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In particle physics, the Higgs mechanism is the process that gives mass to elementary particles. The particles gain mass by interacting with the Higgs field that permeates all space. More precisely, the Higgs mechanism endows gauge bosons in a gauge theory with mass through absorption of Nambu–Goldstone bosons arising in spontaneous symmetry breaking.

The simplest implementation of the mechanism adds an extra Higgs field to the gauge theory. The spontaneous symmetry breaking of the underlying local symmetry triggers conversion of components of this Higgs field to Goldstone bosons which interact with (at least some of) the other fields in the theory, so as to produce mass terms for (at least some of) the gauge bosons. This mechanism may also leave behind elementary scalar (spin-0) particles, known as Higgs bosons.

In the standard model, the phrase "Higgs mechanism" refers specifically to the generation of masses for the W^±, and Z weak gauge bosons through electroweak symmetry breaking.^[1] Although the evidence for the electroweak Higgs mechanism is overwhelming, experiments have yet to discover the single Higgs boson predicted by the standard model. The Large Hadron Collider at CERN is currently searching for Higgs bosons, and attempting to understand the electroweak Higgs mechanism.

The mechanism was proposed in 1962 by Philip Warren Anderson. The relativistic model was developed in 1964 by three independent groups: Robert Brout and Francois Englert; Peter Higgs; and Gerald Guralnik, C. R. Hagen, and Tom Kibble.

Standard model[link]

The Higgs mechanism was incorporated into modern particle physics by Steven Weinberg and Abdus Salam, and is an essential part of the standard model.

In the standard model, at temperatures high enough so that electroweak symmetry is unbroken, all elementary particles are massless. At a critical temperature the Higgs field becomes tachyonic, the symmetry is spontaneously broken by condensation, and the W and Z bosons acquire masses. (EWSB, ElectroWeak Symmetry Breaking, is an abbreviation used for this.)

Fermions, such as the leptons and quarks in the Standard Model, can also acquire mass as a result of their interaction with the Higgs field, but not in the same way as the gauge bosons.

Structure of the Higgs field[link]

In the standard model, the Higgs field is an SU(2) doublet, a complex spinor with four real components (or equivalently with two complex components). Its (weak hypercharge) U(1) charge is 1. That means that it transforms as a spinor under SU(2). Under U(1) rotations, it is multiplied by a phase, which thus mixes the real and imaginary parts of the complex spinor into each other—so this is not the same as two complex spinors mixing under U(1) (which would have eight real components between them), but instead is the spinor representation of the group U(2).

The Higgs field, through the interactions specified (summarized, represented, or even simulated) by its potential, induces spontaneous breaking of three out of the four generators ("directions") of the gauge group SU(2)×U(1): three out of its four components would ordinarily amount to Goldstone bosons, if they were not coupled to gauge fields. However, after symmetry breaking, these three of the four degrees of freedom in the Higgs field mix with the W and Z bosons, and are only observable as spin components of these bosons, which are now massive; while the one remaining degree of freedom becomes the Higgs boson—a new scalar particle.

Part that remains massless[link]

The gauge group of the electroweak part of the standard model is SU(2) × U(1). The group SU(2) is all 2-by-2 unitary matrices, all the orthonormal changes of coordinates in a complex two dimensional vector space.

Rotating the coordinates so that the second basis vector points in the direction of the Higgs boson makes the vacuum expectation value of H the spinor (0,v). The generators for rotations about the x, y, and z axes are by half the Pauli matrices Failed to parse (Missing texvc executable; please see math/README to configure.): \sigma_x, \sigma_y, \sigma_z , so that a rotation of angle θ about the z-axis takes the vacuum to:

Failed to parse (Missing texvc executable; please see math/README to configure.): (0, v e^{\frac{-i}{2} \theta})\,

While the T_x and T_y generators mix up the top and bottom components of the spinor, the T_z rotations only multiply each by opposite phases. This phase can be undone by a U(1) rotation of angle ½θ. Consequently, under both an SU(2) T_z-rotation and a U(1) rotation by an amount ½θ, the vacuum is invariant.

This combination of generators:

Failed to parse (Missing texvc executable; please see math/README to configure.): Q = T_z + \frac{Y}{2}

defines the unbroken part of the gauge group, where T_z is the generator of rotations around the z-axis in the SU(2) and Y is the hypercharge generator of the U(1). This combination of generators (a z rotation in the SU(2) and a simultaneous U(1) rotation by half the angle) preserves the vacuum, and defines the unbroken gauge group in the standard model, namely the electric charge group. The part of the gauge field in this direction stays massless, and amounts to the physical photon.

Consequences for fermions[link]

In spite of the introduction of spontaneous symmetry-breaking, also for fermions the mass terms oppose the chiral gauge invariance. Therefore, also for these fields the mass terms should always be replaced by a gauge-invariant "Higgs" mechanism. An obvious possibility is some kind of "Yukawa coupling" (see below) between the fermion field ψ and the Higgs field Φ, with unknown couplings Failed to parse (Missing texvc executable; please see math/README to configure.): G_{\psi} , which after symmetry-breaking (more precisely: after expansion of the Lagrange density around a suitable ground state) again results in the original mass terms, which are now, however (i.e. by introduction of the Higgs field) written in a gauge-invariant way. The Lagrange density for the "Yukawa"-interaction of a fermion field 'ψ' and the Higgs field 'Φ' is

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathcal{L}_{\mathrm{Fermion}}(\phi , A, \psi ) = \overline{\psi} \gamma^{\mu} D_{\mu} \psi + G_{\psi} \overline{\psi} \phi \psi \,,

where again the gauge field A only enters Failed to parse (Missing texvc executable; please see math/README to configure.): D_\mu

(i.e., it is only indirectly visible). The quantities Failed to parse (Missing texvc executable; please see math/README to configure.): \gamma^{\mu}

are the Dirac matrices, and Failed to parse (Missing texvc executable; please see math/README to configure.): G_{\psi}

is the already-mentioned "Yukawa"-coupling parameter. Already now the mass-generation follows the same principle as above, namely from the existence of a finite expectation value Failed to parse (Missing texvc executable; please see math/README to configure.): |\langle\phi\rangle |

, as described above. Again, this is crucial for the existence of the property "mass".

