False vacuum

In quantum field theory, a false vacuum is a metastable sector of space that appears to be a perturbative vacuum, but is unstable due to instanton effects that may tunnel 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, but not the lowest energy state, even though it may remain stable for some time. This is analogous to metastability for first-order phase transitions.

A scalar field φ in a false vacuum. Note that the energy E is higher 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.

Vacuum metastability event

In their paper,^[1] Coleman and de Luccia noted:

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.

Sidney Coleman & F. de Luccia

The possibility that we are living in a false vacuum has been considered though this is only a possibility and Chaotic Inflation theory 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 instantaneously, without any forewarning.^[1] Thus, this vacuum metastability event is a theoretical doomsday event. This was used in a science-fiction story in 1988 by Geoffrey A. Landis,^[2] in 2000 by Stephen Baxter,^[3] and in 2002 by Greg Egan.^[4]

Particle accelerator

One scenario is that, rather than quantum tunnelling, a particle accelerator, which produces very high energies 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,^[5] however, have determined that because we have observed cosmic ray collisions 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, the so-called Greisen–Zatsepin–Kuzmin limit. John Leslie has argued^[6] 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.^[7] 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.^[8] 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 walls) have a surface tension, 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 4πr² but the negative contribution of the interior increases more quickly, as the volume of a sphere $\textstyle\frac{4}{3} \pi r^3$. 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 and the Universe is undergoing the exponential expansion of de Sitter space. This leads to a number of interesting effects, first studied by Coleman and de Luccia:^[1]

Development of theories

Alan Guth in his original proposal for cosmic inflation^[9] 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^[10] and, independently, Andreas Albrecht and Paul Steinhardt^[11] to propose "new inflation" or "slow roll inflation" in which no tunnelling occurs, and the inflationary scalar field instead rolls down a gentle slope.

See also

• Supercooling
• Superheating
• Schild's Ladder

References

1. ^ ^{a b c} S. Coleman and F. De Luccia (1980). "Gravitational effects on and of vacuum decay". Physical Review D21: 3305. Bibcode 1980PhRvD..21.3305C. doi:10.1103/PhysRevD.21.3305. 
2. ^ Geoffrey A. Landis (1988). "Vacuum States". Analog Science Fact / Science Fiction: July. 
3. ^ Stephen Baxter (2000). Time. ISBN 0765312387. 
4. ^ Greg Egan (2002). Schild's Ladder. ISBN ISBN 0-06-107344-X. 
5. ^ P. Hut, M.J. Rees (1983). "How stable is our vacuum?". Nature 302 (5908): 508–509. Bibcode 1983Natur.302..508H. doi:10.1038/302508a0. 
6. ^ John Leslie (1998). The End of the World:The Science and Ethics of Human Extinction. Routledge. ISBN 0-415-14043-9. 
7. ^ M.S. Turner, F. Wilczek (1982). "Is our vacuum metastable?". Nature 298 (5875): 633–634. Bibcode 1982Natur.298..633T. doi:10.1038/298633a0. 
8. ^ M. Stone (1976). "Lifetime and decay of excited vacuum states". Phys. Rev. D 14 (12): 3568–3573. Bibcode 1976PhRvD..14.3568S. doi:10.1103/PhysRevD.14.3568. P.H. Frampton (1976). "Vacuum Instability and Higgs Scalar Mass". Phys. Rev. Lett. 37 (21): 1378–1380. Bibcode 1976PhRvL..37.1378F. doi:10.1103/PhysRevLett.37.1378.  M. Stone (1977). "Semiclassical methods for unstable states". Phys.Lett. B 67 (2): 186–183. Bibcode 1977PhLB...67..186S. doi:10.1016/0370-2693(77)90099-5. P.H. Frampton (1977). "Consequences of Vacuum Instability in Quantum Field Theory". Phys. Rev. D15 (10): 2922–28. Bibcode 1977PhRvD..15.2922F. doi:10.1103/PhysRevD.15.2922. S. Coleman (1977). "Fate of the false vacuum: Semiclassical theory". Phys. Rev. D15: 2929–36. C. Callan and S. Coleman (1977). "Fate of the false vacuum. II. First quantum corrections". Phys. Rev. D16: 1762–68. 
9. ^ A. H. Guth (1981). "The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems". Phys. Rev. D23: 347. 
10. ^ A. Linde (1982). "A New Inflationary Universe Scenario: A Possible Solution Of The Horizon, Flatness, Homogeneity, Isotropy And Primordial Monopole Problems". Phys. Lett. B108: 389. 
11. ^ A. Albrecht and P. J. Steinhardt (1982). "Cosmology For Grand Unified Theories With Radiatively Induced Symmetry Breaking". Phys. Rev. Lett. 48 (17): 1220. Bibcode 1982PhRvL..48.1220A. doi:10.1103/PhysRevLett.48.1220. 

Further reading

• Johann Rafelski and Berndt Muller (1985). The Structured Vacuum - thinking about nothing. Harri Deutsch. ISBN 3-87144-889-3. 
• Sidney Coleman (1988). Aspects of Symmetry: Selected Erice Lectures. 0521318270. ISBN 0-521-31827-0. 

External links

• Free pdf copy of The Structured Vacuum - thinking about nothing by Johann Rafelski and Berndt Muller (1985) ISBN 3-87144-889-3.
• An Eternity of Bubbles? by Alan Guth
• The Decay of the False Vacuum by Sten Odenwald
• Simulation of False Vacuum Decay by Bubble Nucleation by Joel Thorarinson