False vacuum decay

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/False_vacuum_decay 

A scalar field φ (which represents physical position) in a false vacuum. Note that the energy E is higher in the false vacuum than that in the true vacuum or ground state, but there is a barrier preventing the field from classically rolling down to the true vacuum. Therefore, the transition to the true vacuum must be stimulated by the creation of high-energy particles or through quantum-mechanical tunneling.

In quantum field theory, a false vacuum is a hypothetical vacuum that is stable, but not in the most stable state possible (it is metastable). It may last for a very long time in that state, but could eventually decay to the more stable state, an event known as false vacuum decay. The most common suggestion of how such a decay might happen in our universe is called bubble nucleation – if a small region of the universe by chance reached a more stable vacuum, this "bubble" (also called "bounce") would spread.

A false vacuum exists at a local minimum of energy and is therefore not stable, in contrast to a true vacuum, which exists at a global minimum and is stable.

Definition of true vs false vacuum

A vacuum is defined as a space with as little energy in it as possible. Despite the name, the vacuum still has quantum fields. A true vacuum is stable because it is at a global minimum of energy, and is commonly assumed to coincide with a physical vacuum state we live in. It is possible that a physical vacuum state is a configuration of quantum fields representing a local minimum but not global minimum of energy. This type of vacuum state is called a "false vacuum".

Implications

Existential threat

If our universe is in a false vacuum state rather than a true vacuum state, then the decay from the less stable false vacuum to the more stable true vacuum (called false vacuum decay) could have dramatic consequences. The effects could range from complete cessation of existing fundamental forces, elementary particles and structures comprising them, to subtle change in some cosmological parameters, mostly depending on potential difference between true and false vacuum. Some false vacuum decay scenarios are compatible with survival of structures like galaxies and stars or even biological life while others involve the full destruction of baryonic matter or even immediate gravitational collapse of the universe, although in this more extreme case the likelihood of a “bubble” forming may be very low (i.e. false vacuum decay may be impossible).

A paper by Coleman and de Luccia which attempted to include simple gravitational assumptions into these theories noted that if this was an accurate representation of nature, then the resulting universe "inside the bubble" in such a case would appear to be extremely unstable and would almost immediately collapse:

In general, gravitation makes the probability of vacuum decay smaller; in the extreme case of very small energy-density difference, it can even stabilize the false vacuum, preventing vacuum decay altogether. We believe we understand this. For the vacuum to decay, it must be possible to build a bubble of total energy zero. In the absence of gravitation, this is no problem, no matter how small the energy-density difference; all one has to do is make the bubble big enough, and the volume/surface ratio will do the job. In the presence of gravitation, though, the negative energy density of the true vacuum distorts geometry within the bubble with the result that, for a small enough energy density, there is no bubble with a big enough volume/surface ratio. Within the bubble, the effects of gravitation are more dramatic. The geometry of space-time within the bubble is that of anti-de Sitter space, a space much like conventional de Sitter space except that its group of symmetries is O(3, 2) rather than O(4, 1). Although this space-time is free of singularities, it is unstable under small perturbations, and inevitably suffers gravitational collapse of the same sort as the end state of a contracting Friedmann universe. The time required for the collapse of the interior universe is on the order of ... microseconds or less.

The possibility that we are living in a false vacuum has never been a cheering one to contemplate. Vacuum decay is the ultimate ecological catastrophe; in the new vacuum there are new constants of nature; after vacuum decay, not only is life as we know it impossible, so is chemistry as we know it. However, one could always draw stoic comfort from the possibility that perhaps in the course of time the new vacuum would sustain, if not life as we know it, at least some structures capable of knowing joy. This possibility has now been eliminated.

The second special case is decay into a space of vanishing cosmological constant, the case that applies if we are now living in the debris of a false vacuum which decayed at some early cosmic epoch. This case presents us with less interesting physics and with fewer occasions for rhetorical excess than the preceding one. It is now the interior of the bubble that is ordinary Minkowski space ...

— Sidney Coleman and Frank De Luccia

In a 2005 paper published in Nature, as part of their investigation into global catastrophic risks, MIT physicist Max Tegmark and Oxford philosopher Nick Bostrom calculate the natural risks of the destruction of the Earth at less than 1/10⁹ per year from all natural (i.e. non-anthropogenic) events, including a transition to a lower vacuum state. They argue that due to observer selection effects, we might underestimate the chances of being destroyed by vacuum decay because any information about this event would reach us only at the instant when we too were destroyed. This is in contrast to events like risks from impacts, gamma-ray bursts, supernovae and hypernovae, the frequencies of which we have adequate direct measures.

Inflation

A number of theories suggest that cosmic inflation may be an effect of a false vacuum decaying into the true vacuum. The inflation itself may be the consequence of the Higgs field trapped in a false vacuum state with Higgs self-coupling λ and its β_λ function very close to zero at the planck scale. A future electron-positron collider would be able to provide the precise measurements of the top quark needed for such calculations.

Chaotic Inflation Theory suggests that the universe may be in either a false vacuum or a true vacuum state. Alan Guth, in his original proposal for cosmic inflation, 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 and, independently, Andreas Albrecht and Paul Steinhardt, to propose "new inflation" or "slow roll inflation" in which no tunnelling occurs, and the inflationary scalar field instead graphs as a gentle slope.

In 2014, researchers at the Chinese Academy of Sciences' Wuhan Institute of Physics and Mathematics suggested that the universe could have been spontaneously created from nothing (no space, time, nor matter) by quantum fluctuations of metastable false vacuum causing an expanding bubble of true vacuum.

Vacuum decay varieties

Electroweak vacuum decay

Electroweak vacuum stability landscape as estimated in 2012

 

Electroweak vacuum stability landscape as estimated in 2018. T_RH is grand unification energy. ξ is the degree of non-minimal coupling between fundamental forces.

The stability criteria for the electroweak interaction was first formulated in 1979 as a function of the masses of the theoretical Higgs boson and the heaviest fermion. Discovery of the top quark in 1995 and the Higgs boson in 2012 have allowed physicists to validate the criteria against experiment, therefore since 2012 the electroweak interaction is considered as the most promising candidate for a metastable fundamental force. The corresponding false vacuum hypothesis is called either 'Electroweak vacuum instability' or 'Higgs vacuum instability'. The present false vacuum state is called ${\displaystyle dS}$ (De Sitter space), while tentative true vacuum is called ${\displaystyle AdS}$ (Anti-de Sitter space).

The diagrams show the uncertainty ranges of Higgs boson and top quark masses as oval-shaped lines. Underlying colors indicate if the electroweak vacuum state is likely to be stable, merely long-lived or completely unstable for given combination of masses. The "electroweak vacuum decay" hypothesis was sometimes misreported as the Higgs boson "ending" the universe. A 125.18±0.16 GeV/c²  Higgs boson mass is likely to be on the metastable side of stable-metastable boundary (estimated in 2012 as 123.8–135.0 GeV.) However, a definitive answer requires much more precise measurements of the top quark's pole mass, although improved measurement precision of Higgs boson and top quark masses further reinforced the claim of physical electroweak vacuum being in the metastable state as of 2018. Nonetheless, new physics beyond the Standard Model of Particle Physics could drastically change the stability landscape division lines, rendering previous stability and metastability criteria incorrect.

If measurements of the Higgs boson and top quark suggest that our universe lies within a false vacuum of this kind, this would imply that, more than likely in many billions of years, the bubble's effects will propagate across the universe at nearly the speed of light from its origin in space-time.

Other decay modes

• Decay to smaller Vacuum expectation value, resulting in decrease of Casimir effect and destabilization of proton.
• Decay to vacuum with larger neutrino mass (may have happened relatively recently).
• Decay to vacuum with no dark energy.

Bubble nucleation

When the false vacuum decays, the lower-energy true vacuum forms through a process known as bubble nucleation. In this process, instanton effects cause a bubble containing the true vacuum to appear. The walls of the bubble (or domain walls) have a positive surface tension, as energy is expended as the fields roll over the potential barrier to the true vacuum. The former tends as the cube of the bubble's radius while the latter is proportional to the square of its radius, so there is a critical size ${\displaystyle R_{c}}$ at which the total energy of the bubble is zero; smaller bubbles tend to shrink, while larger bubbles tend to grow. To be able to nucleate, the bubble must overcome an energy barrier of height.

