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Type of quantum mechanics theory
In physics, a hidden-variable theory is a deterministic model which seeks to explain the probabilistic nature of quantum mechanics by introducing additional
Hidden-variable_theory
Topics referred to by the same term
Look up hidden variable in Wiktionary, the free dictionary. Hidden variable may refer to: Confounding, in statistics, an extraneous variable in a statistical
Hidden_variable
Interpretation of quantum mechanics
In the interpretation of quantum mechanics, a local hidden-variable theory is a hidden-variable theory that satisfies the principle of locality. These
Local_hidden-variable_theory
Statistical Markov model
of the hidden variable x(t) at time t, given the values of the hidden variable x at all times, depends only on the value of the hidden variable x(t − 1);
Hidden_Markov_model
Physics phenomenon
produced from quantum entanglement cannot be explained in terms of local hidden variables. Entanglement can produce statistical correlations between events in
Quantum_entanglement
Area of physical and philosophical debate
uncertainty principle constraint. The theory is considered to be a hidden-variable theory, and by embracing non-locality it satisfies Bell's inequality
Interpretations of quantum mechanics
Interpretations_of_quantum_mechanics
Interpretation of quantum mechanics
processes] could be called 'hidden' variables." Bohm and Hiley later stated that they found Bohm's choice of the term "hidden variables" to be too restrictive
De_Broglie–Bohm_theory
Theorem in quantum mechanics
significant for the role it played in showing that wide classes of hidden-variable theories are inconsistent with quantum physics. Multiple variations
Gleason's_theorem
Theorem in physics
which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measurement
Bell's_theorem
Interpretation of quantum mechanics
answer to that question of "hidden variables" was "yes". By contrast, Max Jammer writes "Einstein never proposed a hidden variable theory." Einstein explored
Copenhagen_interpretation
Concept in statistics
In statistics, latent variables (from Latin: present participle of lateo 'lie hidden'[citation needed]) are variables that can only be inferred indirectly
Latent and observable variables
Latent_and_observable_variables
1932 book by John von Neumann
measurements have predictable results. But if hidden variables existed, then knowing the values of the hidden variables would make the results of all measurements
Mathematical Foundations of Quantum Mechanics
Mathematical_Foundations_of_Quantum_Mechanics
Experiments to test Bell's theorem in quantum mechanics
realism, which requires the presence of some additional local variables (called "hidden" because they are not a feature of quantum theory) to explain
Bell_test
Description of physical properties at the atomic and subatomic scale
significantly Bell's theorem, have demonstrated that broad classes of such hidden-variable theories are in fact incompatible with quantum physics. According to
Quantum_mechanics
Deviations from local realism
multipartite quantum system do not allow an interpretation with local hidden variables. Quantum nonlocality has been experimentally verified under a variety
Quantum_nonlocality
Historical critique of quantum mechanics
that it should be possible to construct a theory containing these hidden variables. Resolutions of the paradox have important implications for the interpretation
Einstein–Podolsky–Rosen paradox
Einstein–Podolsky–Rosen_paradox
Ontological concepts for quantum theory
Before developing his implicit order approach, Bohm had proposed a hidden variable theory of quantum physics (see Bohm interpretation). According to Bohm
Implicate_and_explicate_order
Physical principle that only immediate surroundings can influence an object
modern terminology. They reasoned that without additions, now called hidden variables, quantum mechanics would predict illogical relationships between the
Principle_of_locality
Truths and principles of the study of matter, space, time and energy
which determine that quantum mechanics is incompatible with local hidden-variable theories given some basic assumptions about the nature of measurement
Philosophy_of_physics
Testable implication of local hidden-variable theories
of entanglement in quantum mechanics cannot be reproduced by local hidden-variable theories. Experimental verification of the inequality being violated
CHSH_inequality
Northern Irish physicist (1928–1990)
Bell's theorem, an important theorem in quantum physics regarding hidden-variable theories. In 2022, the Nobel Prize in Physics was awarded to Alain
