More general probability sum-rules for describing interference found in quantum mechanics (QM) were formulated by Sorkin in a hierarchy of such rules. The additivity of classical measure theory corresponds to the second sum-rule. QM violates this rule, but satisfies the third and higher sum-rules. This evokes the question of whether there are physical principles that forbid their violation. We show that in a theory that is indistinguishable from quantum mechanics in first and second-order interferences, the violation of higher sum-rules allows for superluminal signaling, essentially because probability measures can be contextual in such theories.More general probability sum-rules for describing interference found in quantum mechanics (QM) were formulated by Sorkin in a hierarchy of such rules. The additivity of classical measure theory corresponds to the second sum-rule. QM violates this rule, but satisfies the third and higher sum-rules. This evokes the question of whether there are physical principles that forbid their violation. We show that in a theory that is indistinguishable from quantum mechanics in first and second-order interferences, the violation of higher sum-rules allows for superluminal signaling, essentially because probability measures can be contextual in such theories.

arXiv:1308.6065International Journal of Quantum InformationAug 1, 20160 citations

The formal rules of quantum mechanics

P. C. W. Davies, David S. Betts

Springer eBooksJan 1, 19940 citations

Epistemic Separability and Everettian Branches: A Critique of Sebens and Carroll

Richard Dawid, Simon Friederich

We discuss the proposal by Sebens and Carroll to derive the Born rule in Everettian quantum mechanics from a principle they call ‘ESP-QM’. We argue that the proposal fails: ESP-QM is not, as Sebens and Carroll argue, a ‘less general version’ of an independently plausible principle, ESP, and can only be motivated by the empirical success of quantum mechanics, including use of the Born rule. Therefore, ESP-QM cannot have the status of a meta-theoretical principle of reasoning and provides no viable basis for deriving the Born rule.We discuss the proposal by Sebens and Carroll to derive the Born rule in Everettian quantum mechanics from a principle they call ‘ESP-QM’. We argue that the proposal fails: ESP-QM is not, as Sebens and Carroll argue, a ‘less general version’ of an independently plausible principle, ESP, and can only be motivated by the empirical success of quantum mechanics, including use of the Born rule. Therefore, ESP-QM cannot have the status of a meta-theoretical principle of reasoning and provides no viable basis for deriving the Born rule.

The British Journal for the Philosophy of ScienceJan 28, 20204 citations

Principles of Quantum Mechanics

Jean-Louis Basdevant

Graduate texts in physicsJan 1, 2016434 citations

Born rule in quantum and classical mechanics

Paul W. Brumer, Jiangbin Gong

Considerable effort has been devoted to deriving the Born rule [i.e., that ${\ensuremath{\mid}\ensuremath{\psi}(x)\ensuremath{\mid}}^{2}dx$ is the probability of finding a system, described by $\ensuremath{\psi}$, between $x$ and $x+dx$ ] in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbert-space formulation of classical mechanics as well. These results provide insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics.Considerable effort has been devoted to deriving the Born rule [i.e., that ${\ensuremath{\mid}\ensuremath{\psi}(x)\ensuremath{\mid}}^{2}dx$ is the probability of finding a system, described by $\ensuremath{\psi}$, between $x$ and $x+dx$] in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbert-space formulation of classical mechanics as well. These results provide insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics.

arXiv:quant-ph/0604178Physical Review AMay 19, 200674 citations

x

and

x+dx

] in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbert-space formulation of classical mechanics as well. These results provide insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics.