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<p>Repair Quantum Collection B backlink template</p> <p><b>New page</b></p><div>{{Quantum book backlink|Advanced and frontier topics}}<br /> 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:<br /> &lt;math&gt;<br /> S \propto A.<br /> &lt;/math&gt;<br /> This suggests that the fundamental degrees of freedom of a region scale with its boundary, not its interior.&lt;ref&gt;{{cite journal |last=Susskind |first=Leonard |title=The World as a Hologram |journal=Journal of Mathematical Physics |year=1995}}&lt;/ref&gt;<br /> [[File:Holografisch principe_ Informatie en volume.jpg|thumb|400px|Holographic principle: information in a volume encoded on its boundary surface.]]<br /> ==Origin==<br /> === Basic idea ===<br /> <br /> The principle states that a physical theory in a volume can be equivalently described by a theory defined on its boundary.<br /> <br /> This is analogous to a hologram, where a two-dimensional surface encodes a three-dimensional image.<br /> <br /> In this sense, spacetime itself may be an emergent phenomenon.<br /> <br /> === AdS/CFT correspondence ===<br /> <br /> The most concrete realization of the holographic principle is the AdS/CFT correspondence.<br /> <br /> It states that:<br /> <br /> * a gravitational theory in anti-de Sitter (AdS) space <br /> * is equivalent to a conformal field theory (CFT) on its boundary <br /> <br /> This duality provides a powerful tool for studying quantum gravity and strongly interacting systems.&lt;ref&gt;{{cite journal |last=Maldacena |first=Juan |title=The Large N Limit of Superconformal Field Theories and Supergravity |journal=Advances in Theoretical and Mathematical Physics |year=1998}}&lt;/ref&gt;<br /> <br /> === Information and entropy ===<br /> <br /> The holographic principle implies that the maximum entropy in a region is bounded by its surface area:<br /> <br /> &lt;math&gt;<br /> S \le \frac{k c^3 A}{4 G \hbar}.<br /> &lt;/math&gt;<br /> <br /> This bound is known as the &#039;&#039;&#039;Bekenstein bound&#039;&#039;&#039;.<br /> <br /> It places a fundamental limit on the amount of information that can be stored in a given region of space.<br /> <br /> === Physical significance ===<br /> <br /> The holographic principle:<br /> <br /> * suggests spacetime may be emergent, <br /> * connects gravity with quantum information, <br /> * provides insight into black hole physics, <br /> * plays a central role in modern quantum gravity. <br /> <br /> =See also=<br /> {{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}<br /> <br /> =References=<br /> {{reflist|3}}<br /> <br /> {{Author|Harold Foppele}}<br /> <br /> {{Sourceattribution|Quantum Holographic principle|1}}</div>

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