found to multiple degrees of freedom, but we believe this should be enough to highlight the power of the reverse physics approach. The first thing to note is how in a couple of pages we have found fundamental connections between classical Hamiltonian mechanics (1), vector calculus (2), differential geometry (6), statistical mechanics (7), thermodynamics (8), information theory ( 9) and plain statistics (12). This helps foster a sense of unity of these disparate disciplines and their perspectives, a sense that is sorely lacking both in research and education: nature is one, and does not care about how we have divided academic knowledge.…”

Section: Determinism Reversibility and Hamiltonian Mechanicsmentioning

confidence: 99%

“…Refs. [4][5][6][7][8][9][10][11][12]), for example in the context of foundations of quantum mechanics, statistical mechanics or the search for quantum gravity, their aim is typically different. Some are focused on a particular field (e.g.…”

Section: Introductionmentioning

confidence: 99%

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Reverse Physics: From Laws to Physical Assumptions

Carcassi,

Aidala

2021

Preprint

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We introduce an approach to the foundations of physics that is more in line with the foundations of mathematics. The idea is to examine current theories and find a set of starting physical assumptions that are sufficient to rederive them, which is the physical equivalent of the reverse mathematics program. This allows us to identify physical starting points (as opposed to mathematical ones), compare their deductive power, and find those that can better serve as a foundation for our theories.

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“…Since by (12) Σ is a constant of motion, we find that during Hamiltonian evolution the uncertainty is bounded.…”

Section: Uncertainty Principle Revisitedmentioning

confidence: 85%

Section: Determinism Reversibility and Hamiltonian Mechanicsmentioning

confidence: 99%

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Reverse Physics: From Laws to Physical Assumptions

Carcassi,

Aidala

2021

Preprint

Self Cite

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“…QM was developed through a process of tackling several inconsistencies mainly in particle physics and thermodynamics which could not be solved by classical principles of physics. Its foundation as a consistent theory rested on a collection of postulates not truly derived from first principles [5,6], and on three fundamental pillars: Energy quantization, the concept and interpretation of the wave function and the uncertainty principle. For the uncertainty principle, classical QM states that the position and momentum of a particle in a trajectory cannot be defined with absolute certainty, which is in direct contradiction with GR.…”

Section: Introduction: General Relativity Quantum Mechanics and The P...mentioning

confidence: 99%

The Uncertainty Principle and the Minimal Space-Time Length Element

Escors¹,

Kochan²

2022

Preprint

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Quantum gravity theories rely on a minimal measurable length for their formulations, which clashes with the classical formulation of the uncertainty principle and with Lorentz invariance from general relativity. These incompatibilities led to the development of the generalized uncertainty principle (GUP) from string theories and its various modifications. GUP and covariant formulations of the uncertainty principle are discussed, together with implications for space-time quantization.

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“…The tensor product postulate of quantum mechanics, also cited as the 'zeroth' axiom in literature [1], describes the Hilbert space of a composite system to be the tensor product of the components' Hilbert spaces [2][3][4]. A recent study, however, logically derives this postulate from the state postulate and the measurement postulate rather than taking it as an independent one [5]. Nevertheless, within this tensor product structure, the unentangled Gleason's theorem assigns state spaces for the composite systems that include density operators (the quantum states) as a proper subset [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Timelike correlations and quantum tensor product structure

Sen¹,

Lobo²,

Patra³

et al. 2022

Preprint

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The state space structure for a composite quantum system is postulated among several mathematically consistent possibilities that are compatible with local quantum description. For instance, unentangled Gleason's theorem allows a state space that includes density operators as a proper subset among all possible composite states. However, bipartite correlations obtained in Bell type experiments from this broader state space are in-fact quantum simulable, and hence such spacelike correlations are no good to make distinction among different compositions. In this work we analyze communication utilities of these different composite models and show that they can lead to distinct utilities in a simple communication game involving two players. Our analysis, thus, establishes that beyond quantum composite structure can lead to beyond quantum correlations in timelike scenario and hence welcomes new principles to isolate the quantum correlations from the beyond quantum ones. We also prove a no-go that the classical information carrying capacity of different such compositions cannot be more than the corresponding quantum composite systems.

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Four Postulates of Quantum Mechanics Are Three

Cited by 22 publications

References 16 publications

Reverse Physics: From Laws to Physical Assumptions

Reverse Physics: From Laws to Physical Assumptions

The Uncertainty Principle and the Minimal Space-Time Length Element

Timelike correlations and quantum tensor product structure

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