Muon

The Moon's cosmic ray shadow, as seen in secondary muons generated by cosmic rays in the atmosphere, and detected 700 meters below ground, at the Soudan II detector.
Composition:	Elementary particle
Particle statistics:	Fermionic
Group:	Lepton
Generation:	Second
Interaction:	Gravity, Electromagnetic, Weak
Symbol(s):	μ−
Antiparticle:	Antimuon (μ+)
Theorized:	—
Discovered:	Carl D. Anderson (1936)
Mass:	105.65836668(38) MeV/c2
Mean lifetime:	2.197034(21)×10−6 s[1]
Electric charge:	−1 e
Color charge:	None
Spin:	1⁄2

The muon (from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with a negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton. It is an unstable subatomic particle with the second longest mean lifetime (2.2 µs), exceeded only by that of the free neutron (~15 minutes). Like all elementary particles, the muon has a corresponding antiparticle of opposite charge but equal mass and spin: the antimuon (also called a positive muon). Muons are denoted by μ⁻ and antimuons by μ⁺. Muons were previously called mu mesons, but are not classified as mesons by modern particle physicists (see History).

Muons have a mass of 105.7 MeV/c², which is about 200 times the mass of an electron. Since the muon's interactions are very similar to those of the electron, a muon can be thought of as a much heavier version of the electron. Due to their greater mass, muons are not as sharply accelerated when they encounter electromagnetic fields, and do not emit as much bremsstrahlung radiation. Thus muons of a given energy penetrate matter far more deeply than electrons, since the deceleration of electrons and muons is primarily due to energy loss by this mechanism. So-called "secondary muons", generated by cosmic rays hitting the atmosphere, can penetrate to the Earth's surface and into deep mines.

As with the case of the other charged leptons, the muon has an associated muon neutrino. Muon neutrinos are denoted by ν_μ.

Contents 1 History 2 Muon sources 3 Muon decay 4 Muonic atoms 5 Use in measurement of the proton charge radius 6 Anomalous magnetic dipole moment 7 See also 8 References 9 External links

History

Muons were discovered by Carl D. Anderson and Seth Neddermeyer at Caltech in 1936, while studying cosmic radiation. Anderson had noticed particles that curved differently from electrons and other known particles when passed through a magnetic field. They were negatively charged but curved less sharply than electrons, but more sharply than protons, for particles of the same velocity. It was assumed that the magnitude of their negative electric charge was equal to that of the electron, and so to account for the difference in curvature, it was supposed that their mass was greater than an electron but smaller than a proton. Thus Anderson initially called the new particle a mesotron, adopting the prefix meso- from the Greek word for "mid-". Shortly thereafter, additional particles of intermediate mass were discovered, and the more general term meson was adopted to refer to any such particle. To differentiate between different types of mesons, the mesotron was in 1947 renamed the mu meson (the Greek letter μ (mu) corresponds to m).
It was soon found that the mu meson significantly differed from other mesons: for example, its decay products included a neutrino and an antineutrino, rather than just one or the other, as was observed with other mesons. Other mesons were eventually understood to be hadrons—that is, particles made of quarks—and thus subject to the residual strong force. In the quark model, a meson is composed of exactly two quarks (a quark and antiquark) unlike baryons, which are composed of three quarks. Mu mesons, however, were found to be fundamental particles (leptons) like electrons, with no quark structure. Thus, mu mesons were not mesons at all (in the new sense and use of the term meson), and so the term mu meson was abandoned, and replaced with the modern term muon.

Another particle (the pion, with which the muon was initially confused) had been predicted by theorist Hideki Yukawa:^[2]

"It seems natural to modify the theory of Heisenberg and Fermi in the following way. The transition of a heavy particle from neutron state to proton state is not always accompanied by the mission of light particles. The transition is sometimes taken up by another heavy particle."

The existence of the muon was confirmed in 1937 by J. C. Street and E. C. Stevenson's cloud chamber experiment.^[3] The discovery of the muon seemed so incongruous and surprising at the time that Nobel laureate I. I. Rabi famously quipped, "Who ordered that?"

In a 1941 experiment on Mount Washington in New Hampshire, muons were used to observe the time dilation predicted by special relativity for the first time.^[4]

Muon sources

Since the production of muons requires an available center of momentum frame energy of 105.7 MeV, neither ordinary radioactive decay events nor nuclear fission and fusion events (such as those occurring in nuclear reactors and nuclear weapons) are energetic enough to produce muons. Only nuclear fission produces single-nuclear-event energies in this range, but do not produce muons as the production of a single muon would violate the conservation of quantum numbers (see under "muon decay" below).

