Negative energy is a concept used in

physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

to explain the nature of certain fields, including the

gravitational field In physics, a gravitational field or gravitational acceleration field is a vector field used to explain the influences that a body extends into the space around itself. A gravitational field is used to explain gravitational phenomena, such as ...

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 Classical mechanics is a Theoretical physics, physical theory describing the motion of objects such as projectiles, parts of Machine (mechanical), machinery, spacecraft, planets, stars, and galaxies. The development of classical mechanics inv ...

, two or more

mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...

es always have a

gravitational potential In classical mechanics, the gravitational potential is a scalar potential associating with each point in space the work (energy transferred) per unit mass that would be needed to move an object to that point from a fixed reference point in the ...

Conservation of energy The law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be Conservation law, ''conserved'' over time. In the case of a Closed system#In thermodynamics, closed system, the principle s ...

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 In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...

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 The universe is all of space and time and their contents. It comprises all of existence, any fundamental interaction, physical process and physical constant, and therefore all forms of matter and energy, and the structures they form, from s ...

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 0 (zero) is a number representing an empty quantity. Adding (or subtracting) 0 to any number leaves that number unchanged; in mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and compl ...

: its amount of positive energy in the form of

matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic pa ...

is exactly cancelled out by its negative energy in the form of

gravity In physics, gravity (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force b ...

. 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

quasar A quasar ( ) is an extremely Luminosity, luminous active galactic nucleus (AGN). It is sometimes known as a quasi-stellar object, abbreviated QSO. The emission from an AGN is powered by accretion onto a supermassive black hole with a mass rangi ...

s is generated.

Quantum field effects

Negative energies and negative energy density are consistent with

quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...

Virtual particles

In quantum theory, the

uncertainty principle The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a limit to the precision with which certain pairs of physical properties, such as position a ...

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 A virtual particle is a theoretical transient particle that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle, which allows the virtual particles to spontaneously emer ...

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.Ford and Roman 2000

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 Paul Adrien Maurice Dirac ( ; 8 August 1902 – 20 October 1984) was an English mathematician and Theoretical physics, theoretical physicist who is considered to be one of the founders of quantum mechanics. Dirac laid the foundations for bot ...

in 1930, the

vacuum A vacuum (: vacuums or vacua) is space devoid of matter. The word is derived from the Latin adjective (neuter ) meaning "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressur ...

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 In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1/2 massive particles, called "Dirac ...

. A year later, after work by Weyl, the negative energy concept was abandoned and replaced by a theory of

antimatter In modern physics, antimatter is defined as matter composed of the antiparticles (or "partners") of the corresponding subatomic particle, particles in "ordinary" matter, and can be thought of as matter with reversed charge and parity, or go ...

. The following year, 1932, saw the discovery of the

positron The positron or antielectron is the particle with an electric charge of +1''elementary charge, e'', a Spin (physics), spin of 1/2 (the same as the electron), and the same Electron rest mass, mass as an electron. It is the antiparticle (antimatt ...

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 Hawking radiation is black-body radiation released outside a black hole's event horizon due to quantum effects according to a model developed by Stephen Hawking in 1974. The radiation was not predicted by previous models which assumed that onc ...

, 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 Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, Philosophy of science, philosopher of science and Nobel Prize in Physics, Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics i ...

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 General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...

in which a "bubble" of

spacetime In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualiz ...

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.

Negative-energy particles

Speculative theoretical studies have suggested that particles with negative energies are consistent with Relativistic quantum theory, with some noting interrelationships with negative mass and/or time reversal. Frédéric Henry-Couannier;
Negative energies and time reversal in Quantum Field Theory and General Relativity: The Dark Side of Gravity
, ''HAL Open Science'', 2004. ⟨hal-00001476v1⟩

References

Inline notes

{{reflist

Bibliography

* Lawrence H. Ford and Thomas A. Roman; "Negative energy, wormholes and warp drive", ''

Scientific American ''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it, with more than 150 Nobel Pri ...

'' January 2000, 282, Pages 46–53. * Roger Penrose; ''The Road to Reality'', ppbk, Vintage, 2005. Chapter 30: Gravity's Role in Quantum State Reduction. Energy (physics)