# Erik Verlinde

Erik Verlinde | |
---|---|

Erik Verlinde in 2009 | |

Born |
Erik Peter Verlinde 21 January 1962 Woudenberg, Netherlands |

Nationality | Dutch |

Fields | Theoretical physics |

Institutions | |

Alma mater | Utrecht University |

Thesis |
Conformal field theory and its application to strings (1988) |

Doctoral advisor | Bernard de Wit |

Doctoral students | Miranda Cheng |

Known for | Entropic gravity |

Notable awards | Spinoza Prize (2011) |

**Erik Peter Verlinde** (Dutch: [ˈeːrɪk ˈpeːtər vərˈlɪndə]; born 21 January 1962) is a Dutch theoretical physicist and string theorist. He is the identical twin brother of physicist Herman Verlinde. The Verlinde formula, which is important in conformal field theory and topological field theory, is named after him. His research deals with string theory, gravity, black holes and cosmology. Currently, he works at the Institute for Theoretical Physics at the University of Amsterdam.

At a symposium at the Dutch Spinoza-institute on 8 December 2009 he introduced a theory of entropic gravity. In this theory, gravity exists because of a difference in concentration of information in the empty space between two masses and its surroundings; he also extrapolates this to general relativity and quantum mechanics. He said in an interview with the newspaper *de Volkskrant*,^{[1]} "On the smallest level Newton's laws don't apply, but they do for apples and planets. You can compare this to pressure of gas. Molecules themselves don't have any pressure, but a barrel of gas has." It appears that Verlinde's approach to explaining gravity leads naturally to the correct observed strength of dark energy.^{[2]}

## Biography

Erik Verlinde was born in the Dutch village of Woudenberg on 21 January 1962, together with his identical twin brother, Herman Verlinde.^{[3]} He went to school in the nearby city of Utrecht, where he graduated from the gymnasium in 1980.

That fall he began his studies in theoretical physics together with his twin brother at Utrecht University. There he studied with his brother Herman, Robbert Dijkgraaf, and Kareljan Schoutens (now dean of the Faculty of Science at the University of Amsterdam). He wrote his Master's thesis with Nobel Laureate Gerard 't Hooft.^{[3]}

In 1985, Verlinde started work on his PhD at Utrecht University under the formal supervision of Bernard de Wit. He worked together with his twin Herman and Robbert Dijkgraaf, and in practice the trio supervised themselves. The original arrangement was that only one of them would be working on the emerging field of string theory, but in the end all three of them wrote their theses on the subject. In September 1988 he defended his PhD thesis, which included the Verlinde formula.^{[3]}^{[4]}^{[5]}

After his PhD, Verlinde joined the Institute for Advanced Study in Princeton as a postdoctoral fellow. In 1993, he was added to the permanent staff of the theory division of CERN in Geneva. At the age of 34 he was appointed full professor of theoretical physics at Utrecht University. Only a few years later, in 1999, he left for Princeton University to take up a professorial position there. In 2003, he returned to the Netherlands to become a professor in the string theory group led by Robbert Dijkgraaf at the University of Amsterdam.^{[3]}^{[4]}^{[5]}

## Major contributions

Verlinde's main field of research is string theory. Over the years he has introduced a number of results that have become important in the development of the theory, and in the study of pure mathematics.

### Verlinde formula

Verlinde's PhD thesis was titled “Conformal Field Theory Applied to Strings”. In it he investigated conformal field theories in two dimensions and their relation to the description of the world sheet of fundamental strings. As part of the project he extended fusion or Verlinde algebras, describing conformal field theories with a finite number of fields.^{[6]} A main result was an explicit formula for the fusion rules of these algebras, now known as the Verlinde formula. This has proven to be a very non-trivial mathematical result. In Verlinde's original work, the formula followed from mainly physical arguments, but since its introduction many formal mathematical proofs have been provided.^{[7]}

### Witten–Dijkgraaf–Verlinde–Verlinde equation

^{[8]}^{[9]}

### Cardy–Verlinde formula

The Cardy formula is an important result in conformal field theory that allows the calculation of the entropy of a 1+1 dimensional conformal field theory. Using the AdS/CFT correspondence correspondence between conformal field theories and quantum gravity in AntideSitter spaces with one additional dimension, it can be used to calculate the (quantum corrections) to the entropy of black holes in 2+1 dimensions. In 2000, Verlinde extended Cardy's result to conformal field theories of arbitrary dimension,^{[10]}
allowing the calculation of entropy of black holes in any dimension.