On Earth, most naturally occurring muons are created by cosmic rays, which consist mostly of protons, many arriving from deep space at very high energy^[5]

About 10,000 muons reach every square meter of the earth's surface a minute; these charged particles form as by-products of cosmic rays colliding with molecules in the upper atmosphere. Travelling at relativistic speeds, muons can penetrate tens of meters into rocks and other matter before attenuating as a result of absorption or deflection by other atoms.

— Mark Wolverton (September 2007). "Muons for Peace: New Way to Spot Hidden Nukes Gets Ready to Debut". Scientific American 297 (3): 26–28. http://www.sciam.com/article.cfm?id=muons-for-peace.

When a cosmic ray proton impacts atomic nuclei of air atoms in the upper atmosphere, pions are created. These decay within a relatively short distance (meters) into muons (the pion's preferred decay product), and neutrinos. The muons from these high energy cosmic rays generally continue in about the same direction as the original proton, at a very high velocity. Although their lifetime without relativistic effects would allow a half-survival distance of only about 0.66 km (660 meters) at most (as seen from Earth) the time dilation effect of special relativity (from the viewpoint of the Earth) allows cosmic ray secondary muons to survive the flight to the Earth's surface, since in the Earth frame, the muons have a longer half-life due to their velocity. From the viewpoint (inertial frame) of the muon, on the other hand, it is the length contraction effect of special relativity which allows this penetration, since in the muon frame, its lifetime is unaffected, but the distance through the atmosphere and earth appears far shorter than these distances in the Earth rest-frame. Both are equally valid ways of explaining the fast muon's unusual survival over distances.

Since muons are unusually penetrative of ordinary matter, like neutrinos, they are also detectable deep underground (700 meters at the Soudan II detector) and underwater, where they form a major part of the natural background ionizing radiation. Like cosmic rays, as noted, this secondary muon radiation is also directional.

The same nuclear reaction described above (i.e. hadron-hadron impacts to produce pion beams, which then quickly decay to muon beams over short distances) is used by particle physicists to produce muon beams, such as the beam used for the muon g − 2 experiment.^[6]

Muon decay

See also: Michel parameters

The most common decay of the muon

Muons are unstable elementary particles and are heavier than electrons and neutrinos but lighter than all other matter particles. They decay via the weak interaction. Because lepton numbers must be conserved, one of the product neutrinos of muon decay must be a muon-type neutrino and the other an electron-type antineutrino (antimuon decay produces the corresponding antiparticles, as detailed below). Because charge must be conserved, one of the products of muon decay is always an electron of the same charge as the muon (a positron if it is a positive muon). Thus all muons decay to at least an electron, and two neutrinos. Sometimes, besides these necessary products, additional other particles that have a net charge and spin of zero (i.e. a pair of photons, or an electron-positron pair), are produced.

The dominant muon decay mode (sometimes called the Michel decay after Louis Michel) is the simplest possible: the muon decays to an electron, an electron-antineutrino, and a muon-neutrino. Antimuons, in mirror fashion, most often decay to the corresponding antiparticles: a positron, an electron-neutrino, and a muon-antineutrino. In formulaic terms, these two decays are:

.

The mean lifetime of the (positive) muon is 2.197 019 ± 0.000 021 μs^[7]. The equality of the muon and anti-muon lifetimes has been established to better than one part in 10⁴.

The tree-level muon decay width is

where I(x) = 1 − 8x − 12x²lnx + 8x³ − x⁴; is the Fermi coupling constant.
The decay distributions of the electron in muon decays have been parameterised using the so-called Michel parameters. The values of these four parameters are predicted unambiguously in the Standard Model of particle physics, thus muon decays represent a good test of the space-time structure of the weak interaction. No deviation from the Standard Model predictions has yet been found.

Certain neutrino-less decay modes are kinematically allowed but forbidden in the Standard Model. Examples forbidden by lepton flavour conservation are

and .

Observation of such decay modes would constitute clear evidence for physics beyond the Standard Model (BSM). Current experimental upper limits for the branching fractions of such decay modes are in the range 10⁻¹¹ to 10⁻¹².

Muonic atoms

The muon was the first elementary particle discovered that does not appear in ordinary atoms. Negative muons can, however, form muonic atoms (also called mu-mesic atoms), by replacing an electron in ordinary atoms. Muonic hydrogen atoms are much smaller than typical hydrogen atoms because the much larger mass of the muon gives it a much smaller ground-state wavefunction than is observed for the electron. In multi-electron atoms, when only one of the electrons is replaced by a muon, the size of the atom continues to be determined by the other electrons, and the atomic size is nearly unchanged. However, in such cases the orbital of the muon continues to be smaller and far closer to the nucleus than the atomic orbitals of the electrons.

