False vacuum

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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.

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. 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.[citation needed]

Stability and instability of the vacuum[edit]

Diagram showing the Higgs boson and top quark masses, which could indicate whether our universe is stable, or a long-lived 'bubble'. The outer dotted line is the current measurement uncertainties; the inner ones show predicted sizes after completion of future physics programs, but their location could be anywhere inside the outer.[1]

For decades, scientific models of our universe have included the possibility that it exists as a long-lived, but not completely stable, sector of space, which could potentially at some time be destroyed upon 'toppling' into a more stable vacuum state.[2][3][4][5][6] The Standard Model of particle physics opens the possibility of calculating from the masses of the Higgs boson and the top quark, whether the universe's present electroweak vacuum state is likely to be stable or merely long-lived.[7][8] (This was sometimes misreported as the Higgs boson "ending" the universe[12]). A 125–127 GeV Higgs mass seems to be extremely close to the boundary for stability (estimated in 2012 as 123.8–135.0 GeV[1]) but a definitive answer requires much more precise measurements of the top quark's pole mass.[1] This catastrophic bubble of "true vacuum" (per quantum models) could theoretically occur at any time or place in the universe, which means (because the bubble of "true vacuum" will expand at the speed of light) the end of such a false vacuum could occur at any time.[13] At present therefore, there are "too large uncertainties which do not allow to draw a firm conclusion on the important question whether the electroweak vacuum is indeed stable or not".[1]

Implications[edit]

If measurements of these particles suggests that our universe lies within a false vacuum of this kind, then it would imply—more than likely in many billions of years[14][Note 1]—that it could cease to exist as we know it, if a true vacuum happened to nucleate.[14]

This is because, if the Standard Model is correct, the particles and forces we observe in our universe exist as they do because of underlying quantum fields. Quantum fields can have states of differing stability, including 'stable', 'unstable', or 'metastable' (meaning, long-lived but capable of being "toppled" in the right circumstances). If a more stable vacuum state were able to arise, then existing particles and forces would no longer arise as they do in the universe's present state. Different particles or forces would arise from (and be shaped by) whatever new quantum states arose. The world we know depends upon these particles and forces, so if this happened, everything around us, from subatomic particles to galaxies, and all fundamental forces, would be reconstituted into new fundamental particles and forces and structures. The universe would lose all of its present structures and become inhabited by new ones (depending upon the exact states involved) based upon the same quantum fields.[citation needed]

It would also have implications for other aspects of physics, and would suggest that the Higgs self-coupling λ and its βλ function could be very close to zero at the Planck scale, with "intriguing" implications, including implications for theories of gravity and Higgs-based inflation.[1]:218 A future electron-positron collider would be able to provide the precise measurements of the top quark needed for such calculations.[1]

Vacuum metastability event[edit]

A hypothetical vacuum metastability event would be theoretically possible if our universe were part of a metastable (false) vacuum in the first place, an issue that was highly theoretical and far from resolved in 1982.[2] A false vacuum is one that appears stable, and is stable within certain limits and conditions, but is capable of being disrupted and entering a different state which is more stable. If this were the case, a bubble of lower-energy vacuum could come to exist by chance or otherwise in our universe, and catalyze the conversion of our universe to a lower energy state in a volume expanding at nearly the speed of light, destroying all that we know without forewarning.[3] Chaotic Inflation theory suggests that the universe may be in either a false vacuum or a true vacuum state.

A paper by Coleman and de Luccia notes that the resulting universe would be extremely unstable and collapse almost immediately:[3]

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

Such an event would be one possible doomsday event. It was used as a plot device in a science-fiction story in 1988 by Geoffrey A. Landis,[15] in 2000 by Stephen Baxter,[16] and in 2002 by Greg Egan.[17]

In theory, either high enough energy concentrations or random chance could trigger the tunneling needed to set this event in motion. However an immense number of ultra-high energy particles and events have occurred in the history of our universe, dwarfing by many orders of magnitude any events at human disposal. Hut and Rees[18] note that, because we have observed cosmic ray collisions 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 accelerations have reached energies of only approximately eight tera electron volts (8×1012 eV). Cosmic ray collisions have been observed at and beyond energies of 1018 eV, a million times more powerful – the so-called Greisen–Zatsepin–Kuzmin limit – and other cosmic events may be more powerful yet. Against this, John Leslie has argued[19] 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.

Bubble nucleation[edit]

In the theoretical physics of the 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.[4][5][20][21][22][23] 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 semi-classical 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.

Joseph Lykken has said that study of the exact properties of the Higgs boson could shed light on the possibility of vacuum collapse.[24]

Expansion of bubble[edit]

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 4 \pi r^2 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 would occur where the walls collide.

