The Spacetime Metric
Lecture 657 min 46 sec

Energy conditions and their violations

The assumptions that turn geometry into physically plausible matter.

See what the classical energy conditions constrain, where quantum field theory permits limited violations, and why scale and duration matter.

Season 1 · remastered lesson

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57 min 46 sec · Captions: English · Español · Português · Français · Polski

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Visual explanation

Explore the central idea

A number line for one observer’s local energy density: negative on the hatched left, zero at the center, positive on the right.
A sign diagram, not measured data or a spatial map. Here ρ(u) is the energy density measured by an observer with four-velocity u. One negative reading violates the weak energy condition; one positive reading does not establish it. The condition must hold for every timelike observer.

Read alongside

Wormholes, Energy Conditions, and the Negative-Energy Budget

The experiments, equations, and original papers behind the lesson.

Open the companion chapter →