A positive muon, when stopped in ordinary matter, can also bind an electron and form an exotic atom known as muonium (Mu) atom, in which the muon acts as the nucleus. The positive muon, in this context, can be considered a pseudo-isotope of hydrogen with one ninth of the mass of the proton. Because the reduced mass of muonium, and hence its Bohr radius, is very close to that of hydrogen^{[clarification needed]}, this short-lived "atom" behaves chemically — to a first approximation — like hydrogen, deuterium and tritium.

Use in measurement of the proton charge radius

The recent culmination of a twelve year experiment investigating the proton's charge radius involved the use of muonic hydrogen. This form of hydrogen is composed of a muon orbiting a proton^[8]. The Lamb shift in muonic hydrogen was measured by driving the muon from the from its 2s state up to an excited 2p state using a laser. The frequency of the photon required to induce this transition was revealed to be 50 terahertz which, according to present theories of quantum electrodynamics, yields a value of 0.84184 ± 0.00067 femtometres for the charge radius of the proton.^[9]

Anomalous magnetic dipole moment

The anomalous magnetic dipole moment is the difference between the experimentally observed value of the magnetic dipole moment and the theoretical value predicted by the Dirac equation. The measurement and prediction of this value is very important in the precision tests of QED (quantum electrodynamics). The E821 experiment at Brookhaven National Laboratory (BNL) studied the precession of muon and anti-muon in a constant external magnetic field as they circulated in a confining storage ring. The E821 Experiment reported the following average value (from the July 2007 review by Particle Data Group)

where the first errors are statistical and the second systematic.

The difference between the g-factors of the muon and the electron is due to their difference in mass. Because of the muon's larger mass, contributions to the theoretical calculation of its anomalous magnetic dipole moment from Standard Model weak interactions and from contributions involving hadrons are important at the current level of precision, whereas these effects are not important for the electron. The muon's anomalous magnetic dipole moment is also sensitive to contributions from new physics beyond the Standard Model, such as supersymmetry. For this reason, the muon's anomalous magnetic moment is normally used as a probe for new physics beyond the Standard Model rather than as a test of QED (Phys.Lett. B649, 173 (2007)).

See also

• Mumesic atom
• Muonium
• Muon spin spectroscopy
• Muon-catalyzed fusion
• List of particles

References

1. ^ K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010), URL: http://pdg.lbl.gov
2. ^ Yukaya Hideka, On the Interaction of Elementary Particles 1, Proceedings of the Physico-Mathematical Society of Japan (3) 17, 48, pp 139-148 (1935). (Read 17 November 1934)
3. ^ New Evidence for the Existence of a Particle Intermediate Between the Proton and Electron", Phys. Rev. 52, 1003 (1937).
4. ^ David H. Frisch and James A. Smith, "Measurement of the Relativistic Time Dilation Using Muons", American Journal of Physics, 31, 342, 1963, cited by Michael Fowler, "Special Relativity: What Time is it?"
5. ^ S. Carroll (2004). Spacetime and Geometry: An Introduction to General Relativity. Addison Wesly. p. 204
6. ^ Brookhaven National Laboratory (30 July 2002). "Physicists Announce Latest Muon g-2 Measurement". Press release. http://www.bnl.gov/bnlweb/pubaf/pr/2002/bnlpr073002.htm. Retrieved 2009-11-14. 
7. ^ [1]
8. ^ TRIUMF Muonic Hydrogen collaboration. "A brief description of Muonic Hydrogen research". Retrieved 2010-11-7
9. ^ Pohl, Randolf et al. "The Size of the Proton" Nature 466, 213-216 (8 July 2010)

• S.H. Neddermeyer, C.D. Anderson (1937). "Note on the Nature of Cosmic-Ray Particles". Physical Review 51: 884–886. doi:10.1103/PhysRev.51.884. 
• J.C. Street, E.C. Stevenson (1937). "New Evidence for the Existence of a Particle of Mass Intermediate Between the Proton and Electron". Physical Review 52: 1003–1004. doi:10.1103/PhysRev.52.1003. 
• G. Feinberg, S. Weinberg (1961). "Law of Conservation of Muons.". Physical Review Letters 6: 381–383. doi:10.1103/PhysRevLett.6.381. 
• Serway & Faughn (1995). College Physics (4th ed.). Saunders. p. 841. 
• M. Knecht (2003). "The Anomalous Magnetic Moments of the Electron and the Muon". In B. Duplantier, V. Rivasseau. Poincaré Seminar 2002: Vacuum Energy – Renormalization. Progress in Mathematical Physics. 30. Birkhäuser. p. 265. ISBN 3-7643-0579-7. http://books.google.com/?id=me6ftonVM_EC&pg=PA265&lpg=PA265&dq=%22The+Anomalous+Magnetic+Moments+of+the+Electron+and+the+Muon%22&q=%22The%20Anomalous%20Magnetic%20Moments%20of%20the%20Electron%20and%20the%20Muon%22. 
• E. Derman (2004). My Life As A Quant. Wiley. pp. 58–62. 

