Gerard 't Hooft

Gerardus (Gerard) 't Hooft (Dutch: [ˈɣeːrɑrt ət ˈɦoːft]; born July 5, 1946) is a Dutch theoretical physicist and professor at Utrecht University, the Netherlands. He shared the 1999 Nobel Prize in Physics with his thesis advisor Martinus J. G. Veltman "for elucidating the quantum structure of electroweak interactions".

His work concentrates on gauge theory, black holes, quantum gravity and fundamental aspects of quantum mechanics. His contributions to physics include a proof that gauge theories are renormalizable, dimensional regularization and the holographic principle.

Gerard 't Hooft
Gerard 't Hooft
November 2008
BornJuly 5, 1946 (age 72)
Den Helder, Netherlands
Alma materUtrecht University
Known forQuantum field theory, Quantum gravity, 't Hooft–Polyakov monopole, 't Hooft symbol, 't Hooft operator, Holographic principle, Renormalization, Dimensional regularization
AwardsHeineman Prize (1979)
Wolf Prize (1981)
Lorentz Medal (1986)
Spinoza Prize (1995)
Franklin Medal (1995)
Nobel Prize in Physics (1999)
Lomonosov Gold Medal (2010)
Scientific career
FieldsTheoretical physics
InstitutionsUtrecht University
Doctoral advisorMartinus J. G. Veltman
Doctoral studentsRobbert Dijkgraaf
Herman Verlinde

Personal life

He is married to Albertha Schik (Betteke) and has two daughters, Saskia and Ellen.


Early life

Gerard 't Hooft was born in Den Helder on July 5, 1946, but grew up in The Hague, the seat of government of the Netherlands. He was the middle child of a family of three. He comes from a family of scholars. His grandmother was a sister of Nobel prize laureate Frits Zernike, and was married to Pieter Nicolaas van Kampen, who was a well-known professor of zoology at Leiden University. His uncle Nico van Kampen was an (emeritus) professor of theoretical physics at Utrecht University, and while his mother did not opt for a scientific career because of her gender,[1] she did marry a maritime engineer.[1] Following his family's footsteps, he showed interest in science at an early age. When his primary school teacher asked him what he wanted to be when he grew up, he boldly declared, "a man who knows everything."[1]

After primary school Gerard attended the Dalton Lyceum, a school that applied the ideas of the Dalton Plan, an educational method that suited him well. He easily passed his science and mathematics courses, but struggled with his language courses. Nonetheless, he passed his classes in English, French, German, classical Greek and Latin. At the age of sixteen he earned a silver medal in the second Dutch Math Olympiad. [1]


After Gerard 't Hooft passed his high school exams in 1964, he enrolled in the physics program at Utrecht University. He opted for Utrecht instead of the much closer Leiden, because his uncle was a professor there and he wanted to attend his lectures. Because he was so focused on science, his father insisted that he join the Utrechtsch Studenten Corps, an elite student association, in the hope that he would do something else besides studying. This worked to some extent, during his studies he was a coxswain with their rowing club "Triton" and organized a national congress for science students with their science discussion club "Christiaan Huygens".

In the course of his studies he decided he wanted to go into what he perceived as the heart of theoretical physics, elementary particles. His uncle had grown to dislike the subject and in particular its practitioners, so when it became time to write his 'doctoraalscriptie' (Dutch equivalent of a master's thesis) in 1968, 't Hooft turned to the newly appointed professor Martinus Veltman, who specialized in Yang–Mills theory, a relatively fringe subject at the time because it was thought that these could not be renormalized. His assignment was to study the Adler–Bell–Jackiw anomaly, a mismatch in the theory of the decay of neutral pions; formal arguments forbid the decay into photons, whereas practical calculations and experiments showed that this was the primary form of decay. The resolution of the problem was completely unknown at the time, and 't Hooft was unable to provide one.

In 1969, 't Hooft started on his doctoral research with Martinus Veltman as his advisor. He would work on the same subject Veltman was working on, the renormalization of Yang–Mills theories. In 1971 his first paper was published.[2] In it he showed how to renormalize massless Yang–Mills fields, and was able to derive relations between amplitudes, which would be generalized by Andrei Slavnov and John C. Taylor, and become known as the Slavnov–Taylor identities.

The world took little notice, but Veltman was excited because he saw that the problem he had been working on was solved. A period of intense collaboration followed in which they developed the technique of dimensional regularization. Soon 't Hooft's second paper was ready to be published,[3] in which he showed that Yang–Mills theories with massive fields due to spontaneous symmetry breaking could be renormalized. This paper earned them worldwide recognition, and would ultimately earn the pair the 1999 Nobel Prize in Physics.

These two papers formed the basis of 't Hooft's dissertation, The Renormalization procedure for Yang–Mills Fields, and he obtained his PhD degree in 1972. In the same year he married his wife, Albertha A. Schik, a student of medicine in Utrecht.[1]


Gerardus t' Hooft at Harvard
Gerard 't Hooft at Harvard

After obtaining his doctorate 't Hooft went to CERN in Geneva, where he had a fellowship. He further refined his methods for Yang–Mills theories with Veltman (who went back to Geneva). In this time he became interested in the possibility that the strong interaction could be described as a massless Yang–Mills theory, i.e. one of a type that he had just proved to be renormalizable and hence be susceptible to detailed calculation and comparison with experiment.

According to 't Hooft's calculations, this type of theory possessed just the right kind of scaling properties (asymptotic freedom) that this theory should have according to deep inelastic scattering experiments. This was contrary to popular perception of Yang–Mills theories at the time, that like gravitation and electrodynamics, their intensity should decrease with increasing distance between the interacting particles; such conventional behaviour with distance was unable to explain the results of deep inelastic scattering, whereas 't Hooft's calculations could.

When 't Hooft mentioned his results at a small conference at Marseilles in 1972, Kurt Symanzik urged him to publish this result;[1] but 't Hooft did not, and the result was eventually rediscovered and published by Hugh David Politzer, David Gross, and Frank Wilczek in 1973, which led to their earning the 2004 Nobel Prize in Physics.[4][5]

In 1974, 't Hooft returned to Utrecht where he became assistant professor. In 1976, he was invited for a guest position at Stanford and a position at Harvard as Morris Loeb lecturer. His eldest daughter, Saskia Anne, was born in Boston, while his second daughter, Ellen Marga, was born in 1978 after he returned to Utrecht, where he was made full professor.[1]

In 2007 't Hooft became editor-in-chief for Foundations of Physics, where he sought to distance the journal from the controversy of ECE theory.[6] 't Hooft held the position until 2016.

On July 1, 2011 he was appointed Distinguished professor by Utrecht University.[7]


In 1999 't Hooft shared the Nobel prize in Physics with his thesis adviser Veltman for "elucidating the quantum structure of the electroweak interactions in physics".[8] Before that time his work had already been recognized by other notable awards. In 1981, he was awarded the Wolf Prize,[9] possibly the most prestigious prize in physics after the Nobel prize. Five years later he received the Lorentz Medal, awarded every four years in recognition of the most important contributions in theoretical physics.[10] In 1995, he was one of the first recipients of the Spinozapremie, the highest award available to scientists in the Netherlands.[11] In the same year he was also honoured with a Franklin Medal.[12]

Since his Nobel Prize, 't Hooft has received a slew of awards, honorary doctorates and honorary professorships.[13] He was knighted commander in the Order of the Netherlands Lion, and officer in the French Legion of Honor. The asteroid 9491 Thooft has been named in his honor,[14] and he has written a constitution for its future inhabitants.[15]

He is a member of the Royal Netherlands Academy of Arts and Sciences (KNAW) since 1982,[16] where he was made academy professor in 2003.[17] He is also a foreign member of many other science academies, including the French Académie des Sciences, the American National Academy of Sciences and American Academy of Arts and Sciences and the Britain and Ireland based Institute of Physics.[13]


't Hooft's research interest can be divided in three main directions: 'gauge theories in elementary particle physics', 'quantum gravity and black holes', and 'foundational aspects of quantum mechanics'.[18]

Gauge theories in elementary particle physics

't Hooft is most famous for his contributions to the development of gauge theories in particle physics. The best known of these is the proof in his PhD thesis that Yang–Mills theories are renormalizable, for which he shared the 1999 Nobel Prize in Physics. For this proof he introduced (with his adviser Veltman) the technique of dimensional regularization.

After his PhD, he became interested in the role of gauge theories in the strong interaction,[1] the leading theory of which is called quantum chromodynamics or QCD. Much of his research focused on the problem of color confinement in QCD, i.e. the observational fact that only color neutral particles are observed at low energies. This led him to the discovery that SU(N) gauge theories simplify in the large N limit,[19] a fact which has proved important in the examination of the conjectured correspondence between string theories in an Anti-de Sitter space and conformal field theories in one lower dimension. By solving the theory in one space and one time dimension, 't Hooft was able to derive a formula for the masses of mesons.[20]

He also studied the role of so-called instanton contributions in QCD. His calculation showed that these contributions lead to an interaction between light quarks at low energies not present in the normal theory.[21] Studying instanton solutions of Yang–Mills theories, 't Hooft discovered that spontaneously breaking a theory with SU(N) symmetry to a U(1) symmetry will lead to the existence of magnetic monopoles.[22] These monopoles are called 't Hooft–Polyakov monopoles, after Alexander Polyakov, who independently obtained the same result.[23]

As another piece in the color confinement puzzle 't Hooft introduced 't Hooft operators, which are the magnetic dual of Wilson loops.[24] Using these operators he was able to classify different phases of QCD, which form the basis of the QCD phase diagram.

In 1986, he was finally able to show that instanton contributions solve the Adler–Bell–Jackiw anomaly, the topic of his master's thesis.[25]

Quantum gravity and black holes

When Veltman and 't Hooft moved to CERN after 't Hooft obtained his PhD, Veltman's attention was drawn to the possibility of using their dimensional regularization techniques to the problem of quantizing gravity. Although it was known that perturbative quantum gravity was not completely renormalizible, they felt important lessons were to be learned by studying the formal renormalization of the theory order by order. This work would be continued by Stanley Deser and another PhD student of Veltman, Peter van Nieuwenhuizen, who later found patterns in the renormalization counter terms, which led to the discovery of supergravity.[1]

In the 1980s, 't Hooft's attention was drawn to the subject of gravity in 3 spacetime dimensions. Together with Deser and Jackiw he published an article in 1984 describing the dynamics of flat space where the only local degrees of freedom were propagating point defects.[26] His attention returned to this model at various points in time, showing that Gott pairs would not cause causality violating timelike loops,[27] and showing how the model could be quantized.[28] More recently he proposed generalizing this piecewise flat model of gravity to 4 spacetime dimensions.[29]

With Stephen Hawking's discovery of Hawking radiation of black holes, it appeared that the evaporation of these objects violated a fundamental property of quantum mechanics, unitarity. 'T Hooft refused to accept this problem, known as the black hole information paradox, and assumed that this must be the result of the semi-classical treatment of Hawking, and that it should not appear in a full theory of quantum gravity. He proposed that it might be possible to study some of the properties of such a theory, by assuming that such a theory was unitary.

Using this approach he has argued that near a black hole, quantum fields could be described by a theory in a lower dimension.[30] This led to the introduction of the holographic principle by him and Leonard Susskind.[31]

Fundamental aspects of quantum mechanics

't Hooft has "deviating views on the physical interpretation of quantum theory".[18] He believes that there could be a deterministic explanation underlying quantum mechanics.[32] Using a speculative model he has argued that such a theory could avoid the usual Bell inequality arguments that would disallow such a local hidden variable theory.[33] In 2016 he published a book length exposition of his ideas[34] which, according to 't Hooft, has encountered mixed reactions.[35]


Popular publications

See also


  1. ^ a b c d e f g h i 't Hooft, G. (1999). "Gerardus 't Hooft — Autobiography". Nobel web. Retrieved 2010-10-06.
  2. ^ 't Hooft, G. . (1971). "Renormalization of massless Yang-Mills fields". Nuclear Physics B. 33 (1): 173–177. Bibcode:1971NuPhB..33..173T. doi:10.1016/0550-3213(71)90395-6.
  3. ^ 't Hooft, G. . (1971). "Renormalizable Lagrangians for massive Yang-Mills fields". Nuclear Physics B. 35 (1): 167–188. Bibcode:1971NuPhB..35..167T. doi:10.1016/0550-3213(71)90139-8. hdl:1874/4733.
  4. ^ "The Nobel Prize in Physics 2004". Nobel Web. 2004. Retrieved 2010-10-24.
  5. ^ Politzer, H. David (2004). "The Dilemma of Attribution" (PDF). Nobel Web. Retrieved 2010-10-24.
  6. ^ ’t Hooft, Gerard (2007). "Editorial note". Foundations of Physics. 38 (1): 1–2. Bibcode:2008FoPh...38....1T. doi:10.1007/s10701-007-9187-8. ISSN 0015-9018.
  7. ^ "Prof. dr. Gerard 't Hooft has been appointed Distinguished Professor". Utrecht University. Archived from the original on 2012-04-19. Retrieved 2012-04-19.
  8. ^ "The Nobel Prize in Physics 1999". Nobel web.
  9. ^ "The 1981 Wolf Foundation Prize in Physics". Wolf Foundation. Archived from the original on 2011-09-27.
  10. ^ "Lorentz medal". Leiden University.
  11. ^ "NWO Spinoza Prize 1995". Netherlands Organisation for Scientific Research. 3 September 2014. Retrieved 2016-01-30.
  12. ^ "Franklin Laureate Database". The Franklin Institute. Archived from the original on 2010-06-01.
  13. ^ a b "Curriculum Vitae Gerard 't Hooft". G. 't Hooft.
  14. ^ "JPL Small-Body Database Browser". NASA.
  15. ^ "9491 THOOFT — Constitution and Bylaws". G. 't Hooft.
  16. ^ "Gerard 't Hooft". Royal Netherlands Academy of Arts and Sciences. Retrieved 2015-07-17.
  17. ^ "Academy Professorships Programme - 2003". Royal Netherlands Academy of Arts and Sciences. Archived from the original on 2010-11-24.
  18. ^ a b 't Hooft, G. "Gerard 't Hooft". Retrieved 2010-10-24.
  19. ^ 't Hooft, G. (1974). "A planar diagram theory for strong interactions". Nuclear Physics B. 72 (3): 461–470. Bibcode:1974NuPhB..72..461T. doi:10.1016/0550-3213(74)90154-0.
  20. ^ 't Hooft, G. (1974). "A two-dimensional model for mesons". Nuclear Physics B. 75 (3): 461–863. Bibcode:1974NuPhB..75..461T. doi:10.1016/0550-3213(74)90088-1.
  21. ^ 't Hooft, G. (1976). "Computation of the quantum effects due to a four-dimensional pseudoparticle". Physical Review D. 14 (12): 3432–3450. Bibcode:1976PhRvD..14.3432T. doi:10.1103/PhysRevD.14.3432.
  22. ^ 't Hooft, G. (1974). "Magnetic monopoles in unified gauge theories". Nuclear Physics B. 79 (2): 276–284. Bibcode:1974NuPhB..79..276T. doi:10.1016/0550-3213(74)90486-6. hdl:1874/4686.
  23. ^ Polyakov, A.M. (1974). "Particle spectrum in quantum field theory". Journal of Experimental and Theoretical Physics Letters. 20: 194. Bibcode:1974JETPL..20..194P.
  24. ^ 't Hooft, G. (1978). "On the phase transition towards permanent quark confinement". Nuclear Physics B. 138 (1): 1–2. Bibcode:1978NuPhB.138....1T. doi:10.1016/0550-3213(78)90153-0.
  25. ^ 't Hooft, G. (1986). "How instantons solve the U(1) problem". Physics Reports. 142 (6): 357–712. Bibcode:1986PhR...142..357T. doi:10.1016/0370-1573(86)90117-1.
  26. ^ Deser, S.; Jackiw, R.; 't Hooft, G. (1984). "Three-dimensional Einstein gravity: Dynamics of flat space". Annals of Physics. 152 (1): 220. Bibcode:1984AnPhy.152..220D. doi:10.1016/0003-4916(84)90085-X. hdl:1874/4772.
  27. ^ 't Hooft, G. (1992). "Causality in (2+1)-dimensional gravity". Classical and Quantum Gravity. 9 (5): 1335–1348. Bibcode:1992CQGra...9.1335T. doi:10.1088/0264-9381/9/5/015. hdl:1874/4627.
  28. ^ 't Hooft, G. (1993). "Canonical quantization of gravitating point particles in 2+1 dimensions". Classical and Quantum Gravity. 10 (8): 1653–1664. arXiv:gr-qc/9305008. Bibcode:1993CQGra..10.1653T. doi:10.1088/0264-9381/10/8/022.
  29. ^ 't Hooft, G. (2008). "A Locally Finite Model for Gravity". Foundations of Physics. 38 (8): 733–757. arXiv:0804.0328. Bibcode:2008FoPh...38..733T. doi:10.1007/s10701-008-9231-3.
  30. ^ Stephens, C. R.; 't Hooft, G.; Whiting, B. F. (1994). "Black hole evaporation without information loss". Classical and Quantum Gravity. 11 (3): 621–648. arXiv:gr-qc/9310006. Bibcode:1994CQGra..11..621S. doi:10.1088/0264-9381/11/3/014.
  31. ^ Susskind, L. (1995). "The world as a hologram". Journal of Mathematical Physics. 36 (11): 6377–6396. arXiv:hep-th/9409089. Bibcode:1995JMP....36.6377S. doi:10.1063/1.531249.
  32. ^ 't Hooft, G. (2007). "A mathematical theory for deterministic quantum mechanics". Journal of Physics: Conference Series. 67 (1): 012015. arXiv:quant-ph/0604008. Bibcode:2007JPhCS..67a2015T. doi:10.1088/1742-6596/67/1/012015.
  33. ^ Gerard 't Hooft (2009). "Entangled quantum states in a local deterministic theory". arXiv:0908.3408 [quant-ph].
  34. ^ Gerard 't Hooft, 2016, The Cellular Automaton Interpretation of Quantum Mechanics, Springer International Publishing, DOI 10.1007/978-3-319-41285-6, Open access-[1]
  35. ^ Baldwin, Melinda (2017-07-11). "Q&A: Gerard 't Hooft on the future of quantum mechanics". Physics Today. doi:10.1063/pt.6.4.20170711a.

External links

't Hooft operator

In theoretical physics, a 't Hooft operator, introduced by Gerard 't Hooft in the 1978 paper "On the phase transition towards permanent quark confinement", is a dual version of the Wilson loop in which the electromagnetic potential A is replaced by its electromagnetic dual Amag, where the exterior derivative of A is equal to the Hodge dual of the exterior derivative of Amag. In d spacetime dimensions, Amag is a (d-3)-form and so the 't Hooft operator is the integral of Amag over a (d-3)-dimensional surface.

't Hooft–Polyakov monopole

In theoretical physics, the 't Hooft–Polyakov monopole is a topological soliton similar to the Dirac monopole but without any singularities. It arises in the case of a Yang–Mills theory with a gauge group G, coupled to a Higgs field which spontaneously breaks it down to a smaller group H via the Higgs mechanism. It was first found independently by Gerard 't Hooft and Alexander Polyakov.

Unlike the Dirac monopole, the 't Hooft–Polyakov monopole is a smooth solution with a finite total energy. The solution is localized around . Very far from the origin, the gauge group G is broken to H, and the 't Hooft–Polyakov monopole reduces to the Dirac monopole.

However, at the origin itself, the G gauge symmetry is unbroken and the solution is non-singular also near the origin. The Higgs field

is proportional to

where the adjoint indices are identified with the three-dimensional spatial indices. The gauge field at infinity is such that the Higgs field's dependence on the angular directions is pure gauge. The precise configuration for the Higgs field and the gauge field near the origin is such that it satisfies the full Yang–Mills–Higgs equations of motion.

AdS/CFT correspondence

In theoretical physics, the anti-de Sitter/conformal field theory correspondence, sometimes called Maldacena duality or gauge/gravity duality, is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter spaces (AdS) which are used in theories of quantum gravity, formulated in terms of string theory or M-theory. On the other side of the correspondence are conformal field theories (CFT) which are quantum field theories, including theories similar to the Yang–Mills theories that describe elementary particles.

The duality represents a major advance in our understanding of string theory and quantum gravity. This is because it provides a non-perturbative formulation of string theory with certain boundary conditions and because it is the most successful realization of the holographic principle, an idea in quantum gravity originally proposed by Gerard 't Hooft and promoted by Leonard Susskind.

It also provides a powerful toolkit for studying strongly coupled quantum field theories. Much of the usefulness of the duality results from the fact that it is a strong-weak duality: when the fields of the quantum field theory are strongly interacting, the ones in the gravitational theory are weakly interacting and thus more mathematically tractable. This fact has been used to study many aspects of nuclear and condensed matter physics by translating problems in those subjects into more mathematically tractable problems in string theory.

The AdS/CFT correspondence was first proposed by Juan Maldacena in late 1997. Important aspects of the correspondence were elaborated in articles by Steven Gubser, Igor Klebanov, and Alexander Polyakov, and by Edward Witten. By 2015, Maldacena's article had over 10,000 citations, becoming the most highly cited article in the field of high energy physics.

Anomaly matching condition

In quantum field theory, the anomaly matching condition by Gerard 't Hooft states that the calculation of any chiral anomaly for the flavor symmetry must not depend on what scale is chosen for the calculation if it is done by using the degrees of freedom of the theory at some energy scale. It is also known as the 't Hooft condition and the 't Hooft UV-IR anomaly matching condition.

Asymptotic freedom

In particle physics, asymptotic freedom is a property of some gauge theories that causes interactions between particles to become asymptotically weaker as the energy scale increases and the corresponding length scale decreases.

Asymptotic freedom is a feature of quantum chromodynamics (QCD), the quantum field theory of the strong interaction between quarks and gluons, the fundamental constituents of nuclear matter. Quarks interact weakly at high energies, allowing perturbative calculations. At low energies the interaction becomes strong, leading to the confinement of quarks and gluons within composite hadrons.

The asymptotic freedom of QCD was discovered in 1973 by David Gross and Frank Wilczek,

and independently by David Politzer in the same year.

For this work all three shared the 2004 Nobel Prize in Physics.

Black hole complementarity

Black hole complementarity is a conjectured solution to the black hole information paradox, proposed by Leonard Susskind, Larus Thorlacius, and Gerard 't Hooft.

Einstein–Cartan–Evans theory

Einstein–Cartan–Evans theory or ECE theory was an attempted unified theory of physics proposed by the Welsh chemist and physicist Myron Wyn Evans (born May 26, 1950), which claimed to unify general relativity, quantum mechanics and electromagnetism. The hypothesis was largely published in the journal Foundations of Physics Letters between 2003 and 2005. Several of Evans' central claims were later shown to be mathematically incorrect and, in 2008, the new editor of Foundations of Physics, Nobel laureate Gerard 't Hooft, published an editorial note effectively retracting the journal's support for the hypothesis.

Foundations of Physics

Foundations of Physics is a monthly journal "devoted to the conceptual bases and fundamental theories of modern physics and cosmology, emphasizing the logical, methodological, and philosophical premises of modern physical theories and procedures". The journal publishes results and observations based on fundamental questions from all fields of physics, including: quantum mechanics, quantum field theory, special relativity, general relativity, string theory, M-theory, cosmology, thermodynamics, statistical physics, and quantum gravity

Foundations of Physics has been published since 1970. Its founding editors were Henry Margenau and Wolfgang Yourgrau. The 1999 Nobel laureate Gerard 't Hooft was editor-in-chief from January 2007. At that stage, it absorbed the associated journal for shorter submissions Foundations of Physics Letters, which had been edited by Alwyn Van der Merwe since its foundation in 1988. Past editorial board members (which include several Nobel laureates) include Louis de Broglie, Robert H. Dicke, Murray Gell-Mann, Abdus Salam, Ilya Prigogine and Nathan Rosen. Carlo Rovelli was announced as new editor-in-chief in February 2016.

Franklin Medal

The Franklin Medal was a science award presented from 1915 through 1997 by the Franklin Institute located in Philadelphia, Pennsylvania, U.S. It was founded in 1914 by Samuel Insull.

The Franklin Medal was the most prestigious of the various awards presented by the Franklin Institute. Together with other historical awards, it was merged into the Benjamin Franklin Medal, initiated in 1998.

Holographic principle

The holographic principle is a principle of string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region—preferably a light-like boundary like a gravitational horizon. First proposed by Gerard 't Hooft, it was given a precise string-theory interpretation by Leonard Susskind who combined his ideas with previous ones of 't Hooft and Charles Thorn. As pointed out by Raphael Bousso, Thorn observed in 1978 that string theory admits a lower-dimensional description in which gravity emerges from it in what would now be called a holographic way. The prime example of holography is the AdS/CFT correspondence.

The holographic principle was inspired by black hole thermodynamics, which conjectures that the maximal entropy in any region scales with the radius squared, and not cubed as might be expected. In the case of a black hole, the insight was that the informational content of all the objects that have fallen into the hole might be entirely contained in surface fluctuations of the event horizon. The holographic principle resolves the black hole information paradox within the framework of string theory.

However, there exist classical solutions to the Einstein equations that allow values of the entropy larger than those allowed by an area law, hence in principle larger than those of a black hole. These are the so-called "Wheeler's bags of gold". The existence of such solutions conflicts with the holographic interpretation, and their effects in a quantum theory of gravity including the holographic principle are not yet fully understood.


Hooft or 't Hooft is a Dutch surname meaning "(the) head" (hoofd in modern Dutch). Notable people with the surname include:

HooftCornelis Hooft (1547–1627), Dutch statesman, father of P.C. Hooft

Pieter Corneliszoon Hooft (1581–1647), Dutch historian, poet and playwright

Henrick Hooft (1617–1678), Dutch mayor of Amsterdam,

Catharina Hooft (1618–1691), woman of the Dutch Golden Age

Hendrik Daniëlsz Hooft (1716–1794), Dutch politician during the Patriottentijd

Jeannette Hooft (1888–1939), Dutch traveler, mountaineer, and writer't Hooft / Visser 't Hooft / Van 't HooftWillem Visser 't Hooft (1900–1985), Dutch theologian and the first secretary general of the World Council of Churches

Haas Visser 't Hooft (1905–1977), Dutch field hockey player

Francis van 't Hooft (born 1940), Dutch field hockey player

Gerard 't Hooft (born 1946), Dutch theoretical physicist and Nobel Laureate

Jotie T'Hooft (1956–1977), Flemish Belgian neo-romantic poetVan Hooft / Van der HooftHans van Hooft (born 1941), Dutch Socialist Party politician

Anna Van Hooft (born 1980s), Canadian actress

Elroy van der Hooft (born 1990), Dutch football forward

Jeffrey Epstein VI Foundation

The Jeffrey Epstein VI Foundation is a private science foundation known for establishing the Program for Evolutionary Dynamics at Harvard University with a $30 million gift to the university. The Program for Evolutionary Dynamics is considered the first department of its kind to study the evolution of molecular biology with the sole use of mathematics. It is also one of the first departments to develop mathematical models of how human cancer cells evolve as well as infectious bacteria and viruses such as HIV.The Jeffrey Epstein VI Foundation is also known for giving one of the largest amounts of funding to individual scientists around the world. Since 2000, the Foundation has given approximately $200 million a year to many notable scientists including Stephen Hawking, Marvin Minsky, Eric Lander, Lawrence Krauss, Lee Smolin, George Church, Ben Goertzel, Kip Thorne, Gregory Benford and numerous Nobel laureates, including, Gerald Edelman, Murray Gell-Mann, Gerard ’t Hooft, David Gross, and Frank Wilczek. Over the years, the Foundation has convened many of these scientists in conferences to discuss the consensus on fundamental science topics such as gravity, global threats to the Earth and language.

Little Saint James, U.S. Virgin Islands

Little Saint James is an island of the United States Virgin Islands, located off the east end of St. Thomas.

The island is privately owned by American financier and convicted sex offender Jeffrey Epstein. There is a luxury estate on the Island and it is often used for conferences held by the Jeffrey Epstein VI Foundation, which sponsors cutting-edge science and medical research. Recent conferences have included topics such as gravity, language evolution and global threats to the Earth. Many notable scientists have attended the conferences, including Marvin Minsky, Gerard 't Hooft and Stephen Hawking.The island hosts a helipad, a lagoon and cabanas. It also has a library, a Japanese bathhouse, and cinema.

Lorentz Medal

Lorentz Medal is a distinction awarded every four years by the Royal Netherlands Academy of Arts and Sciences. It was established in 1925 on the occasion of the 50th anniversary of the doctorate of Hendrik Lorentz. The medal is given for important contributions to theoretical physics, though in the past there have been some experimentalists among its recipients.Many of the award winners later received a Nobel Prize.

Max Welling

Max Welling (born 1968) is a Dutch computer scientist in machine learning at the University of Amsterdam. In August 2017, the university spin-off, “Scyfer BV”, co-founded by Welling was acquired by Qualcommand he has since then served as a VP Technologies at Qualcomm Netherlands.Welling received his PhD in quantum physics under the supervision of Nobel laureate Gerard 't Hooft (1998) at the Utrecht University. He has published over 250 peer-reviewed articles in machine learning, computer vision, statistics and physics.

Niels Bohr Institute

The Niels Bohr Institute (Danish: Niels Bohr Institutet) is a research institute of the University of Copenhagen. The research of the institute spans astronomy, geophysics, nanotechnology, particle physics, quantum mechanics and biophysics.

Pauli–Villars regularization

In theoretical physics, Pauli–Villars regularization (P–V) is a procedure that isolates divergent terms from finite parts in loop calculations in field theory in order to renormalize the theory. Wolfgang Pauli and Felix Villars published the method in 1949, based on earlier work by Richard Feynman, Ernst Stueckelberg and Dominique Rivier.In this treatment, a divergence arising from a loop integral (such as vacuum polarization or electron self-energy) is modulated by a spectrum of auxiliary particles added to the Lagrangian or propagator. When the masses of the fictitious particles are taken as an infinite limit (i.e., once the regulator is removed) one expects to recover the original theory.

This regulator is gauge invariant due to the auxiliary particles being minimally coupled to the photon field through the gauge covariant derivative. It is not gauge covariant, though, so Pauli–Villars regularization cannot be used in QCD calculations. P–V serves as an alternative to the more favorable dimensional regularization in specific circumstances, such as in chiral phenomena, where a change of dimension alters the properties of the Dirac gamma matrices.

Gerard 't Hooft and Martinus J. G. Veltman invented, in addition to dimensional regularization, the method of unitary regulators, which is a Lagrangian-based Pauli–Villars method with a discrete spectrum of auxiliary masses, using the path-integral formalism.

Slavnov–Taylor identities

In quantum field theory, a Slavnov-Taylor identity is the non-Abelian generalisation of a Ward-Takahashi identity, which in turn is an identity between correlation functions that follows from the global or gauged symmetries of a theory, and which remains valid after renormalization. The identity was originally discovered by Gerard 't Hooft , and it is named after Andrei Slavnov and John C. Taylor who rephrased the identity to hold off the mass shell. .


In quantum mechanics, superdeterminism is a hypothetical class of theories that evade Bell's theorem by virtue of being completely deterministic. It is conceivable that someone could exploit this loophole to construct a local hidden variable theory that reproduces the predictions of quantum mechanics. Superdeterminists do not recognize the existence of genuine chances or possibilities anywhere in the cosmos.

Bell's theorem assumes that the types of measurements performed at each detector can be chosen independently of each other and of the hidden variable being measured. In order for the argument for Bell's inequality to follow, it is necessary to be able to speak meaningfully of what the result of the experiment would have been, had different choices been made. This assumption is called counterfactual definiteness. But in a fully deterministic theory, the measurements the experimenters choose at each detector are predetermined by the laws of physics. It can therefore be argued that it is erroneous to speak of what would have happened had different measurements been chosen; no other measurement choices were physically possible. Since the chosen measurements can be determined in advance, the results at one detector can be affected by the type of measurement done at the other without any need for information to travel faster than the speed of light.

Thus, it is conceivable that freedom of choice has been restricted since the beginning of the universe in the Big Bang, with every future measurement predetermined by correlations established at the Big Bang. This would make superdeterminism untestable, since experimenters would never be able to eliminate correlations that were created at the beginning of the universe: the freedom-of-choice loophole could never be completely eliminated.

In the 1980s, John Bell discussed superdeterminism in a BBC interview:

There is a way to escape the inference of superluminal speeds and spooky action at a distance. But it involves absolute determinism in the universe, the complete absence of free will. Suppose the world is super-deterministic, with not just inanimate nature running on behind-the-scenes clockwork, but with our behavior, including our belief that we are free to choose to do one experiment rather than another, absolutely predetermined, including the "decision" by the experimenter to carry out one set of measurements rather than another, the difficulty disappears. There is no need for a faster than light signal to tell particle A what measurement has been carried out on particle B, because the universe, including particle A, already "knows" what that measurement, and its outcome, will be.

Although he acknowledged the loophole, he also argued that it was implausible. Even if the measurements performed are chosen by deterministic random number generators, the choices can be assumed to be "effectively free for the purpose at hand," because the machine's choice is altered by a large number of very small effects. It is unlikely for the hidden variable to be sensitive to all of the same small influences that the random number generator was.Nobel Prize winner Gerard 't Hooft discussed this loophole with John Bell in the early '80s. "I raised the question: Suppose that also Alice’s and Bob’s decisions have to be seen as not coming out of free will, but being determined by everything in the theory. John said, well, you know, that I have to exclude. If it’s possible, then what I said doesn’t apply. I said, Alice and Bob are making a decision out of a cause. A cause lies in their past and has to be included in the picture."The implications of superdeterminism, if it is true, would bring into question the value of science itself by destroying falsifiability, as Anton Zeilinger has commented:

[W]e always implicitly assume the freedom of the experimentalist... This fundamental assumption is essential to doing science. If this were not true, then, I suggest, it would make no sense at all to ask nature questions in an experiment, since then nature could determine what our questions are, and that could guide our questions such that we arrive at a false picture of nature.

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