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Spacetime with complexified coordinates
Complex spacetime is a mathematical framework that combines the concepts of complex numbers and spacetime in physics. In this framework, the usual real-valued
Complex_spacetime
Topological structure of 4D spacetime
Spacetime topology is the topological structure of spacetime, a topic studied primarily in general relativity. This physical theory models gravitation
Spacetime_topology
Mathematical model combining space and time
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of
Spacetime
Topics referred to by the same term
may also refer to: Complex spacetime, a theoretical extension of spacetime into complex-valued space and time coordinates Spacetime diagram, a diagram
Spacetime_(disambiguation)
Mathematical theory of the geometry of space and time
In physics, curved spacetime is the mathematical model in which, with Einstein's theory of general relativity, gravity naturally arises, as opposed to
Curved_spacetime
Hypothetical topological feature of spacetime
connects disparate points in spacetime. It can be visualized as a tunnel with two ends at separate points in spacetime (i.e., different locations, different
Wormhole
Condition in which spacetime itself breaks down
singularity, spacetime singularity, or simply singularity, is a theoretical condition in which gravity is predicted to be so intense that spacetime itself would
Gravitational_singularity
2014 American science documentary television series presented by Neil deGrasse Tyson
Cosmos: A Spacetime Odyssey is a 2014 American science documentary television series. The show is a follow-up to the 1980 television series Cosmos: A
Cosmos:_A_Spacetime_Odyssey
Number with a real and an imaginary part
mechanics – make use of complex numbers. In special relativity and general relativity, some formulas for the metric on spacetime become simpler if one takes
Complex_number
Specific quantum state of a quantum harmonic oscillator
Física. 23 (1–2): 143–187. G. Kaiser, Quantum Physics, Relativity, and Complex Spacetime: Towards a New Synthesis, North-Holland, Amsterdam, 1990. S.T. Ali
Coherent_state
Unified field theory
of a fifth dimension of space beyond the conventional four-dimensional spacetime of general relativity. According to this proposal, there are three dimensions
Kaluza–Klein_theory
Mathematical description of spacetime used in relativity
In physics, Minkowski spacetime (or Minkowski space; /mɪŋˈkɔːfski, -ˈkɒf-/) is the main mathematical description of spacetime in the absence of gravitation
Minkowski_spacetime
Concept in mathematical group theory
group of spacetime has been denoted C(1,3) Isaak Yaglom has contributed to the mathematics of spacetime conformal transformations in split-complex and dual
Conformal_group
Mathematical trick using imaginary numbers to simplify certain formulas in physics
dimensions. Circular points at infinity § Imaginary transformation Complex spacetime Imaginary time Schwinger function Zee, Anthony (2010). Quantum Field
Wick_rotation
Property of a mathematical space
found necessary to describe electromagnetism. The four dimensions (4D) of spacetime consist of events that are not absolutely defined spatially and temporally
Dimension
Theory proposed by Roger Penrose
non-commutative holomorphic twistor quantum algebra.) Background independence Complex spacetime History of loop quantum gravity Robinson congruences Spin network
Twistor_theory
Compact astronomical body
of general relativity, which describes gravitation as the curvature of spacetime, predicts that any sufficiently compact mass will form a black hole. The
Black_hole
Geometric space with five dimensions
such a space extends the familiar three spatial dimensions plus time (4D spacetime) by introducing an additional degree of freedom, which is often used to
Five-dimensional_space
Field-equations in general relativity
related the local spacetime curvature (expressed by the Einstein tensor) with the local energy, momentum and stress within that spacetime (expressed by the
Einstein_field_equations
Theory of interwoven space and time by Albert Einstein
gravitational effects as the geometric curvature of spacetime. Special relativity is restricted to the flat spacetime known as Minkowski space. As long as the universe
