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Description of quantum mechanics in which the present depends on both the past and future
The two-state vector formalism (TSVF) is a description of quantum mechanics in terms of a causal relation in which the present is caused by quantum states
Two-state_vector_formalism
Japanese physicist
laws. He developed the Double Inferential Vector Formalism (DIVF), later known as the Two-state vector formalism (TSVF), which is sometimes interpreted as
Satoshi_Watanabe_(physicist)
Mathematical technique in physics
associated with the Double Inferential state-Vector Formalism (DIVF), later known as the two-state vector formalism (TSVF) in quantum mechanics, where the
Retrocausality
Area of physical and philosophical debate
Thus a leading exponent of the two-state vector formalism, Lev Vaidman, states that the two-state vector formalism dovetails well with Hugh Everett's
Interpretations of quantum mechanics
Interpretations_of_quantum_mechanics
Israeli physicist (born 1932)
that appear to be random are caused by events in the future (two-state vector formalism). Verifying a present effect of a future cause requires a measurement
Yakir_Aharonov
Quantity in quantum mechanics
1988, published in Physical Review Letters and is related to the two-state vector formalism. The first experimental realization came from researchers at Rice
Weak_value
Notation in general relativity
of the NP formalism, the vector basis chosen is a null tetrad: a set of four null vectors—two real, and a complex-conjugate pair. The two real members
Newman–Penrose_formalism
Mathematical entity to describe the probability of each possible measurement on a system
formal quantum mechanics (see § Formalism in quantum physics below) the theory develops in terms of abstract 'vector space', avoiding any particular representation
Quantum_state
Gauge fixing procedure
In quantum field theory, the Gupta–Bleuler formalism is a way of quantizing the electromagnetic field. The formulation is due to theoretical physicists
Gupta–Bleuler_formalism
Simple quantum mechanical system
These two complex numbers may be considered coordinates in a two-dimensional complex Hilbert space. Thus the state vector corresponding to the state | ψ
Two-state_quantum_system
Motion of a certain space that preserves at least one point
was stated above, Euclidean rotations are applied to rigid body dynamics. Moreover, most of mathematical formalism in physics (such as the vector calculus)
Rotation_(mathematics)
Notation for quantum states
denotes a vector, v {\displaystyle {\boldsymbol {v}}} , in an abstract (complex) vector space V {\displaystyle V} , and physically it represents a state of some
Bra–ket_notation
Interpretation of quantum mechanics
transactional interpretation is superficially similar to the two-state vector formalism (TSVF) which has its origin in work by Yakir Aharonov, Peter Bergmann
Transactional_interpretation
Interpretation of electrodynamics
Symmetry in physics and T-symmetry Transactional interpretation Two-state vector formalism Wheeler, J. A.; Feynman, R. P. (July 1949). "Classical Electrodynamics
Wheeler–Feynman absorber theory
Wheeler–Feynman_absorber_theory
Mathematical space representing physical quantum systems
superposition. In the formalism of quantum mechanics these state vectors are often written using Dirac's compact bra–ket notation. The spin state of a silver atom
Quantum_state_space
Ways to represent 3D rotations
needs to track a target. Consider a rigid body, with three orthogonal unit vectors fixed to its body (representing the three axes of the object's local coordinate
Rotation formulations in three dimensions
Rotation_formulations_in_three_dimensions
Tensor operator generalizes the notion of operators which are scalars and vectors
scalars, vectors, and tensors, must be represented by scalar, vector, and tensor operators, respectively. Whether something is a scalar, vector, or tensor
Tensor_operator
Family of linear transformations
latter two with eigenvalue 1. When the boost velocity v {\displaystyle {\boldsymbol {v}}} is in an arbitrary vector direction with the boost vector β = v
Lorentz_transformation