History of research[link]

Background[link]

Spontaneous symmetry breaking offered a framework to introduce bosons into relativistic quantum field theories. However, according to Goldstone's theorem, these bosons should be massless.^[2] The only observed particles which could be approximately interpreted as Goldstone bosons were the pions, which Yoichiro Nambu related to chiral symmetry breaking.

A similar problem arises with Yang–Mills theory (also known as nonabelian gauge theory), which predicts massless spin-1 gauge bosons. Massless weakly interacting gauge bosons lead to long-range forces, which are only observed for electromagnetism and the corresponding massless photon. Gauge theories of the weak force needed a way to describe massive gauge bosons in order to be consistent.

Discovery[link]

Five of the six 2010 APS Sakurai Prize Winners- (L to R) Kibble, Guralnik, Hagen, Englert, and Brout

Number six: P. Higgs 2009

Wikinews has related news: Prospective Nobel Prize for Higgs boson work disputed

The Higgs mechanism is also called the Brout–Englert–Higgs mechanism, or Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism,^[3] or Anderson–Higgs mechanism. The mechanism was proposed in 1962 by Philip Warren Anderson,^[4] who discussed its consequences for particle physics but did not work out an explicit relativistic model. The relativistic model was developed in 1964 by Peter Higgs,^[5] and independently by Robert Brout and Francois Englert,^[6] and Gerald Guralnik, C. R. Hagen, and Tom Kibble,^[7] who worked out the results by the spring of 1963.^[8] The mechanism is closely analogous to phenomena previously discovered by Yoichiro Nambu involving the "vacuum structure" of quantum fields in superconductivity.^[9] A similar but distinct effect, known as the Stueckelberg mechanism, had previously been studied by Ernst Stueckelberg. These physicists discovered that when a gauge theory is combined with an additional field breaking spontaneously the symmetry group, the gauge bosons can consistently acquire a finite mass. In spite of the large values involved (see below) this permits a gauge theory description of the weak force, which was independently developed by Steven Weinberg and Abdus Salam in 1967. Higgs's original article presenting the model was rejected by Physics Letters. When revising the article before resubmitting it to Physical Review Letters, he added a sentence at the end,^[10] mentioning that it implies the existence of one or more new, massive scalar bosons, which do not form complete representations of the symmetry group; these are the Higgs bosons.

The three papers by Brout and Englert; Higgs; and Guralnik, Hagen, and Kibble were each recognized as "milestone letters" by Physical Review Letters in 2008.^[11] While each of these seminal papers took similar approaches, the contributions and differences among the 1964 PRL symmetry breaking papers are noteworthy. All six physicists were jointly awarded the 2010 J. J. Sakurai Prize for Theoretical Particle Physics for this work.^[12]

Benjamin W. Lee is often credited with first naming the "Higgs-like" mechanism, although there is debate around when this first occurred.^[13][14][15] One of the first times the Higgs name appeared in print was in 1972 when Gerardus 't Hooft and Martinus J. G. Veltman referred to it as the "Higgs-Kibble mechanism" in their Nobel winning paper.^[16][17]

Examples[link]

The Higgs mechanism occurs whenever a charged field has a vacuum expectation value. In the nonrelativistic context, this is the Landau model of a charged Bose-Einstein condensate, also known as a superconductor. In the relativistic condensate, the condensate is a scalar field, and is relativistically invariant.

Landau model[link]

The Higgs mechanism is a type of superconductivity which occurs in the vacuum. It occurs when all of space is filled with a sea of particles which are charged, or, in field language, when a charged field has a nonzero vacuum expectation value. Interaction with the quantum fluid filling the space prevents certain forces from propagating over long distances (as it does in a superconducting medium, e.g. in the Ginzburg–Landau theory).

A superconductor expels all magnetic fields from its interior, a phenomenon known as the Meissner effect. This was mysterious for a long time, because it implies that electromagnetic forces somehow become short-range inside the superconductor. Contrast this with the behavior of an ordinary metal. In a metal, the conductivity shields electric fields by rearranging charges on the surface until the total field cancels in the interior. But magnetic fields can penetrate to any distance, and if a magnetic monopole (an isolated magnetic pole) is surrounded by a metal the field can escape without collimating into a string. In a superconductor, however, electric charges move with no dissipation, and this allows for permanent surface currents, not just surface charges. When magnetic fields are introduced at the boundary of a superconductor, they produce surface currents which exactly neutralize them. The Meissner effect is due to currents in a thin surface layer, whose thickness, the London penetration depth, can be calculated from a simple model (the Ginzburg–Landau theory).

This simple model treats superconductivity as a charged Bose–Einstein condensate. Suppose that a superconductor contains bosons with charge q. The wavefunction of the bosons can be described by introducing a quantum field, ψ, which obeys the Schrödinger equation as a field equation (in units where Failed to parse (Missing texvc executable; please see math/README to configure.): \hbar , the Planck quantum divided by 2π, is replaced by 1):

Failed to parse (Missing texvc executable; please see math/README to configure.): i{\partial \over \partial t} \psi = {(\nabla - iqA)^2 \over 2m} \psi

The operator ψ(x) annihilates a boson at the point x, while its adjoint Failed to parse (Missing texvc executable; please see math/README to configure.): \psi^\dagger

creates a new boson at the same point. The wavefunction of the Bose–Einstein condensate is then the expectation value ψ of ψ(x), which is a classical function that obeys the same equation. The interpretation of the expectation value is that it is the phase that one should give to a newly created boson so that it will coherently superpose with all the other bosons already in the condensate.