${\displaystyle \Phi _{c}={\frac {3\gamma }{4R^{2}}}-\Delta \Phi ,}$

(Eq. 1)

where ${\displaystyle \Delta \Phi }$ is the difference in energy between the true and false vacuums, ${\displaystyle \gamma }$ is the unknown (possibly extremely large) surface tension of the domain wall, and ${\displaystyle R}$ is the radius of the bubble. Rewriting Eq. 1 gives the critical radius as

${\displaystyle R_{c}={\sqrt {\frac {3\gamma }{4\Delta \Phi }}}.}$

(Eq. 2)

The height of the potential barrier between true and false vacuum ${\displaystyle \Phi _{c}}$ was estimated to be around 10²⁰ eV, based on theoretical calculations in 2020.

A bubble smaller than the critical size can overcome the potential barrier via quantum tunnelling of instantons to lower energy states. For a large potential barrier, the tunneling rate per unit volume of space is given by

${\displaystyle \omega \approx {\frac {1}{\gamma }}{\sqrt {\frac {2\Phi _{c}}{\hbar }}}e^{-\Phi _{c}/\hbar },}$

(Eq. 3)

where ${\displaystyle \hbar }$ is the reduced Planck constant. As soon as a bubble of lower-energy vacuum grows beyond the critical radius defined by Eq. 2, the bubble's wall will begin to accelerate outward. Due to the typically large difference in energy between the false and true vacuums, the speed of the wall approaches the speed of light extremely quickly. The bubble does not produce any gravitational effects because the negative energy density of the bubble interior is cancelled out by the positive kinetic energy of the wall.

Small bubbles of true vacuum can be inflated to critical size by providing energy, although required energy densities are several orders of magnitude larger than what is attained in any natural or artificial process. It is also thought that certain environments can catalyze bubble formation by lowering the potential barrier.

Nucleation seeds

Further information: Relativistic Heavy Ion Collider § Critics of high energy experiments, and Safety of particle collisions at the Large Hadron Collider

In a study in 2015, it was pointed out that the vacuum decay rate could be vastly increased in the vicinity of black holes, which would serve as a nucleation seed. According to this study, a potentially catastrophic vacuum decay could be triggered at any time by primordial black holes, should they exist. The authors note however that if primordial black holes cause a false vacuum collapse then it should have happened long before humans evolved on Earth. A subsequent study in 2017 indicated that the bubble would collapse into a primordial black hole rather than originate from it, either by ordinary collapse or by bending space in such a way that it breaks off into a new universe. In 2019, it was found that although small non-spinning black holes may increase true vacuum nucleation rate, rapidly spinning black holes will stabilize false vacuums to decay rates lower than expected for flat space-time. Proposed alternative nucleation seeds include cosmic strings and magnetic monopoles.

If particle collisions produce mini black holes then energetic collisions such as the ones produced in the Large Hadron Collider (LHC) could trigger such a vacuum decay event, a scenario which has attracted the attention of the news media. It is likely to be unrealistic, because if such mini black holes can be created in collisions, they would also be created in the much more energetic collisions of cosmic radiation particles with planetary surfaces or during the early life of the universe as tentative primordial black holes. Hut and Rees note that, because cosmic ray collisions have been observed at much higher energies than those produced in terrestrial particle accelerators, these experiments should not, at least for the foreseeable future, pose a threat to our current vacuum. Particle accelerators have reached energies of only approximately eight tera electron volts (8×10¹² eV). Cosmic ray collisions have been observed at and beyond energies of 5×10¹⁹ eV, six million times more powerful – the so-called Greisen–Zatsepin–Kuzmin limit – and cosmic rays in vicinity of origin may be more powerful yet. 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. Fears of this kind were raised by critics of both the Relativistic Heavy Ion Collider and the Large Hadron Collider at the time of their respective proposal, and determined to be unfounded by scientific inquiry.