John_Stewart_Bell
Interpretation of quantum mechanics
other decoherence interpretations, the Copenhagen interpretation, and hidden variable theories such as Bohmian mechanics. In the many-worlds interpretation
Many-worlds_interpretation
Quantum states of two qubits
pair given above – namely this "agreement", called more formally a hidden variable. In his famous paper of 1964, John S. Bell showed by simple probability
Bell_state
Topics referred to by the same term
Look up Variable, variable, or variables in Wiktionary, the free dictionary. Wikiversity has learning resources about Variable Variable may refer to:
Variable
American-Brazilian-British scientist (1917–1992)
"interpretation in terms of hidden variables" to be too restrictive, especially since their variables, position and momentum, "are not actually hidden". Bohm's work
David_Bohm
Calculation rule in quantum mechanics
significant for the role it played in showing that wide classes of hidden-variable theories are inconsistent with quantum physics. Several other researchers
Born_rule
Theorem constraining types of hidden-variable theories
in 1967. It places certain constraints on the permissible types of hidden-variable theories, which try to explain the predictions of quantum mechanics
Kochen–Specker_theorem
2D fighting video game
mobile title was released in 2017 for Android and iOS, developed by Hidden Variable Studios. Development of Skullgirls 2nd Encore continues in the form
Skullgirls
Statement that is taken to be true
the Hidden variable case. The experiment was conducted first by Alain Aspect in the early 1980s, and the result excluded the simple hidden variable mop:
Axiom
German mathematician (1901–1984)
quantum mechanics. This work led to her critique of Von Neumann's no hidden variables proof. Her criticism was long ignored; it was discovered in 1974 by
Grete_Hermann
Quantum mechanics experiment
that it should be possible to construct a theory containing these hidden variables. Resolutions of the paradox have important implications for the interpretation
Aspect's_experiment
Dutch physicist (1913–1991)
physicist and a professor at Purdue University. He was a proponent of the hidden variable interpretation of quantum mechanics. Belinfante was born in the Hague
Frederik_Belinfante
"Highly entangled" quantum state of 3 or more qubits
experiments that directly contradict predictions by every classical local hidden-variable theory. The state has applications in quantum computing. The four-particle
Greenberger–Horne–Zeilinger state
Greenberger–Horne–Zeilinger_state
Process by which a quantum system takes on a definitive state
group includes hidden-variable theories like de Broglie–Bohm theory; here random outcomes only result from unknown values of hidden variables. Results from
Wave_function_collapse
2011 video game
Bag It! is a puzzle game developed by American studio Hidden Variable Studios and released on October 15, 2011 for iOS and Android. The player is tasked
Bag_It!
Series of public disputes between physicists Niels Bohr and Albert Einstein
local hidden variable theories, Bohm's theory was not ruled out. A 2007 experiment ruled out a large class of non-Bohmian non-local hidden variable theories
Bohr–Einstein_debates
Theorem pertaining to the ontology of quantum mechanics
the predictions of quantum mechanics with local hidden variable theories and noncontextual hidden variable theories. Similarly, the PBR theorem could be
Pusey–Barrett–Rudolph_theorem
Property of states in quantum mechanics
as the scenario having a local hidden state model which is, in some sense, a generalisation of the local hidden variable model for Bell nonlocality and
Quantum_steering
Concept in physics
nevertheless affect the outcome of experiments. In the words of Bell, "If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it
Action_at_a_distance
Study of speech signals and the processing methods of these signals
of the hidden variable x(t) at time t, given the values of the hidden variable x at all times, depends only on the value of the hidden variable x(t − 1)
Speech_processing
Non-mathematical introduction
the results of these experiments are incompatible with any local hidden variable theory. The idea of quantum field theory began in the late 1920s with
Introduction to quantum mechanics
Introduction_to_quantum_mechanics
Fact that observing a situation changes it
self-adjoint operator that represents the possible results of a random variable. Observer (special relativity) Dirac, P.A.M. (1967). The Principles of
Observer_effect_(physics)
American physicist (1944–2012)
Bell's inequality, which distinguishes orthodox quantum mechanics from hidden variable theories. Following the proposal of Clauser, Horne, Shimony, and Holt