The tunnelling 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[edit]

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:[3]

Development of theories[edit]

Alan Guth, in his original proposal for cosmic inflation,[25] 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[26] and, independently, Andreas Albrecht and Paul Steinhardt,[27] 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[edit]

Notes[edit]

  1. ^ The bubble's effects would be expected to propagate across the universe at the speed of light from wherever it occurred. However space is vast—with even the nearest galaxy being over 2 million lightyears from us, and others being many billions of lightyears distant, so the effect of such an event would be unlikely to arise here for billions of years after first occurring.[13][14]

References[edit]

  1. ^ a b c d e f Alekhin, Djouadi and Moch (2012-08-13). "The top quark and Higgs boson masses and the stability of the electroweak vacuum". Physics Letters B. doi:10.1016/j.physletb.2012.08.024. Retrieved 13 January 2013. 
  2. ^ a b M.S. Turner; F. Wilczek (1982). "Is our vacuum metastable?". Nature 298 (5875): 633–634. Bibcode:1982Natur.298..633T. doi:10.1038/298633a0. 
  3. ^ a b c d Coleman, Sidney; De Luccia, Frank (1980-06-15). "Gravitational effects on and of vacuum decay". Physical Review D D21 (12): 3305–3315. Bibcode:1980PhRvD..21.3305C. doi:10.1103/PhysRevD.21.3305. 
  4. ^ a b 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. 
  5. ^ a b 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. 
  6. ^ 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. 
  7. ^ Ellis, Espinosa, Giudice, Hoecker, & Riotto (2009). "The Probable Fate of the Standard Model". Phys. Lett. B 679: 369–375. arXiv:0906.0954. Bibcode:2009PhLB..679..369E. doi:10.1016/j.physletb.2009.07.054. 
  8. ^ Masina, Isabella (2013-02-12). "Higgs boson and top quark masses as tests of electroweak vacuum stability". Phys. Rev. D. doi:10.1103/physrevd.87.053001. 
  9. ^ Irene Klotz (editing by David Adams and Todd Eastham) (2013-02-18). "Universe Has Finite Lifespan, Higgs Boson Calculations Suggest". Huffington Post. Reuters. Retrieved 21 February 2013. Earth will likely be long gone before any Higgs boson particles set off an apocalyptic assault on the universe 
  10. ^ Hoffman, Mark (2013-02-19). "Higgs Boson Will Destroy The Universe Eventually". ScienceWorldReport. Retrieved 21 February 2013. 
  11. ^ "Higgs boson will aid in creation of the universe—and how it will end". Catholic Online/NEWS CONSORTIUM. 2013-02-20. Retrieved 21 February 2013. [T]he Earth will likely be long gone before any Higgs boson particles set off an apocalyptic assault on the universe 
  12. ^ For example, Huffington Post/Reuters[9] and others[10][11]
  13. ^ a b Peralta, Eyder (2013-02-19). "If Higgs Boson Calculations Are Right, A Catastrophic 'Bubble' Could End Universe". NPR.org. NPR. Retrieved 12 March 2013.  Article cites Fermilab's Joseph Lykken: "The bubble forms through an unlikely quantum fluctuation, at a random time and place," Lykken tells us. "So in principle it could happen tomorrow, but then most likely in a very distant galaxy, so we are still safe for billions of years before it gets to us."
  14. ^ a b c Boyle, Alan (2013-02-19). "Will our universe end in a 'big slurp'? Higgs-like particle suggests it might". NBC News' Cosmic log. Retrieved 21 February 2013. [T]he bad news is that its mass suggests the universe will end in a fast-spreading bubble of doom. The good news? It'll probably be tens of billions of years . The article quotes Fermilab's Joseph Lykken: "[T]he parameters for our universe, including the Higgs [and top quark's masses] suggest that we're just at the edge of stability, in a "metastable" state. Physicists have been contemplating such a possibility for more than 30 years. Back in 1982, physicists Michael Turner and Frank Wilczek wrote in Nature that "without warning, a bubble of true vacuum could nucleate somewhere in the universe and move outwards..."
  15. ^ Geoffrey A. Landis (1988). "Vacuum States". Isaac Asimov's Science Fiction: July. 
  16. ^ Stephen Baxter (2000). Time. ISBN 0-7653-1238-7. 
  17. ^ Greg Egan (2002). Schild's Ladder. ISBN 0-06-107344-X. 
  18. ^ P. Hut, M.J. Rees (1983). "How stable is our vacuum?". Nature 302 (5908): 508–509. Bibcode:1983Natur.302..508H. doi:10.1038/302508a0. 
  19. ^ John Leslie (1998). The End of the World:The Science and Ethics of Human Extinction. Routledge. ISBN 0-415-14043-9. 
  20. ^ 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. 
  21. ^ 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. 
  22. ^ S. Coleman (1977). "Fate of the false vacuum: Semiclassical theory". Phys. Rev. D15: 2929–36. 
  23. ^ C. Callan and S. Coleman (1977). "Fate of the false vacuum. II. First quantum corrections". Phys. Rev. D16: 1762–68. 
  24. ^ "Cosmos may be 'inherently unstable'."
  25. ^ A. H. Guth (1981-01-15). "The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems". Physical Review D23: 347. doi:10.1103/physrevd.23.347. OCLC 4433735058. 
  26. ^ 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. 
  27. ^ 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. 

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