Quantum vacuum state

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Quantum_vacuum_state

In quantum field theory, the quantum vacuum state (also called the quantum vacuum or vacuum state) is the quantum state with the lowest possible energy. Generally, it contains no physical particles. the word Zero-point field is sometimes used as a synonym for the vacuum state of a quantized field which is completely individual.

According to present-day understanding of what is called the vacuum state or the quantum vacuum, it is "by no means a simple empty space". According to quantum mechanics, the vacuum state is not truly empty but instead contains fleeting electromagnetic waves and particles that pop into and out of the quantum field.

The QED vacuum of quantum electrodynamics (or QED) was the first vacuum of quantum field theory to be developed. QED originated in the 1930s, and in the late 1940s and early 1950s it was reformulated by Feynman, Tomonaga and Schwinger, who jointly received the Nobel prize for this work in 1965. Today the electromagnetic interactions and the weak interactions are unified (at very high energies only) in the theory of the electroweak interaction.

The Standard Model is a generalization of the QED work to include all the known elementary particles and their interactions (except gravity). Quantum chromodynamics (or QCD) is the portion of the Standard Model that deals with strong interactions, and QCD vacuum is the vacuum of quantum chromodynamics. It is the object of study in the Large Hadron Collider and the Relativistic Heavy Ion Collider, and is related to the so-called vacuum structure of strong interactions.

Non-zero expectation value

Play media

The video of an experiment showing vacuum fluctuations (in the red ring) amplified by spontaneous parametric down-conversion.

If the quantum field theory can be accurately described through perturbation theory, then the properties of the vacuum are analogous to the properties of the ground state of a quantum mechanical harmonic oscillator, or more accurately, the ground state of a measurement problem. In this case the vacuum expectation value (VEV) of any field operator vanishes. For quantum field theories in which perturbation theory breaks down at low energies (for example, Quantum chromodynamics or the BCS theory of superconductivity) field operators may have non-vanishing vacuum expectation values called condensates. In the Standard Model, the non-zero vacuum expectation value of the Higgs field, arising from spontaneous symmetry breaking, is the mechanism by which the other fields in the theory acquire mass.

Energy

Main article: Vacuum energy

The vacuum state is associated with a zero-point energy, and this zero-point energy (equivalent to the lowest possible energy state) has measurable effects. In the laboratory, it may be detected as the Casimir effect. In physical cosmology, the energy of the cosmological vacuum appears as the cosmological constant. In fact, the energy of a cubic centimeter of empty space has been calculated figuratively to be one trillionth of an erg (or 0.6 eV). An outstanding requirement imposed on a potential Theory of Everything is that the energy of the quantum vacuum state must explain the physically observed cosmological constant.

Symmetry

For a relativistic field theory, the vacuum is Poincaré invariant, which follows from Wightman axioms but can be also proved directly without these axioms. Poincaré invariance implies that only scalar combinations of field operators have non-vanishing VEV's. The VEV may break some of the internal symmetries of the Lagrangian of the field theory. In this case the vacuum has less symmetry than the theory allows, and one says that spontaneous symmetry breaking has occurred. See Higgs mechanism, standard model.

Non-linear permittivity

Main article: Schwinger limit

Quantum corrections to Maxwell's equations are expected to result in a tiny nonlinear electric polarization term in the vacuum, resulting in a field-dependent electrical permittivity ε deviating from the nominal value ε₀ of vacuum permittivity. These theoretical developments are described, for example, in Dittrich and Gies. The theory of quantum electrodynamics predicts that the QED vacuum should exhibit a slight nonlinearity so that in the presence of a very strong electric field, the permitivity is increased by a tiny amount with respect to ε₀. Subject to ongoing experimental efforts is the effect that a strong electric field would modify the effective permeability of free space, becoming anisotropic with a value slightly below μ₀ in the direction of the electric field and slightly exceeding μ₀ in the perpendicular direction. The quantum vacuum exposed to an electric field thereby exhibits birefringence for an electromagnetic wave travelling in a direction other than that of the electric field. The effect is similar to the Kerr effect but without matter being present. This tiny nonlinearity can be interpreted in terms of virtual pair production A characteristic electric field strength for which the nonlinearities become sizable is predicted to be enormous, about ${\displaystyle 1.32\times 10^{18}}$V/m, known as the Schwinger limit; the equivalent Kerr constant has been estimated, being about 10²⁰ times smaller than the Kerr constant of water. Explanations for dichroism from particle physics, outside quantum electrodynamics, also have been proposed. Experimentally measuring such an effect is very difficult, and has not yet been successful.