Special_relativity
Reals with an extra square root of +1 adjoined
semi-complex numbers, F. Antonuccio (1994) paracomplex numbers, Cruceanu, Fortuny & Gadea (1996) split-complex numbers, B. Rosenfeld (1997) spacetime numbers
Split-complex_number
Framework of superstring theory
consequence of the geometry of spacetime. In spite of the fact that the universe is well described by four-dimensional spacetime, there are several reasons
M-theory
Description of gravity using discrete values
gravity as curvature of spacetime: in the slogan of John Archibald Wheeler, "Spacetime tells matter how to move; matter tells spacetime how to curve." On the
Quantum_gravity
Theory of subatomic structure
relativity, a theory that explains the force of gravity and the structure of spacetime at the macro-level. The other is quantum mechanics, a completely different
String_theory
American physicist (1929–2021)
metric. In 1973 he advocated the use of complex numbers in relativity, and consideration of complex spacetime. Some of his most interesting recent work
Ezra_T._Newman
Attraction of masses and energy
of the curvature of spacetime, caused by the uneven distribution of mass. The most extreme example of this curvature of spacetime is a black hole, from
Gravity
Setting of relativistic physics in geometric algebra
physics, spacetime algebra (STA) is the application of Clifford algebra Cl1,3(R), or equivalently the geometric algebra G(M4) of physics. Spacetime algebra
Spacetime_algebra
Hypothetical travel into the past or future
it, such as a rotating black hole. Traveling to an arbitrary point in spacetime has very limited support in theoretical physics, and is usually connected
Time_travel
Theoretical framework in physics
changes in the spacetime metric. QFTs in curved spacetime generally change according to the geometry (local structure) of the spacetime background, while
Quantum_field_theory
Totality of existing entities
in this field differ both concerning their notion of spacetime and of the contents of spacetime. The theory of relativity plays a central role in modern
World
Framework of distances and directions
with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to
Space
Theory in theoretical physics
that are not spheres vanish unless the complex dimension of the spacetime is three, and so spacetimes with complex dimension three are the most interesting
Topological_string_theory
Opposition of a circuit to a current when a voltage is applied
circuit element is the ratio of the complex representation of the sinusoidal voltage between its terminals, to the complex representation of the current flowing
Electrical_impedance
Equations describing classical electromagnetism
mechanics, or for use in quantum mechanics. The covariant formulation (on spacetime rather than space and time separately) makes the compatibility of Maxwell's
Maxwell's_equations
Branch of mathematics
investigate or measure the properties of the metric of spacetime through the analysis of masses within spacetime, linking with the earlier observation of Euler
Differential_geometry
Method in evaluating divergent integrals
them that are meromorphic functions of a complex parameter d, the analytic continuation of the number of spacetime dimensions. Dimensional regularization
Dimensional_regularization
Relativistic quantum mechanical wave equation
vectors or on spacetime. Another representation is a set of 4 × 4 {\displaystyle 4\times 4} complex matrices acting on Dirac spinors in the complex vector space
Dirac_equation
Lie group of Lorentz transformations
Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (non-gravitational) physical
Lorentz_group
theories to break down under extreme conditions, such as within known spacetime gravitational singularities like those at the Big Bang and at the centers
List of unsolved problems in physics
List_of_unsolved_problems_in_physics
Study of complex manifolds and several complex variables
dimensions of spacetime in 10-dimensional models of string theory. Examples of Calabi–Yau manifolds are given by elliptic curves, K3 surfaces, and complex Abelian
Complex_geometry
Hypothetical approach to quantum gravity with emergent spacetime
