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Higgs lede

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The Higgs boson or Higgs particle is an elementary particle in the Standard Model of Partical physics. Its main relevance is that it is the smallest possible excitation of the Higgs field;[1][2] A field that unlike the more familiar electromagnetic field cannot be "turned off", but instead takes a constant value almost everywhere. Its existence explains why some fundamental particles have mass when the symmetries controlling their interactions should require them to be massless, and why the weak force has a much shorter range than the electromagnetic force.

Despite being present everywhere, the existence of the Higgs field has been very hard to confirm, because it is extremely hard to create excitations (i.e. Higgs particles). The search for this elusive particle has taken more than 40 years and led to the construction of one of the world's most expensive and complex experimental facilities to date, the Large Hadron Collider,[3] able to create Higgs bosons and other particles for observation and study. On 4 July 2012, it was announced that a previously unknown particle with a mass between 125 and 127 GeV/c2 (134.2 and 136.3 amu) had been detected; physicists suspected at the time that it was the Higgs boson.[4][5][6] By March 2013, the particle had been proven to behave, interact and decay in many of the ways predicted by the Standard Model, and was also tentatively confirmed to have positive parity and zero spin,[7] two fundamental attributes of a Higgs boson. This appears to be the first elementary scalar particle discovered in nature.[8] More data is needed to know if the discovered particle exactly matches the predictions of the Standard Model, or whether, as predicted by some theories, multiple Higgs bosons exist.[9]

References

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  1. ^ Onyisi, P. (23 October 2012). "Higgs boson FAQ". University of Texas ATLAS group. Retrieved 2013-01-08.
  2. ^ Strassler, M. (12 October 2012). "The Higgs FAQ 2.0". ProfMattStrassler.com. Retrieved 2013-01-08. [Q] Why do particle physicists care so much about the Higgs particle?
    [A] Well, actually, they don't. What they really care about is the Higgs field, because it is so important. [emphasis in original]
  3. ^ Strassler, M. (8 October 2011). "The Known Particles – If The Higgs Field Were Zero". ProfMattStrassler.com. Retrieved 13 November 2012. The Higgs field: so important it merited an entire experimental facility, the Large Hadron Collider, dedicated to understanding it.
  4. ^ Biever, C. (6 July 2012). "It's a boson! But we need to know if it's the Higgs". New Scientist. Retrieved 2013-01-09. 'As a layman, I would say, I think we have it,' said Rolf-Dieter Heuer, director general of CERN at Wednesday's seminar announcing the results of the search for the Higgs boson. But when pressed by journalists afterwards on what exactly 'it' was, things got more complicated. 'We have discovered a boson – now we have to find out what boson it is'
    Q: 'If we don't know the new particle is a Higgs, what do we know about it?' We know it is some kind of boson, says Vivek Sharma of CMS [...]
    Q: 'are the CERN scientists just being too cautious? What would be enough evidence to call it a Higgs boson?' As there could be many different kinds of Higgs bosons, there's no straight answer.
    [emphasis in original]
    [dead link]
  5. ^ Cite error: The named reference ScienceNews was invoked but never defined (see the help page).
  6. ^ Del Rosso, A. (19 November 2012). "Higgs: The beginning of the exploration". CERN Bulletin. Retrieved 2013-01-09. Even in the most specialized circles, the new particle discovered in July is not yet being called the "Higgs boson". Physicists still hesitate to call it that before they have determined that its properties fit with those the Higgs theory predicts the Higgs boson has.
  7. ^ Cite error: The named reference CERN March 2013 was invoked but never defined (see the help page).
  8. ^ Naik, G. (14 March 2013). "New Data Boosts Case for Higgs Boson Find". The Wall Street Journal. Retrieved 2013-03-15. 'We've never seen an elementary particle with spin zero,' said Tony Weidberg, a particle physicist at the University of Oxford who is also involved in the CERN experiments.
  9. ^ Cite error: The named reference Huffington 14 March 2013 was invoked but never defined (see the help page).

Big bang lede

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The Big Bang theory is the prevailing cosmological model for the early development of the universe.[1] The main idea is that the universe is expanding. Consequently, the universe was denser and hotter in the past. In particular, the Big Bang model suggests that at some moment all matter in the universe was contained in a point. Modern measurements place this moment at approximately 13.82 billion years ago, which is thus considered the age of the universe.[2] After the initial expansion, the universe cooled sufficiently to allow the formation of subatomic particles, including protons, neutrons, and electrons. Though simple atomic nuclei formed within the first three minutes after the Big Bang, thousands of years passed before the first electrically neutral atoms formed. The majority of atoms that were produced by the Big Bang are hydrogen, along with helium and traces of lithium. Giant clouds of these primordial elements later coalesced through gravity to form stars and galaxies, and the heavier elements were synthesized either within stars or during supernovae.