Virtual particles

Main article: Virtual particle

The presence of virtual particles can be rigorously based upon the non-commutation of the quantized electromagnetic fields. Non-commutation means that although the average values of the fields vanish in a quantum vacuum, their variances do not. The term "vacuum fluctuations" refers to the variance of the field strength in the minimal energy state, and is described picturesquely as evidence of "virtual particles". It is sometimes attempted to provide an intuitive picture of virtual particles, or variances, based upon the Heisenberg energy-time uncertainty principle:

${\displaystyle \Delta E\Delta t\geq \hbar \ ,}$

(with ΔE and Δt being the energy and time variations respectively; ΔE is the accuracy in the measurement of energy and Δt is the time taken in the measurement, and ħ is the Reduced Planck constant) arguing along the lines that the short lifetime of virtual particles allows the "borrowing" of large energies from the vacuum and thus permits particle generation for short times. Although the phenomenon of virtual particles is accepted, this interpretation of the energy-time uncertainty relation is not universal. One issue is the use of an uncertainty relation limiting measurement accuracy as though a time uncertainty Δt determines a "budget" for borrowing energy ΔE. Another issue is the meaning of "time" in this relation, because energy and time (unlike position q and momentum p, for example) do not satisfy a canonical commutation relation (such as [q, p] = i ħ). Various schemes have been advanced to construct an observable that has some kind of time interpretation, and yet does satisfy a canonical commutation relation with energy. The very many approaches to the energy-time uncertainty principle are a long and continuing subject.

Physical nature of the quantum vacuum

According to Astrid Lambrecht (2002): "When one empties out a space of all matter and lowers the temperature to absolute zero, one produces in a Gedankenexperiment [thought experiment] the quantum vacuum state." According to Fowler & Guggenheim (1939/1965), the third law of thermodynamics may be precisely enunciated as follows:

It is impossible by any procedure, no matter how idealized, to reduce any assembly to the absolute zero in a finite number of operations.

Photon-photon interaction can occur only through interaction with the vacuum state of some other field, for example through the Dirac electron-positron vacuum field; this is associated with the concept of vacuum polarization. According to Milonni (1994): "... all quantum fields have zero-point energies and vacuum fluctuations." This means that there is a component of the quantum vacuum respectively for each component field (considered in the conceptual absence of the other fields), such as the electromagnetic field, the Dirac electron-positron field, and so on. According to Milonni (1994), some of the effects attributed to the vacuum electromagnetic field can have several physical interpretations, some more conventional than others. The Casimir attraction between uncharged conductive plates is often proposed as an example of an effect of the vacuum electromagnetic field. Schwinger, DeRaad, and Milton (1978) are cited by Milonni (1994) as validly, though unconventionally, explaining the Casimir effect with a model in which "the vacuum is regarded as truly a state with all physical properties equal to zero." In this model, the observed phenomena are explained as the effects of the electron motions on the electromagnetic field, called the source field effect. Milonni writes:

The basic idea here will be that the Casimir force may be derived from the source fields alone even in completely conventional QED, ... Milonni provides detailed argument that the measurable physical effects usually attributed to the vacuum electromagnetic field cannot be explained by that field alone, but require in addition a contribution from the self-energy of the electrons, or their radiation reaction. He writes: "The radiation reaction and the vacuum fields are two aspects of the same thing when it comes to physical interpretations of various QED processes including the Lamb shift, van der Waals forces, and Casimir effects."

This point of view is also stated by Jaffe (2005): "The Casimir force can be calculated without reference to vacuum fluctuations, and like all other observable effects in QED, it vanishes as the fine structure constant, α, goes to zero."

