Physics:Quantum Holographic principle

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The holographic principle was motivated by the discovery that black hole entropy is proportional to the area of the event horizon rather than the volume: $S\propto A.$ This suggests that the fundamental degrees of freedom of a region scale with its boundary, not its interior.

Holographic principle: information in a volume encoded on its boundary surface.

Origin

Basic idea

The principle states that a physical theory in a volume can be equivalently described by a theory defined on its boundary.

This is analogous to a hologram, where a two-dimensional surface encodes a three-dimensional image.

In this sense, spacetime itself may be an emergent phenomenon.

AdS/CFT correspondence

The most concrete realization of the holographic principle is the AdS/CFT correspondence.

It states that:

• a gravitational theory in anti-de Sitter (AdS) space
• is equivalent to a conformal field theory (CFT) on its boundary

This duality provides a powerful tool for studying quantum gravity and strongly interacting systems.

Information and entropy

The holographic principle implies that the maximum entropy in a region is bounded by its surface area:

$S\le \frac{k{c}^{3}A}{4G\hslash }.$

This bound is known as the Bekenstein bound.

It places a fundamental limit on the amount of information that can be stored in a given region of space.

Physical significance

The holographic principle:

• suggests spacetime may be emergent,
• connects gravity with quantum information,
• provides insight into black hole physics,
• plays a central role in modern quantum gravity.

Table of contents (175 articles)

Index

Core theory

1. Foundations
2. Conceptual and interpretations
3. Mathematical structure and systems
4. Atomic and spectroscopy
5. Wavefunctions and modes
6. Quantum dynamics and evolution
7. Measurement and information
8. Quantum information and computing

Matter (by scale)

9. Matter (by scale)

Applications and extensions

10. Quantum optics and experiments
11. Open quantum systems
12. Quantum field theory
13. Statistical mechanics and kinetic theory
14. Condensed matter and solid-state physics
15. Plasma and fusion physics
16. Timeline
17. Advanced and frontier topics

Methods and tools

18. Methods and tools

Full contents

1. Foundations (11)↑

1. Physics:Quantum basics
2. Physics:Quantum Postulates
3. Physics:Quantum Hilbert space
4. Physics:Quantum Observables and operators
5. Physics:Quantum mechanics
6. Physics:Quantum mechanics measurements
7. Physics:Quantum state
8. Physics:Quantum system
9. Physics:Quantum superposition
10. Physics:Quantum probability
11. Physics:Quantum Mathematical Foundations of Quantum Theory

2. Conceptual and interpretations (13)↑

12. Physics:Quantum Interpretations of quantum mechanics
13. Physics:Quantum Wave–particle duality
14. Physics:Quantum Complementarity principle
15. Physics:Quantum Uncertainty principle
16. Physics:Quantum Measurement problem
17. Physics:Quantum Bell's theorem
18. Physics:Quantum Hidden variable theory
19. Physics:Quantum nonlocality
20. Physics:Quantum contextuality
21. Physics:Quantum Darwinism
22. Physics:Quantum A Spooky Action at a Distance
23. Physics:Quantum A Walk Through the Universe
24. Physics:Quantum The Secret of Cohesion and How Waves Hold Matter Together

3. Mathematical structure and systems (13)↑

25. Physics:Quantum Density matrix
26. Physics:Quantum Exactly solvable quantum systems
27. Physics:Quantum Formulas Collection
28. Physics:Quantum A Matter Of Size
29. Physics:Quantum Symmetry in quantum mechanics
30. Physics:Quantum Angular momentum operator
31. Physics:Quantum Runge–Lenz vector
32. Physics:Quantum Approximation Methods
33. Physics:Quantum Matter Elements and Particles
34. Physics:Quantum Dirac equation
35. Physics:Quantum Klein–Gordon equation
36. Physics:Quantum pendulum
37. Physics:Quantum configuration space

4. Atomic and spectroscopy (14)↑

Quantum atomic structure and spectroscopy: orbitals, energy levels, and emission and absorption spectra.

38. Physics:Quantum Atomic structure and spectroscopy
39. Physics:Quantum Hydrogen atom
40. Physics:Quantum number
41. Physics:Quantum Multi-electron atoms
42. Physics:Quantum Fine structure
43. Physics:Quantum Hyperfine structure
44. Physics:Quantum Isotopic shift
45. Physics:Quantum defect
46. Physics:Quantum Zeeman effect
47. Physics:Quantum Stark effect
48. Physics:Quantum Spectral lines and series
49. Physics:Quantum Selection rules
50. Physics:Quantum Fermi's golden rule
51. Physics:Quantum beats

5. Wavefunctions and modes (9)↑

A quantum wavefunction showing probability amplitude in space; the square of its magnitude gives the probability density.

52. Physics:Quantum Wavefunction
53. Physics:Quantum Superposition principle
54. Physics:Quantum Eigenstates and eigenvalues
55. Physics:Quantum Boundary conditions and quantization
56. Physics:Quantum Standing waves and modes
57. Physics:Quantum Normal modes and field quantization
58. Physics:Number of independent spatial modes in a spherical volume
59. Physics:Quantum Density of states
60. Physics:Quantum carpet

6. Quantum dynamics and evolution (17)↑

61. Physics:Quantum Time evolution
62. Physics:Quantum Schrödinger equation
63. Physics:Quantum Time-dependent Schrödinger equation
64. Physics:Quantum Stationary states
65. Physics:Quantum Perturbation theory
66. Physics:Quantum Time-dependent perturbation theory
67. Physics:Quantum Adiabatic theorem
68. Physics:Quantum Scattering theory
69. Physics:Quantum S-matrix
70. Physics:Quantum tunnelling
71. Physics:Quantum speed limit
72. Physics:Quantum revival
73. Physics:Quantum reflection
74. Physics:Quantum oscillations
75. Physics:Quantum jump
76. Physics:Quantum boomerang effect
77. Physics:Quantum chaos