Stuart_Freedman
Context dependence in quantum measurements
revealing pre-existing values. Any attempt to do so in a realistic hidden-variable theory leads to values that are dependent upon the choice of the other
Quantum_contextuality
Quantum physics theorem on causality
and Landsman regarding hidden-variable theories: "There has been a similar tension between the idea that the hidden variables (in the pertinent causal
Free_will_theorem
Thought experiment in quantum mechanics
demonstrate how quantum mechanics cannot be explained using a local hidden variable theory. In this way Mermin's device is a pedagogical tool to introduce
Mermin's_device
Interaction of a quantum system with a classical observer
measurement results cannot be explained away as due to ignorance about local hidden variables within quantum systems. Measuring a quantum system generally changes
Measurement in quantum mechanics
Measurement_in_quantum_mechanics
Class of theories in quantum mechanics
on them, the assumptions of the theorem are no longer fulfilled. A hidden-variable theory which is superdeterministic can thus fulfill Bell's notion of
Superdeterminism
Philosophical view that events are determined by prior events
Specker, which argues that hidden variable theories cannot be "sensible", meaning that the values of the hidden variables inherently depend on the devices
Determinism
Apparent lack of definite state before measurement of quantum systems
by experiment: because Bell's inequalities are violated, any such hidden variable(s) cannot be local (see Bell test experiments). The answer to 2) depends
Quantum_indeterminacy
from John Archibald Wheeler about quantum information. "Bohm-like" (hidden variable) theories as a whole are a "minority view" as compared to Copenhagen-type
Minority interpretations of quantum mechanics
Minority_interpretations_of_quantum_mechanics
Hungarian and American mathematician and physicist (1903–1957)
out hidden variable theories. The validity of Bub's argument is, in turn, disputed. Gleason's theorem of 1957 provided an argument against hidden variables
John_von_Neumann
Interpretation of quantum mechanics
structure we could arrive at a universal description (the troubled hidden variables approach). Yet another option is to give a preferred status to a particular
Relational_quantum_mechanics
Algorithm in mathematics
the i-th hidden variable given the (i − 1)-th hidden variable is independent of previous hidden variables, and the current observation variables depend
Baum–Welch_algorithm
Theory of logic to account for observations from quantum theory
sprung up, either hoping that quantum logic would provide a viable hidden-variable theory, or obviate the need for one. Their work proved fruitless, and
Quantum_logic
Quantum search algorithm
not contained in BQP. It has been shown that a class of non-local hidden variable quantum computers could implement a search of an N {\displaystyle N}
Grover's_algorithm
Computer programming, a variable only usable in a portion of a program (the scope)
with private variables, functions, constants and types hidden within them, either by nested blocks or nested functions. Local variables are fundamental
Local_variable
Theoretical upper limit to non-local correlations in quantum mechanics
violates Bell inequalities (i.e., it cannot be described by a local hidden-variable theory), a natural question to ask is how large can the violation be
Tsirelson's_bound
Solvability theorem for finite systems of linear inequalities
of necessary and sufficient conditions for the existence of a local hidden-variable theory, given data from any specific set of measurements. Generalizations
Farkas'_lemma
Phenomenon resulting from the superposition of two waves
collapse Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Many-worlds Objective-collapse Quantum logic Superdeterminism Relational
Wave_interference
American physicist
to note how the three-particle GHZ state demonstrates that no local hidden-variable theory can explain quantum correlations, and together with Asher Peres
N._David_Mermin
Kavli Institute of Nanoscience reported that the failure of the local hidden-variable hypothesis is supported at the 96% confidence level based on a "loophole-free
List of unsolved problems in physics
List_of_unsolved_problems_in_physics
Quantum mechanical state change
ISSN 0031-9007. Clauser, John F. (1969). "Proposed Experiment to Test Local Hidden-Variable Theories". Physical Review Letters. 23 (15): 880–884. Bibcode:1969PhRvL
Spontaneous_emission
Aspect of quantum measurement
