Negative energy

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

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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. [1]

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. [2] 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. [3]

Quantum field effects

Negative energies and negative energy density are consistent with quantum field theory. [4]

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. [5]

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. [5]

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. [6] : 9  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. [7]

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. [8] [9]

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. [10]

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. [5]

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. [11] [12] [13]

See also

Related Research Articles

A wormhole is a hypothetical structure connecting disparate points in spacetime, and is based on a special solution of the Einstein field equations.

<span class="mw-page-title-main">Gravitational singularity</span> Condition in which spacetime itself breaks down

A gravitational singularity, spacetime singularity or simply singularity is a condition in which gravity is predicted to be so intense that spacetime itself would break down catastrophically. As such, a singularity is by definition no longer part of the regular spacetime and cannot be determined by "where" or "when". Gravitational singularities exist at a junction between general relativity and quantum mechanics; therefore, the properties of the singularity cannot be described without an established theory of quantum gravity. Trying to find a complete and precise definition of singularities in the theory of general relativity, the current best theory of gravity, remains a difficult problem. A singularity in general relativity can be defined by the scalar invariant curvature becoming infinite or, better, by a geodesic being incomplete.

Timeline of black hole physics

<i>A Brief History of Time</i> 1988 book by Stephen Hawking

A Brief History of Time: From the Big Bang to Black Holes is a book on theoretical cosmology by the physicist Stephen Hawking. It was first published in 1988. Hawking wrote the book for readers who had no prior knowledge of physics.

In general relativity, a white hole is a hypothetical region of spacetime and singularity that cannot be entered from the outside, although energy-matter, light and information can escape from it. In this sense, it is the reverse of a black hole, from which energy-matter, light and information cannot escape. White holes appear in the theory of eternal black holes. In addition to a black hole region in the future, such a solution of the Einstein field equations has a white hole region in its past. This region does not exist for black holes that have formed through gravitational collapse, however, nor are there any observed physical processes through which a white hole could be formed.

The Penrose–Hawking singularity theorems are a set of results in general relativity that attempt to answer the question of when gravitation produces singularities. The Penrose singularity theorem is a theorem in semi-Riemannian geometry and its general relativistic interpretation predicts a gravitational singularity in black hole formation. The Hawking singularity theorem is based on the Penrose theorem and it is interpreted as a gravitational singularity in the Big Bang situation. Penrose was awarded the Nobel Prize in Physics in 2020 "for the discovery that black hole formation is a robust prediction of the general theory of relativity", which he shared with Reinhard Genzel and Andrea Ghez.

Vacuum energy is an underlying background energy that exists in space throughout the entire universe. The vacuum energy is a special case of zero-point energy that relates to the quantum vacuum.

<span class="mw-page-title-main">Quantum foam</span> Fluctuation of spacetime on very small scales

Quantum foam or spacetime foam is a theoretical quantum fluctuation of spacetime on very small scales due to quantum mechanics. The theory predicts that at these small scales, particles of matter and antimatter are constantly created and destroyed. These subatomic objects are called virtual particles. The idea was devised by John Wheeler in 1955.

The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which makes exact solutions very difficult to find.

The chronology protection conjecture is a hypothesis first proposed by Stephen Hawking that laws of physics beyond those of standard general relativity prevent time travel on all but microscopic scales—even when the latter theory states that it should be possible. The permissibility of time travel is represented mathematically by the existence of closed timelike curves in some solutions to the field equations of general relativity. The chronology protection conjecture should be distinguished from chronological censorship under which every closed timelike curve passes through an event horizon, which might prevent an observer from detecting the causal violation.

<span class="mw-page-title-main">Quantum field theory in curved spacetime</span> Extension of quantum field theory to curved spacetime

In theoretical physics, quantum field theory in curved spacetime (QFTCS) is an extension of quantum field theory from Minkowski spacetime to a general curved spacetime. This theory uses a semi-classical approach; it treats spacetime as a fixed, classical background, while giving a quantum-mechanical description of the matter and energy propagating through that spacetime. A general prediction of this theory is that particles can be created by time-dependent gravitational fields (multigraviton pair production), or by time-independent gravitational fields that contain horizons. The most famous example of the latter is the phenomenon of Hawking radiation emitted by black holes.

Fuzzballs are hypothetical objects in superstring theory, intended to provide a fully quantum description of the black holes predicted by general relativity.

