[Paper Review] Violations of the Null Energy Condition in QFT and their Implications

Dimitrios Krommydas|arXiv (Cornell University)|May 31, 2018

Black Holes and Theoretical Physics20 references3 citations

TL;DR

This thesis investigates violations of the Null Energy Condition (NEC) in Quantum Field Theory (QFT), proposing a conjecture that NEC-violating states are incompatible with semi-classical gravity due to large stress-energy tensor fluctuations. It introduces a semi-local bound on the smeared stress-energy tensor that incorporates quantum variance, offering a consistent framework to constrain exotic spacetimes like traversable wormholes.

ABSTRACT

We study violations of the Null Energy Condition (NEC) in Quantum Field Theory (QFT) and their implications. For the first part of the project, we examine these violations for classes of already known and novel (first discussed here) QFT states. Next, we discuss the implications of these violations focusing on the example of Wormhole Traversability. After reviewing the current literature on the existing restrictions on these violations, we conjecture that NEC violating states are incompatible with the Semi-Classical Gravity approximation. We argue that this conjecture provides the only way out of the problems introduced by the violations of NEC in this regime. Building on this, we propose a bound that should hold for all QFT states. Finally, we show that both our conjecture and bound hold for some relevant classes of QFT states.

Motivation & Objective

• To investigate the implications of NEC violations in QFT, particularly in relation to traversable wormholes.
• To address the incompatibility of NEC-violating states with the semi-classical gravity approximation, which lacks a fundamental mechanism to suppress such violations.
• To propose a new, semi-local bound on the stress-energy tensor that accounts for quantum fluctuations and probability distributions.
• To test the validity of this bound across various QFT states, including coherent states, Casimir configurations, and perturbed vacua.
• To reconcile NEC violations with known energy conditions and quantum inequalities in a way that preserves key theorems of classical GR in the semi-classical regime.

Proposed method

• Derives the NEC in QFT using the stress-energy tensor in 1+1 CFT and coherent states, analyzing its form under quantum superpositions.
• Applies the Raychaudhuri equation and focusing theorem to connect NEC violations to spacetime singularities and causal structure breakdown.
• Introduces the concept of smearing the stress-energy tensor to define a semi-local observable, reducing ultraviolet divergences and enabling probabilistic analysis.
• Uses the variance of the smeared stress-energy tensor to construct a bound that includes both expectation value and quantum fluctuations.
• Tests the conjecture via explicit calculations in coherent states and perturbed vacuum states, showing the bound holds when fluctuations are large.
• Compares the proposed bound with existing constraints like QNEC, ANEC, and quantum inequalities (QIs), arguing for its superiority in semi-local control of NEC violations.

Experimental results

Research questions

• RQ1 Can NEC-violating states in QFT be consistently embedded in semi-classical gravity, or do they signal a breakdown of the approximation?
• RQ2 What is the role of quantum fluctuations in the stress-energy tensor in suppressing or allowing NEC violations?
• RQ3 How can a semi-local bound on the smeared stress-energy tensor be constructed to constrain exotic spacetime geometries like traversable wormholes?
• RQ4 Why do some superposed QFT states violate NEC while others do not, and what determines the phase-space dependence of this behavior?
• RQ5 Does the proposed bound resolve the tension between NEC violations and the validity of semi-classical gravity, especially in cases like Hawking radiation?

Key findings

• NEC violations occur in QFT for coherent states, superpositions of vacuum and particles, and Casimir configurations, primarily due to oscillatory interference terms.
• The variance of the stress-energy tensor in NEC-violating states is large, suggesting that quantum fluctuations must be included in any consistent bound.
• The proposed semi-local bound, which combines the expectation value and standard deviation of the smeared stress-energy tensor, holds for coherent states and perturbed vacuum states.
• The bound is stronger than QNEC and QIs and more robust than ANEC, as it accounts for both local and non-local features of the stress-energy distribution.
• The conjecture that NEC-violating states are incompatible with semi-classical gravity is supported by the fact that only states with large fluctuations satisfy the proposed bound.
• Hawking radiation remains a potential counterexample, as it violates NEC and exhibits large fluctuations, but its consistency with the conjecture remains an open question.