False vacuum

# False vacuum

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Encyclopedia
In quantum field theory
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

, a false vacuum is a metastable
Metastability
Metastability describes the extended duration of certain equilibria acquired by complex systems when leaving their most stable state after an external action....

sector of space
Space
Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum...

that appears to be a perturbative vacuum
Vacuum state
In quantum field theory, the vacuum state is the quantum state with the lowest possible energy. Generally, it contains no physical particles...

, but is unstable due to instanton
Instanton
An instanton is a notion appearing in theoretical and mathematical physics. Mathematically, a Yang–Mills instanton is a self-dual or anti-self-dual connection in a principal bundle over a four-dimensional Riemannian manifold that plays the role of physical space-time in non-abelian gauge theory...

effects that may tunnel
Quantum tunnelling
Quantum tunnelling refers to the quantum mechanical phenomenon where a particle tunnels through a barrier that it classically could not surmount. This plays an essential role in several physical phenomena, such as the nuclear fusion that occurs in main sequence stars like the sun, and has important...

to a lower energy state. This tunneling can be caused by quantum fluctuations or the creation of high-energy particles. Simply put, the false vacuum is a local minimum
Maxima and minima
In mathematics, the maximum and minimum of a function, known collectively as extrema , are the largest and smallest value that the function takes at a point either within a given neighborhood or on the function domain in its entirety .More generally, the...

, but not the lowest energy state, even though it may remain stable for some time. This is analogous to metastability for first-order phase transition
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....

s.

## Vacuum metastability event

In their paper, Coleman and de Luccia noted:
The possibility that we are living in a false vacuum has been considered though this is only a possibility and Chaotic Inflation theory
Chaotic inflation theory
The Chaotic Inflation theory is a variety of the inflationary universe model, which is itself an outgrowth of the Big Bang theory. Chaotic Inflation, proposed by physicist Andrei Linde, models our universe as one of many that grew as part of a multiverse owing to a vacuum that had not decayed to...

suggests that the universe may be a false vacuum or a true vacuum. If a bubble of lower energy vacuum were nucleated, it would approach at nearly the speed of light and destroy the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

instantaneously, without any forewarning. Thus, this vacuum metastability event is a theoretical doomsday event
Doomsday event
A doomsday event is a specific, plausibly verifiable or hypothetical occurrence which has an exceptionally destructive effect on the human race...

. This was used in a science-fiction story in 1988 by Geoffrey A. Landis
Geoffrey A. Landis
Geoffrey A. Landis is an American scientist, working for the National Aeronautics and Space Administration on planetary exploration, interstellar propulsion, solar power and photovoltaics...

, in 2000 by Stephen Baxter
Stephen Baxter
Stephen Baxter is a prolific British hard science fiction author. He has degrees in mathematics and engineering.- Writing style :...

, and in 2002 by Greg Egan
Greg Egan
Greg Egan is an Australian science fiction author.Egan published his first work in 1983. He specialises in hard science fiction stories with mathematical and quantum ontology themes, including the nature of consciousness...

.

### Particle accelerator

One scenario is that, rather than quantum tunnelling, a particle accelerator
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...

, which produces very high energies
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

in a very small volume, could create sufficiently high energy density as to penetrate the barrier and stimulate the decay of the false vacuum to the lower-energy vacuum. Hut and Rees, however, have determined that because we have observed cosmic ray collisions
Cosmic ray
Cosmic rays are energetic charged subatomic particles, originating from outer space. They may produce secondary particles that penetrate the Earth's atmosphere and surface. The term ray is historical as cosmic rays were thought to be electromagnetic radiation...

at much higher energies than those produced in terrestrial particle accelerators, that these experiments will not, at least for the foreseeable future, pose a threat to our vacuum. Particle accelerations have reached energies of only approximately seven tera electron volts (7×1012 eV). Cosmic ray collisions have been observed at and beyond energies of 1018 eV
Electronvolt
In physics, the electron volt is a unit of energy equal to approximately joule . By definition, it is equal to the amount of kinetic energy gained by a single unbound electron when it accelerates through an electric potential difference of one volt...

, the so-called Greisen–Zatsepin–Kuzmin limit
Greisen–Zatsepin–Kuzmin limit
The Greisen–Zatsepin–Kuzmin limit is a theoretical upper limit on the energy of cosmic rays coming from "distant" sources. The limit is 5×1019 eV, or about 8 joules. The limit is set by slowing-interactions of cosmic ray protons with the microwave background radiation over long distances...

. John Leslie has argued that if present trends continue, particle accelerators will exceed the energy given off in naturally occurring cosmic ray collisions by the year 2150.

This event would be contingent on our living in a metastable vacuum, an issue which is far from resolved. Worries about the vacuum metastability event are reminiscent of the controversy concerning the activation of the Relativistic Heavy Ion Collider. This is merely one subtle way in which one such event can occur.

