Negative energy

Key takeaways

Negative energy belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Negative energy to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Negative energy from memory before moving on to harder problems.

Reference excerpt

Negative energy is a concept used in physics to explain the nature of certain fields, including the gravitational field and various quantum field effects.

Gravitational energy

Gravitational energy, or gravitational potential energy, is the potential energy a massive object has because it is within a gravitational field. In classical mechanics, two or more masses always have a gravitational potential. Conservation of energy requires that this gravitational field energy is always negative, so that it is zero when the objects are infinitely far apart. As two objects move apart and the distance between them approaches infinity, the gravitational force between them approaches zero from the positive side of the real number line and the gravitational potential approaches zero from the negative side. Conversely, as two massive objects move towards each other, the motion accelerates under gravity causing an increase in the (positive) kinetic energy of the system and, in order to conserve the total sum of energy, the increase of the same amount in the gravitational potential energy of the object is treated as negative. A universe in which positive energy dominates will eventually collapse in a Big Crunch, while an "open" universe in which negative energy dominates will either expand indefinitely or eventually disintegrate in a Big Rip. In the zero-energy universe model ("flat" or "Euclidean"), the total amount of energy in the universe is exactly zero: its amount of positive energy in the form of matter is exactly cancelled out by its negative energy in the form of gravity. It is unclear which, if any, of these models accurately describes the real universe.

Black hole ergosphere

For a classically rotating black hole, the rotation creates an ergosphere outside the event horizon, in which spacetime itself begins to rotate, in a phenomenon known as frame-dragging. Since the ergosphere is outside the event horizon, particles can escape from it. Within the ergosphere, a particle's energy may become negative (via the relativistic rotation of its Killing vector). The negative-energy particle then crosses the event horizon into the black hole, with the law of conservation of energy requiring that an equal amount of positive energy should escape. In the Penrose process, a body divides in two, with one half gaining negative energy and falling in, while the other half gains an equal amount of positive energy and escapes. This is proposed as the mechanism by which the intense radiation emitted by quasars is generated.

Quantum field effects Negative energies and negative energy density are consistent with quantum field theory.

Virtual particles

In quantum theory, the uncertainty principle allows the vacuum of space to be filled with virtual particle-antiparticle pairs which appear spontaneously and exist for only a short time before, typically, annihilating themselves again. Some of these virtual particles can have negative energy. This behaviour plays a role in several important phenomena, as described below.

Casimir effect

In the Casimir effect, two flat plates placed very close together restrict the wavelengths of quanta which can exist between them. This in turn restricts the types and hence number and density of virtual particle pairs which can form in the intervening vacuum and can result in a negative energy density. Since this restriction does not exist or is much less significant on the opposite sides of the plates, the forces outside the plates are greater than those between the plates. This causes the plates to appear to pull on each other, which has been measured. More accurately, the vacuum energy caused by the virtual particle pairs is pushing the plates together, and the vacuum energy between the plates is too small to negate this effect since fewer virtual particles can exist per unit volume between the plates than can exist outside them.

Squeezed light

It is possible to arrange multiple beams of laser light such that destructive quantum interference suppresses the vacuum fluctuations. Such a squeezed vacuum state involves negative energy. The repetitive waveform of light leads to alternating regions of positive and negative energy.

Dirac sea

According to the theory of the Dirac sea, developed by Paul Dirac in 1930, the vacuum of space is full of negative energy. This theory was developed to explain the anomaly of negative-energy quantum states predicted by the Dirac equation. A year later, after work by Weyl, the negative energy concept was abandoned and replaced by a theory of antimatter. The following year, 1932, saw the discovery of the positron by Carl Anderson.

Quantum gravity phenomena The intense gravitational fields around black holes create phenomena which are attributed to both gravitational and quantum effects. In these situations, a particle's Killing vector may be rotated such that its energy becomes negative.

Hawking radiation

Virtual particles can exist for a short period. When a pair of such particles appears next to a black hole's event horizon, one of them may get drawn in. This rotates its Killing vector so that its energy becomes negative and the pair have no net energy. This allows them to become real and the positive particle escapes as Hawking radiation, while the negative-energy particle reduces the black hole's net energy. Thus, a black hole may slowly evaporate.

Speculative suggestions

Wormholes

Negative energy appears in the speculative theory of wormholes, where it is needed to keep the wormhole open. A wormhole directly connects two locations which may be separated arbitrarily far apart in both space and time, and in principle allows near-instantaneous travel between them. However physicists such as Roger Penrose regard such ideas as unrealistic, more fiction than speculation.

Warp drive

A theoretical principle for a faster-than-light (FTL) warp drive for spaceships has been suggested, using negative energy. The Alcubierre drive is based on a solution to the Einstein field equations of general relativity in which a "bubble" of spacetime is constructed using a hypothetical negative energy. The bubble is then moved by expanding space behind it and shrinking space in front of it. The bubble may travel at arbitrary speeds and is not constrained by the speed of light. This does not contradict general relativity, as the bubble's contents do not actually move through their local spacetime.

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Negative energy

Start with the simplest possible case. Write down what Negative energy claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Negative energy before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Negative energy ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Negative energy

In research: Negative energy appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Negative energy in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Negative energy is common in secondary-school and first-year university syllabi. It links to neighbouring topics Energy (physics), so understanding it makes those chapters shorter.
In everyday life: Look for Negative energy outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Negative energy in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Negative energy means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Negative energy out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Negative energy in simple terms?

Negative energy is a concept used in physics to explain the nature of certain fields, including the gravitational field and various quantum field effects. Gravitational energy Gravitational energy, or gravitational potential energy, is the potential energy a massive object has because it is within…

Why does Negative energy matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Negative energy?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Negative energy.