[Paper Review] The response of a Unruh-deWitt particle detector in a thin-shell wormhole spacetime

Robert Blaga|arXiv (Cornell University)|May 2, 2017

Quantum Electrodynamics and Casimir Effect3 references3 citations

TL;DR

This paper investigates the response of a Unruh-deWitt particle detector in a thin-shell wormhole spacetime using quantum field theory in curved spacetime. It shows that the detector's transition probability exhibits a peak at the wormhole throat and damped oscillations afterward, stabilizing to a nonzero constant—despite the detector's inertial motion—due entirely to the spacetime's nontrivial topology, not acceleration or curvature effects.

ABSTRACT

We investigate the transition probability of a Unruh-deWitt particle detector evolving in flat space and in a wormhole spacetime, in various scenarios. In Minkowski space, we look at the response of the detector on trajectories having discontinuities and rapid variations, as well as the effect of finite-time coupling. It is found that these features induce spurious oscillations in the probability and rate of transition. At large times the oscillations are damped and the probability tends to a constant value. Next, we look at the response of an inertial detector on a radial trajectory that passes through a thin-shell wormhole. After finding the appropriate modes, we look at the renormalized detector response, defined by subtracting the flat space analogues from the partial probabilities. The resulting curve has a peak around the wormhole throat followed by a period of damped oscillations, before stabilizing to a constant value. This is very similar to the flat space results, which is surprising given that in this case the trajectory is continuous. The features of the transition probability are due entirely to the nontrivial topology induced by the wormhole.

Motivation & Objective

• To investigate how nontrivial spacetime topology—specifically a thin-shell wormhole—affects the response of a Unruh-deWitt particle detector.
• To examine the transition probability and rate of an inertial detector traversing the wormhole throat, comparing it to flat spacetime behavior.
• To isolate the contribution of topological features by renormalizing the detector response against Minkowski space analogues.
• To analyze the role of spherical mode decomposition and finite coupling time in shaping the detector’s response in both flat and wormhole spacetimes.

Proposed method

• Model the detector as a point-like two-level system coupled to a massless scalar field via a monopole interaction Hamiltonian.
• Solve the Klein-Gordon equation in the wormhole spacetime using spherical harmonic decomposition to obtain mode solutions.
• Compute the detector’s transition probability using the standard Unruh-deWitt formalism, integrating over the field’s Wightman function.
• Apply renormalization by subtracting the Minkowski-space transition probability to isolate topology-induced effects.
• Use numerical summation over multipole modes (l) up to a maximum cutoff L_max, with convergence monitored via a 1% error threshold.
• Analyze the transition probability for inertial radial trajectories, focusing on behavior near and across the wormhole throat.

Experimental results

Research questions

• RQ1 How does the transition probability of an inertial Unruh-deWitt detector change when traversing a thin-shell wormhole compared to Minkowski spacetime?
• RQ2 To what extent do spurious oscillations in the detector response arise from finite-time coupling or discontinuous trajectories in flat spacetime?
• RQ3 What is the role of spacetime topology in generating a non-zero, non-thermal detector response in the absence of acceleration or curvature?
• RQ4 How do higher-order spherical modes (l > 0) contribute to the detector’s response, especially near the wormhole throat?
• RQ5 Does the detector response stabilize to a constant value after crossing the wormhole, and if so, what determines its final value?

Key findings

• The detector’s transition probability in Minkowski space exhibits spurious oscillations due to finite-time coupling or abrupt velocity changes, which damp over time.
• In the wormhole spacetime, the transition probability peaks sharply at the wormhole throat, indicating a strong topological influence.
• After crossing the throat, the probability undergoes damped oscillations before stabilizing to a constant, nonzero value, even though the detector is inertial.
• The renormalized transition probability—defined by subtracting the Minkowski-space analogue—reveals that the observed features are due solely to the wormhole’s topology.
• Convergence of the mode sum requires high L_max near the throat, but stabilizes quickly at large times, with L_max = 4 sufficient for 1% accuracy in late-time regimes.
• The response structure closely resembles that in flat space, but the origin is fundamentally different: topology-induced rather than motion-induced.