A review of Takesaki crossed product duality plus an unproven conjecture that modular Hamiltonian evolution of vacuum fluctuations is the microscopic mechanism of gravitational time dilation.
von Neumann:On rings of operators IV, Ann.Math.44(1943)716
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The Crossed Product, Modular (Tomita) Dynamics and its Role in the Transition of Type $III$ to Type $II_{\infty}$ v.Neumann Algebras and Connections to Quantum Gravity
A review of Takesaki crossed product duality plus an unproven conjecture that modular Hamiltonian evolution of vacuum fluctuations is the microscopic mechanism of gravitational time dilation.