Straight path on a curved surface or a Riemannian manifold
is constrained in various ways. This article presents the mathematical formalism involved in defining, finding, and proving the existence of geodesics
Geodesic
Circulation density in a vector field
In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional
Curl_(mathematics)
Formulation to quantize gauge field theories in physics
In theoretical physics, the BRST formalism, or BRST quantization (where the BRST refers to the last names of Carlo Becchi, Alain Rouet, Raymond Stora
BRST_quantization
Theory of quantum gravity merging quantum mechanics and general relativity
dimensions, a direct comparison between the two has not been possible. It is possible to extend mainstream LQG formalism to higher-dimensional supergravity, general
Loop_quantum_gravity
Equations describing classical electromagnetism
the original equations by Maxwell is no longer included. The vector calculus formalism below, the work of Oliver Heaviside, has become standard. It is
Maxwell's_equations
Differential form of degree one or section of a cotangent bundle
one. One-forms are dual to vector fields on the same manifold, in the sense that a one-form pairs naturally with a vector field to produce a real valued
One-form
Specification of a derivative along a tangent vector of a manifold
covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing
Covariant_derivative
Non-tensorial representation of the spin group
its original state. Spinors are therefore often described heuristically as "square roots" of (geometric) vectors, and a geometric vector can be constructed
Spinor
Mathematical function, in linear algebra
compatible with addition of vectors, and multiplication of vectors by scalars. When the two vector spaces are the same, a linear map is also called a linear
Linear_map
Mathematical operation on vector spaces
{\displaystyle V\otimes W} of two vector spaces V {\displaystyle V} and W {\displaystyle W} (over the same field) is a vector space to which is associated
Tensor_product
Matrix representing a Euclidean rotation
Axis–angle representation Rotation group SO(3) Rotation formalisms in three dimensions Rotation operator (vector space) Transformation matrix Yaw-pitch-roll system
Rotation_matrix
Study of curves from a differential point of view
curvature and the arc length, are expressed via derivatives and integrals using vector calculus. One of the most important tools used to analyze a curve is the
Differentiable_curve
Mathematical description of spacetime used in relativity
form a four-vector. The 3-space electric field, E, combines with the 3-space magnetic field, B, to create a tensor in the four-vector formalism. This approach
Minkowski_spacetime
Ways of writing certain laws of physics
form that is manifestly invariant under Lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems. These
Covariant formulation of classical electromagnetism
Covariant_formulation_of_classical_electromagnetism
Mathematical structures that allow quantum mechanics to be explained
mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
Representation of a tensor in Euclidean space
tensor formed by the tensor product ⊗ of two Cartesian vectors a and b, written T = a ⊗ b. Analogous to vectors, it can be written as a linear combination
Cartesian_tensor
Mathematical model combining space and time
four-vectors, namely four-position, four-velocity, and four-force. He did not pursue the 4-dimensional formalism in subsequent papers, however, stating that
Spacetime
Base space for supersymmetric theories
bracket may be defined between any two elements of this vector space, and that this bracket reduces to the commutator on two even coordinates and on one even
Superspace
Physical theory with fields invariant under the action of local "gauge" Lie groups
path-ordered operator. The formalism of gauge theory carries over to a general setting. For example, it is sufficient to ask that a vector bundle have a metric
Gauge_theory
Conserved physical quantity; rotational analogue of linear momentum
the cross product of the particle's position vector r (relative to some origin) and its momentum vector; the latter is p = mv in Newtonian mechanics.
