Generalized Dualities in 1T-Physics as Holographic Predictions from 2T-Physics

Abstract

In the conventional formalism of physics, with 1-time, systems with different Hamiltonians or Lagrangians have different physical interpretations and are considered to be independent systems unrelated to each other. However, in this paper we construct explicitly canonical maps in 1T phase space (including timelike components, specifically the Hamiltonian) to show that it is appropriate to regard various 1T-physics systems, with different Lagrangians or Hamiltonians, as being duals of each other. This concept is similar in spirit to dualities discovered in more complicated examples in field theory or string theory. Our approach makes it evident that such generalized dualities are widespread. This suggests that, as a general phenomenon, there are hidden relations and hidden symmetries that conventional 1T-physics does not capture, implying the existence of a more unified formulation of physics that naturally supplies the hidden information. In fact, we show that 2T-physics in (d+2)-dimensions is the generator of these dualities in 1T-physics in d-dimensions by providing a holographic perspective that unifies all the dual 1T systems into one. The unifying ingredient is a gauge symmetry in phase space. Via such dualities it is then possible to gain new insights toward new physical predictions not suspected before, and suggest new methods of computation that yield results not obtained before. As an illustration, we will provide concrete examples of 1T-systems in classical mechanics that are solved analytically for the first time via our dualities. These dualities in classical mechanics have counterparts in quantum mechanics and field theory, and in some simpler cases they have already been constructed in field theory. We comment on the impact of our approach on the meaning of spacetime and on the development of new computational methods based on dualities.

55 pages. More references in v2

References in corpus (19)

• Local Conformal Symmetry in Physics and Cosmology
• The Standard Model of Particles and Forces in the Framework of 2T-physics
• Cyclic Cosmology, Conformal Symmetry and the Metastability of the Higgs
• Sailing through the big crunch-big bang transition
• Gravity in 2T-Physics
• Gauge Symmetry in Phase Space, Consequences for Physics and Spacetime
• Geometry and Symmetry Structures in 2T Gravity
• The Big Bang and Inflation United by an Analytic Solution
• Field Theory in 2T-physics with N=1 Supersymmetry
• A Calculus for Higher Spin Interactions
• Dual Field Theories In (d-1)+1 Emergent Spacetimes From A Unifying Field Theory In d+2 Spacetime
• Dualities among 1T-Field Theories with Spin, Emerging from a Unifying 2T-Field Theory
• Conformal theories including conformal gravity as gauge theories on the hypercone
• Constraints on Interacting Scalars in 2T Field Theory and No Scale Models in 1T Field Theory
• Supersymmetric Field Theory in 2T-physics
• Traversing Cosmological Singularities, Complete Journeys Through Spacetime Including Antigravity
• Generalized Twistor Transform And Dualities, With A New Description of Particles With Spin, Beyond Free and Massless
• N=2,4 Supersymmetric Gauge Field Theory in 2T-physics
• The Standard Model as a 2T-physics Theory

Cited by in corpus (9)

• Dynamical String Tension in String Theory with Spacetime Weyl Invariance
• Duality Between Hydrogen Atom and Oscillator Systems via Hidden SO(d,2) Symmetry and 2T-physics
• Is Quantum Gravity a Chern-Simons Theory?
• Implications of Kleinian relativity
• CPTM symmetry, closed time paths and cosmological constant problem in the formalism of extended manifold
• Huygens triviality of the time-independent Schrödinger equation. Applications to atomic and high energy physics
• Looking for Carroll particles in two time spacetime
• Lifting the Eisenhart-Duval Lift to a Minimal Brane
• Chronons in M-theory and F-theory