### Entropic gravity

In 2009, Verlinde showed that the laws of gravity may be derived by assuming a form of the holographic principle and the laws of thermodynamics.^{[11]} This may imply that gravity is not a true fundamental force of nature (like e.g. electromagnetism), but instead is a consequence of the universe striving to maximize entropy.

### Emergent gravity and the dark universe

On 8 November 2016 Erik Verlinde published his new theory of gravity.^{[12]} In this work, he argues that unlike in anti-de Sitter (AdS) space, holography and the area law do not apply exactly in de Sitter space (which models our universe) because there is an additional entropy associated with the cosmological horizon. If this entropy were evenly distributed throughout space, it would contribute a volume law term to the entropy which becomes dominant at large lengths scales and is related to dark energy. He further argues that this entropy modifies emergent gravity, introducing residual forces when gravity is very weak.^{[13]}
The result provides a candidate explanation for dark matter similar to the Modified Newtonian dynamics proposal and explains the empirical relationship between dark matter and the Hubble constant.

## Awards and honors

In June 2011, the Netherlands Organisation for Scientific Research (NWO) awarded Verlinde the Spinoza Prize, the highest award available to Dutch scientists including a 2.5 million euro grant for future research.^{[14]} The committee cited his work on the Verlinde formula, the Witten–Dijkgraaf–Verlinde–Verlinde equations, the Cardy-Verlinde formula and entropic gravity as the major achievements leading to the award.

## References

- ↑ "De Volkskrant 27 January 2010" (in Dutch). Archived from the original on 11 November 2013. Retrieved 11 September 2011.
- ↑ Koelman, Johannes. "It from bit: how to get rid of dark energy". Retrieved 20 August 2011.
- 1 2 3 4 Verlinde, Erik. "Curriculum Vitae".
*Website of Erik Verlinde*. Archived from the original on 14 July 2014. - 1 2 "Erik Verlinde". NWO.
- 1 2 "Biografie Erik Verlinde". Quantum Universe.
- ↑ Verlinde, Erik (1988). "Fusion Rules and Modular Transformations in 2D Conformal Field Theory".
*Nucl. Phys. B*.**300**. Bibcode:1988NuPhB.300..360V. doi:10.1016/0550-3213(88)90603-7. - ↑ Schottenloher, Martin (2008).
*A Mathematical Introduction to Conformal Field Theory*. Springer. ISBN 9783540686255. - ↑ Witten, Edward (1991). "Two-dimensional gravity and intersection theory on moduli space".
*Surveys Diff. Geom*.**1**: 243–310. Bibcode:1990SDGeo...1..243W. doi:10.4310/SDG.1990.v1.n1.a5. - ↑ Dijkgraaf, Robbert; Verlinde, Herman; Verlinde, Erik (1990). "Topological strings in d < 1".
*Nucl. Phys. B*.**345**: 59–86. Bibcode:1991NuPhB.352...59D. doi:10.1016/0550-3213(91)90129-L. - ↑ Erik, Verlinde (2000). "On the Holographic Principle in a Radiation Dominated Universe". arXiv:hep-th/0008140.
- ↑ E.P. Verlinde. "On the Origin of Gravity and the Laws of Newton".
*JHEP*.**2011**(04): 29. arXiv:1001.0785. Bibcode:2011JHEP...04..029V. doi:10.1007/JHEP04(2011)029. - ↑ New theory of gravity might explain dark matter, E. P. Verlinde, 2016 Nov 8
- ↑ Erik, Verlinde (2016). "Emergent Gravity and the Dark Universe". arXiv:1611.02269.
- ↑ "NWO-Spinoza Laureates 2011". Retrieved 20 August 2011.

## External links

- University of Amsterdam faculty page
- Blog on Verlinde's publication 'On the Origin of Gravity and the Laws of Newton
- Blog discussing Verlinde's holographic derivation of Newtonian gravity
- A Scientist Takes On Gravity
- Scientific publications of Erik Verlinde on INSPIRE-HEP
- It from bit and fit from bit. On the origin and impact of information in the average evolution (Yves Decadt, 2000). Book published in Dutch with English paper summary in The Information Philosopher