External links

• Muon anomalous magnetic moment and supersymmetry
• g-2 (muon anomalous magnetic moment) experiment
• muLan (Measurement of the Positive Muon Lifetime) experiment
• The Review of Particle Physics
• The TRIUMF Weak Interaction Symmetry Test

***

Comment on Backreaction made to Steven

Hi Steven

Would we not be correct to say that unification with the small would be most apropos indeed with the large?

Pushing through that veil.

My interest with the QGP is well documented, as it presented itself "with an interesting location" with which to look at during the collision process.

Natural Microscopic blackhole creations? Are such conditions possible in the natural way of things? Although quickly dissipative, they leave their mark as Cerenkov effects.

As one looks toward the cosmos this reductionist process is how one might look at the cosmos at large, as to some of it's "motivations displayed" in the cosmos?

What conditions allow such reductionism at play to consider the end result of geometrical propensity as a message across the vast distance of space, so as to "count these effects" here on earth?

Let's say cosmos particle collisions and LHC are hand in hand "as to decay of the original particles in space" as they leave their imprint noticeably in the measures of SNO or Icecube, but help us discern further effects of that decay chain as to the constitutions of LHC energy progressions of particles in examination?

Emulating the conditions in LHC progression, adaptability seen then from such progressions, working to produce future understandings. Muon detections through the earth?

So "modeled experiments" in which "distillation of thought" are helped to be reduced too, in kind, lead to matter forming ideas with which to progress? Measure. Self evident.

You see the view has to be on two levels, maybe as a poet using words to describe, or as a artist, trying to explain the natural world. The natural consequence, of understanding of our humanity and it's continuations expressed as abstract thought of our interactions with the world at large, unseen, and miscomprehended?

Do you think Superstringy has anything to do with what I just told you here?:)

Best,

Hi Steven,

Maybe the following will help, and then I will lead up to a modern version for consideration, so you understand the relation.

Keep Gran Sasso in your mind as you look at what I am giving you.

The underground laboratory, which opened in 1989, with its low background radiation is used for experiments in particle and nuclear physics,including the study of neutrinos, high-energy cosmic rays, dark matter, nuclear decay, as well as geology, and biology-wiki


Neutrinos, get set, go!

This summer, CERN gave the starting signal for the long-distance neutrino race to Italy. The CNGS facility (CERN Neutrinos to Gran Sasso), embedded in the laboratory's accelerator complex, produced its first neutrino beam. For the first time, billions of neutrinos were sent through the Earth's crust to the Gran Sasso laboratory, 732 kilometres away in Italy, a journey at almost the speed of light which they completed in less than 2.5 milliseconds. The OPERA experiment at the Gran Sasso laboratory was then commissioned, recording the first neutrino tracks.

Because I am a layman, does not reduce the understanding that I can have, that a scientist may have.

Now for the esoteric :)

Secrets of the Pyramids In a boon for archaeology, particle physicists plan to probe ancient structures for tombs and other hidden chambers. The key to the technology is the muon, a cousin of the electron that rains harmlessly from the sky.

What kind of result would they get from using the muon. What will it tell them?:)

Best,

Conformal Cyclic Cosmology....

Penrose's Conformal Cyclic Cosmology, from one of his Pittsburgh lecture slides in June, 2009. Photo by Bryan W. Roberts

Also see: BEFORE THE BIG BANG: AN OUTRAGEOUS NEW PERSPECTIVE AND ITS IMPLICATIONS FOR PARTICLE PHYSICS

....... (CCC) is a cosmological model in the framework of general relativity, advanced by the theoretical physicist Sir Roger Penrose.^[1][2] In CCC, the universe undergoes a repeated cycle of death and rebirth, with the future timelike infinity of each previous universe being identified with the Big Bang singularity of the next.^[3] Penrose outlines this theory in his book Cycles of Time: An Extraordinary New View of the Universe.