spacetime fabric itself evolves. There is evidence that, at large scales, CDT approximates the familiar 4-dimensional spacetime but shows spacetime to
Causal dynamical triangulation
Causal_dynamical_triangulation
Family of linear transformations
six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former
Lorentz_transformation
Contraction of length in the direction of propagation in Minkowski space
all relativistic effects by introducing his concept of four-dimensional spacetime. The numerous and confusing visual effects of combination of length contraction
Length_contraction
Algebraic structure in linear algebra
ISBN 978-0-7167-0344-0 Naber, Gregory L. (2003), The geometry of Minkowski spacetime, New York: Dover Publications, ISBN 978-0-486-43235-9, MR 2044239 Schönhage
Vector_space
Electromagnetism in general relativity
physics, Maxwell's equations in curved spacetime govern the dynamics of the electromagnetic field in curved spacetime (where the metric may deviate from the
Maxwell's equations in curved spacetime
Maxwell's_equations_in_curved_spacetime
Structure from which the geometry of the universe arises
Ninomiya Spacetime is described as having a deeper pregeometric structure based on three dynamical variables, vertices of an abstract simplicial complex, and
Pregeometry_(physics)
geodesics of the spacetime – straight lines in the case of flat Minkowski spacetime and their closest equivalent in the curved spacetime of general relativity
Introduction to the mathematics of general relativity
Introduction_to_the_mathematics_of_general_relativity
Hypothetical physical concept
the structure of spacetime and fundamental particles through complex geometric objects called twistors. Instead of treating spacetime points as fundamental
Theory_of_everything
Concept in special relativity
of complex numbers was not properly understood." — H.S.M. Coxeter In the Minkowski spacetime model adopted by the theory of relativity, spacetime is represented
Imaginary_time
Riemannian manifold with SU(n) holonomy
physics. Particularly in superstring theory, the extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau
Calabi–Yau_manifold
Extended physical object in string theory
higher-dimensional objects. Branes are dynamical objects which can propagate through spacetime according to the rules of quantum mechanics. They have mass and can have
Brane
Reformulation of general relativity
momentum–energy is the source of spacetime curvature, large fluctuations in energy and momentum mean the spacetime "fabric" could potentially become
Hamilton–Jacobi–Einstein equation
Hamilton–Jacobi–Einstein_equation
Concept that there might be more than one dimension of time
dimension, changing time from a real number line into a complex plane. Introducing it into Minkowski spacetime allows a generalization of Kaluza–Klein theory.
Multiple_time_dimensions
Hypothetical quantum cosmological effect
zero size, leaving behind a warped spacetime devoid of any matter; a classical black hole is pure empty spacetime, and the simplest (nonrotating and uncharged)
Hawking_radiation
Four-dimensional number system
In mathematics, the quaternions form a number system similar to the complex numbers, with the usual arithmetical operations of addition, subtraction,
Quaternion
Linear transformation of spacetime coordinates
relativity, a Lorentz transformation is a real linear transformation of the spacetime cartesian coordinates t {\displaystyle t} , x {\displaystyle x}
Biquaternion Lorentz transformation
Biquaternion_Lorentz_transformation
Concept in general relativity
In general relativity, the pp-wave spacetimes, or pp-waves for short, are an important family of exact solutions of Einstein's field equation. The term
Pp-wave_spacetime
Penrose (1967, 1968, 1969), is a complex analogue of the Radon transform that relates massless fields on spacetime, or more precisely the space of solutions
Penrose_transform
Topics referred to by the same term
Spacetime curvature due to gravity, a central aspect of the general theory of relativity Space-time folding, a physical concept of non-flat spacetime
Space_folding
Algebraic structure designed for geometry
relativity. Examples of geometric algebras applied in physics include the spacetime algebra (and the less common algebra of physical space). Geometric calculus