## Bubble nucleation

In a physical theory in a false vacuum, the system moves to a lower energy state – either the true vacuum, or another, lower energy vacuum – through a process known as bubble nucleation
Nucleation
Nucleation is the extremely localized budding of a distinct thermodynamic phase. Some examples of phases that may form by way of nucleation in liquids are gaseous bubbles, crystals or glassy regions. Creation of liquid droplets in saturated vapor is also characterized by nucleation...

. In this, instanton effects cause a bubble to appear in which fields have their true vacuum values inside. Therefore, the interior of the bubble has a lower energy. The walls of the bubble (or domain wall
Domain wall
A domain wall is a term used in physics which can have one of two distinct but similar meanings in magnetism, optics, or string theory. These phenomena can all be generically described as topological solitons which occur whenever a discrete symmetry is spontaneously broken.-Magnetism:In magnetism,...

s) have a surface tension
Surface tension
Surface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface...

, as energy is expended as the fields roll over the potential barrier to the lower energy vacuum. The most likely size of the bubble is determined in the semiclassical approximation to be such that the bubble has zero total change in the energy: the decrease in energy by the true vacuum in the interior is compensated by the tension of the walls.

### Expansion of bubble

Any increase in size of the bubble will decrease its potential energy, as the energy of the wall increases as the area of a sphere but the negative contribution of the interior increases more quickly, as the volume of a sphere . Therefore, after the bubble is nucleated, it quickly begins expanding at very nearly the speed of light. The excess energy contributes to the very large kinetic energy of the walls. If two bubbles are nucleated and they eventually collide, it is thought that particle production occurs where the walls impact.

The tunneling rate is increased by increasing the energy difference between the two vacua and decreased by increasing the height or width of the barrier.

## Gravitational effects

The addition of gravity to the story leads to a considerably richer variety of phenomena. The key insight is that a false vacuum with positive potential energy density is a de Sitter vacuum, in which the potential energy acts as a cosmological constant
Cosmological constant
In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...

and the Universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...

is undergoing the exponential expansion of de Sitter space
De Sitter space
In mathematics and physics, a de Sitter space is the analog in Minkowski space, or spacetime, of a sphere in ordinary, Euclidean space. The n-dimensional de Sitter space , denoted dS_n, is the Lorentzian manifold analog of an n-sphere ; it is maximally symmetric, has constant positive curvature,...

. This leads to a number of interesting effects, first studied by Coleman
Sidney Coleman
Sidney Richard Coleman was an American theoretical physicist who studied under Murray Gell-Mann.- Life and work :Sidney Coleman grew up on the Far North Side of Chicago...

and de Luccia:

### Development of theories

Alan Guth
Alan Guth
Alan Harvey Guth is an American theoretical physicist and cosmologist. Guth has researched elementary particle theory...

in his original proposal for cosmic inflation
Cosmic inflation
In physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized extremely rapid exponential expansion of the early universe by a factor of at least 1078 in volume, driven by a negative-pressure vacuum energy density. The inflationary epoch comprises the first part...

proposed that inflation could end through quantum mechanical bubble nucleation of the sort described above. See History of Chaotic inflation theory. It was soon understood that a homogeneous and isotropic universe could not be preserved through the violent tunneling process. This led Andrei Linde
Andrei Linde
Andrei Dmitriyevich Linde is a Russian-American theoretical physicist and professor of Physics at Stanford University. Dr. Linde is best known for his work on the concept of the inflationary universe. He received his Bachelor of Science degree from Moscow State University. In 1975, Linde was...

and, independently, Andreas Albrecht and Paul Steinhardt
Paul Steinhardt
Paul J. Steinhardt is the Albert Einstein Professor of Science at Princeton University and a professor of theoretical physics. He received his B.S. at the California Institute of Technology and his Ph.D. in Physics at Harvard University...

to propose "new inflation" or "slow roll inflation" in which no tunnelling occurs, and the inflationary scalar field instead rolls down a gentle slope.

• Free pdf copy of The Structured Vacuum - thinking about nothing by Johann Rafelski
Johann Rafelski
Johann Rafelski is a German-American theoretical physicist and author. He is Professor of Physics at The University of Arizona in Tucson, guest scientist at CERN , and has been LMU-Excellent Guest Professor at the Ludwig Maximilian University of Munich in Munich, Germany.Rafelski’s current...

and Berndt Muller (1985) ISBN 3-87144-889-3.
• An Eternity of Bubbles? by Alan Guth
Alan Guth
Alan Harvey Guth is an American theoretical physicist and cosmologist. Guth has researched elementary particle theory...

• The Decay of the False Vacuum by Sten Odenwald
Sten Odenwald
Sten Odenwald is an astronomer who runs the website Astronomy Cafe, and is a researcher studying the cosmic infrared background and space weather. Since receiving his Ph.D. in astronomy from Harvard University in 1982, he has been an astronomer in the Washington, D.C...

• Simulation of False Vacuum Decay by Bubble Nucleation by Joel Thorarinson