[Paper Review] From Vacuum Fluctuations to Radiation: Accelerated Detectors and Black Holes

S. Massar, R. Parentani|arXiv (Cornell University)|Apr 28, 1994

Quantum Electrodynamics and Casimir Effect6 citations

TL;DR

This paper investigates how vacuum fluctuations give rise to radiation in two contexts: accelerated detectors and black hole horizons. Using the weak measurement formalism, it shows that each transition in a uniformly accelerated atom emits a Minkowski photon, and in black hole scenarios, vacuum fluctuations split into Hawking quanta (positive energy) and their partners (negative energy), with exponentially growing energy densities implying significant backreaction effects.

ABSTRACT

The vacuum fluctuations that induce the transitions and the thermalisation of a uniformly accelerated two level atom are studied in detail. Their energy content is revealed through the weak measurement formalism of Aharonov et al. It is shown that each time the detector makes a transition it radiates a Minkowski photon. The same analysis is then applied to the conversion of vacuum fluctuations into real quanta in the context of black hole radiation. Initially these fluctuations are located around the light like geodesic that shall generate the horizon and carry zero total energy. However upon exiting from the star they break up into two pieces one of which gradually acquires positive energy and becomes a Hawking quantum, the other, its ''partner", ends up in the singularity. As time goes by the vacuum fluctuations generating Hawking quanta have exponentially large energy densities. This implies that back reaction effects are large.

Motivation & Objective

• To understand the origin of radiation from vacuum fluctuations in relativistic quantum field theory.
• To analyze the energy content of vacuum fluctuations that induce transitions in accelerated two-level detectors.
• To extend the analysis to black hole spacetimes, particularly the mechanism by which vacuum fluctuations produce Hawking radiation.
• To assess the role of energy conservation and backreaction in the generation of real quanta from vacuum fluctuations near horizons.
• To apply the weak measurement formalism to reveal the energy carried by individual quantum transitions.

Proposed method

• Utilizes the weak measurement formalism of Aharonov et al. to extract energy content from vacuum fluctuations.
• Analyzes a uniformly accelerated two-level detector coupled to a quantum field in Minkowski spacetime.
• Traces the evolution of vacuum fluctuations near the future horizon of a collapsing star.
• Identifies the splitting of fluctuations into two parts: one escaping to infinity as a Hawking quantum, the other falling into the singularity.
• Calculates the energy density of vacuum fluctuations over time, showing exponential growth.
• Applies the formalism to both inertial and accelerated frames to compare radiation emission in different reference frames.

Experimental results

Research questions

• RQ1 How do vacuum fluctuations generate detectable radiation in the case of a uniformly accelerated detector?
• RQ2 What is the energy content of vacuum fluctuations that trigger transitions in an accelerated detector?
• RQ3 How do vacuum fluctuations near a black hole horizon evolve into real quanta such as Hawking radiation?
• RQ4 What is the role of energy conservation and the partner particle in the radiation process?
• RQ5 To what extent do backreaction effects become significant due to the energy density of vacuum fluctuations?

Key findings

• Each transition in a uniformly accelerated two-level detector corresponds to the emission of a Minkowski photon, as revealed by weak measurement.
• Vacuum fluctuations near the horizon of a collapsing star are initially centered on a light-like geodesic and carry zero total energy.
• Upon exiting the star, these fluctuations split into two parts: one acquires positive energy and becomes a Hawking quantum, the other carries negative energy and falls into the singularity.
• The energy density of the vacuum fluctuations generating Hawking quanta increases exponentially over time.
• The exponentially growing energy density implies that backreaction effects on the spacetime geometry are large and cannot be neglected.
• The analysis confirms that the radiation process is fundamentally tied to the dynamics of vacuum fluctuations and their energy distribution.