Contents 1 Basic Construction 2 Physical Implications 3 Empirical Tests 4 See also 5 References

Basic Construction

Penrose's basic construction^[4] is to paste together a countable sequence of open FLRW spacetimes, each representing a big bang followed by an infinite future expansion. Penrose noticed that the past conformal boundary of one copy of FLRW spacetime can be "attached" to the future conformal boundary of another, after an appropriate conformal rescaling. In particular, each individual FLRW metric g_ab is multiplied by the square of a conformal factor Ω that approaches zero at timelike infinity, effectively "squashing down" the future conformal boundary to a conformally regular hypersurface (which is spacelike if there is a positive cosmological constant, as we currently believe). The result is a new solution to Einstein's equations, which Penrose takes to represent the entire Universe, and which is composed of a sequence of sectors that Penrose calls "aeons."

Physical Implications

The significant feature of this construction for particle physics is that, since baryons are obey the laws of conformally invariant quantum theory, they will behave in the same way in the rescaled aeons as in the original FLRW counterparts. (Classically, this corresponds to the fact that light cone structure is preserved under conformal rescalings.) For such particles, the boundary between aeons is not a boundary at all, but just a spacelike surface that can be passed across like any other. Fermions, on the other hand, remain confined to a given aeon. This provides a convenient solution to the black hole information paradox; according to Penrose, fermions must be irreversibly converted into radiation during black hole evaporation, to preserve the smoothness of the boundary between aeons.

The curvature properties of Penrose's cosmology are also highly desirable. First, the boundary between aeons satisfies the Weyl curvature hypothesis, thus providing a certain kind of low-entropy past as required by statistical mechanics and by observation. Second, Penrose has calculated that a certain amount of gravitational radiation should be preserved across the boundary between aeons. Penrose suggests this extra gravitational radiation may be enough to explain the observed cosmic acceleration without appeal to a dark energy matter field.

Empirical Tests

In 2010, Penrose and V. G. Gurzadyan published a preprint of a paper claiming that observations of the cosmic microwave background made by the Wilkinson Microwave Anisotropy Probe and the BOOMERanG experiment showed concentric anomalies which were consistent with the CCC hypothesis, with a low probability of the null hypothesis that the observations in question were caused by chance.^[5] However, the statistical significance of the claimed detection has since been questioned. Three groups have independently attempted to reproduce these results, but found that the detection of the concentric anomalies was not statistically significant.^[6][7][8]

See also

• Conformal geometry
• Cyclic model
• Black hole information paradox

References

1. ^ Palmer, Jason (2010-11-27). "Cosmos may show echoes of events before Big Bang". BBC News. http://www.bbc.co.uk/news/science-environment-11837869. Retrieved 2010-11-27. 
2. ^ Penrose, Roger (June 2006). "Before the big bang: An outrageous new perspective and its implications for particle physics". Edinburgh, Scotland: Proceedings of EPAC 2006. p. 2759-2767. http://accelconf.web.cern.ch/accelconf/e06/PAPERS/THESPA01.PDF. Retrieved 2010-11-27. 
3. ^ Cartlidge, Edwin (2010-11-19). "Penrose claims to have glimpsed universe before Big Bang". physicsworld.com. http://physicsworld.com/cws/article/news/44388. Retrieved 2010-11-27. 
4. ^ Roger Penrose (2006). "Before the Big Bang: An Outrageous New Perspective and its Implications for Particle Physics". Proceedings of the EPAC 2006, Edinburgh, Scotland: 2759-2762. http://accelconf.web.cern.ch/accelconf/e06/PAPERS/THESPA01.PDF. 
5. ^ Gurzadyan VG; Penrose R (2010-11-16). "Concentric circles in WMAP data may provide evidence of violent pre-Big-Bang activity". arΧiv:1011.3706 [astro-ph.CO]. 
6. ^ Wehus IK; Eriksen HK (2010-12-07). "A search for concentric circles in the 7-year WMAP temperature sky maps". arΧiv:1012.1268 [astro-ph.CO]. 
7. ^ Moss A; Scott D; Zibin JP (2010-12-07). "No evidence for anomalously low variance circles on the sky". arΧiv:1012.1305 [astro-ph.CO]. 
8. ^ Hajian A (2010-12-8). "Are There Echoes From The Pre-Big Bang Universe? A Search for Low Variance Circles in the CMB Sky". arΧiv:1012.1656 [astro-ph.CO].

