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Collision in the interior of wormhole

Ying Zhao

TL;DR

The paper develops a quantum-circuit perspective on the interior dynamics of a Schwarzschild wormhole by mapping the perturbed thermofield double to a bulk tensor-network description and an epidemic-model of perturbations. It argues that the meeting of infalling signals in the interior corresponds to the overlap of two growing perturbations in the circuit, and it shows a quantitative match between the spacetime volume of the post-collision region and the number of healthy gates in the circuit across multiple time regimes. This supports a circuit-based account of interior physics in AdS/CFT and ER=EPR, linking complexity growth and bulk geometry to perturbation propagation. The work also outlines future directions, including charged black holes, diagnostics for perturbation overlap, and extensions toward traversable-wormhole phenomena in more general quantum systems.

Abstract

The Schwarzschild wormhole has been interpreted as an entangled state. If Alice and Bob fall into each of the black hole, they can meet in the interior. We interpret this meeting in terms of the quantum circuit that prepares the entangled state. Alice and Bob create growing perturbations in the circuit, and we argue that the overlap of these perturbations represents their meeting. We compare the gravity picture with circuit analysis, and identify the post-collision region as the region storing the gates that are not affected by any of the perturbations.

Collision in the interior of wormhole

TL;DR

The paper develops a quantum-circuit perspective on the interior dynamics of a Schwarzschild wormhole by mapping the perturbed thermofield double to a bulk tensor-network description and an epidemic-model of perturbations. It argues that the meeting of infalling signals in the interior corresponds to the overlap of two growing perturbations in the circuit, and it shows a quantitative match between the spacetime volume of the post-collision region and the number of healthy gates in the circuit across multiple time regimes. This supports a circuit-based account of interior physics in AdS/CFT and ER=EPR, linking complexity growth and bulk geometry to perturbation propagation. The work also outlines future directions, including charged black holes, diagnostics for perturbation overlap, and extensions toward traversable-wormhole phenomena in more general quantum systems.

Abstract

The Schwarzschild wormhole has been interpreted as an entangled state. If Alice and Bob fall into each of the black hole, they can meet in the interior. We interpret this meeting in terms of the quantum circuit that prepares the entangled state. Alice and Bob create growing perturbations in the circuit, and we argue that the overlap of these perturbations represents their meeting. We compare the gravity picture with circuit analysis, and identify the post-collision region as the region storing the gates that are not affected by any of the perturbations.

Paper Structure

This paper contains 15 sections, 16 equations, 24 figures.

Table of Contents

  1. Introduction
  2. Perturbed theomofield double and quantum circuit
  3. Bulk tensor network and quantum circuit
  4. Epidemic model
  5. Quantum circuit from the point of view of Alice
  6. Quantum circuit from the point of view of Bob
  7. Size and interior trajectory
  8. Collision in the interior
  9. The spreading of two epidemics: overlap of two perturbations in the quantum circuit
  10. Post-collision region and the number of healthy gates in the circuit
  11. More detailed match of time dependence
  12. Conclusion and Discussion
  13. Geodesic distance
  14. Geodesic distance 1
  15. Geodesic distance 2

Figures (24)

  • Figure 1: The two perturbations have overlap in the quantum circuit.
  • Figure 2: The quantum circuit in (a) becomes bulk tensor network in (b) in the interior.
  • Figure 3: Thermofield double perturbed by Alice at time $t_w$
  • Figure 4: The wormhole grows as the circuit grows.
  • Figure 5: Penrose diagram and quantum circuit of perturbed thermofield double
  • ...and 19 more figures