Religious Implications (ec)

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The Big Bang is a scientific theory, and as such is dependent on its agreement with observations. But as a theory which addresses the origins of reality, it has always carried theological implications, most notably, those based upon the philosophical[3][4] concept of creation ex nihilo (a Latin phrase meaning "out of nothing").[5][6][7][8][9] Since the acceptance of the Big Bang as the dominant physical cosmological paradigm, there have been a variety of reactions by religious groups as to its implications for their respective religious cosmologies. Some accept the scientific evidence at face value, while others seek to reconcile the Big Bang with their religious tenets, and others completely reject or ignore the evidence for the Big Bang theory.[10]

A tachyon /ˈtæki.ɒn/ (or tachyonic particle), is a hypothetical particle that always moves faster than light. Most physicists do not believe that such particles exist, or are consistent with the known laws of physics.[11] Tachyons could be used to send signals faster than light, and (according to special relativity) this leads to violations of causality.[11]

The first hypothesis regarding tachyons is attributed to German physicist Arnold Sommerfeld,[12] and more recent discussions include.[13][14] The term itself was coined by Gerald Feinberg in a 1967 paper.[15] The name comes from the Greek: ταχύς (tachys, “swift, quick, fast, rapid”). Conventional massive particles that travel slower than the speed of light are sometimes termed "bradyons" or "tardyons" in contrast, although these terms are only used in the context of discussions about tachyons.

In the language of special relativity, a tachyon would have space-like four-momentum and imaginary proper time, and would be constrained to the spacelike portion of the energy-momentum graph. Therefore, it cannot slow down to subluminal speeds.[15]

In his 1967 paper Feinberg proposed that tachyons could occur as the quanta of a field with imaginary mass. It was however later shown that the excitations of this field do not propagate faster than light, but instead represent an instability of the ground state of the field (see tachyon condensation).[16] Today, the fields of the type proposed by Feinberg still play a role in theoretical physics and are referred to as tachyonic fields (or sometimes as simply tachyons). Potentially consistent theories that allow faster-than-light particles include those that break Lorentz invariance, the symmetry underlying special relativity, so that the speed of light is not a barrier.

Despite the theoretical arguments against the existence of faster than light particles, experimental searches have been conducted to search for them. Until recently, no compelling experimental evidence for their existence had been found.[17] Following the results of the September 2011 observation of faster-than-light neutrino velocities, the faster-than-light neutrino anomaly, the value of the neutrino velocity is now an active subject of theoretical and experimental studies.[18]

Motivating Examples (tensor)

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Tensors generalize the concept of scalars, vectors, and linear maps. This section reviews the properties of these objects that will be relevant to all tensors.

Vector

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A vector is a quantity that has a direction and a magnitude. Vectors can be added together through vector addition and can be scaled through scalar multiplication. In three dimensions, if you choose three linearly independent vectors, e1, e2, and e3, any other vector v can be written as a linear combination of these vectors,

v = c1e1 + c2e2 + c3e3.

Such a set {e1, e2, e3} of linearly independent vectors is called a basis.

When dealing with vectors it is common to fix a choice of basis, e.g. vectors of unit length in the x, y, and z directions, and identify a vector by its coefficients, c1, c2, and c3, with respect to that basis, also called its components. This is commonly denoted by placing the components in a column,

.

A different choice of basis vectors {ê1, ê2, ê3} leads to different components, ĉ1, ĉ2, and ĉ3. The components with respect to new basis are related to the components with respect to the old basis, because the vectors in the new basis can be expressed as linear combinations of the old basis,

êi = Ri1e1 + Ri2e2 + Ri3e3 = Rijej,

where i runs from 1 to 3, and last part introduces a notational shorthand called Einstein notation, which implies that any repeated indices (in this case j) are summed over their range (in this case 1 to 3). This notational shorthand is very convenient when dealing with tensors and is used throughout the rest of this article. It follows from this relation that the coefficients ci can be expressed in terms of the coefficients ĉi as follows,

ci = Rijĉj,

or conversely,

ĉi = (R-1)ijcj,

where (R-1)ij is the inverse transformation of Rij (which is defined by the condition (R-1)ikRkj = Id). The coefficients of a vector does transform with de inverse transformation with respect to the basis transformation. They are said to transform contravariantly.

Covector

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For every vector space V there exists a dual vector space V* defined as the space of all linear functions on V, the elements of which are called covectors. If V has a basis e1, ..., en then there exists a dual basis ε1, ..., εn of V* defined by the condition,

εi(ej) = 1 if i = j and 0 otherwise.

If ω is a covector with coefficients ω1, ..., ωn then its effect of a vector v with components v1, ..., vn is given by

ω(v) = ωivi,

or expressed as a matrix multiplication,

For this reason covectors are often referred to as row vectors.

