This paper presents a formal mathematical and epistemological refutation of canonical and path-integral field quantization protocols. The work demonstrates that forcing discrete quantum operators onto a continuous manifold ( $\mathbb{R}^4$ ) constitutes a profound category error—an Aristotelian logical refutation showing that the Planck scale is merely the forced discretization of an artificial continuous cosmos. Furthermore, it exposes the foundational impedance mismatch between Schrödinger’s continuous Wave Mechanics and Heisenberg’s native discrete Matrix Mechanics, proving that infinite potentials, ultraviolet divergences, and renormalization schemes serve as unfalsifiable pseudo-scientific hypotheses designed to rescue broken differential equations from collapse.This paper presents a formal mathematical and epistemological refutation of canonical and path-integral field quantization protocols. The work demonstrates that forcing discrete quantum operators onto a continuous manifold ($\mathbb{R}^4$) constitutes a profound category error—an Aristotelian logical refutation showing that the Planck scale is merely the forced discretization of an artificial continuous cosmos. Furthermore, it exposes the foundational impedance mismatch between Schrödinger’s continuous Wave Mechanics and Heisenberg’s native discrete Matrix Mechanics, proving that infinite potentials, ultraviolet divergences, and renormalization schemes serve as unfalsifiable pseudo-scientific hypotheses designed to rescue broken differential equations from collapse.

Aug 19, 20260 citations

HEISENBERG ON THE RUN

Michigan State University Press eBooksMar 1, 20260 citations

Dodging Heisenberg

N. MacDonald

NatureApr 1, 19782 citations

Rescuing a black hole in the large-q coupled SYK model

Yuri D. Lensky

In this paper, we develop a general effective theory for two copies of the Sachdev-Ye-Kitaev (SYK) model with a time-dependent bilinear coupling. For a quantum quench problem with an initial state of the thermofield double state, we show how the evolution of the system is described by a complex reparametrization field with a classical Hamiltonian. We study correlation functions in this system and compare the large-q theory with the bulk low energy effective theory. In particular, we study the special case of a “rescued black hole”, which describes how a time-evolved thermofield double state can evolve to the ground state of a coupled SYK model by a carefully tuned time-dependent coupling. In the low energy region, there is a holographic dual interpretation, which is a geometry that crosses over from an eternal black hole to a global AdS2 vacuum. This family of geometries allow us to access the bulk region that would be the black hole interior without the rescue process. By comparing the large-q and low energy theory, we find that even in the low energy region the deviation from the low energy theory cannot be neglected if the rescue process starts late. This provides evidence that the low energy effective theory of the bulk fails near the inner horizon of the black hole. We note the possibility of a connection to a two-dimensional analog of the higher-dimensional black hole singularity.In this paper, we develop a general effective theory for two copies of the Sachdev-Ye-Kitaev (SYK) model with a time-dependent bilinear coupling. For a quantum quench problem with an initial state of the thermofield double state, we show how the evolution of the system is described by a complex reparametrization field with a classical Hamiltonian. We study correlation functions in this system and compare the large-q theory with the bulk low energy effective theory. In particular, we study the special case of a “rescued black hole”, which describes how a time-evolved thermofield double state can evolve to the ground state of a coupled SYK model by a carefully tuned time-dependent coupling. In the low energy region, there is a holographic dual interpretation, which is a geometry that crosses over from an eternal black hole to a global AdS2 vacuum. This family of geometries allow us to access the bulk region that would be the black hole interior without the rescue process. By comparing the large-q and low energy theory, we find that even in the low energy region the deviation from the low energy theory cannot be neglected if the rescue process starts late. This provides evidence that the low energy effective theory of the bulk fails near the inner horizon of the black hole. We note the possibility of a connection to a two-dimensional analog of the higher-dimensional black hole singularity.

Nov 25, 202414 citations

HUNTING HEISENBERG

Michigan State University Press eBooksMar 1, 20260 citations

Rescuing a black hole in the large-q coupled SYK model

Yuri D. Lensky, Xiao-Liang Qi

Abstract In this paper, we develop a general effective theory for two copies of the Sachdev-Ye-Kitaev (SYK) model with a time-dependent bilinear coupling. For a quantum quench problem with an initial state of the thermofield double state, we show how the evolution of the system is described by a complex reparametrization field with a classical Hamiltonian. We study correlation functions in this system and compare the large-qtheory with the bulk low energy effective theory. In particular, we study the special case of a “rescued black hole”, which describes how a time-evolved thermofield double state can evolve to the ground state of a coupled SYK model by a carefully tuned time-dependent coupling. In the low energy region, there is a holographic dual interpretation, which is a geometry that crosses over from an eternal black hole to a global AdS2vacuum. This family of geometries allow us to access the bulk region that would be the black hole interior without the rescue process. By comparing the large-qand low energy theory, we find that even in the low energy region the deviation from the low energy theory cannot be neglected if the rescue process starts late. This provides evidence that the low energy effective theory of the bulk fails near the inner horizon of the black hole. We note the possibility of a connection to a two-dimensional analog of the higher-dimensional black hole singularity.Abstract In this paper, we develop a general effective theory for two copies of the Sachdev-Ye-Kitaev (SYK) model with a time-dependent bilinear coupling. For a quantum quench problem with an initial state of the thermofield double state, we show how the evolution of the system is described by a complex reparametrization field with a classical Hamiltonian. We study correlation functions in this system and compare the large-qtheory with the bulk low energy effective theory. In particular, we study the special case of a “rescued black hole”, which describes how a time-evolved thermofield double state can evolve to the ground state of a coupled SYK model by a carefully tuned time-dependent coupling. In the low energy region, there is a holographic dual interpretation, which is a geometry that crosses over from an eternal black hole to a global AdS2vacuum. This family of geometries allow us to access the bulk region that would be the black hole interior without the rescue process. By comparing the large-qand low energy theory, we find that even in the low energy region the deviation from the low energy theory cannot be neglected if the rescue process starts late. This provides evidence that the low energy effective theory of the bulk fails near the inner horizon of the black hole. We note the possibility of a connection to a two-dimensional analog of the higher-dimensional black hole singularity.

arXiv:2012.15798Journal of High Energy PhysicsApr 1, 202115 citations

\mathbb{R}^4

) constitutes a profound category error—an Aristotelian logical refutation showing that the Planck scale is merely the forced discretization of an artificial continuous cosmos. Furthermore, it exposes the foundational impedance mismatch between Schrödinger’s continuous Wave Mechanics and Heisenberg’s native discrete Matrix Mechanics, proving that infinite potentials, ultraviolet divergences, and renormalization schemes serve as unfalsifiable pseudo-scientific hypotheses designed to rescue broken differential equations from collapse.