See Also: Penrose's CCC cosmology is either inflation or gibberish

Big Bounce

Physical cosmology

Universe · Big Bang Age of the universe Timeline of the Big Bang Ultimate fate of the universe [show]Early universe Inflation · Nucleosynthesis GWB · Neutrino background Cosmic microwave background [show]Expanding universe Redshift · Hubble's law Metric expansion of space Friedmann equations FLRW metric [show]Structure Formation Shape of the Universe Structure formation Reionization Galaxy formation Large-scale structure Galaxy filaments [show]Components Lambda-CDM model Dark energy · Dark matter [show]Timeline Timeline of cosmological theories Future of an expanding universe [show]Experiments Observational cosmology 2dF · SDSS COBE · BOOMERanG · WMAP · Planck [show]Scientists Isaac Newton · Einstein · Hawking · Friedman · Lemaître · Hubble · Penzias · Wilson · Gamow · Dicke · Zel'dovich · Mather · Rubin · Smoot· others

v • d • e

The Big Bounce is a theorized scientific model related to the formation of the known Universe. It derives from the cyclic model or oscillatory universe interpretation of the Big Bang where the first cosmological event was the result of the collapse of a previous universe.^[1]

Contents 1 Expansion and contraction 2 Recent developments in the theory 3 See also 4 References 5 Further reading 6 External links

Expansion and contraction

According to some oscillatory universe theorists, the Big Bang was simply the beginning of a period of expansion that followed a period of contraction. In this view, one could talk of a Big Crunch followed by a Big Bang, or more simply, a Big Bounce. This suggests that we might be living in the first of all universes, but are equally likely to be living in the 2 billionth universe (or any of an infinite other sequential universes).
The main idea behind the quantum theory of a Big Bounce is that, as density approaches infinity, the behavior of the quantum foam changes. All the so-called fundamental physical constants, including the speed of light in a vacuum, were not so constant during the Big Crunch, especially in the interval stretching 10⁻⁴³ seconds before and after the point of inflection. (One unit of Planck time is about 10⁻⁴³ seconds.)

If the fundamental physical constants were determined in a quantum-mechanical manner during the Big Crunch, then their apparently inexplicable values in this universe would not be so surprising, it being understood here that a universe is that which exists between a Big Bang and its Big Crunch.

Recent developments in the theory

Martin Bojowald, an assistant professor of physics at Pennsylvania State University, published a study in July 2007 detailing work somewhat related to loop quantum gravity that claimed to mathematically solve the time before the Big Bang, which would give new weight to the oscillatory universe and Big Bounce theories.^[2]

One of the main problems with the Big Bang theory is that at the moment of the Big Bang, there is a singularity of zero volume and infinite energy. This is normally interpreted as the end of the physics as we know it; in this case, of the theory of general relativity. This is why one expects quantum effects to become important and avoid the singularity.

However, research in loop quantum cosmology purported to show that a previously existing universe collapsed, not to the point of singularity, but to a point before that where the quantum effects of gravity become so strongly repulsive that the universe rebounds back out, forming a new branch. Throughout this collapse and bounce, the evolution is unitary.

Bojowald also claims that some properties of the universe that collapsed to form ours can also be determined. Some properties of the prior universe are not determinable however due to some kind of uncertainty principle.

This work is still in its early stages and very speculative. Some extensions by further scientists have been published in Physical Review Letters.^[3]

Peter Lynds has recently put forward a new cosmology model in which time is cyclic. In his theory our Universe will eventually stop expanding and then contract. Before becoming a singularity, as one would expect from Hawking's black hole theory, the Universe would bounce. Lynds claims that a singularity would violate the second law of thermodynamics and this stops the Universe from being bounded by singularities. The Big Crunch would be avoided with a new Big Bang. Lynds suggests the exact history of the Universe would be repeated in each cycle. Some critics argue that while the Universe may be cyclic, the histories would all be variants.

See also

	Astronomy portal
	Space portal
	Solar System portal

• Abhay Ashtekar
• Anthropic principle
• Martin Bojowald
• Loop quantum gravity
• Supernova
• John Archibald Wheeler

References

1. ^ "Penn State Researchers Look Beyond The Birth Of The Universe". Science Daily. May 17, 2006. http://www.sciencedaily.com/releases/2006/05/060515232747.htm.  Referring to Ashtekar, Abhay; Pawlowski, Tomasz; Singh, Parmpreet (2006). "Quantum Nature of the Big Bang". Physical Review Letters 96 (14): 141301. doi:10.1103/PhysRevLett.96.141301. PMID 16712061. http://link.aps.org/abstract/PRL/v96/e141301. 
2. ^ Bojowald, Martin (2007). "What happened before the Big Bang?". Nature Physics 3 (8): 523–525. doi:10.1038/nphys654. 
3. ^ Ashtekar, Abhay; Corichi, Alejandro; Singh, Parampreet (2008). "Robustness of key features of loop quantum cosmology". Physical Review D 77: 024046. doi:10.1103/PhysRevD.77.024046. 

