A point particle (ideal particle or point-like particle, often spelled pointlike particle) is an idealization of particles heavily used in physics. Its defining feature is that it lacks spatial extension: being zero-dimensional, it does not take up space. A point particle is an appropriate representation of any object whose size, shape, and structure is irrelevant in a given context. For example, from far enough away, an object of any shape will look and behave as a point-like object.

In the theory of gravity, physicists often discuss a point mass, meaning a point particle with a nonzero mass and no other properties or structure. Likewise, in electromagnetism, physicists discuss a point charge, a point particle with a nonzero charge.

Sometimes due to specific combinations of properties extended objects behave as point-like even in their immediate vicinity. For example, spherical objects interacting in 3-dimensional space whose interactions are described by the inverse square law behave in such a way as if all their matter were concentrated in their geometric centers. In Newtonian gravitation and classical electromagnetism, for example, the respective fields outside of a spherical object are identical to those of a point particle of equal charge/mass located at the center of the sphere.

In quantum mechanics, the concept of a point particle is complicated by the Heisenberg uncertainty principle: Even an elementary particle, with no internal structure, occupies a nonzero volume. For example, a 1s electron in a hydrogen atom occupies a volume of ~10^-30 m³. There is nevertheless a distinction between elementary particles such as electrons or quarks, which have no internal structure, versus composite particles such as protons, which do have internal structure: A proton is made of three quarks. Elementary particles are sometimes called "point particles", but this is in a different sense than discussed above. For more details see elementary particle.

Point mass

Point mass (pointlike mass) is an idealistic term used to describe either matter which is infinitely small, or an object which can be thought of as infinitely small. This concept in terms of size is similar to that of point particles, however unlike point particles the object need only be considered infinitely small.

Application

Physics

A common use for point mass lies in the analysis of the gravitational force fields. When analyzing the gravitational forces in a system, it becomes impossible to account for every unit of mass individually. When none of the objects in the system have overlapping center of mass circumferences, it is possible to consider the object as a zero-dimensional point mass.

Mathematics

A point mass in statistics is a discontinuous segment in a probability distribution. To calculate such point mass, an integration is carried out over the entire range of the random variable, on the probability distribution of the continuous part. After equating this integral to 1, the point mass can be found by further calculation.

Point charge

A point charge is an idealized model of a particle which has an electric charge. A point charge is an electric charge at a mathematical point with no dimensions.

The fundamental equation of electrostatics is Coulomb's law, which describes the electric force between two point charges. The electric field associated with a classical point charge increases to infinity as the distance from the point charge decreases towards zero making energy (thus mass) of point charge infinite. In quantum electrodynamics, developed in part by Richard Feynman, the mathematical method of renormalization eliminates the infinite divergence of the point charge.

Earnshaw's theorem states that a collection of point charges cannot be maintained in an equilibrium configuration solely by the electrostatic interaction of the charges.

In quantum mechanics

In quantum mechanics, there is a distinction between an elementary particle (also called "point particle") and a composite particle. An elementary particle, such as an electron, quark, or photon, is a particle with no internal structure, whereas a composite particle, such as a proton or neutron, has an internal structure (see figure). However, neither elementary nor composite particles are spatially localized, because of the Heisenberg uncertainty principle. The particle wavepacket always occupies a nonzero volume. For example, see atomic orbital: The electron is an elementary particle, but its quantum states form three-dimensional patterns.

Nevertheless, there is good reason that an elementary particle is often called a point particle. Even if an elementary particle has a delocalized wavepacket, the wavepacket is in fact a quantum superposition of quantum states wherein the particle is exactly localized. This is not true for a composite particle, which can never be represented as a superposition of exactly-localized quantum states. It is in this sense that physicists can discuss the intrinsic "size" of a particle: The size of its internal structure, not the size of its wavepacket. The "size" of an elementary particle, in this sense, is exactly zero.

For example, for the electron, experimental evidence shows that the size of an electron is less than 10^-18 m. This is consistent with the expected value of exactly zero. (This should not be confused with the classical electron radius, which, despite the name, is unrelated to the actual size of an electron.)

See also

Elementary Particle

* Quark

* Lepton

Charge (physics) (general concept, not limited to ''electric charge'')

Self-propelled particle

Notes and references

Notes

Bibliography

Further reading

Eric W. Weisstein, "''Point Charge''".

F. H. J. Cornish, "''Classical radiation theory and point charges''". Proc. Phys. Soc. 86 427-442, 1965. doi:10.1088/0370-1328/86/3/301

O. D. Jefimenko, "''Direct calculation of the electric and magnetic fields of an electric point charge moving with constant velocity''". Am. J. Phys.62 (1994), 79.