\lambda )B(b,\lambda )} where a and b are detector settings and λ is the hidden variable, drawn from a distribution ρ(λ). The quantum correlation is the key
Quantum_correlation
Facts provided or learned about something or someone
of Bell's theorem, determinists reconciled with this behavior using hidden variable theories, which argued that the information necessary to predict the
Information
Concept in quantum mechanics
showed that the results of experiments intended to test the idea of hidden variables would be predicted to fall within certain limits based on all three
Counterfactual_definiteness
German-born theoretical physicist (1879–1955)
entangled pair, then the assumption that the outcomes depend upon hidden variables within each half implies a mathematical constraint on how the outcomes
Albert_Einstein
Austrian philosopher of science (1924–1994)
became an outspoken defender of Bohm's interpretation and argued that hidden variable approaches to quantum mechanics should be pursued to increase the testability
Paul_Feyerabend
Experiment verifying the wave-particle duality of matter
collapse Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Many-worlds Objective-collapse Quantum logic Superdeterminism Relational
Davisson–Germer_experiment
Epistemic model
The Spekkens toy model is a conceptually simple toy hidden-variable theory introduced by Robert Spekkens in 2004, to argue in favour of the epistemic
Spekkens_toy_model
Branch of mathematics
collapse Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Local Superdeterminism Many-worlds Objective collapse Quantum logic
Quantum_calculus
Force resulting from the quantisation of a field
collapse Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Many-worlds Objective-collapse Quantum logic Superdeterminism Relational
Casimir_effect
Indian philosopher, scientist and environmentalist
titled "Hidden Variables and Locality in Quantum Theory" in which she discussed the mathematical and philosophical implications of hidden variable theories
Vandana_Shiva
The hidden transformation reformulates a constraint satisfaction problem in such a way all constraints have at most two variables. The new problem is
Hidden_transformation
Set of mathematical concepts in quantum gravity
collapse Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Many-worlds Objective-collapse Quantum logic Superdeterminism Relational
Quantum_geometry
Philosophical concept
John S. Bell was able to define a theoretical test for these local hidden variable theories, which was reformulated as a workable experimental test through
Indeterminism
Mathematical structures that allow quantum mechanics to be explained
incomplete, which motivated research into so-called hidden-variable theories. The issue of hidden variables has become in part an experimental issue with the
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
Investigations by Albert Einstein
Stewart Bell proved his Bell's theorem that would allow to test local hidden-variable theory. Conclusive experimental evidence was obtained in 1982 with
Einstein's unsuccessful investigations
Einstein's_unsuccessful_investigations
American writer (born 1970)
performed by One Ring Zero, and "The Gibbons Girl", by Chris Ewen's The Hidden Variable. In 2017, Handler wrote the play Imaginary Comforts, and The Story
Daniel_Handler
Theoretical problem in quantum physics
collapse Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Many-worlds Objective-collapse Quantum logic Superdeterminism Relational
Measurement_problem
Quantum mechanics principle
collapse Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Many-worlds Objective-collapse Quantum logic Superdeterminism Relational
Pauli_exclusion_principle
Experimentally violated inequality of correlations of entangled particles
inequality Leggett–Garg inequality Leggett, A. J. (2003). "Nonlocal Hidden-Variable Theories and Quantum Mechanics: An Incompatibility Theorem". Foundations
Leggett_inequality
1993 physics textbook by Asher Peres
is incompatible with local hidden-variable theories. (Within its substantial discussion of the failure of hidden variable theories, the book includes
Quantum Theory: Concepts and Methods
Quantum_Theory:_Concepts_and_Methods
Mathematical entity to describe the probability of each possible measurement on a system
mechanics. A classical dynamical state consists of a set of dynamical variables with well-defined real values at each instant of time. For example, the
Quantum_state
Principle of quantum mechanics
|n\rangle } are the energy eigenstates of the Hamiltonian. For continuous variables like position eigenstates, | x ⟩ {\displaystyle |x\rangle } : | α ⟩ =
Quantum_superposition
Loss of quantum coherence
