On Gravity, Holography and the Quantum

TL;DR

This paper explores the holographic principle, proposing that the boundary degrees of freedom are not fundamental and that stochastic quantization may explain the bulk-boundary mapping, with gravity influencing this relationship.

Contribution

It introduces a stochastic quantization framework for understanding the holographic mapping and discusses how gravity affects this process, challenging the notion of fundamental boundary degrees of freedom.

Findings

Stochastic quantization can describe the bulk-boundary mapping in holography.

Gravity causes differences in the quantization process compared to flat spacetime.

The boundary degrees of freedom are not fundamental but emerge from a more complex process.

Abstract

The holographic principle states that the number of degrees of freedom describing the physics inside a volume (including gravity) is bounded by the area of the boundary (also called the screen) which encloses this volume. A stronger statement is that these (quantum) degrees of freedom live on the boundary and describe the physics inside the volume completely. The obvious question is, what mechanism is behind the holographic principle. Recently, 't Hooft argued that the quantum degrees of freedom on the boundary are not fundamental. We argue that this interpretation opens up the possibility that the mapping between the theory in the bulk (the holographic theory) and the theory on the screen (the dual theory) is always given by a (generalized) procedure of stochastic quantization. We show that gravity causes differences to the situation in Minkowski/Euclidean spacetime and argue that the fictitious coordinate needed in the stochastic quantization procedure can be spatial. The diffusion coefficient of the stochastic process is in general a function of this coordinate. While a mapping of a bulk theory onto a (quantum) boundary theory can be possible, such a mapping does not make sense in spacetimes in which the area of the screen is growing with time. This is connected to the average process in the formalism of stochastic quantization. We show where the stochastic quantization procedure breaks down and argue, in agreement with `t Hooft, that the quantum degrees of freedom are not fundamental degrees of freedom. They appear as a limit of a more complex process.