Notations

The vacuum state is written as ${\displaystyle |0\rangle }$ or ${\displaystyle |\rangle }$. The vacuum expectation value (see also Expectation value) of any field ${\displaystyle \phi }$ should be written as ${\displaystyle \langle 0|\phi |0\rangle }$.

Vacuum energy

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Vacuum_energy

 

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.

 

Unsolved problem in physics:

Why does the zero-point energy of the vacuum not cause a large cosmological constant? What cancels it out?

The effects of vacuum energy can be experimentally observed in various phenomena such as spontaneous emission, the Casimir effect and the Lamb shift, and are thought to influence the behavior of the Universe on cosmological scales. Using the upper limit of the cosmological constant, the vacuum energy of free space has been estimated to be 10⁻⁹ joules (10⁻² ergs), or ~5 GeV per cubic meter. However, in quantum electrodynamics, consistency with the principle of Lorentz covariance and with the magnitude of the Planck constant suggest a much larger value of 10¹¹³ joules per cubic meter. This huge discrepancy is known as the cosmological constant problem.

Origin

Quantum field theory states that all fundamental fields, such as the electromagnetic field, must be quantized at each and every point in space. A field in physics may be envisioned as if space were filled with interconnected vibrating balls and springs, and the strength of the field is like the displacement of a ball from its rest position. The theory requires "vibrations" in, or more accurately changes in the strength of, such a field to propagate as per the appropriate wave equation for the particular field in question. The second quantization of quantum field theory requires that each such ball–spring combination be quantized, that is, that the strength of the field be quantized at each point in space. Canonically, if the field at each point in space is a simple harmonic oscillator, its quantization places a quantum harmonic oscillator at each point. Excitations of the field correspond to the elementary particles of particle physics. Thus, according to the theory, even the vacuum has a vastly complex structure and all calculations of quantum field theory must be made in relation to this model of the vacuum.

The theory considers vacuum to implicitly have the same properties as a particle, such as spin or polarization in the case of light, energy, and so on. According to the theory, most of these properties cancel out on average leaving the vacuum empty in the literal sense of the word. One important exception, however, is the vacuum energy or the vacuum expectation value of the energy. The quantization of a simple harmonic oscillator requires the lowest possible energy, or zero-point energy of such an oscillator to be

${\displaystyle {E}={\frac {1}{2}}h\nu .}$

Summing over all possible oscillators at all points in space gives an infinite quantity. To remove this infinity, one may argue that only differences in energy are physically measurable, much as the concept of potential energy has been treated in classical mechanics for centuries. This argument is the underpinning of the theory of renormalization. In all practical calculations, this is how the infinity is handled.

Vacuum energy can also be thought of in terms of virtual particles (also known as vacuum fluctuations) which are created and destroyed out of the vacuum. These particles are always created out of the vacuum in particle–antiparticle pairs, which in most cases shortly annihilate each other and disappear. However, these particles and antiparticles may interact with others before disappearing, a process which can be mapped using Feynman diagrams. Note that this method of computing vacuum energy is mathematically equivalent to having a quantum harmonic oscillator at each point and, therefore, suffers the same renormalization problems.

Additional contributions to the vacuum energy come from spontaneous symmetry breaking in quantum field theory.

Implications

Vacuum energy has a number of consequences. In 1948, Dutch physicists Hendrik B. G. Casimir and Dirk Polder predicted the existence of a tiny attractive force between closely placed metal plates due to resonances in the vacuum energy in the space between them. This is now known as the Casimir effect and has since been extensively experimentally verified. It is therefore believed that the vacuum energy is "real" in the same sense that more familiar conceptual objects such as electrons, magnetic fields, etc., are real. However, alternative explanations for the Casimir effect have since been proposed.

Other predictions are harder to verify. Vacuum fluctuations are always created as particle–antiparticle pairs. The creation of these virtual particles near the event horizon of a black hole has been hypothesized by physicist Stephen Hawking to be a mechanism for the eventual "evaporation" of black holes. If one of the pair is pulled into the black hole before this, then the other particle becomes "real" and energy/mass is essentially radiated into space from the black hole. This loss is cumulative and could result in the black hole's disappearance over time. The time required is dependent on the mass of the black hole (the equations indicate that the smaller the black hole, the more rapidly it evaporates) but could be on the order of 10¹⁰⁰ years for large solar-mass black holes.