Geometric_algebra
Geometric figure
purposes of analytic geometry. A prominent instance is the depiction of spacetime as a pseudo-Euclidean space. There the asymptotes of the unit hyperbola
Unit_hyperbola
Topological structure in loop quantum gravity
describe the quantum geometry of space. Spin foam does the same job for spacetime. Spacetime can be defined as a superposition of spin foams, which is a generalized
Spin_foam
Group of flat spacetime symmetries
defined by Hermann Minkowski (1908) as the isometry group of Minkowski spacetime. It is a ten-dimensional non-abelian Lie group that is of importance as
Poincaré_group
American television producer, director, and screenwriter
served as an executive producer on the Fox primetime series, Cosmos: A Spacetime Odyssey, a re-launch of the 1980 miniseries hosted by Carl Sagan for which
Brannon_Braga
Greek physicist (born 1971)
no concept of spacetime as we know it exists. As the universe cools, the model undergoes a phase transition to Phase II where spacetime emerges as low
Fotini_Markopoulou-Kalamara
Tool from special relativity
hyperbolic acceleration of a uniformly accelerating reference frame in flat spacetime. In relativistic physics the coordinates of a hyperbolically accelerated
Rindler_coordinates
of Minkowski spacetime are commonly represented: as a four-vector with 4 real coordinates, as a four-vector with 3 real and one complex coordinate, or
Formulations of special relativity
Formulations_of_special_relativity
Vector in relativity
reference frame). Four-vectors describe, for instance, position xμ in spacetime modeled as Minkowski space, a particle's four-momentum pμ, the amplitude
Four-vector
Notation in general relativity
_{20},\Phi _{12},\Phi _{21}} (complex). In many situations—especially algebraically special spacetimes or vacuum spacetimes—the Newman–Penrose formalism
Newman–Penrose_formalism
Mathematical space with two coordinates
Lorentzian surfaces look locally like a two-dimensional slice of relativistic spacetime with one spatial and one time dimension; constant-curvature examples are
Two-dimensional_space
Abstract coordinate system
expansion like a Fourier series. In a physical problem, they could be spacetime coordinates or normal mode amplitudes. In a robot design, they could be
Frame_of_reference
Physical quantities taking values at each point in space and time
formulated in terms of two interacting vector fields at each point in spacetime, or as a single rank-2 tensor field. In the modern framework of the quantum
Field_(physics)
26-dimensional string theory
general spacetime dimension displays inconsistencies due to the conformal anomaly. But, as was first noticed by Claud Lovelace, in a spacetime of 26 dimensions
Bosonic_string_theory
Tensor describing energy momentum density in spacetime
describes the density and flux of energy and momentum at each point in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute
Stress–energy_tensor
Solution of Einstein field equations
The Kerr–Newman metric describes the spacetime geometry around a mass that is electrically charged and rotating. It is a vacuum solution that generalizes
Kerr–Newman_metric
Hypothetical phenomenon
evolution of spacetime near a singularity. In generic black holes, this is not a problem, as an outside viewer cannot observe the spacetime within the event
Naked_singularity
Hypothesis about sapient life and the universe
a "weak" one that referred only to anthropic selection of privileged spacetime locations in the universe, and a more controversial "strong" form that
Anthropic_principle
Formulation in general relativity
is a pair of complex null vectors. These tetrad vectors respect the following normalization and metric conditions assuming the spacetime signature ( −
Construction of a complex null tetrad
Construction_of_a_complex_null_tetrad
Physical principle that only immediate surroundings can influence an object
quantum mechanics, which Einstein himself had helped to create. Simple spacetime diagrams can help clarify the issues related to locality. A way to describe
Principle_of_locality
Aspect of general relativity
Solutions of the Einstein field equations are metrics of spacetimes that result from solving the Einstein field equations (EFE) of general relativity.
