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Restrictions on Negative Energy Density in Flat Spacetime
General Relativity and Quantum Cosmology · Submitted 1 Jul 1996
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Similar ``quantum inequality'' bounds on negative energy density are derived for the electromagnetic field, and for the massive scalar field in both two and four-dimensional Minkowski spacetime.
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The abstract, sentence by sentence
In a previous paper, a bound on the negative energy density seen by an arbitrary inertial observer was derived for the free massless, quantized scalar field in four-dimensional Minkowski spacetime. This constraint has the form of an uncertainty principle-type limitation on the magnitude and duration of the negative energy density. That result was obtained after a somewhat complicated analysis. The goal of the current paper is to present a much simpler method for obtaining such constraints. Similar ``quantum inequality'' bounds on negative energy density are derived for the electromagnetic field, and for the massive scalar field in both two and four-dimensional Minkowski spacetime.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In a previous paper, a bound on the negative energy density seen by an arbitrary inertial observer was derived for the free massless, quantized scalar field in four-dimensional Minkowski spacetime. | background 1.00 | 0.22 | 0.05 | asserted 1.00 |
| s1 | This constraint has the form of an uncertainty principle-type limitation on the magnitude and duration of the negative energy density. | background 0.56 | 0.17 | 0.09 | asserted 1.00 |
| s2 | That result was obtained after a somewhat complicated analysis. | background 0.88 | 0.30 | 0.02 | asserted 1.00 |
| s3 | The goal of the current paper is to present a much simpler method for obtaining such constraints. | contribution 0.96 | 0.35 | 0.11 | asserted 0.89 |
| s4 | Similar ``quantum inequality'' bounds on negative energy density are derived for the electromagnetic field, and for the massive scalar field in both two and four-dimensional Minkowski spacetime. | result 0.52 | 0.94 | 0.52 | asserted 1.00 |
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Original abstract
In a previous paper, a bound on the negative energy density seen by an arbitrary inertial observer was derived for the free massless, quantized scalar field in four-dimensional Minkowski spacetime. This constraint has the form of an uncertainty principle-type limitation on the magnitude and duration of the negative energy density. That result was obtained after a somewhat complicated analysis. The goal of the current paper is to present a much simpler method for obtaining such constraints. Similar ``quantum inequality'' bounds on negative energy density are derived for the electromagnetic field, and for the massive scalar field in both two and four-dimensional Minkowski spacetime.
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References
How the literature uses it
18 arXiv papers cite this in 18 sentences
Papers citing it · 9 sentences without a confident label
Compares with it 3 papers
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The QEI bounds we have obtained depend on the state, in contrast to the original QEIs, [ref] that provide state-independent lower bounds.
Quantum strong energy inequalities · KMS states and temperature scaling · 1.00
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This bound is also similar in flavor to the so-called quantum inequalities that have been proposed by Ford & Roman for theories without gravity [ref] .
Upper and Lower Bounds on the Integrated Null Energy in Gravity · Introduction and Summary · 0.97
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These integral variants of the NEC are also qualitatively very different from the standard averaged null energy condition (ANEC), see for instance [ref] , or the Ford–Roman quantum inequalities [ref] , or their variants [ref] , or even the recent non-linear energy conditions explored in [ref] .
Clausius entropy for arbitrary bifurcate null surfaces · Generalized second law · 0.92
Cites it as support 1 paper
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Therefore, there is no physical way to create an Alcubierre drive [ref] .
Introducing Physical Warp Drives · Introduction · 0.97
Cites it as background 5 papers
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In [ref] , ANEC-type inequalities were initially proposed to hold for two and four-dimensional, free, massless quantized scalar fields.
A Holographic Dual of the Quantum Inequalities · Introduction and Summary · 0.97
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QEIs have been established for free (minimally coupled) Klein–Gordon [ref] , Dirac [ref] , Maxwell [ref] and Proca fields [ref] in both flat and curved spacetimes, for the Rarita–Schwinger field in Minkowski space [ref] , and for the whole class of unitary positive-energy conformal field theories in two-dimensional Minkowski space [ref] (generalising a special case [ref] ).
Quantum Energy Inequality for the Massive Ising Model · Introduction · 0.92
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Several quantum replacements for the NEC have been suggested — such as the averaged null energy condition (ANEC) [ref] and “quantum inequalities” [ref] — which involve integrating \(⟨T_kk|⟩ over a region of spacetime, and others [ref] .
The Quantum Null Energy Condition in Curved Space · Introduction and Summary · 0.99
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