The vacuum energy also has important consequences for physical cosmology. General relativity predicts that energy is equivalent to mass, and therefore, if the vacuum energy is "really there", it should exert a gravitational force. Essentially, a non-zero vacuum energy is expected to contribute to the cosmological constant, which affects the expansion of the universe. In the special case of vacuum energy, general relativity stipulates that the gravitational field is proportional to ρ + 3p (where ρ is the mass–energy density, and p is the pressure). Quantum theory of the vacuum further stipulates that the pressure of the zero-state vacuum energy is always negative and equal in magnitude to ρ. Thus, the total is ρ + 3p = ρ − 3ρ = −2ρ, a negative value. If indeed the vacuum ground state has non-zero energy, the calculation implies a repulsive gravitational field, giving rise to acceleration of the expansion of the universe,. However, the vacuum energy is mathematically infinite without renormalization, which is based on the assumption that we can only measure energy in a relative sense, which is not true if we can observe it indirectly via the cosmological constant.

The existence of vacuum energy is also sometimes used as theoretical justification for the possibility of free-energy machines. It has been argued that due to the broken symmetry (in QED), free energy does not violate conservation of energy, since the laws of thermodynamics only apply to equilibrium systems. However, consensus amongst physicists is that this is unknown as the nature of vacuum energy remains an unsolved problem. In particular, the second law of thermodynamics is unaffected by the existence of vacuum energy.

History

In 1934, Georges Lemaître used an unusual perfect-fluid equation of state to interpret the cosmological constant as due to vacuum energy. In 1948, the Casimir effect provided an experimental method for a verification of the existence of vacuum energy; in 1955, however, Evgeny Lifshitz offered a different origin for the Casimir effect. In 1957, Lee and Yang proved the concepts of broken symmetry and parity violation, for which they won the Nobel prize. In 1973, Edward Tryon proposed the zero-energy universe hypothesis: that the Universe may be a large-scale quantum-mechanical vacuum fluctuation where positive mass–energy is balanced by negative gravitational potential energy. During the 1980s, there were many attempts to relate the fields that generate the vacuum energy to specific fields that were predicted by attempts at a Grand unification theory and to use observations of the Universe to confirm one or another version. However, the exact nature of the particles (or fields) that generate vacuum energy, with a density such as that required by inflation theory, remains a mystery.

Vacuum energy in fiction

• Arthur C. Clarke's novel The Songs of Distant Earth features a starship powered by a "quantum drive" based on aspects of this theory.
• In the Sci-Fi television series Stargate Atlantis, the Zero Point Module (ZPM) is a power source that extracts vacuum energy from a micro parallel universe.
• The book Star Trek: Deep Space Nine Technical Manual describes the operating principle of the so-called Quantum torpedo. In this fictional weapon, an antimatter reaction is used to create a multi-dimensional membrane in a vacuum that releases at its decomposition more energy than was needed to produce it. The missing energy is removed from the vacuum. Usually about twice as much energy is released in the explosion, as would correspond to the initial antimatter matter annihilation.

 

Virtual black hole

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Virtual_black_hole 

In quantum gravity, a virtual black hole is a hypothetical micro black hole that exists temporarily as a result of a quantum fluctuation of spacetime. It is an example of quantum foam and is the gravitational analog of the virtual electron–positron pairs found in quantum electrodynamics. Theoretical arguments suggest that virtual black holes should have mass on the order of the Planck mass, lifetime around the Planck time, and occur with a number density of approximately one per Planck volume.

The emergence of virtual black holes at the Planck scale is a consequence of the uncertainty relation

${\displaystyle \Delta R_{\mu }\Delta x_{\mu }\geq \ell _{P}^{2}={\frac {\hbar G}{c^{3}}}}$

where ${\displaystyle R_{\mu }}$ is the radius of curvature of spacetime small domain, ${\displaystyle x_{\mu }}$ is the coordinate of the small domain, ${\displaystyle \ell _{P}}$ is the Planck length, ${\displaystyle \hbar }$ is the reduced Planck constant, ${\displaystyle G}$ is Newton's gravitational constant, and ${\displaystyle c}$ is the speed of light. These uncertainty relations are another form of Heisenberg's uncertainty principle at the Planck scale.