Category:Introductory physics Category:Electromagnetism Category:Fundamental physics concepts Category:Classical mechanics Category:Mass Category:Physics

ca:Partícula puntual cs:Bodová částice el:Υλικό σημείο es:Punto material fa:ذره نقطه‌ای fr:Particule ponctuelle ko:점입자 it:Punto materiale pt:Ponto material ckb:وردیلەی نوقتەیی zh:點粒子

name	Brian Greene
birth date	February 09, 1963
birth place	New York City, U.S.
residence	United States
nationality	USA
field	Physics
alma mater	Stuyvesant High School Harvard UniversityOxford University
work institution	Cornell UniversityColumbia University
doctoral advisor	Graham G. Ross (Oxford University)James Binney
known for	String theory''The Elegant Universe''''The Fabric of the Cosmos''
footnotes	}}

Brian Greene (born February 9, 1963) is an American theoretical physicist and string theorist. He has been a professor at Columbia University since 1996. Greene has worked on mirror symmetry, relating two different Calabi-Yau manifolds (concretely, relating the conifold to one of its orbifolds). He also described the flop transition, a mild form of topology change, showing that topology in string theory can change at the conifold point. He has become known to a wider audience through his books for the general public, ''The Elegant Universe'', ''Icarus at the Edge of Time'', ''The Fabric of the Cosmos,'' ''The Hidden Reality,'' and a related PBS television special. Greene also appeared on The Big Bang Theory episode "The Herb Garden Germination."

Biography

Greene was born in New York City. His father, Alan Greene, was a one-time vaudeville performer and high school dropout who later worked as a voice coach and composer. After attending Stuyvesant High School, where he was a classmate of Lisa Randall, Greene entered Harvard in 1980 to major in physics. After completing his bachelor's degree, Greene earned his doctorate from Oxford University as a Rhodes Scholar, graduating in 1987. While at Oxford, Greene also studied piano with the concert pianist Jack Gibbons.

Greene joined the physics faculty of Cornell University in 1990, and was appointed to a full professorship in 1995. The following year, he joined the staff of Columbia University as a full professor. At Columbia, Greene is co-director of the university's Institute for Strings, Cosmology, and Astroparticle Physics (ISCAP), and is leading a research program applying superstring theory to cosmological questions. He is also one of the FQXi large grant awardees, his project title being "Arrow of Time in the Quantum Universe". His co-investigators are David Albert and Maulik Parikh.

Greene is married to former ABC producer Tracy Day. He became vegan in 1997 after touring Farm Sanctuary in Watkins Glen, NY.

Work

Research

Greene's area of research is string theory, a candidate for a theory of quantum gravity. String theory attempts to explain the different particle species of the standard model of particle physics as different aspects of a single type of one-dimensional, vibrating string. One peculiarity of string theory is that it postulates the existence of extra dimensions of space – instead of the usual four dimensions, there must be ten spatial dimensions and one dimension of time to allow for a consistently defined string theory. The theory has several explanations to offer for why we do not perceive these extra dimensions, one being that they are "curled up" (compactified, to use the technical term) and are hence too small to be readily noticeable.

In the field, Greene is best known for his contribution to the understanding of the different shapes the curled-up dimensions of string theory take on. The most important of these shapes are so-called Calabi-Yau manifolds; when the extra dimensions take on those particular form, physics in three dimensions exhibits an abstract symmetry known as supersymmetry.

Greene has worked on a particular class of symmetry relating two different Calabi-Yau manifolds, known as mirror symmetry (concretely, relating the conifold to one of its orbifolds). He is also known for his research on the flop transition, a mild form of topology change, showing that topology in string theory can change at the conifold point.

Currently, Greene studies string cosmology, especially the imprints of trans Planckian physics on the cosmic microwave background, and brane-gas cosmologies that could explain why the space around us has three large dimensions, expanding on the suggestion of a black hole electron, namely that the electron may be a black hole.

Communicating science

Greene is well known to a wider audience for his work on popularizing theoretical physics, in particular string theory and the search for a unified theory of physics. His first book, ''The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory'', published in 1999, is a popularization of superstring theory and M-theory. It was a finalist for the Pulitzer Prize in nonfiction, and winner of ''The Aventis Prizes for Science Books'' in 2000. ''The Elegant Universe'' was later made into a PBS television special of the same name, hosted and narrated by Greene, which won a 2003 Peabody Award.

Greene's second book, ''The Fabric of the Cosmos: Space, Time, and the Texture of Reality'' (2004), is about space, time, and the nature of the universe. Aspects covered in this book include non-local particle entanglement as it relates to special relativity and basic explanations of string theory. It is an examination of the very nature of matter and reality, covering such topics as spacetime and cosmology, origins and unification, and including an exploration into reality and the imagination.

