Quantum Mechanics from a Holographic Principle

Abstract: In 1953, Richard Feynman introduced a mathematical trick through which quantum mechanical many-body problems could be solved using classical statistical mechanics by treating the inverse of the thermal energy in the partition function as an imaginary time dimension (a Wick rotation). This opened the door for modern quantum simulation methods such as path integral Monte Carlo, centroid molecular dynamics and ring polymer molecular dynamics which are solved classically by using the extra, fictitious, dimension. Practitioners of this quantum-classical isomorphism often refer to the quantum particles they are simulating as “ring polymers” since the imaginary time parameter describes a one-dimensional trajectory that starts and stops at the same position in space, forming a closed loop when projected into 3D. It has been shown that polymer self-consistent field theory (SCFT) also obeys the quantum-classical isomorphism, and is, under the right conditions, also equivalent to quantum density functional theory (DFT). Since the theorems of DFT guarantee equivalence between the predictions of DFT and those of of quantum mechanics, the mathematics of SCFT in a 5D thermal-space-time must be dual to those of 4D non-relativistic quantum mechanics — a holographic principle. This requires speculating that Feynman’s thermal dimension is physically real instead of just a trick of the math. The 5D picture requires fewer postulates than most descriptions of quantum mechanics and uses only classical concepts, albeit in a higher dimensional space. I will give an introductions to the SCFT approach, show some numerical solutions to the non-linear SCFT equations, and consider the prospects, applications and significant limitations of the methodology.

mathematical physicsgeneral physicsquantum physics

Audience: researchers in the topic

( video )

---

QM Foundations & Nature of Time seminar

Series comments: Description: Physics foundations discussion seminar

Current access link in th.if.uj.edu.pl/~dudaj/QMFNoT

---