On Sunday, May 10, 2020 at 9:09:51 AM UTC-5, Philip Thrift wrote: > > > > On Sunday, May 10, 2020 at 7:20:16 AM UTC-5, Bruno Marchal wrote: >> >> >> On 10 May 2020, at 13:45, Philip Thrift <cloud...@gmail.com> wrote: >> >> >> >> >> cf. >> https://www.researchgate.net/publication/325907723_A_gentle_introduction_to_Schwinger's_formulation_of_quantum_mechanics_The_groupoid_picture >> >> >> >> >> *Schwinger’s picture of Quantum Mechanics* >> https://arxiv.org/pdf/2002.09326.pdf >> >> >> >> >> Those are good papers. >> >> (I am not entirely sure why you refer to them, but Swinger is very good >> on this). When I teach quantum mechanics, I use an informal version of >> this, based on a textbook by Thomson (but I failed to find it right now). >> This helps to understand than both complex numbers and three dimension >> marry well together to make the quantum weirdness hard to avoid. It >> provides short path to the violation of Bell’s inequality. >> >> Bruno >> >> >> >> *In this paper we will present the main features of what can be called >> Schwinger's foundational approach to Quantum Mechanics. The basic >> ingredients of this formulation are the selective measurements, whose >> algebraic composition rules define a mathematical structure called >> groupoid, which is associated with any physical system. After the >> introduction of the basic axioms of a groupoid, the concepts of observables >> and states, statistical interpretation and evolution are derived. An >> example is finally introduced to support the theoretical description of >> this approach.* >> >> Finally, we will introduce *a quantum measure* associated with the state >> ρ >> >> First, we realize that the state ρ on C∗(G) defines a decoherence >> functional D on the σ-algebra Σ of events of the groupoid G >> >> We define a quantum measure µ on Σ >> >> ... >> >> >> >> @philipthrift >> Click >> >> >> >> @philipthrift >> >> >> > A measure theory on *the appropriate measure space* underlies both > probability theory and what has been called quantum-probability theory. > > @philipthrift >
*Quantum measures and the coevent interpretation* https://arxiv.org/abs/1005.2242 A quantum measure µ describes the dynamics of a quantum system in the sense that µ(A) gives the propensity that the event A occurs. Denoting the set of events by A, a coevent is a potential reality for the system given by a truth function φ: A → Z₂ where Z₂ is the two element Boolean algebra {0, 1}. Due to quantum interference, a q-measure need not satisfy the usual additivity condition of an ordinary measure but satisfies the more general grade-2 additivity condition (2.1) instead. Let (Ω, A) be a measurable space, where Ω is a set of outcomes and A is a σ-algebra of subsets of Ω called events for a physical system. If A, B ∈ A are disjoint, we denote their union by A ⩁ B. A nonnegative set function µ: A → R+ is grade-2 additive if µ (A ⩁ B ⩁ C) = µ (A ⩁ B) + µ (A ⩁ C) + µ (B ⩁ C) − µ(A) − µ(B)- µ(C) (2.1) for all mutually disjoint A, B, C ∈ A [examples] @philipthrift -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/487195d6-f60c-4b13-9af9-8b9df12ed8f7%40googlegroups.com.