1952). "A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. II". Physical Review. 85 (2): 180–193. Bibcode:1952PhRv...85..180B
Quantum_decoherence
American physicist (born 1942)
J.; Clauser, John F. (April 3, 1972). "Experimental Test of Local Hidden-Variable Theories". Physical Review Letters. 28 (14): 938-941. Bibcode:1972PhRvL
John_Clauser
Problem in physics and quantum mechanics
collapse Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Many-worlds Objective-collapse Quantum logic Superdeterminism Relational
Many-body_problem
American mathematical physicist (1935–2026)
Bell's theorem in which the hidden variables are a priori assumed to not influence detector settings, denying hidden variable causality from the beginning
Carl_H._Brans
foundations, the KCBS pentagram is an example disproving noncontextual hidden variable models. It was discovered by Alexander Klyachko, M. Ali Can, Sinem
KCBS_pentagram
Variation of classical electrodynamics
collapse Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Many-worlds Objective-collapse Quantum logic Superdeterminism Relational
Stochastic_electrodynamics
Description of a quantum-mechanical system
appreciated in a single dimension. In canonical quantization, the classical variables x {\displaystyle x} and p {\displaystyle p} are promoted to self-adjoint
Schrödinger_equation
Topics referred to by the same term
(disambiguation) The Hidden Reality (book) 2011 physics book by Brian Greene Hidden sector (physics), the hidden part of the universe Hidden-variable theory (physics)
Hidden_universe
2014 video game
by Sirvo for iOS on February 6, 2014, and ported by indie developer Hidden Variable Studios for Android on March 12, 2014. The team chose to release for
Threes
Type of mathematical filter
state-space models are defined based on a switching variable which evolves independent of the hidden variable. The probabilistic model of such variant of SKF
Switching_Kalman_filter
Swiss mathematician (1920–2011)
Kochen–Specker theorem in quantum mechanics, showing that certain types of hidden-variable theories are impossible. He also proved the ordinal partition relation
Ernst_Specker
Formula for spectral line wavelengths in alkali metals
of the screening of inner electrons for outer-electron transitions is variable and cannot be compensated for in the simple manner above. The correction
Rydberg_formula
Interdisciplinary theory behind quantum computing
collapse Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Many-worlds Objective-collapse Quantum logic Superdeterminism Relational
Quantum_information_science
Similar behavior of quantum systems to droplets bouncing on a fluid
deterministic theory and is entirely nonlocal. It is an example of a hidden variable theory, and all non-relativistic quantum mechanics can be accounted
Hydrodynamic_quantum_analogs
Topics referred to by the same term
Vehicle, a type of commercial vehicle in the United Kingdom Local hidden-variable theory, a hypothetical manifestation of unknown classical physical
LHV
HIDDEN VARIABLE
HIDDEN VARIABLE
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : habitational name from Hebden in North Yorkshire or Hebden Bridge in West Yorkshire, both named from Old English hēope ‘rose-hip’ + denu ‘valley’.
Surname or Lastname
English (mainly Sussex and Kent)
English (mainly Sussex and Kent) : topographic name from Middle English hilder ‘dweller on a slope’ (from Old English hylde ‘slope’).
Surname or Lastname
English
English : habitational name from Hidden in Berkshire or Clayhidon in Devon, recorded in Domesday Book as Hidone, from Old English hī(e)g ‘hay’ + dūn ‘hill’.
Boy/Male
English
Hidden.
Girl/Female
English
The linden tree.
Surname or Lastname
English
English : habitational name from various places such as Headon, Nottinghamshire, Hedon in East Yorkshire, and Heddon on the Wall and Black Heddon. Northumberland. The first is probably named from Old English hēah ‘high’ + dūn ‘hill’; the others have the same second element, combined with Old English hǣþ ‘heath’, ‘heather’.North German (Frisian) : variant of Hadden.
Male
German
Middle High German byname HEIDEN means "heathen." The composer Josef Haydn's surname was a respelling of this name.
Surname or Lastname
Scottish
Scottish : habitational name from a place so called near Kelso on the border with England. Early forms include Hadden, Hauden, and Halden; the place name is probably from Old English halh ‘nook’, ‘recess’ + denu ‘valley’.English : habitational name from a place in East Yorkshire, so named from Old Norse hǫfuð ‘head’ (replacing Old English hēafod) + Old English denu ‘valley’; the first element may have been used in the sense ‘principal’, ‘top’, or ‘end’.Americanized form of Norwegian Hovden.