When there is a charged condensate, the electromagnetic interactions are screened. To see this, consider the effect of a gauge transformation on the field. A gauge transformation rotates the phase of the condensate by an amount which changes from point to point, and shifts the vector potential by a gradient.

Failed to parse (Missing texvc executable; please see math/README to configure.): \psi \rightarrow e^{iq\phi(x)} \psi

Failed to parse (Missing texvc executable; please see math/README to configure.): A \rightarrow A + \nabla \phi

When there is no condensate, this transformation only changes the definition of the phase of ψ at every point. But when there is a condensate, the phase of the condensate defines a preferred choice of phase.

The condensate wave function can be written as

Failed to parse (Missing texvc executable; please see math/README to configure.): \psi(x) = \rho(x)\, e^{i\theta(x)},

where ρ is real amplitude, which determines the local density of the condensate. If the condensate were neutral, the flow would be along the gradients of θ, the direction in which the phase of the Schrödinger field changes. If the phase θ changes slowly, the flow is slow and has very little energy. But now θ can be made equal to zero just by making a gauge transformation to rotate the phase of the field.

The energy of slow changes of phase can be calculated from the Schrödinger kinetic energy,

Failed to parse (Missing texvc executable; please see math/README to configure.): H= {1\over 2m} |{(qA+\nabla )\psi|^2},

and taking the density of the condensate ρ to be constant,

Failed to parse (Missing texvc executable; please see math/README to configure.): H \approx {\rho^2 \over 2m} (qA + \nabla \theta)^2.

Fixing the choice of gauge so that the condensate has the same phase everywhere, the electromagnetic field energy has an extra term,

Failed to parse (Missing texvc executable; please see math/README to configure.): {q^2 \rho^2 \over 2m} A^2.

When this term is present, electromagnetic interactions become short-ranged. Every field mode, no matter how long the wavelength, oscillates with a nonzero frequency. The lowest frequency can be read off from the energy of a long wavelength A mode,

Failed to parse (Missing texvc executable; please see math/README to configure.): E\approx {{\dot A}^2\over 2} + {q^2 \rho^2 \over 2m} A^2.

This is a harmonic oscillator with frequency:

Failed to parse (Missing texvc executable; please see math/README to configure.): \sqrt{\frac{1}{m} q^2 \rho^2}.

The quantity |ψ|² (=ρ²) is the density of the condensate of superconducting particles.

In an actual superconductor, the charged particles are electrons, which are fermions not bosons. So in order to have superconductivity, the electrons need to somehow bind into Cooper pairs. The charge of the condensate q is therefore twice the electron charge e. The pairing in a normal superconductor is due to lattice vibrations, and is in fact very weak; this means that the pairs are very loosely bound. The description of a Bose–Einstein condensate of loosely bound pairs is actually more difficult than the description of a condensate of elementary particles, and was only worked out in 1957 by Bardeen, Cooper and Schrieffer in the famous BCS theory.

Abelian Higgs mechanism[link]

Gauge invariance means that certain transformations of the gauge field do not change the energy at all. If an arbitrary gradient is added to A, the energy of the field is exactly the same. This makes it difficult to add a mass term, because a mass term tends to push the field toward the value zero. But the zero value of the vector potential is not a gauge invariant idea. What is zero in one gauge is nonzero in another.

So in order to give mass to a gauge theory, the gauge invariance must be broken by a condensate. The condensate will then define a preferred phase, and the phase of the condensate will define the zero value of the field in a gauge invariant way. The gauge invariant definition is that a gauge field is zero when the phase change along any path from parallel transport is equal to the phase difference in the condensate wavefunction.

The condensate value is described by a quantum field with an expectation value, just as in the Landau–Ginzburg model.

In order for the phase of the vacuum to define a gauge, the field must have a phase (also referred to as 'to be charged'). In order for a scalar field Φ to have a phase, it must be complex, or (equivalently) it should contain two fields with a symmetry which rotates them into each other. The vector potential changes the phase of the quanta produced by the field when they move from point to point. In terms of fields, it defines how much to rotate the real and imaginary parts of the fields into each other when comparing field values at nearby points.

The only renormalizable model where a complex scalar field Φ acquires a nonzero value is the Mexican-hat model, where the field energy has a minimum away from zero.

Failed to parse (Missing texvc executable; please see math/README to configure.): S(\phi ) = \int {1\over 2} |\partial \phi|^2 - \lambda\cdot (|\phi|^2 - \Phi^2)^2

This defines the following Hamiltonian:

Failed to parse (Missing texvc executable; please see math/README to configure.): H(\phi ) = {1\over 2} |\dot\phi|^2 + |\nabla \phi|^2 + V(|\phi|)

The first term is the kinetic energy of the field. The second term is the extra potential energy when the field varies from point to point. The third term is the potential energy when the field has any given magnitude.

This potential energy V(z, Φ) = λ • (|z|² - Φ²)² has a graph which looks like a Mexican hat, which gives the model its name. In particular, the minimum energy value is not at z = 0, but on the circle of points where the magnitude of z is Φ.

Higgs potential V. For a fixed value of λ the potential is presented against the real and imaginary parts of Φ. The Mexican-hat or champagne-bottle profile at the ground should be noted.

When the field Φ(x) is not coupled to electromagnetism, the Mexican-hat potential has flat directions. Starting in any one of the circle of vacua and changing the phase of the field from point to point costs very little energy. Mathematically, if

Failed to parse (Missing texvc executable; please see math/README to configure.): \phi(x) = \Phi e^{i\theta(x)}

with a constant prefactor, then the action for the field θ(x), i.e., the "phase" of the Higgs field Φ(x), has only derivative terms. This is not a surprise. Adding a constant to θ(x) is a symmetry of the original theory, so different values of θ(x) cannot have different energies. This is an example of Goldstone's theorem: spontaneously broken continuous symmetries normally produce massless excitations.

The Abelian Higgs model is the Mexican-hat model coupled to electromagnetism:

Failed to parse (Missing texvc executable; please see math/README to configure.): S(\phi ,A) = \int {1\over 4} F^{\mu\nu} F_{\mu\nu} + |(\partial - i q A)\phi|^2 + \lambda\cdot (|\phi|^2 - \Phi^2)^2.

The classical vacuum is again at the minimum of the potential, where the magnitude of the complex field φ is equal to Φ. But now the phase of the field is arbitrary, because gauge transformations change it. This means that the field θ(x) can be set to zero by a gauge transformation, and does not represent any actual degrees of freedom at all.

Furthermore, choosing a gauge where the phase of the vacuum is fixed, the potential energy for fluctuations of the vector field is nonzero. So in the abelian Higgs model, the gauge field acquires a mass. To calculate the magnitude of the mass, consider a constant value of the vector potential A in the x direction in the gauge where the condensate has constant phase. This is the same as a sinusoidally varying condensate in the gauge where the vector potential is zero. In the gauge where A is zero, the potential energy density in the condensate is the scalar gradient energy:

Failed to parse (Missing texvc executable; please see math/README to configure.): E = {1 \over 2} \left |\partial \left (\Phi e^{iqAx} \right ) \right |^2 = {1 \over 2} q^2\Phi^2 A^2

And this energy is the same as a mass term ½m²A² where m = qΦ.

Nonabelian Higgs mechanism[link]

The Nonabelian Higgs model has the following action:

Failed to parse (Missing texvc executable; please see math/README to configure.): S(\phi ,\mathbf A) = \int {1\over 4g^2} \mathop{\textrm{tr}}(F^{\mu\nu}F_{\mu\nu}) + |D\phi|^2 + V(|\phi|)

where now the nonabelian field A is contained in D and in the tensor components Failed to parse (Missing texvc executable; please see math/README to configure.): F^{\mu \nu}

and Failed to parse (Missing texvc executable; please see math/README to configure.): F_{\mu \nu}
(the relation between A and those components is well-known from the Yang–Mills theory).

It is exactly analogous to the Abelian Higgs model. Now the field φ is in a representation of the gauge group, and the gauge covariant derivative is defined by the rate of change of the field minus the rate of change from parallel transport using the gauge field A as a connection.

Failed to parse (Missing texvc executable; please see math/README to configure.): D\phi = \partial \phi - i A^k t_k \phi

Again, the expectation value of Φ defines a preferred gauge where the vacuum is constant, and fixing this gauge, fluctuations in the gauge field A come with a nonzero energy cost.

Depending on the representation of the scalar field, not every gauge field acquires a mass. A simple example is in the renormalizable version of an early electroweak model due to Julian Schwinger. In this model, the gauge group is SO(3) (or SU(2)--- there are no spinor representations in the model), and the gauge invariance is broken down to U(1) or SO(2) at long distances. To make a consistent renormalizable version using the Higgs mechanism, introduce a scalar field φ^a which transforms as a vector (a triplet) of SO(3). If this field has a vacuum expectation value, it points in some direction in field space. Without loss of generality, one can choose the z-axis in field space to be the direction that φ is pointing, and then the vacuum expectation value of φ is (0, 0, A), where A is a constant with dimensions of mass (Failed to parse (Missing texvc executable; please see math/README to configure.): c = \hbar = 1 ).

Rotations around the z-axis form a U(1) subgroup of SO(3) which preserves the vacuum expectation value of φ, and this is the unbroken gauge group. Rotations around the x and y-axis do not preserve the vacuum, and the components of the SO(3) gauge field which generate these rotations become massive vector mesons. There are two massive W mesons in the Schwinger model, with a mass set by the mass scale A, and one massless U(1) gauge boson, similar to the photon.

The Schwinger model predicts magnetic monopoles at the electroweak unification scale, and does not predict the Z meson. It doesn't break electroweak symmetry properly as in nature. But historically, a model similar to this (but not using the Higgs mechanism) was the first in which the weak force and the electromagnetic force were unified.

Affine Higgs mechanism[link]

This unreferenced section requires citations to ensure verifiability.

Ernst Stueckelberg discovered a version of the Higgs mechanism by analyzing the theory of quantum electrodynamics with a massive photon. Stueckelberg's model is a limit of the regular Mexican hat Abelian Higgs model, where the vacuum expectation value H goes to infinity and the charge of the Higgs field goes to zero in such a way that their product stays fixed. The mass of the Higgs boson is proportional to H, so the Higgs boson becomes infinitely massive and disappears. The vector meson mass is equal to the product eH, and stays finite.

The interpretation is that when a U(1) gauge field does not require quantized charges, it is possible to keep only the angular part of the Higgs oscillations, and discard the radial part. The angular part of the Higgs field θ has the following gauge transformation law:

Failed to parse (Missing texvc executable; please see math/README to configure.): \theta \rightarrow \theta + e\alpha\,

Failed to parse (Missing texvc executable; please see math/README to configure.): A \rightarrow A + \alpha \,

The gauge covariant derivative for the angle (which is actually gauge invariant) is:

Failed to parse (Missing texvc executable; please see math/README to configure.): D\theta = \partial \theta - e A\,

In order to keep θ fluctuations finite and nonzero in this limit, θ should be rescaled by H, so that its kinetic term in the action stays normalized. The action for the theta field is read off from the Mexican hat action by substituting Failed to parse (Missing texvc executable; please see math/README to configure.): \phi \;=\; He^{\frac{1}{H}i\theta} .

Failed to parse (Missing texvc executable; please see math/README to configure.): S = \int {1 \over 4}F^2 + {1 \over 2}(D\theta)^2 = \int {1 \over 4}F^2 + {1 \over 2}(\partial \theta - He A)^2 = \int {1 \over 4}F^2 + {1 \over 2}(\partial \theta - m A)^2

since eH is the gauge boson mass. By making a gauge transformation to set θ = 0, the gauge freedom in the action is eliminated, and the action becomes that of a massive vector field:

Failed to parse (Missing texvc executable; please see math/README to configure.): S= \int {1 \over 4} F^2 + {1 \over 2} m^2 A^2\,

To have arbitrarily small charges requires that the U(1) is not the circle of unit complex numbers under multiplication, but the real numbers R under addition, which is only different in the global topology. Such a U(1) group is non-compact. The field θ transforms as an affine representation of the gauge group. Among the allowed gauge groups, only non-compact U(1) admits affine representations, and the U(1) of electromagnetism is experimentally known to be compact, since charge quantization holds to extremely high accuracy.

The Higgs condensate in this model has infinitesimal charge, so interactions with the Higgs boson do not violate charge conservation. The theory of quantum electrodynamics with a massive photon is still a renormalizable theory, one in which electric charge is still conserved, but magnetic monopoles are not allowed. For nonabelian gauge theory, there is no affine limit, and the Higgs oscillations cannot be too much more massive than the vectors.

See also[link]

• 1964 PRL symmetry breaking papers
• Electromagnetic mass
• Ginzburg–Landau theory
• Goldstone boson
• Higgs boson
• Higgs bundle
• QCD vacuum
• Quantum triviality
• Symmetry breaking
• Tachyonic field
• Tachyon condensation
• Top quark condensate
• Yang–Mills–Higgs equations

References[link]

Further reading[link]

• Schumm, Bruce A. (2004) Deep Down Things. Johns Hopkins Univ. Press. Chpt. 9.

External links[link]

• Guralnik, G.S.; Hagen, C.R.; Kibble, T.W.B. (1964). "Global Conservation Laws and Massless Particles". Physical Review Letters 13 (20): 585–87. Bibcode 1964PhRvL..13..585G. DOI:10.1103/PhysRevLett.13.585. 
• Mark D. Roberts (1999) "A Generalized Higgs Model."
• Sakurai Prize Videos
• In CERN Courier, Steven Weinberg reflects on spontaneous symmetry breaking
• Steven Weinberg on LHC
• Steven Weinberg Praises Teams for Higgs Boson Theory.
• Physical Review Letters – 50th Anniversary Milestone Papers.
• Imperial College London on PRL 50th Anniversary Milestone Papers.
• "Introducing the little Higgs." Physics World.
• Englert-Brout-Higgs-Guralnik-Hagen-Kibble Mechanism on Scholarpedia.
• History of Englert-Brout-Higgs-Guralnik-Hagen-Kibble Mechanism on Scholarpedia.
• The Hunt for the Higgs at Tevatron
• The Mystery of Empty Space on YouTube. A lecture with UCSD physicist Kim Griest (43 minutes).

Stephen Hawking
Stephen Hawking at NASA, 1980s
Born	Stephen William Hawking (1942-01-08) 8 January 1942 (age 70) Oxford, England, United Kingdom
Residence	United Kingdom
Nationality	British
Fields	Mathematics Theoretical physics
Institutions	Cambridge University California Institute of Technology Perimeter Institute for Theoretical Physics
Alma mater	Oxford University Cambridge University
Doctoral advisor	Dennis Sciama
Other academic advisors	Robert Berman
Known for	Black holes Theoretical cosmology Quantum gravity Hawking radiation
Influences	Dikran Tahta
Notable awards	Albert Einstein Award (1978) Wolf Prize (1988) Prince of Asturias Award (1989) Copley Medal (2006) Presidential Medal of Freedom (2009)
Spouse	Jane Hawking (m. 1965–1991, divorced) Elaine Mason (m. 1995–2006, divorced)

Stephen William Hawking, CH, CBE, FRS, FRSA (born 8 January 1942) is a British theoretical physicist, cosmologist, and author. His key scientific works to date have included providing, with Roger Penrose, theorems regarding gravitational singularities in the framework of general relativity, and the theoretical prediction that black holes should emit radiation, which is today known as Hawking radiation (or sometimes as Bekenstein–Hawking radiation).

He is an Honorary Fellow of the Royal Society of Arts, a lifetime member of the Pontifical Academy of Sciences, and in 2009 was awarded the Presidential Medal of Freedom, the highest civilian award in the United States. Hawking was the Lucasian Professor of Mathematics at the University of Cambridge between 1979 and 2009. Subsequently, he became research director at the university's Centre for Theoretical Cosmology.

Hawking has a motor neurone disease related to amyotrophic lateral sclerosis, a condition that has progressed over the years. He is now almost completely paralysed and communicates through a speech generating device. He has been married twice and has three children. Hawking has achieved success with works of popular science in which he discusses his own theories and cosmology in general; these include A Brief History of Time, which stayed on the British Sunday Times best-sellers list for a record-breaking 237 weeks.

Early life and education[link]

Stephen Hawking was born on 8 January 1942 to Frank Hawking, a research biologist, and Isobel Hawking.^[1] He has two younger sisters, Philippa and Mary, and an adopted brother, Edward.^[2] Although Hawking's parents were living in North London, he was born in Oxford as his parents felt it was safer to stay in Oxford for the later stages of the pregnancy. (London was under attack at the time by the Luftwaffe).^[3]

When his father became head of the division of parasitology at the National Institute for Medical Research^[1] in 1950, Hawking and his family moved to St Albans, Hertfordshire.^[3] Hawking attended St Albans High School for Girls from 1950 to 1953 (At that time, boys could attend the girls' school until the age of 10).^[2] and then from the age of 11, he attended St Albans School, where he was a good, but not exceptional, student.^[3]

Inspired by his mathematics teacher, Hawking originally wanted to study the subject at university. However, Hawking's father wanted him to apply to University College, Oxford, where his father had attended. As University College did not have a mathematics fellow at that time, applications were not accepted from students who wished to study that discipline. Hawking therefore applied to read natural sciences with an emphasis in Physics. He was accepted and gained a scholarship.^[3] While at Oxford, he coxed a rowing team, which, he stated, helped relieve his immense boredom at the university.^[4] His physics tutor, Robert Berman, later said "It was only necessary for him to know that something could be done, and he could do it without looking to see how other people did it. ... his mind was completely different from all of his contemporaries".^[3]

Hawking's unimpressive study habits resulted in a final examination score on the borderline between first and second class honours, making an "oral examination" necessary.^[3] Berman said of the oral examination: "And of course the examiners then were intelligent enough to realize they were talking to someone far more clever than most of themselves".^[3] After receiving his B.A. degree at Oxford in 1962, he left for graduate work at Trinity Hall, Cambridge.^[3]

Career[link]

1962-1975[link]

Hawking in Cambridge

Hawking with string theorists David Gross and Edward Witten

Although Hawking started developing symptoms of amyotrophic lateral sclerosis as soon as he arrived at Cambridge and did not distinguish himself in his first two years at Cambridge, he returned to working on his PhD after the disease had stabilised and with the help of his doctoral tutor, Dennis William Sciama.^[5]

When Hawking began his graduate studies In the 1960s, there was much debate in the physics community about the opposing theories of the creation of the universe: big bang, and steady state.^[5] Hawking and his Cambridge friend and colleague, Roger Penrose, showed in 1970 that if the universe obeys general relativity and if the universe fits any of the Friedmann models, then the universe must have begun as a singularity.^[6] This work showed that, far from being mathematical curiosities which appear only in special cases, singularities are a fairly generic feature of general relativity.^[7]

Hawking's work with Brandon Carter, Werner Israel and D. Robinson, strongly supported John Wheeler's no-hair theorem – that any black hole is fully described by the three properties of mass, angular momentum, and electric charge.^[8] With Bardeen and Carter, he proposed the four laws of black hole mechanics, drawing an analogy with thermodynamics.^[9] In 1974, he calculated that black holes should thermally create and emit subatomic particles, known today as Bekenstein-Hawking radiation, until they exhaust their energy and evaporate.^[6]

Hawking was elected one of the youngest Fellows of the Royal Society in 1974,^[10] and in the same year he accepted the Sherman Fairchild Distinguished Scholar visiting professorship at the California Institute of Technology (Caltech) to work with his friend, Kip Thorne, who was a faculty member there.^[11] He continues to have ties with Caltech, spending a month each year there since 1992.^[12]

1975-present[link]

The mid to late 1970s were a period of growing fame and success for Hawking, his work was now much talked about, he was appearing in popular television documentaries and in 1979 he was made the Lucasian Professor of Mathematics at the University of Cambridge, a post he held for 30 years until his retirement in 2009.^[13][14] Hawking's inaugural lecture as Lucasian Professor of Mathematics had the title "Is the end in sight for Theoretical Physics" and promoted the idea that supergravity would help resolve many of the outstanding problems physicists were studying. ^[14]

In collaboration with Jim Hartle, Hawking developed a model in which the universe had no boundary in space-time, replacing the initial singularity of the classical Big Bang models with a region akin to the North Pole: one cannot travel north of the North Pole, as there is no boundary.^[15] While originally the no-boundary proposal predicted a closed universe, discussions with Neil Turok led to the realisation that the no-boundary proposal is also consistent with a universe which is not closed.^[16]

Along with Thomas Hertog at CERN, in 2006 Hawking proposed a theory of "top-down cosmology", which says that the universe had no unique initial state, and therefore it is inappropriate for physicists to attempt to formulate a theory that predicts the universe's current configuration from one particular initial state.^[17] Top-down cosmology posits that in some sense, the present "selects" the past from a superposition of many possible histories. In doing so, the theory suggests a possible resolution of the fine-tuning question.^[18]

Thorne–Hawking–Preskill bet[link]

U.S. President Barack Obama talks with Stephen Hawking in the Blue Room of the White House before a ceremony presenting him and 15 others the Presidential Medal of Freedom on 12 August 2009. The Medal of Freedom is the United States' highest civilian honour.

In 1997 Hawking made a public scientific wager with Thorne and John Preskill of Caltech concerning the black hole information paradox.^[19] Thorne and Hawking argued that since general relativity made it impossible for black holes to radiate, and lose information, the mass-energy and information carried by Hawking Radiation must be "new", and must not originate from inside the black hole event horizon. Since this contradicted the idea under quantum mechanics of microcausality, quantum mechanics would need to be rewritten. Preskill argued the opposite, that since quantum mechanics suggests that the information emitted by a black hole relates to information that fell in at an earlier time, the view of black holes given by general relativity must be modified in some way.^[20] The winner of the bet was to receive an encyclopedia of the loser's choice, from which information may be accessed.^[19]

In 2004, Hawking announced that he was conceding the bet, and that he now believed that black hole horizons should fluctuate and leak information, in doing so providing Preskill with a copy of Total Baseball.^[19] Comparing the useless information obtainable from a black hole to "burning an encyclopedia", Hawking commented, "I gave John an encyclopedia of baseball, but maybe I should just have given him the ashes".^[19]

Recognition[link]

Acclaim[link]

On 19 December 2007, a statue of Hawking by artist Ian Walters was unveiled at the Centre for Theoretical Cosmology, University of Cambridge.^[21] The Stephen W. Hawking Science Museum in San Salvador, El Salvador, is named in honour of Stephen Hawking, citing his scientific distinction and perseverance in dealing with adversity.^[22] The Stephen Hawking Building in Cambridge opened on 17 April 2007. The building belongs to Gonville and Caius College and is used as an undergraduate accommodation and conference facility.^[23]

Awards and honours[link]

Personal life[link]

Stephen Hawking being presented by his daughter Lucy Hawking at the lecture he gave for NASA's 50th anniversary

Hawking has stated that, having been diagnosed with ALS during an early stage of his graduate work, he did not see much point in obtaining a doctorate if he were to die soon after. Hawking later said that the real turning point was his 1965 marriage to Jane Wilde, a language student.^[29] Jane cared for him until 1990 when the couple separated.^[1] They had three children: Robert, Lucy, and Timothy.^[1] Hawking married his personal care assistant, Elaine Mason, in 1995; ^[1] the couple divorced In October 2006^[30] amid claims by former nurses that she had abused him.^[31] In 1999, Jane Hawking published a memoir, Music to Move the Stars, detailing the marriage and its breakdown; in 2010 she published a revised version, Travelling to Infinity, My Life with Stephen.^[32]

Hawking supports the children's charity SOS Children's Villages UK^[33] and has stated that his view on how to live life is to "seek the greatest value of our action".^[34] He strongly opposed the Iraq War, calling it "a war crime" and "based on two lies" at a demonstration in Trafalgar Square, where he participated in a public reading of the names of Iraqi war victims.^[35][36]

Hawking has named his secondary school mathematics teacher Dikran Tahta as an inspiration.^[37] He maintains his connection with St Albans School, giving his name to one of the four houses and to an extracurricular science lecture series.^[38]

Illness[link]

Hawking on 5 May 2006, during the press conference at the Bibliothèque nationale de France to inaugurate the Laboratory of Astronomy and Particles in Paris and the French release of his work God Created the Integers

Hawking has a motor neurone disease that is related to amyotrophic lateral sclerosis (ALS), a condition that has progressed over the years. He is now almost completely paralysed and communicates through a speech generating device. Hawking's illness has progressed more slowly than typical cases of ALS: survival for more than 10 years after diagnosis is uncommon.^[39][40]

Symptoms of the disorder first appeared while he was enrolled at University of Cambridge; he lost his balance and fell down a flight of stairs, hitting his head.^[4] The diagnosis of motor neurone disease came when Hawking was 21, shortly before his first marriage, and doctors said he would not survive more than two or three years. By 1974, he was unable to feed himself or get out of bed. His speech became slurred so that he could be understood only by people who knew him well. During a visit to CERN in Geneva in 1985, Hawking contracted pneumonia, which in his condition was life-threatening as it further restricted his already limited respiratory capacity. He had an emergency tracheotomy, and as a result lost what remained of his ability to speak.^[41] A speech generating device was built in Cambridge, using software from an American company, that enabled Hawking to write onto a computer with small movements of his body, and then have a voice synthesiser speak what he typed.^[42]

The particular voice synthesiser hardware he uses, which has an American English accent, is no longer being produced. Asked why he has still kept the same voice after so many years, Hawking stated that he has not heard a voice he likes better and that he identifies with it even though the synthesiser is both large and fragile by current standards. Although a mid-2009 corporate press release said that he had chosen NeoSpeech's VoiceText speech synthesiser as his new voice,^[43] a 30 December 2011 interview with Hawking's technician indicates that Hawking is still using an older synthesiser containing a card "which dates back to the 1980s" and that any upgrade would have to be the same voice, otherwise "it wouldn't be Stephen's voice any more".^[44]

For lectures and media appearances, Hawking appears to speak fluently through his synthesiser; however when preparing answers his system produces words at a rate of about one per minute.^[44] Hawking's setup uses a predictive text entry system, which requires only the first few characters in order to auto-complete the word, but as he is only able to use his cheek for data entry, constructing complete sentences takes time.^[44] During a TED Conference talk, it took him seven minutes to provide a brief answer to a question.^[45]

He describes himself as lucky, despite his disease. Its slow progression has allowed him time to make influential discoveries and has not hindered him from having, in his own words, "a very attractive family".^[42]

In popular culture[link]

Hawking in 2007, experiencing weightlessness

Hawking has played himself on numerous television shows and has been portrayed in many more. He has played himself on a Red Dwarf anniversary special, played a hologram of himself on the episode "Descent" of Star Trek: The Next Generation,^[46] and appeared on the Discovery Channel special Alien Planet.^[47] He has also played himself in several episodes of The Simpsons and Futurama, and has had an action figure made of his Simpsons likeness.^[48] The 2004 BBC4 TV film Hawking dealt with his early life and the onset of his illness. He was portrayed by Benedict Cumberbatch. In 2008, Hawking was the subject of and featured in the documentary series Stephen Hawking, Master of the Universe for Channel 4. In September 2008, Hawking presided over the unveiling of the 'Chronophage' (time-eating) Corpus Clock at Corpus Christi College Cambridge.^[49] His actual synthesiser voice was used on parts of the Pink Floyd song "Keep Talking" from the 1994 album The Division Bell, as well as on Turbonegro's "Intro: The Party Zone" on their 2005 album Party Animals, Wolfsheim's "Kein Zurück (Oliver Pinelli Mix)". On 5 April 2012 he appeared as a guest star in an episode of The Big Bang Theory.^[50]

Space and spaceflight[link]

At the celebration of his 65th birthday on 8 January 2007, Hawking announced his plan to take a zero-gravity flight that year, with an intention to later take a sub-orbital spaceflight. Billionaire Richard Branson pledged to pay all expenses for a future flight on Virgin Galactic's space service, costing an estimated £100,000.^[51] Stephen Hawking's zero-gravity flight in a "Vomit Comet" of Zero Gravity Corporation, during which he experienced weightlessness eight times, took place on 26 April 2007.^[52] He became the first quadriplegic to float in zero gravity. The fee is normally US$3,750 for 10 to 15 plunges, but Hawking was not required to pay. Hawking was quoted before the flight saying:

Many people have asked me why I am taking this flight. I am doing it for many reasons. First of all, I believe that life on Earth is at an ever-increasing risk of being wiped out by a disaster such as sudden nuclear war, a genetically engineered virus, or other dangers. I think the human race has no future if it doesn't go into space. I therefore want to encourage public interest in space.^[53]

In an interview with The Daily Telegraph, he suggested that space was the Earth's long term hope.^[54] He continued this theme at a 2008 Charlie Rose interview.^[55]

Hawking has indicated that he is almost certain that alien life exists in other parts of the universe, "To my mathematical brain, the numbers alone make thinking about aliens perfectly rational. The real challenge is to work out what aliens might actually be like".^[56] He believes alien life not only certainly exists on planets but perhaps even in other places, like within stars or even floating in outer space. He has also warned that a few of these species might be intelligent and threaten Earth.^[57] "If aliens visit us, the outcome would be much as when Columbus landed in America, which didn't turn out well for the Native Americans," he said.^[56] He has advocated that, rather than try to establish contact, humans should try to avoid contact with alien life forms.^[56] At a George Washington University lecture in honour of NASA's fiftieth anniversary, Hawking discussed the existence of extraterrestrial life, believing that "primitive life is very common and intelligent life is fairly rare".^[58]

Religious views[link]

In his early work, Hawking spoke of God in a metaphorical sense, such as in A Brief History of Time: "If we discover a complete theory, it would be the ultimate triumph of human reason – for then we should know the mind of God."^[59] In the same book he suggested the existence of God was unnecessary to explain the origin of the universe.^[60] In the Channel 4 documentary Genius of Britain, in his 2010 book The Grand Design, and in interviews with the Telegraph, Hawking has clarified that he does not believe in a "personal" God.^[61] Hawking writes, "The question is: is the way the universe began chosen by God for reasons we can't understand, or was it determined by a law of science? I believe the second."^[61] He adds, "Because there is a law such as gravity, the Universe can and will create itself from nothing."^[62]

His ex-wife, Jane, has described him as an atheist.^[63] Hawking has stated that he is "not religious in the normal sense" and he believes that "the universe is governed by the laws of science. The laws may have been decreed by God, but God does not intervene to break the laws."^[64] In an interview published in The Guardian newspaper, Hawking regarded the concept of Heaven as a myth, believing that there is "no heaven or afterlife" and that such a notion was a "fairy story for people afraid of the dark."^[59][65] Hawking contrasted religion and science in 2010, saying: "There is a fundamental difference between religion, which is based on authority, [and] science, which is based on observation and reason. Science will win because it works."^[66]

Philosophical views[link]

At Google’s Zeitgeist Conference in 2011, Hawking said that "philosophy is dead." He believes philosophers "have not kept up with modern developments in science" and that scientists "have become the bearers of the torch of discovery in our quest for knowledge.” He said that philosophical problems can be answered by science, particularly new scientific theories which "lead us to a new and very different picture of the universe and our place in it”.^[67]

Publications[link]

Hawking's first popular science book, A Brief History of Time, was published on 1 April 1988. It stayed on the British Sunday Times best-sellers list for a record-breaking 237 weeks.^[68] A Brief History of Time was followed by The Universe in a Nutshell (2001). A collection of essays titled Black Holes and Baby Universes (1993) was also popular. His book, A Briefer History of Time (2005), co-written by Leonard Mlodinow, updated his earlier works to make them accessible to a wider audience. In 2007 Hawking and his daughter, Lucy Hawking, published George's Secret Key to the Universe, a children's book focusing on science that Lucy Hawking described as "a bit like Harry Potter but without the magic."^[69]

Popular[link]

• A Brief History of Time, (1988)
• Black Holes and Baby Universes and Other Essays, (1994)
• The Universe in a Nutshell, (2001)
• On The Shoulders of Giants. The Great Works of Physics and Astronomy, (2002)
• A Briefer History of Time, (2005)
• God Created the Integers: The Mathematical Breakthroughs That Changed History, (2005)^[70]
• The Grand Design, (2010)^[70]

Children's fiction[link]

These are co-written with his daughter Lucy.

• George's Secret Key to the Universe, (2007)
• George's Cosmic Treasure Hunt, (2009)^[70]
• George and the Big Bang, (2011)

Films and series[link]

• A Brief History of Time (1991)
• Stephen Hawking's Universe (1997)
• Horizon: The Hawking Paradox^[71] (2005)
• Masters of Science Fiction (2007)
• Stephen Hawking: Master of the Universe^[72] (2008)
• Into the Universe with Stephen Hawking^[73] (2010)
• Brave New World with Stephen Hawking

See also[link]

• Many-worlds interpretation, or flexiverse
• Gibbons–Hawking ansatz
• Gibbons–Hawking space

References[link]

Bibliography[link]

Further reading[link]

External links[link]

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• Stephen Hawking's web site
• Appearances on C-SPAN
• Stephen Hawking at the Internet Movie Database
• Stephen Hawking at the Mathematics Genealogy Project
• Works by or about Stephen Hawking in libraries (WorldCat catalog)
• Stephen Hawking collected news and commentary at The Guardian
• Stephen Hawking collected news and commentary at The New York Times
• Archival material relating to Stephen Hawking listed at the UK National Register of Archives
• Portraits of Stephen William Hawking at the National Portrait Gallery, London