7. Measurement and information (8)↑

78. Physics:Quantum Measurement theory
79. Physics:Quantum Measurement operators
80. Physics:Quantum Projective measurement
81. Physics:Quantum POVM
82. Physics:Quantum Weak measurement
83. Physics:Quantum Measurement collapse
84. Physics:Quantum Zeno effect
85. Physics:Quantum limit

8. Quantum information and computing (10)↑

86. Physics:Quantum information theory
87. Physics:Quantum Qubit
88. Physics:Quantum Entanglement
89. Physics:Quantum Gates and circuits
90. Physics:Quantum Computing Algorithms in the NISQ Era
91. Physics:Quantum Noisy Qubits
92. Physics:Quantum random access code
93. Physics:Quantum pseudo-telepathy
94. Physics:Quantum network
95. Physics:Quantum money

9. Quantum optics and experiments (5)↑

Experimental quantum physics: qubits, dilution refrigerators, quantum communication, and laboratory systems.

96. Physics:Quantum Nonlinear King plot anomaly in calcium isotope spectroscopy
97. Physics:Quantum optics beam splitter experiments
98. Physics:Quantum Ultra fast lasers
99. Physics:Quantum Experimental quantum physics
100. Physics:Quantum optics
Template:Quantum optics operators

10. Open quantum systems (9)↑

101. Physics:Quantum Open systems
102. Physics:Quantum Master equation
103. Physics:Quantum Lindblad equation
104. Physics:Quantum Decoherence
105. Physics:Quantum dissipation
106. Physics:Quantum Markov semigroup
107. Physics:Quantum Markovian dynamics
108. Physics:Quantum Non-Markovian dynamics
109. Physics:Quantum Trajectories

11. Quantum field theory (19)↑

Structural dependency map of quantum field theory.

110. Physics:Quantum field theory (QFT) basics
111. Physics:Quantum field theory (QFT) core
112. Physics:Quantum Fields and Particles
113. Physics:Quantum Second quantization
114. Physics:Quantum Harmonic Oscillator field modes
115. Physics:Quantum Creation and annihilation operators
116. Physics:Quantum vacuum fluctuations
117. Physics:Quantum Propagators in quantum field theory
118. Physics:Quantum Feynman diagrams
119. Physics:Quantum Path integral formulation
120. Physics:Quantum Renormalization in field theory
121. Physics:Quantum Renormalization group
122. Physics:Quantum Field Theory Gauge symmetry
123. Physics:Quantum Non-Abelian gauge theory
124. Physics:Quantum Electrodynamics (QED)
125. Physics:Quantum chromodynamics (QCD)
126. Physics:Quantum Electroweak theory
127. Physics:Quantum Standard Model
128. Physics:Quantum triviality

12. Statistical mechanics and kinetic theory (9)↑

129. Physics:Quantum Statistical mechanics
130. Physics:Quantum Partition function
131. Physics:Quantum Distribution functions
132. Physics:Quantum Liouville equation
133. Physics:Quantum Kinetic theory
134. Physics:Quantum Boltzmann equation
135. Physics:Quantum BBGKY hierarchy
136. Physics:Quantum Relaxation and thermalization
137. Physics:Quantum Thermodynamics

13. Condensed matter and solid-state physics (13)↑

138. Physics:Quantum Band structure
139. Physics:Quantum Fermi surfaces
140. Physics:Quantum Semiconductor physics
141. Physics:Quantum Phonons
142. Physics:Quantum Electron-phonon interaction
143. Physics:Quantum Superconductivity
144. Physics:Quantum Topological phases of matter
145. Physics:Quantum well
146. Physics:Quantum spin liquid
147. Physics:Quantum spin Hall effect
148. Physics:Quantum phase transition
149. Physics:Quantum critical point
150. Physics:Quantum dot

14. Plasma and fusion physics (8)↑

Conceptual illustration of plasma physics in a fusion context, showing magnetically confined ionized gas in a tokamak and the collective behavior governed by electromagnetic fields and transport processes.

151. Physics:Quantum Fusion reactions and Lawson criterion
152. Physics:Quantum Plasma (fusion context)
153. Physics:Quantum Magnetic confinement fusion
154. Physics:Quantum Inertial confinement fusion
155. Physics:Quantum Plasma instabilities and turbulence
156. Physics:Quantum Tokamak core plasma
157. Physics:Quantum Tokamak edge physics and recycling asymmetries
158. Physics:Quantum Stellarator

15. Timeline (8)↑

159. Physics:Quantum mechanics/Timeline
160. Physics:Quantum mechanics/Timeline/Pre-quantum era
161. Physics:Quantum mechanics/Timeline/Old quantum theory
162. Physics:Quantum mechanics/Timeline/Modern quantum mechanics
163. Physics:Quantum mechanics/Timeline/Quantum field theory era
164. Physics:Quantum mechanics/Timeline/Quantum information era
165. Physics:Quantum mechanics/Timeline/Quantum technology era
166. Physics:Quantum mechanics/Timeline/Quiz

16. Advanced and frontier topics (8)↑

167. Physics:Quantum topology
168. Physics:Quantum battery
169. Physics:Quantum Supersymmetry
170. Physics:Quantum Black hole thermodynamics
171. Physics:Quantum Holographic principle
172. Physics:Quantum gravity
173. Physics:Quantum De Sitter invariant special relativity
174. Physics:Quantum Doubly special relativity

References

Author: Harold Foppele