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Full-Text Articles in Physics
Conservation Laws And The Foundations Of Quantum Mechanics, Yakir Aharonov, Sandu Popescu, Daniel Rohrlich
Conservation Laws And The Foundations Of Quantum Mechanics, Yakir Aharonov, Sandu Popescu, Daniel Rohrlich
Mathematics, Physics, and Computer Science Faculty Articles and Research
In a recent paper, [Y. Aharonov, S. Popescu, D. Rohrlich, Proc. Natl. Acad. Sci. U.S.A.118 e1921529118 (2021)], it was argued that while the standard definition of conservation laws in quantum mechanics, which is of a statistical character, is perfectly valid, it misses essential features of nature and it can and must be revisited to address the issue of conservation/nonconservation in individual cases. Specifically, in the above paper, an experiment was presented in which it can be proven that in some individual cases, energy is not conserved, despite being conserved statistically. It was felt however that this is worrisome and …
Uncertainty From The Aharonov–Vaidman Identity, Matthew S. Leifer
Uncertainty From The Aharonov–Vaidman Identity, Matthew S. Leifer
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this article, I show how the Aharonov–Vaidman identity A|ψ>=<A⟩|ψ>+ΔA| ψ⊥A> can be used to prove relations between the standard deviations of observables in quantum mechanics. In particular, I review how it leads to a more direct and less abstract proof of the Robertson uncertainty relation ΔAΔB≥12|< [A,B]>| than the textbook proof. I discuss the relationship between these two proofs and show how the Cauchy–Schwarz inequality can be derived from the Aharonov–Vaidman identity. I give Aharonov–Vaidman based proofs of the Maccone–Pati uncertainty relations …
Is There Causation In Fundamental Physics? New Insights From Process Matrices And Quantum Causal Modelling, Emily Adlam
Is There Causation In Fundamental Physics? New Insights From Process Matrices And Quantum Causal Modelling, Emily Adlam
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this article we set out to understand the significance of the process matrix formalism and the quantum causal modelling programme for ongoing disputes about the role of causation in fundamental physics. We argue that the process matrix programme has correctly identified a notion of ‘causal order’ which plays an important role in fundamental physics, but this notion is weaker than the common-sense conception of causation because it does not involve asymmetry. We argue that causal order plays an important role in grounding more familiar causal phenomena. Then we apply these conclusions to the causal modelling programme within quantum foundations, …