Angular_momentum
Proposed theories of gravity
contrived. Bekenstein introduced a tensor–vector–scalar model (TeVeS) that attempted to reproduce MOND in 2004. This has two scalar fields φ {\displaystyle \varphi
Alternatives to general relativity
Alternatives_to_general_relativity
Force directed to the center of rotation
each one is perpendicular to its respective position vector, simple vector subtraction implies two similar isosceles triangles with congruent angles –
Centripetal_force
Theory of gravitation as curved spacetime
at two loops", Phys. Lett., 160B (1–3): 81–86, Bibcode:1985PhLB..160...81G, doi:10.1016/0370-2693(85)91470-4 Gourgoulhon, Eric (2007). "3+1 Formalism and
General_relativity
Interaction between electronic and nuclear vibrational motion in a molecule
Yingli; Peng, Qian; Shuai, Zhigang (2008). "Promoting-mode free formalism for excited state radiationless decay process with Duschinsky rotation effect"
Vibronic_coupling
Theorem in vector calculus
known as the Kelvin–Stokes theorem, is a theorem in vector calculus that relates the behavior of a vector field along the edge of a surface to the behavior
Stokes'_theorem
Theorem in calculus
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through
Divergence_theorem
Tensor in differential geometry
that takes smooth vector fields X {\displaystyle X} , Y {\displaystyle Y} , and Z {\displaystyle Z} , and returns the vector field R ( X , Y )
Ricci_curvature
Geometric model of the physical space
textbook Vector Analysis written by Edwin Bidwell Wilson based on Gibbs' lectures. Further development came in the abstract formalism of vector spaces,
Three-dimensional_space
Mathematical description of quantum state
and are present in other quantum state formalisms. For N distinguishable particles (no two being identical, i.e. no two having the same set of quantum numbers)
Wave_function
Specialized notation for multivariable calculus
respect to a vector as a column vector or a row vector. Both of these conventions are possible even when the common assumption is made that vectors should be
Matrix_calculus
Field theory in physics that aims to unify the fundamental forces and particles
are themselves the quanta of fields. Different fields in physics include vector fields such as the electromagnetic field, spinor fields whose quanta are
Unified_field_theory
semi-classical vector model which is not able to predict many of the results in NMR spectroscopy and is a simplification of the complete density matrix formalism. In
Product_operator_formalism
Statement about integration on manifolds
In vector calculus and differential geometry the generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called
Generalized_Stokes_theorem
Influence that can change motion of an object
magnitude and direction of a force are both important, force is a vector quantity (force vector). The SI unit of force is the newton (N), and force is often
Force
Model in statistical mechanics generalizing the Ising model
dimensions. Some of the formalism is also broad enough to handle related models, such as the XY model, the Heisenberg model and the N-vector model. Let Q = {1
Potts_model
Differential operator in mathematics
rotations and reflections. In two dimensions, this says that for every angle θ {\displaystyle \theta } and every translation vector ( a , b ) {\displaystyle
Laplace_operator
Hypothetical physical concept
such laws could in principle allow deterministic prediction of the future state of the universe. Any "theory of everything" is similarly expected to be
Theory_of_everything
Contraction of an astronomical object due to the influence of its gravity
thermal pressure balances the gravitational forces. The star then exists in a state of thermodynamic equilibrium. During the star's evolution a star might collapse
Gravitational_collapse
Polynomial-time algorithm for the assignment problem
(both formalisms), in Brilliant website. R. A. Pilgrim, Munkres' Assignment Algorithm. Modified for Rectangular Matrices, Course notes, Murray State University
Hungarian_algorithm
Representation of mechanical stress at every point within a deformed 3D object
{\displaystyle \sigma _{ij}} and relates a unit-length direction vector e to the traction vector T(e) across a surface perpendicular to e: T ( e ) = e ⋅ σ or
Cauchy_stress_tensor
Quantization giving rise to photons
})^{n}|0\rangle .} A photon number state (or a Fock state) is an eigenstate of the number operator. This is why the formalism described here is often referred
Quantization of the electromagnetic field
Quantization_of_the_electromagnetic_field
Concept in differential geometry
exterior derivative to the setting of a differentiable principal bundle or vector bundle with a connection. Let G be a Lie group and P → M be a principal