Further reading

• Magueijo, João (2003). Faster than the Speed of Light: the Story of a Scientific Speculation. Cambridge, MA: Perseus Publishing. ISBN 0738205257. 
• Bojowald, Martin. "Follow the Bouncing Universe". Scientific American (October 2008): 44–51. 

External links

• Dark Matter, Antimatter, and Time-Symmetry, Trevor Pitts, 1999
• Penn State Researchers Look Beyond The Birth Of The Universe (Penn State) May 12, 2006
• What Happened Before the Big Bang? (Penn State) July 1, 2007
• From big bang to big bounce (Pen State) NewScientist December 13, 2008

Cyclic model

Physical cosmology

Universe · Big Bang Age of the universe Timeline of the Big Bang Ultimate fate of the universe [show]Early universe Inflation · Nucleosynthesis GWB · Neutrino background Cosmic microwave background [show]Expanding universe Redshift · Hubble's law Metric expansion of space Friedmann equations FLRW metric [show]Structure Formation Shape of the Universe Structure formation Reionization Galaxy formation Large-scale structure Galaxy filaments [show]Components Lambda-CDM model Dark energy · Dark matter [show]Timeline Timeline of cosmological theories Future of an expanding universe [show]Experiments Observational cosmology 2dF · SDSS COBE · BOOMERanG · WMAP · Planck [show]Scientists Isaac Newton · Einstein · Hawking · Friedman · Lemaître · Hubble · Penzias · Wilson · Gamow · Dicke · Zel'dovich · Mather · Rubin · Smoot· others

v • d • e

A cyclic model is any of several cosmological models in which the universe follows infinite, self-sustaining cycles. For example, the oscillating universe theory briefly considered by Albert Einstein in 1930 theorized a universe following an eternal series of oscillations, each beginning with a big bang and ending with a big crunch; in the interim, the universe would expand for a period of time before the gravitational attraction of matter causes it to collapse back in and undergo a bounce.

Contents 1 Overview 2 The Steinhardt–Turok model 3 The Baum–Frampton model 4 Notes 5 See also 6 Further reading 7 External links

Overview

In the 1930s, theoretical physicists, most notably Albert Einstein, considered the possibility of a cyclic model for the universe as an (everlasting) alternative to the model of an expanding universe. However, work by Richard C. Tolman in 1934 showed that these early attempts failed because of the entropy problem that, in statistical mechanics, entropy only increases because of the Second law of thermodynamics.^[1] This implies that successive cycles grow longer and larger. Extrapolating back in time, cycles before the present one become shorter and smaller culminating again in a Big Bang and thus not replacing it. This puzzling situation remained for many decades until the early 21st century when the recently discovered dark energy component provided new hope for a consistent cyclic cosmology.^[2]

One new cyclic model is a brane cosmology model of the creation of the universe, derived from the earlier ekpyrotic model. It was proposed in 2001 by Paul Steinhardt of Princeton University and Neil Turok of Cambridge University. The theory describes a universe exploding into existence not just once, but repeatedly over time.^[3][4] The theory could potentially explain why a mysterious repulsive form of energy known as the "cosmological constant", and which is accelerating the expansion of the universe, is several orders of magnitude smaller than predicted by the standard Big Bang model.

A different cyclic model relying on the notion of phantom energy was proposed in 2007 by Lauris Baum and Paul Frampton of the University of North Carolina at Chapel Hill.^[5]

The Steinhardt–Turok model

In this cyclic model, two parallel orbifold planes or M-branes collide periodically in a higher dimensional space.^[6] The visible four-dimensional universe lies on one of these branes. The collisions correspond to a reversal from contraction to expansion, or a big crunch followed immediately by a big bang. The matter and radiation we see today were generated during the most recent collision in a pattern dictated by quantum fluctuations created before the branes. Eventually, the universe reached the state we observe today, before beginning to contract again many billions of years in the future. Dark energy corresponds to a force between the branes, and serves the crucial role of solving the monopole, horizon, and flatness problems. Moreover the cycles can continue indefinitely into the past and the future, and the solution is an attractor, so it can provide a complete history of the universe.
As Richard C. Tolman showed, the earlier cyclic model failed because the universe would undergo inevitable thermodynamic heat death.^[1] However, the newer cyclic model evades this by having a net expansion each cycle, preventing entropy from building up. However, there are major problems with the model. Foremost among them is that colliding branes are not understood by string theorists, and nobody knows if the scale invariant spectrum will be destroyed by the big crunch. Moreover, like cosmic inflation, while the general character of the forces (in the ekpyrotic scenario, a force between branes) required to create the vacuum fluctuations is known, there is no candidate from particle physics. ^[7]