Proof

If virtual black holes exist, they provide a mechanism for proton decay. This is because when a black hole's mass increases via mass falling into the hole, and is theoretised to decrease when Hawking radiation is emitted from the hole, the elementary particles emitted are, in general, not the same as those that fell in. Therefore, if two of a proton's constituent quarks fall into a virtual black hole, it is possible for an antiquark and a lepton to emerge, thus violating conservation of baryon number.

The existence of virtual black holes aggravates the black hole information loss paradox, as any physical process may potentially be disrupted by interaction with a virtual black hole.

 

Quantum foam

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Quantum_foam

Quantum foam (also known as spacetime foam or spacetime bubble) is the quantum fluctuation of spacetime on very small scales due to quantum mechanics. Matter and antimatter is constantly created and destroyed. These subatomic objects are called virtual particles. The idea was devised by John Wheeler in 1955.

Background

With an incomplete theory of quantum gravity, it is impossible to be certain what spacetime would look like at small scales. However, there is no definitive reason that spacetime needs to be fundamentally smooth. It is possible that instead, in a quantum theory of gravity, spacetime would consist of many small, ever-changing regions in which space and time are not definite, but fluctuate in a foam-like manner.

Wheeler suggested that the uncertainty principle might imply that over sufficiently small distances and sufficiently brief intervals of time, the "very geometry of spacetime fluctuates". These fluctuations could be large enough to cause significant departures from the smooth spacetime seen at macroscopic scales, giving spacetime a "foamy" character.

Experimental results

What Hendrik Casimir predicted and can be verified with the casimir experiment is strong evidence that virtual particles do exist. Another measurement supports the virtual particle idea, by predicting the strength of a magnet formed by an electron or muon. The g2 experiment targets this measurement.

In 2005 MAGIC (Major Atmospheric Gamma-ray Imaging Cherenkov) telescopes detected that among gamma-ray photons arriving from the blazar Markarian 501, some photons at different energy levels arrived at different times, suggesting that some of the photons had moved more slowly and thus contradicting the theory of general relativity's notion of the speed of light being constant, a discrepancy which could be explained by the irregularity of quantum foam. More recent experiments were, however, unable to confirm the supposed variation on the speed of light due to graininess of space.

Other experiments involving the polarization of light from distant gamma ray bursts have also produced contradictory results. More Earth-based experiments are ongoing or proposed.

Constraints and limits

The large fluctuations characteristic of a spacetime foam would be expected to occur on a length scale on the order of the Planck length. A foamy spacetime would have limits on the accuracy with which distances can be measured because the size of the many quantum bubbles through which light travels will fluctuate. Depending on the spacetime model used, the spacetime uncertainties accumulate at different rates as light travels through the vast distances.

X-ray and gamma-ray observations of quasars used data from NASA’s Chandra X-ray Observatory, the Fermi Gamma-ray Space Telescope and ground-based gamma-ray observations from the Very Energetic Radiation Imaging Telescope Array (VERITAS) show that spacetime is uniform down to distances 1000 times smaller than the nucleus of a hydrogen atom.

Observations of radiation from nearby quasars by Floyd Stecker of NASA's Goddard Space Flight Center have placed strong experimental limits on the possible violations of Einstein's special theory of relativity implied by the existence of quantum foam. Thus experimental evidence so far has given a range of values in which scientists can test for quantum foam.

Random diffusion model

Chandra's X-ray detection of quasars at distances of billions of light years rules out the model where photons diffuse randomly through spacetime foam, similar to a light diffusing by passing through the fog.

Holographic model

Measurements of quasars at shorter gamma-ray wavelengths with Fermi, and shorter wavelengths with VERITAS, rule out a second model, called a holographic model with less diffusion.

Relation to other theories

The vacuum fluctuations provide vacuum with a non-zero energy known as vacuum energy.

Spin foam theory is a modern attempt to make Wheeler's idea quantitative.