Exterior_covariant_derivative
Electric and magnetic fields produced by moving charged objects
(electromagnetic fields), is governed by Maxwell's equations. In the vector field formalism, these are: Gauss's law ∇ ⋅ E = ρ ε 0 {\displaystyle \nabla \cdot
Electromagnetic_field
Physics phenomenon
c_{ij}\neq c_{i}^{A}c_{j}^{B}.} If a state is inseparable, it is called an 'entangled state'. For example, given two basis vectors { | 0 ⟩ A , | 1 ⟩ A } {\displaystyle
Quantum_entanglement
is an extension of vector algebra, providing additional algebraic structures on vector spaces, with geometric interpretations. Vector algebra uses all dimensions
Comparison of vector algebra and geometric algebra
Comparison_of_vector_algebra_and_geometric_algebra
Mathematical object that describes the electromagnetic field in spacetime
tensor simplifies and reduces Maxwell's equations as four vector calculus equations into two tensor field equations. In electrostatics and electrodynamics
Electromagnetic_tensor
Theory of interwoven space and time by Albert Einstein
above formalism applies to any direction; and three orthogonal directions allow dealing with all directions in space by decomposing the velocity vectors to
Special_relativity
Field-equations in general relativity
or contracting. This effort was unsuccessful because: any desired steady state solution described by this equation is unstable, and observations by Edwin
Einstein_field_equations
Geometric system used in black hole physics
M {\displaystyle M} , there are precisely 3 rotational Killing vector fields. Stated in another way, the dimension of the Killing algebra K ( M ) {\displaystyle
Spherically symmetric spacetime
Spherically_symmetric_spacetime
4-dimensional vector space either is simple, or can be written as F = v ∧ w + x ∧ y, where v, w, x, and y are linearly independent; the two cases are mutually
Classification of electromagnetic fields
Classification_of_electromagnetic_fields
German-born theoretical physicist (1879–1955)
geometric terms as a theory of spacetime. Einstein adopted Minkowski's formalism in his 1915 general theory of relativity. General relativity (GR) is a
Albert_Einstein
Certain vector fields are the sum of an irrotational and a solenoidal vector field
theorem of vector calculus states that certain differentiable vector fields can be resolved into the sum of an irrotational (curl-free) vector field and
Helmholtz_decomposition
Classical statement of gravity as force
the vector form, which becomes particularly useful if more than two objects are involved (such as a rocket between the Earth and the Moon). For two objects
Newton's law of universal gravitation
Newton's_law_of_universal_gravitation
Formulation of quantum mechanics
addition was the quantum state vector, now written |ψ⟩, which is the vector that the matrices act on. Without the state vector, it is not clear which particular
Matrix_mechanics
On finding a maximal set of solutions of a system of first-order homogeneous linear PDEs
partial differential equations. In modern geometric terms, given a family of vector fields, the theorem gives necessary and sufficient integrability conditions
Frobenius theorem (differential topology)
Frobenius_theorem_(differential_topology)
Extraction of information from a running system to verify certain properties
specifications are typically expressed in trace predicate formalisms, such as finite-state machines, regular expressions, context-free patterns, linear
Runtime_verification
Array of numbers
expressed as multiplication of a two-component vector with a two-by-two matrix called ray transfer matrix analysis: the vector's components are the light ray's
Matrix_(mathematics)
Invariant measure of fractal dimension
the Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an n-dimensional inner product
Hausdorff_dimension
Hypothetical FTL transportation by warping space
external gravitational field, such as that of a black hole. Using the ADM formalism of general relativity, the spacetime is described by a foliation of space-like
Alcubierre_drive
Theorem in quantum mechanics
representation. Within the formalism of quantum field theory (QFT) such a picture generally does not exist, because these two representations are unitarily
Haag's_theorem
Type of physical quantity
improper rotation to see the behaviour of a pseudotensor, but it works only if vector space dimensions is odd otherwise inversion is a proper rotation without
Pseudotensor
Quantum mechanical phenomenon
Jaynes–Cummings model and the Bloch vector formalism. More generally, the introduction of an oscillatory driving field to a two-level system can be viewed as
Rabi_cycle
Kinetic theory of gravity
