## “Probing Planck Scale Shifts in Horizon Structure with Unruh-DeWitt Det

arXiv:2403.12136v1 Announce Type: new

Abstract: One of the foremost concern in the analysis of quantum gravity is whether the locations of classical horizons are stable under a full quantum analysis. In principle, any classical description, when interpolated to the microscopic level, can become prone to fluctuations. The curious question in that case is if there indeed are such fluctuations at the Planck scale, do they have any significance for physics taking place at scales much away from the Planck scale? In this work, we try to attempt the question of small scales and address whether there are definitive signatures of Planck scale shifts in the horizon structure. In a recent work (arXiv:2107.03406), it was suggested that in a nested sequence of Rindler causal wedges, the vacua of preceding Rindler frames appear thermally populated to a shifted Rindler frame. The Bogoliubov analysis used relies on the global notion of the quantum field theory and might be unable to see the local character of such horizon shifts. We investigate this system by means of the Unruh-DeWitt detector and see if this local probe of the quantum field theory is sensitive enough to the shift parameters to reveal any microscopic effects. For the case of infinite-time response, we recover the thermal spectrum, thus reaffirming that the infinite-time response probes the global properties of the field. On the other hand, the finite-time response turns out to be sensitive to the shift parameter in a peculiar way that any detector with energy gap $Omega c/a sim 1$ and is operational for time scale $T a/c sim 1$ has a measurably different response for a macroscopic and microscopic shift of the horizon, giving us direct probe to the tiniest separation between the causal domains of such Rindler wedges. Thus, this study provides an operational method to identify Planck scale effects which can be generalized to various other interesting gravitational settings.

**Quantum Gravity and the Stability of Classical Horizons**

In the analysis of quantum gravity, one of the key concerns is whether the locations of classical horizons remain stable under a full quantum analysis. When a classical description is extrapolated to the microscopic level, it becomes susceptible to fluctuations. Therefore, it is important to investigate whether these fluctuations at the Planck scale have any significant impact on physics at scales far removed from the Planck scale.

**Searching for Signatures of Planck Scale Shifts in Horizon Structure**

In a recent work (arXiv:2107.03406), it was proposed that in a nested sequence of Rindler causal wedges, the vacua of preceding Rindler frames appear thermally populated to a shifted Rindler frame. However, the analysis used in this work relies on the global notion of quantum field theory and may overlook the local character of such horizon shifts. Therefore, it is necessary to investigate this system using a local probe, such as the Unruh-DeWitt detector, to determine if it is sensitive enough to the shift parameters to reveal any microscopic effects.

**Investigating the Sensitivity of the Unruh-DeWitt Detector**

We conducted a study using the Unruh-DeWitt detector to examine the sensitivity of this local probe to the shift parameters of the horizon structure. The results showed that for the case of infinite-time response, the detector recovered the thermal spectrum, confirming that it probes the global properties of the field. However, the finite-time response exhibited a peculiar sensitivity to the shift parameter. We observed that any detector with an energy gap of $Omega c/a sim 1$ and operational for a time scale of $T a/c sim 1$ had a measurably different response for both macroscopic and microscopic shifts of the horizon.

**Identifying Planck Scale Effects and Generalization**

Our study provides a practical method to identify Planck scale effects using the Unruh-DeWitt detector. This method can be extended to various other interesting gravitational settings and allows for the detection of the tiniest separation between the causal domains of Rindler wedges. By investigating these microscopic effects, we can gain a deeper understanding of the stability and behavior of classical horizons under quantum analysis.

**Future Roadmap**

- Further refine the Unruh-DeWitt detector methodology for enhanced sensitivity and accuracy.
- Explore other gravitational settings and test the applicability of the method in different scenarios.
- Investigate the implications of Planck scale shifts in horizon structure for various physical phenomena.
- Collaborate with experimentalists to design and conduct experiments to validate the findings.
- Integrate the findings into the broader framework of quantum gravity and continue the quest to understand the fundamental nature of the universe.

**Challenges and Opportunities**

**Challenges:**

- Developing experimental setups that can measure the tiniest separation between causal domains.
- Overcoming technical limitations and noise in detector measurements.
- Understanding the implications of Planck scale shifts for different gravitational settings and phenomena.

**Opportunities:**

- Understanding the stability and behavior of classical horizons under quantum analysis.
- Gaining insights into the fundamental nature of the universe through the exploration of quantum gravity.
- Opening up new avenues for experimental verification and validation of theoretical predictions.
- Potential applications in other areas of physics beyond quantum gravity.

**Overall, the study of Planck scale shifts in horizon structure and the detection of associated microscopic effects offer exciting prospects for advancing our understanding of quantum gravity and its implications for the broader framework of physics.**