<span class="mw-page-title-main">Ergosphere</span> Region outside of a rotating black holes event horizon

In astrophysics, the ergosphere is a region located outside a rotating black hole's outer event horizon. Its name was proposed by Remo Ruffini and John Archibald Wheeler during the Les Houches lectures in 1971 and is derived from Ancient Greek ἔργον (ergon) 'work'. It received this name because it is theoretically possible to extract energy and mass from this region. The ergosphere touches the event horizon at the poles of a rotating black hole and extends to a greater radius at the equator. A black hole with modest angular momentum has an ergosphere with a shape approximated by an oblate spheroid, while faster spins produce a more pumpkin-shaped ergosphere. The equatorial (maximal) radius of an ergosphere is the Schwarzschild radius, the radius of a non-rotating black hole. The polar (minimal) radius is also the polar (minimal) radius of the event horizon which can be as little as half the Schwarzschild radius for a maximally rotating black hole.

In physics, there is a speculative hypothesis that, if there were a black hole with the same mass, charge and angular momentum as an electron, it would share other properties of the electron. Most notably, Brandon Carter showed in 1968 that the magnetic moment of such an object would match that of an electron. This is interesting because calculations ignoring special relativity and treating the electron as a small rotating sphere of charge give a magnetic moment roughly half the experimental value.

<span class="mw-page-title-main">Penrose process</span> Hypothetical mechanism for extracting energy from rotating black holes

The Penrose process is theorised by Sir Roger Penrose as a means whereby energy can be extracted from a rotating black hole. The process takes advantage of the ergosphere – a region of spacetime around the black hole dragged by its rotation faster than the speed of light, meaning that from the point of view of an outside observer any matter inside is forced to move in the direction of the rotation of the black hole.

The following outline is provided as an overview of and topical guide to black holes:

A black star is a gravitational object composed of matter. It is a theoretical alternative to the black hole concept from general relativity. The theoretical construct was created through the use of semiclassical gravity theory. A similar structure should also exist for the Einstein–Maxwell–Dirac equations system, which is the (super) classical limit of quantum electrodynamics, and for the Einstein–Yang–Mills–Dirac system, which is the (super) classical limit of the standard model.

The zero-energy universe hypothesis proposes that the total amount of energy in the universe is exactly zero: its amount of positive energy in the form of matter is exactly canceled out by its negative energy in the form of gravity. Some physicists, such as Lawrence Krauss, Stephen Hawking or Alexander Vilenkin, call or called this state "a universe from nothingness", although the zero-energy universe model requires both a matter field with positive energy and a gravitational field with negative energy to exist. The hypothesis is broadly discussed in popular sources. Other cancellation examples include the expected symmetric prevalence of right- and left-handed angular momenta of objects, the observed flatness of the universe, the equal prevalence of positive and negative charges, opposing particle spin in quantum mechanics, as well as the crests and troughs of electromagnetic waves, among other possible examples in nature.

<span class="mw-page-title-main">Nikodem Popławski</span> Polish physicist

Nikodem Janusz Popławski is a Polish theoretical physicist, most widely noted for the hypothesis that every black hole could be a doorway to another universe and that the universe was formed within a black hole which itself exists in a larger universe. This hypothesis was listed by National Geographic and Science magazines among their top ten discoveries of 2010.

References

Inline notes

  1. ↑ Alan Guth The Inflationary Universe: The Quest for a New Theory of Cosmic Origins (1997), Random House, ISBN   0-224-04448-6 Appendix A: Gravitational Energy demonstrates the negativity of gravitational energy.
  2. ↑ Hawking, Stephen (2010). The Grand Design. p. 180.
  3. ↑ Penrose 2005, pp. 836-9
  4. ↑ Everett, Allen; Roman, Thomas (2012). Time Travel and Warp Drives . University of Chicago Press. p.  167. ISBN   978-0-226-22498-5.
  5. 1 2 3 Ford and Roman 2000
  6. ↑ Duck, Ian; Sudarshan, E C G (March 1998). Pauli and the Spin-Statistics Theorem. WORLD SCIENTIFIC. doi:10.1142/3457. ISBN   978-981-02-3114-9.
  7. ↑ Penrose 2005, pp. 833-4, 836-7
  8. ↑ Stephen Hawking; A Brief History of Time, Bantam 1988, Pages 105-107. ISBN   0-593-01518-5
  9. ↑ Penrose 2005, pp. 836-7
  10. ↑ Penrose 2005, pp.833-4. "... an (in my opinion misguided) intention to show that some kind of science-fiction 'wormhole' travel between universes..."
  11. ↑ N Debergh, J-P Petit and G D’Agostini; "On evidence for negative energies and masses in the Dirac equation through a unitary time-reversal operator", Journal of Physics Communications, Volume 2, Number 11, 2018.
  12. ↑ Hongwei Yu and Weixing Shu; "Quantum states with negative energy density in the Dirac field and quantum inequalities", Physics Letters B, Volume 570, Issues 1–2, 18 September 2003, Pages 123-128'
  13. ↑ 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⟩

Bibliography

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