impacting all material objects from all directions. According to this model, any two material bodies partially shield each other from the impinging corpuscles
Le Sage's theory of gravitation
Le_Sage's_theory_of_gravitation
Later developments of Heisenberg's principle
incompatible on the state of the system. The Heisenberg–Robertson–Schrödinger uncertainty relation was proved at the dawn of quantum formalism and is ever-present
Stronger uncertainty relations
Stronger_uncertainty_relations
Attraction of masses and energy
force of gravity experienced by objects on Earth's surface is the vector sum of two forces: (a) The gravitational attraction in accordance with Newton's
Gravity
Graph of space and time in special relativity
in two papers in 1921. Relativistic effects such as length contraction and time dilation and some relations to covariant and contravariant vectors were
Spacetime_diagram
Physical quantities taking values at each point in space and time
the electric field is another vector field, while electrodynamics can be formulated in terms of two interacting vector fields at each point in spacetime
Field_(physics)
Property of a mathematical space
dimension of a vector space is the number of vectors in any basis for the space, i.e. the number of coordinates necessary to specify any vector. This notion
Dimension
Mathematical model of the time dependence of a point in space
system has a state representing a point in an appropriate state space. This state is often given by a tuple of real numbers or by a vector in a geometrical
Dynamical_system
Formulation of the quantum many-body problem
quantization, also referred to as occupation number representation, is a formalism used to describe and analyze quantum many-body systems. In quantum field
Second_quantization
und Physik 62, 225 Walter, S. (2007). Renn, J. (ed.). "Breaking in the 4-vectors: the four-dimensional movement in gravitation, 1905–1910" (PDF). The Genesis
History of gravitational theory
History_of_gravitational_theory
Quantum error correction code
import classical codes in this way. The entanglement-assisted stabilizer formalism can also overcome this difficulty. Algebraic-geometry codes provide another
Stabilizer_code
Mathematical description of fermions
invariant of the Lorentz group (an eigenstate of the energy), while the vector combination carries momentum and current, being covariant under the action
Dirac_spinor
Object in differential geometry
torsion tensor is a bilinear map of two input vectors X , Y {\displaystyle X,Y} , that produces an output vector T ( X , Y ) {\displaystyle T(X,Y)} representing
Torsion_tensor
Algebraic structure designed for geometry
multivectors. Compared to other formalisms for manipulating geometric objects, geometric algebra is noteworthy for supporting vector division (though generally
Geometric_algebra
Theory in modern physics that describes gravity as an entropic force
positive dark energy that lifts the vacuum energy of space from its ground state value. A central tenet of the theory is that the positive dark energy leads
Entropic_gravity
Relativistic correction
velocities in relativity is hyperbolic, and so parallel transport of a vector (the gyroscope's angular velocity) around a circle (its linear velocity)
Thomas_precession
Database query language
object-oriented databases (e.g. in db4o). QBE is based on the logical formalism called tableau query, although QBE adds some extensions to that, much
Query_by_Example
Description of gravity using discrete values
gravity, the metric is dynamical, so that whether two points are spacelike separated depends on the state. In fact, they can be in a quantum superposition
Quantum_gravity
Application of quantum theory mathematics to cognitive phenomena
Quantum cognition uses the mathematical formalism of quantum probability theory to model psychology phenomena when classical probability theory fails
Quantum_cognition
Description of large objects' physics
refer to a particular formalism based on Newton's laws of motion. Newtonian mechanics in this sense emphasizes force as a vector quantity. In contrast
Classical_mechanics
Theorem in physics showing the conservation of energy for the electromagnetic field
that the spatially averaged microscopic Poynting vector is exactly predicted by a macroscopic formalism. This result is strictly valid in the limit of low-loss
Poynting's_theorem
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TWO STATE-VECTOR-FORMALISM
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TWO STATE-VECTOR-FORMALISM
TWO STATE-VECTOR-FORMALISM
TWO STATE-VECTOR-FORMALISM
TWO STATE-VECTOR-FORMALISM
TWO STATE-VECTOR-FORMALISM
TWO STATE-VECTOR-FORMALISM
TWO STATE-VECTOR-FORMALISM
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