Machine learning-assisted approximation of symmetrized quantum time correlation functions

Open-chain imaginary-time path-integral sampling approach known with the acronym OPSCF (J. Chem. Phys. 148, 102340 (2018)) is an approach to the calculation of approximate symmetrized quantum time correlation functions. In OPSCF approach, the real time t is treated as a parameter, and therefore for each real time t, a separate simulation on the imaginary time axis is needed to be run, which makes the OPSCF approach quite expensive and as a result, the approach loses the advantage of being a standard path-integral sampling approach. In this study, I propose that the use of OPSCF approach in combination with machine learning can reduce the computational cost by 75% to 90% (depending on the problem at hand). Combining OPSCF approach with ML is very straight forward which gives an upper hand to OPSCF approach over the trajectory-based methods such as the centroid molecular dynamics (CMD) and the ring-polymer molecular dynamics (RPMD).

The Surjective Mapping Conjecture and the Measurement Problem in Quantum Mechanics

Accepting a time-symmetric quantum dynamical world with ontological wave functions or fields, we follow arguments that naturally lead to a two-boundary interpretation of quantum mechanics. The usual two boundary picture is a valid superdeterministic interpretation. It has, however, one unsatisfactory feature. The random selection of a chosen measurement path of the universe is far too complicated. To avoid it, we propose an alternate two-boundary concept called surjective mapping conjecture. It takes as fundamental a quantum-time running forward like the usual time on the wave-function side and backward on the complex conjugate side. Unrelated fixed arbitrary boundary conditions at the initial and the final quantum times then determine the measurement path of the expanding and contracting quantum-time universe in the required way.

Decoding the wave particle duality

The action reaction principle (ARP), a fundamental ingredient of Physics, is taken for granted, because it is automatically fulfilled along the ordinary Hamiltonian, classical or quantum, time evolution law. But in quantum mechanics, there is an extraordinary evolution law, the projection of state rule along quantum measurements, which is not Hamiltonian. Consequently, the ARP is not automatically fulfilled along quantum measurements, and it must be checked case by case. Surprisingly, very simple quantum measurements, both theoretical processes and experiments, show an apparent violation of the ARP, so that the hidden reaction must be found. In the analyzed experiment, the ARP is restored if some new system, the quantum or de Broglie wave, exists and locally interacts with the detector. There cannot be interaction at a spatial distance between the particle (photon or electron) and the obstacle‐detector.