Solutions of the Einstein field equations
Solutions_of_the_Einstein_field_equations
In physics, a non-relativistic spacetime is any mathematical model that fuses n–dimensional space and m–dimensional time into a single continuum other
Non-relativistic_spacetime
Force acting on charged particles in electric and magnetic fields
{\displaystyle \gamma _{0}} . This can be settled through spacetime algebra (or the geometric algebra of spacetime), a type of Clifford algebra defined on a pseudo-Euclidean
Lorentz_force
Candidate unified theory of physics
introducing physical objects on a preexisting spacetime manifold, the general concept is to derive spacetime as well as all the objects therein as secondary
Causal_fermion_systems
British science fiction television series (2006–2011)
episodes "Boom Town" and "Utopia" to refuel, and is the location of the spacetime rift first seen in "The Unquiet Dead". The Cardiff Rift becomes "the first
Torchwood
Relation of space and time in relativity theory
space. Since Hermann Minkowski's foundation for spacetime study in 1908, the concept of points in a spacetime plane being hyperbolic-orthogonal to a timeline
Hyperbolic_orthogonality
representations of a Lie supergroup. The general supersymmetry algebra for spacetime dimension d, and with the fermionic piece consisting of a sum of N irreducible
Supersymmetry_algebra
Relativistic wave equation in quantum mechanics
also act on a complex scalar field χ ( x ) {\displaystyle \chi (x)} , which is a field that assigns to each point in spacetime a complex number. In this
Klein–Gordon_equation
Exact spherically symmetric solution in GR
general relativity, the Vaidya metric describes the non-empty external spacetime of a spherically symmetric and nonrotating star which is either emitting
Vaidya_metric
Type of vector space in math
Academic Press. Wald, Robert M. (1994), Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, Chicago Lectures in Physics, University
Hilbert_space
Generators of the Clifford algebra for relativistic quantum mechanics
algebra of spacetime acts. This in turn makes it possible to represent infinitesimal spatial rotations and Lorentz boosts. Spinors facilitate spacetime computations
Gamma_matrices
Element of a unital algebra over the field of real numbers
three-dimensional Euclidean space, and the algebra of the Pauli matrices); and the spacetime algebra Cl 1 , 3 ( R ) {\displaystyle {\text{Cl}}_{1,3}(\mathbb {R}
Hypercomplex_number
Method for producing composition algebras
produced by this process are known as Cayley–Dickson algebras, for example complex numbers, quaternions, and octonions. These examples are useful composition
Cayley–Dickson_construction
Theory of gravity
parallelism, also referred to as absolute or teleparallelism. In this theory, a spacetime is characterized by a curvature-free linear connection in conjunction
Teleparallelism
Physical theory with fields invariant under the action of local "gauge" Lie groups
invariant under a transformation identically performed at every point in the spacetime in which the physical processes occur, they are said to have a global
Gauge_theory
which is a generalization of the Laplacian to four-dimensional spacetime. In flat spacetime with Euclidean coordinates, this may mean either − ∂ 2 ∂ t 2
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Theory of a quantum origin of consciousness
has its own piece of spacetime curvature, a blister in spacetime. Penrose suggests that gravity exerts a force on these spacetime blisters, which become
Orchestrated objective reduction
Orchestrated_objective_reduction
Type of massless subatomic particle
In contrast to the case of the breaking of internal symmetries, when spacetime symmetries such as Lorentz, conformal, rotational, or translational symmetries
Goldstone_boson
Assignment of numbers to points in space
the value of the scalar field at the same absolute point in space (or spacetime) regardless of their respective points of origin. Examples used in physics
Scalar_field
Algebra of 4D spacetime
three-dimensional Euclidean space as a model for (3+1)-dimensional spacetime, representing a point in spacetime via a paravector (3-dimensional vector plus a 1-dimensional
Algebra_of_physical_space
Mathematical description of fermions
action of the Lorentz group, which describes the symmetries of Minkowski spacetime. They occur in the relativistic spin-1/2 wave function solutions to
Dirac_spinor
COMPLEX SPACETIME
COMPLEX SPACETIME
Boy/Male
Indian
Complete
Girl/Female
Tamil
Sompurna | ஸோமபà¯à®°à¯à®¨à®¾
Complete
Sompurna | ஸோமபà¯à®°à¯à®¨à®¾
Surname or Lastname
English
English : habitational name, probably from Comley in Shropshire or Combley on the Isle of Wight; both are named with Old English cumb ‘valley’ + lēah ‘woodland clearing’.