Female
English
Anglicized form of Irish Gaelic ÉtaÃn, AIDEEN means "face."
Girl/Female
English
Hidden.
Surname or Lastname
Scottish
Scottish : variant of Howden 1.English : variant of Haddon.Irish (Ulster and County Louth) : though mainly Scottish, this surname is sometimes used as an Anglicized form of Gaelic Ó hÉidÃn ‘descendant of ÉidÃn’ (see Hayden).North German (Frisian) : from the personal name Hadder, a derivative of any of the Germanic compound names formed with had ‘battle’, ‘strife’ as the first element.
Boy/Male
Muslim
Hidden
Surname or Lastname
Dutch, German, and Jewish (Ashkenazic)
Dutch, German, and Jewish (Ashkenazic) : variant (plural) of Linde.English : variant spelling of Lindon.Belgian and Dutch (van Linden) : habitational name from places called Linden in Brabant and North Brabant.Dutch (van der Linden) : habitational name from any of numerous places called Ter Linde.Irish : reduced form of McLinden.Swedish (Lindén) : ornamental name from lind ‘lime tree’ + the common suffix -én, from the Latin adjectival ending -enius.
Girl/Female
English
Hidden.
Girl/Female
American, Australian, British, Christian, English
Lives by the Linden Tree Hill
Girl/Female
Muslim
Hidden
Male
English
Variant spelling of English Lyndon, LINDEN means "lime tree hill." Or from the vocabulary word, linden, meaning "lime tree."
Boy/Male
American, Australian, British, English
From the Linden Tree Hill
Male
English
Variant spelling of English Aidan, AIDEN means "little fire."
Girl/Female
English
Hidden.
HIDDEN VARIABLE
HIDDEN VARIABLE
Girl/Female
Muslim
Star
Boy/Male
Anglo, Australian, British, English
Name of a King; A Stream of Praise; A Period of Time
Boy/Male
Scottish
Dear one.
Girl/Female
Indian, Modern
Blessings of Goddess Durga
Boy/Male
Indian, Tamil
Name of Lord Buddha; A Strength
Boy/Male
Arabic
Early Imam (Leader) of Islam
Male
Gypsy/Romani
 Probably a Romani form of French Louis, LOIZA means "famous warrior."Â
Boy/Male
Hindu, Indian, Marathi
Warrior
Boy/Male
Indian
This was the name of the makes of astrolabes
Boy/Male
Indian, Punjabi, Sikh
Moments Spent with Lord
HIDDEN VARIABLE
HIDDEN VARIABLE
HIDDEN VARIABLE
HIDDEN VARIABLE
HIDDEN VARIABLE
imp. & p. p.
of Hide
v. t.
To make hard or harder; to make firm or compact; to indurate; as, to harden clay or iron.
a.
Hidden; secret.
n.
A coarse kind of linen; -- called also harden.
a.
Hidden; secret; occult.
n.
One who hides or conceals.
v. t.
To make wide or wider; to extend in breadth; to increase the width of; as, to widen a field; to widen a breach; to widen a stocking.
adv.
In a hidden manner.
a.
Controlled or oppressed by priests; as, a priest-ridden people.
p. p.
Boiled; seethed; also, soaked; heavy with moisture; saturated; as, sodden beef; sodden bread; sodden fields.
v. i.
To be seethed; to become sodden.
n.
Same as Hoiden.
p. p. & a.
from Hide. Concealed; put out of view; secret; not known; mysterious.
n.
An accumulation of refuse about a dwelling place; especially, an accumulation of shells or of cinders, bones, and other refuse on the supposed site of the dwelling places of prehistoric tribes, -- as on the shores of the Baltic Sea and in many other places. See Kitchen middens.
p. p.
of Hide
a.
Hidden; secret.
a.
Ridden by a hag or witch; hence, afflicted with nightmare.
a.
Hidden; concealed; secret.
a.
Of or belonging to that part or end which is in the rear, or which follows; as, the hinder part of a wagon; the hinder parts of a horse.