Linear maps

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Notes

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References

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  1. ^ Wollack, E. J. (10 December 2010). "Cosmology: The Study of the Universe". Universe 101: Big Bang Theory. NASA. Archived from the original on 14 May 2011. Retrieved 27 April 2011. The second section discusses the classic tests of the Big Bang theory that make it so compelling as the likely valid description of our universe.
  2. ^ "Planck reveals an almost perfect universe". Planck. ESA. 2013-03-21. Retrieved 2013-03-21.
  3. ^ Ellis, G.F.R. (2007). "Issues in the philosophy of cosmology". Philosophy of Physics: 1183–1285. doi:10.1016/B978-044451560-5/50014-2. ISBN 9780444515605.
  4. ^ A., Vilenkin (1982). "Creation of universes from nothing". Physics Letters B. 117 (1–2): 25–28. doi:10.1016/0370-2693(82)90866-8. ISSN 0370-2693.
  5. ^ Russell, R.J. (2008). Cosmology: From Alpha to Omega. Fortress Press. ISBN 9780800662738. Amazingly, some secularists attribute to t=0 a direct implication. The June 1978 issue of the New York Times contained an article by NASA's Robert Jastrow, an avowed agnostic, entitled "Found God?" Here Jastrow depicts the theologians to be "delighted" that astronomical evidence "leads to a biblical view of Genesis." Though claiming to be agnostic, he argued without reservation for the religious significance of t=0: It is beyond science and leads to some sort of creator.
  6. ^ Corey, M. (1993). God and the New Cosmology. Rowman & Littlefield. ISBN 9780847678020. Indeed, creation ex nihilo is a fundamental tenet of orthodox Christian theology. Incredibly enough, modern theoretical physicists have also speculated that the universe may have been produced through a sudden quantum appearance "out of nothing." Physicist Paul Davies has claimed that the particular physicis involved in the Big Bang necessitates creation ex nihilo.
  7. ^ Lerner, E.J. (1992). The Big Bang Never Happened: A Startling Refutation of the Dominant Theory of the Origin of the Universe. Vintage Books. ISBN 9780679740490. From theologians to physicists to novelists, it is widely believed that the Big Bang theory supports Christian concepts of a creator. In February 1989, for example, the front-page article of the New York Times Book Review argued that scientists and novelists were returning to God, in large part through the influence of the Big Bang.
  8. ^ Manson, N.A. (1993). God and Design: The Teleological Argument and Modern Science. Routledge. ISBN 9780415263443. The Big Bang theory strikes many people as having theological implications, as shown by those who do not welcome those implications.
  9. ^ Davis, J.J. (2002). The Frontiers of Science & Faith. InterVarsity Press. ISBN 9780830826643. Genesis' concept of a singular, ex nihilo beginning of the universe essentially stands alone among the cosmologies of the ancient world and exhibits, at this point, convergence with recent big bang cosmological models.
  10. ^ Wright, E.L (24 May 2009). "Cosmology and Religion". Ned Wright's Cosmology Tutorial. Retrieved 2009-10-15.
  11. ^ a b Tipler, Paul A.; Llewellyn, Ralph A. (2008). Modern Physics (5th ed.). New York, NY: W.H. Freeman & Co. p. 54. ISBN 978-0-7167-7550-8. ... so existence of particles v > c ... Called tachyons ... would present relativity with serious ... problems of infinite creation energies and causality paradoxes.
  12. ^ Sommerfeld, A. (1904). "Simplified deduction of the field and the forces of an electron moving in any given way". KNKL. Acad. Wetensch. 7: 345–367.
  13. ^ Bilaniuk, O.-M. P.; Sudarshan, E. C. G. (1969). "Particles beyond the Light Barrier". Physics Today. 22 (5): 43–51. doi:10.1063/1.3035574.
  14. ^ Bilaniuk, O.-M. P.; Deshpande, V. K.; Sudarshan, E. C. G. (1962). "'Meta' Relativity". American Journal of Physics. 30 (10): 718. Bibcode:1962AmJPh..30..718B. doi:10.1119/1.1941773.
  15. ^ a b Feinberg, G. (1967). "Possibility of Faster-Than-Light Particles". Physical Review. 159 (5): 1089–1105. Bibcode:1967PhRv..159.1089F. doi:10.1103/PhysRev.159.1089.
  16. ^ Aharonov, Y.; Komar, A.; Susskind, L. (1969). "Superluminal Behavior, Causality, and Instability". Phys. Rev. 182 ({5}). American Physical Society: 1400–1403. doi:10.1103/PhysRev.182.1400.
  17. ^ Feinberg, G. (1997). "Tachyon". Encyclopedia Americana. Vol. 26. Grolier. p. 210.
  18. ^ http://www.newscientist.com/article/dn21064-neutrino-watch-speed-claim-baffles-cern-theoryfest.html