Greene's third book, ''The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos'' published Jan 25th 2011 deals in greater depth with multiple universes, or, as it is sometimes referred to collectively, the multiverse.

A book for a younger audience, ''Icarus at the Edge of Time'' ISBN 978-0307268884, which is a futuristic re-telling of the Icarus myth, was published September 2, 2008. In addition to authoring popular-science books, Greene is an occasional Op-Ed Contributor for the New York Times, writing on his work and other scientific topics.

The popularity of his books and his natural on-camera demeanor has resulted in many media appearances, including ''Charlie Rose'', ''The Colbert Report'', ''The NewsHour with Jim Lehrer'', ''The Century with Peter Jennings'', CNN, ''TIME'', ''Nightline in Primetime'', ''Late Night with Conan O'Brien'', and ''The Late Show with David Letterman''. It has also led to Greene helping John Lithgow with scientific dialogue for the television series ''3rd Rock from the Sun'', and becoming a technical consultant for the film ''Frequency'', in which he also had a cameo role. Recently, he was a consultant in the time-travel movie ''Déjà Vu.'' He also had a cameo appearance as an Intel scientist in 2007's ''The Last Mimzy''. Greene was also mentioned in the 2002 ''Angel'' episode "Supersymmetry" and in the 2008 Stargate Atlantis episode "Trio". Through his film credits, combined with his research publications in mathematical physics, Greene is one of the few people to have a defined Erdős–Bacon number.

Greene often lectures outside of the collegiate setting, at both a general and a technical level, in more than twenty-five countries. One of his latest projects is to organize an annual science festival held in New York City, the World Science Festival. The first such festival took place in May/June 2008.

In 2010, Greene was named a "Citizen of the Next Century" by Future-ish.

Bibliography

Technical articles

For a full list of technical articles, consult the publication list in the SPIRES database

R. Easther, B. R. Greene, M. G. Jackson and D. Kabat, "String windings in the early universe''. JCAP {0502}, 009 (2005).

R. Easther, B. Greene, W. Kinney, G. Shiu, "A Generic Estimate of Trans-Planckian Modifications to the Primordial Power Spectrum in Inflation". Phys. Rev. D66 (2002). 023518.

R. Easther, B. Greene, W. Kinney, G. Shiu, "Inflation as a Probe of Short Distance Physics". Phys. Rev. D64 (2001) 103502.

Brian R. Greene, "D-Brane Topology Changing Transitions". Nucl. Phys. B525 (1998) 284-296.

Michael R. Douglas, Brian R. Greene, David R. Morrison, "Orbifold Resolution by D-Branes". Nucl.Phys. B506 (1997) 84-106.

Brian R. Greene, David R. Morrison, Andrew Strominger, "Black Hole Condensation and the Unification of String Vacua". Nucl.Phys. B451 (1995) 109-120.

P.S. Aspinwall, B.R. Greene, D.R. Morrison, "Calabi-Yau Moduli Space, Mirror Manifolds and Spacetime Topology Change in String Theory". Nucl.Phys. B416 (1994) 414-480.

B.R.Greene and M.R.Plesser, "Duality in Calabi-Yau Moduli Space". Nucl. Phys. B338 (1990) 15.

Books for general readers

1999. ''The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory''.

2005. ''The Fabric of the Cosmos: Space, Time, and the Texture of Reality''.

2008. ''Icarus at the Edge of Time''.

2011. ''The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos''.

See also

List of physicists

List of theoretical physicists

String Theory

Theory of everything

Unified Field Theory

References

External links

Brian Greene faculty homepage

Category:1963 births Category:Alumni of Magdalen College, Oxford Category:American agnostics Category:American Jews Category:American physicists Category:American Rhodes scholars Category:American science writers Category:American vegans Category:Calculating prodigies Category:Columbia University faculty Category:Cornell University faculty Category:Harvard University alumni Category:Jewish American scientists Category:Living people Category:String theorists Category:Stuyvesant High School alumni Category:Theoretical physicists Category:Westinghouse Science Talent Search winners

ar:براين غرين bg:Брайън Грийн ca:Brian Greene cs:Brian Greene de:Brian Greene el:Μπράιαν Γκριν es:Brian Greene fa:برایان گرین fr:Brian Greene ko:브라이언 그린 is:Brian Greene it:Brian Greene he:בריאן גרין ht:Brian Greene hu:Brian Greene nl:Brian Greene ja:ブライアン・グリーン no:Brian Greene pl:Brian Greene pt:Brian Greene ru:Грин, Брайан sl:Brian Greene fi:Brian Greene sv:Brian Greene