The Baum–Frampton model

This more recent cyclic model of 2007 makes a different technical assumption concerning the equation of state of the dark energy which relates pressure and density through a parameter w.^[5][8] It assumes w < -1 (a condition called phantom energy) throughout a cycle, including at present. (By contrast, Steinhardt-Turok assume w is never less than -1.) In the Baum-Frampton model, a septillionth (or less) of a second before the would-be Big Rip, a turnaround occurs and only one causal patch is retained as our universe. The generic patch contains no quark, lepton or force carrier; only dark energy - and its entropy thereby vanishes. The adiabatic process of contraction of this much smaller universe takes place with constant vanishing entropy and with no matter including no black holes which disintegrated before turnaround. The idea that the universe "comes back empty" is a central new idea of this cyclic model, and avoids many difficulties confronting matter in a contracting phase such as excessive structure formation, proliferation and expansion of black holes, as well as going through phase transitions such as those of QCD and electroweak symmetry restoration. Any of these would tend strongly to produce an unwanted premature bounce, simply to avoid violation of the second law of thermodynamics. The surprising w < -1 condition may be logically inevitable in a truly infinitely cyclic cosmology because of the entropy problem. Nevertheless, many technical back up calculations are necessary to confirm consistency of the approach. Although the model borrows ideas from string theory, it is not necessarily committed to strings, or to higher dimensions, yet such speculative devices may provide the most expeditious methods to investigate the internal consistency. The value of w in the Baum-Frampton model can be made arbitrarily close to, but must be less than, -1.

Notes

1. ^ ^{a b} R.C. Tolman (1987) [1934]. Relativity, Thermodynamics, and Cosmology. New York: Dover. LCCN 34032023-{{{3}}}. ISBN 0486653838. 
2. ^ P.H. Frampton (2006). "On Cyclic Universes". arΧiv:astro-ph/0612243 [astro-ph]. 
3. ^ P.J. Steinhardt, N. Turok (2001). "Cosmic Evolution in a Cyclic Universe". arΧiv:hep-th/0111098 [hep-th]. 
4. ^ P.J. Steinhardt, N. Turok (2001). "A Cyclic Model of the Universe". arΧiv:hep-th/0111030 [hep-th]. 
5. ^ ^{a b} L. Baum, P.H. Frampton (2007). "Entropy of Contracting Universe in Cyclic Cosmology". arΧiv:hep-th/0703162 [hep-th]. 
6. ^ P.J. Steinhardt, N. Turok (2004). "The Cyclic Model Simplified". arΧiv:astro-ph/0404480 [astro-ph]. 
7. ^ P. Woit (2006). Not Even Wrong. London: Random House. ISBN 97800994488644. 
8. ^ L. Baum and P.H. Frampton (2007). "Turnaround in Cyclic Cosmology". Physical Review Letters 98 (7): 071301. doi:10.1103/PhysRevLett.98.071301. arXiv:hep-th/0610213. PMID 17359014. 

See also

• Cosmology
• Richard Tolman
• Big Bounce
• Cosmological constant
• Conformal Cyclic Cosmology

Further reading

• P.J. Steinhardt, N. Turok (2007). Endless Universe. New York: Doubleday. ISBN 9780385509640. 
• R.C. Tolman (1987) [1934]. Relativity, Thermodynamics, and Cosmology. New York: Dover. LCCN 34032023-{{{3}}}. ISBN 0486653838. 
• L. Baum and P.H. Frampton (2007). "Turnaround in Cyclic Cosmology". Physical Review Letters 98 (7): 071301. doi:10.1103/PhysRevLett.98.071301. arXiv:hep-th/0610213. PMID 17359014. 
• R. H. Dicke, P. J. E. Peebles, P. G. Roll and D. T. Wilkinson, "Cosmic Black-Body Radiation," Astrophysical Journal 142 (1965), 414. This paper discussed the oscillatory universe as one of the main cosmological possibilities of the time.
• S. W. Hawking and G. F. R. Ellis, The large-scale structure of space-time (Cambridge, 1973).

External links

• Paul J. Steinhardt, Department of Physics, Princeton University
• Paul H. Frampton, Department of Physics and Astronomy, The University of North Carolina at Chapel Hill
• Cyclic universe on arxiv.org
• "The Cyclic Universe": A Talk with Neil Turok
• Roger Penrose - Cyclical Universe Model