Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Is Time Reversal in de Sitter Space a Spontaneously Broken Gauge Symmetry?

Leonard Susskind

Abstract

I'll begin with some well-deserved acknowledgements: I am grateful to Daniel Harlow for discussions of time-reversal holonomies. I have also benefited from a long ongoing correspondence with Edward Witten, but frankly in both cases I can't tell whether they agree with me or not. I have often been accused of imprecision, especially toward the later parts of a paper, where I expect that my readers have ``caught on." That does eventually happen -- the readers catching on and I thank them -- but I'm now almost 86 and I can't wait. So I've tried to maintain a level of conceptual if not mathematical rigor throughout. Mathematical rigor(mortis) can sometimes be the enemy of conceptual clarity. I thank my friend Richard Feynman for reminding me of that lesson. Finally I thank the chatbot who gave me the definition of scaffold in section \ref{Scaff}. It was better than anything I was able to do. Symmetries of a Holographic theory; whether continuous or discrete, local or global, are gauge symmetries of the bulk. This includes discrete space-time symmetries such as C and P. But time-reversal is sufficiently different from other symmetries that we may question the standard wisdom and ask whether symmetries involving T should be gauged in the bulk. Harlow and Numasawa \cite{Harlow:2023hjb} say yes; time-reversal is a gauge symmetry. Witten \cite{Witten:2025ayw} says no: time reversal is different and does not manifest as a gauge symmetry of the bulk. My view is -- yes -- but with a twist: Time-reversal is indeed a gauge symmetry; but it is hidden by spontaneous symmetry breaking. In this paper I will review the case for spontaneous symmetry breaking of time-reversal and explain the ``smoking gun" -- a closed curve and a holonomy which flips forward-going clocks to backward going clocks, and vice versa.

Is Time Reversal in de Sitter Space a Spontaneously Broken Gauge Symmetry?

Abstract

I'll begin with some well-deserved acknowledgements: I am grateful to Daniel Harlow for discussions of time-reversal holonomies. I have also benefited from a long ongoing correspondence with Edward Witten, but frankly in both cases I can't tell whether they agree with me or not. I have often been accused of imprecision, especially toward the later parts of a paper, where I expect that my readers have ``caught on." That does eventually happen -- the readers catching on and I thank them -- but I'm now almost 86 and I can't wait. So I've tried to maintain a level of conceptual if not mathematical rigor throughout. Mathematical rigor(mortis) can sometimes be the enemy of conceptual clarity. I thank my friend Richard Feynman for reminding me of that lesson. Finally I thank the chatbot who gave me the definition of scaffold in section \ref{Scaff}. It was better than anything I was able to do. Symmetries of a Holographic theory; whether continuous or discrete, local or global, are gauge symmetries of the bulk. This includes discrete space-time symmetries such as C and P. But time-reversal is sufficiently different from other symmetries that we may question the standard wisdom and ask whether symmetries involving T should be gauged in the bulk. Harlow and Numasawa \cite{Harlow:2023hjb} say yes; time-reversal is a gauge symmetry. Witten \cite{Witten:2025ayw} says no: time reversal is different and does not manifest as a gauge symmetry of the bulk. My view is -- yes -- but with a twist: Time-reversal is indeed a gauge symmetry; but it is hidden by spontaneous symmetry breaking. In this paper I will review the case for spontaneous symmetry breaking of time-reversal and explain the ``smoking gun" -- a closed curve and a holonomy which flips forward-going clocks to backward going clocks, and vice versa.
Paper Structure (16 sections, 31 equations, 8 figures)

This paper contains 16 sections, 31 equations, 8 figures.

Table of Contents

  1. The Scaffold
  2. Static Patch Holography
  3. Time-Reversal
  4. Gauge Symmetry
  5. Gauge Symmetries: Local or Global
  6. A Tension
  7. LRO and Time-Reversal
  8. Forward-Going and Backward-Going Clocks
  9. Dressing
  10. Cluster Decomposition
  11. Symmetry Revealed
  12. The Partially-Fixed Unitary Gauge
  13. The Smoking Gun
  14. Does the Holonomy Cause Disorder?
  15. Is the Gauge Invariance Local?
  16. ...and 1 more sections

Figures (8)

  • Figure 1: The de Sitter Penrose diagram showing the Right and Left Static patches together with the pode and antipode.
  • Figure 2: The de Sitter Penrose diagram and a Forward-Going-Clock located in the RSP.
  • Figure 3: Transporting the FGC around the bifurcate horizon. But something important has been left out.
  • Figure 4:
  • Figure 5: Maximum entanglement implies that if a FGC is present at the pode a BGC is automatically present at the antipode.
  • ...and 3 more figures