On the Possibility of a Trans-Planckian Duality

TL;DR

This paper explores a theoretical duality between space-time and energy-momentum manifolds, proposing a geometric framework where gravity has a dual counterpart on the momentum space, with analysis of its classical properties.

Contribution

It introduces a mathematical framework for trans-Planckian duality, connecting space-time and momentum manifolds, and analyzes its classical behavior.

Findings

Proposes a duality exchanging space-time and momentum manifolds.

Develops a mathematical framework for this duality.

Analyzes classical behavior of the dual gravitational theory.

Abstract

We investigate the possibility of a trans-Planckian duality, which exchanges a manifold of events (space-time), with a manifold of momenta (energy-momentum). Gravity has a dual counter-part, that is, a geometric theory defined on the manifold of momenta. We provide a mathematical framework that can possibly realize this idea, and analyze its classical behaviour.