Girl/Female
Tamil
Complete
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : habitational name from any of various places called Copley, for example in County Durham, Staffordshire, and Yorkshire, from the Old English personal name Coppa (apparently a byname for a tall man) or from copp ‘hilltop’ + lēah ‘woodland clearing’.
Girl/Female
Tamil
Complete
Surname or Lastname
English
English : habitational name from Coppull in Lancashire, recorded in the 13th century as Cophill, from Old English copp ‘peak’ + hyll ‘hill’.English : nickname from Old French curt peil ‘short hair’.Probably an Americanized spelling of German and Jewish Koppel or German and Dutch Kappel.
Boy/Male
Tamil
Poornan | பூரà¯à®¨à®¾à®¨
Complete
Poornan | பூரà¯à®¨à®¾à®¨
Girl/Female
Tamil
Complete
Girl/Female
Arabic, Muslim
Complex; Zigzag; Curling
Surname or Lastname
English
English : unexplained.Americanized form of German Koppler.
Girl/Female
Hindu, Indian
Complex
Boy/Male
Tamil
Complete
Boy/Male
Tamil
Complete
Girl/Female
Bengali, Indian
Good Complex
Girl/Female
Muslim
Complex, Zigzag, Curling
Girl/Female
Tamil
Complete
Boy/Male
Tamil
Complete
Girl/Female
Tamil
Shesha Harani | ஷேஷ ஹரணீÂ
Complete
Shesha Harani | ஷேஷ ஹரணீÂ
Boy/Male
Indian
Complete
COMPLEX SPACETIME
COMPLEX SPACETIME
Boy/Male
Gujarati, Hindu, Indian, Kannada, Marathi
Lovable
Boy/Male
Teutonic American English German
Strong as an eagle.
Boy/Male
Hindu
Name of the emperor, With beautiful banner
Girl/Female
French, German
Renowned in Battle; Famous Fighter; Famous Warrior; Form of Louise
Girl/Female
Arabic, Muslim, Parsi
Captivating; Attractive
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Punjabi, Sanskrit, Sikh, Telugu
Lord Indra
Boy/Male
Hindu, Indian, Telugu
Sweetness; Nectar
Male
English
Variant spelling of English Ricky, RICKEY means "powerful ruler."
Surname or Lastname
English
English : habitational name from Shirecliff in Sheffield, South Yorkshire.
Boy/Male
American, British, English
Charcoal Merchant; Coal Seller
COMPLEX SPACETIME
COMPLEX SPACETIME
COMPLEX SPACETIME
COMPLEX SPACETIME
COMPLEX SPACETIME
n.
One who compiles; esp., one who makes books by compilation.
imp. & p. p.
of Couple
a.
Complex, complicated.
a.
That which joins or links two things together; a bond or tie; a coupler.
a.
Intricate; entangled; complicated; complex.
adv.
In a complex manner; not simply.
n.
Two taken together; a pair or couple; especially two lines of verse that rhyme with each other.
a.
See Couple-close.
a.
Not complex; uncompounded; simple.
a.
Finished; ended; concluded; completed; as, the edifice is complete.
a.
One of the pairs of plates of two metals which compose a voltaic battery; -- called a voltaic couple or galvanic couple.
n.
One who complies, yields, or obeys; one of an easy, yielding temper.
n.
A complex; an aggregate of parts; a complication.
imp. & p. p.
of Compile
imp. & p. p.
of Comply
v. t.
To bring to a state in which there is no deficiency; to perfect; to consummate; to accomplish; to fulfill; to finish; as, to complete a task, or a poem; to complete a course of education.
n.
One who couples; that which couples, as a link, ring, or shackle, to connect cars.
n.
Composed of two or more parts; composite; not simple; as, a complex being; a complex idea.
pl.
of Couple-close
a.
Repeatedly compound; made up of complex constituents.