Physics:Quantum basics - Revision history

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	{{Quantum book backlink\|Foundations}}		{{Quantum book backlink\|Foundations}}
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	{{Short description\|Learning project introducing the quantum concept and the fundamental principles of quantum mechanics, from quantization to quantum technologies}}~~Book I~~		{{Short description\|Learning project introducing the quantum concept and the fundamental principles of quantum mechanics, from quantization to quantum technologies}}

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	{{Quantum book backlink\|Foundations}}		{{Quantum book backlink\|Foundations}}

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	*[[Physics:Quantum\|'''Quantum''']]: The smallest unit of a physical property. Imagine a single “portion” of energy or matter that cannot be broken down any further. <br>[https://www.fisica.net/mecanica-quantica/Griffiths%20-%20Introduction%20to%20quantum%20mechanics.pdf For introduction to Quantum Mechanics (QM) and learning about its behaviour this course is highly recommended]		*[[Physics:Quantum\|'''Quantum''']]: The smallest unit of a physical property. Imagine a single “portion” of energy or matter that cannot be broken down any further. <br>[https://www.fisica.net/mecanica-quantica/Griffiths%20-%20Introduction%20to%20quantum%20mechanics.pdf For introduction to Quantum Mechanics (QM) and learning about its behaviour this course is highly recommended]
	* [https://oyc.yale.edu/physics/phys-201/lecture-24#:~:text=Overview,of%20definite%20energy)%20is%20discussed. Above lecture does not include Schödingers Time Dependant formula, if you follow this lecture it will show you a formula to predict the future.]		* [https://oyc.yale.edu/physics/phys-201/lecture-24#:~:text=Overview,of%20definite%20energy)%20is%20discussed. Above lecture does not include Schödingers Time Dependant formula, if you follow this lecture it will show you a formula to predict the future.]
	* '''Physics''' is the ~~[[Wikipedia:~~scientific~~\|scientific]]~~ study of [[Physics:Quantum matter/state of matter\|matter]], its [[Physics:Quantum elementary particle\|fundamental constituents]], its [[Physics:Quantum dynamics\|motion]] and behavior through [[Physics:Quantum spacetime\|space]] and ~~[[Wikipedia:~~time~~\|time]]~~, and the related entities of ~~[[Wikipedia:~~energy~~\|energy]]~~ and ~~[[Wikipedia:~~force~~\|force]]~~.<ref name="maxwell1878-physicalscience">{{harvnb\|Maxwell\|1878\|p=9}} "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events."</ref> It is one of the most fundamental scientific disciplines.<ref name="youngfreedman2014p1">{{harvnb \|Young\|Freedman\|2014\|p=1}} "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."</ref><ref name="youngfreedman2014p2">{{harvnb \|Young\|Freedman\|2014\|p=2}} "Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena."</ref><ref name="holzner2003-physics">{{harvnb\|Holzner\|2006\|p=7}} "Physics is the study of your world and the world and universe around you."</ref>		* '''Physics''' is the scientific study of [[Physics:Quantum matter/state of matter\|matter]], its [[Physics:Quantum elementary particle\|fundamental constituents]], its [[Physics:Quantum dynamics\|motion]] and behavior through [[Physics:Quantum spacetime\|space]] and time, and the related entities of energy and force.<ref name="maxwell1878-physicalscience">{{harvnb\|Maxwell\|1878\|p=9}} "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events."</ref> It is one of the most fundamental scientific disciplines.<ref name="youngfreedman2014p1">{{harvnb \|Young\|Freedman\|2014\|p=1}} "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."</ref><ref name="youngfreedman2014p2">{{harvnb \|Young\|Freedman\|2014\|p=2}} "Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena."</ref><ref name="holzner2003-physics">{{harvnb\|Holzner\|2006\|p=7}} "Physics is the study of your world and the world and universe around you."</ref>
	* '''Quantum Physics (QP)''' studies energy and matter at the fundamental level. To reveal the behaviors and properties of the building blocks of the universe. Quantum experiments involve very small objects, named electrons and photons, quantum phenomena are everywhere,  on every scale.		* '''Quantum Physics (QP)''' studies energy and matter at the fundamental level. To reveal the behaviors and properties of the building blocks of the universe. Quantum experiments involve very small objects, named electrons and photons, quantum phenomena are everywhere,  on every scale.
	[[file:Wignerfunction_fock_4.png\|thumb\|Wigner function for a Fock state with photon number n = 4 (shows structure for non-vacuum Fock states).]]		[[file:Wignerfunction_fock_4.png\|thumb\|Wigner function for a Fock state with photon number n = 4 (shows structure for non-vacuum Fock states).]]
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	== The Quantum Revolution ==		== The Quantum Revolution ==

	For centuries, scientists saw the universe as a precise, predictable apparatus. ~~[[Wikipedia:Classical mechanics\|~~Newtonian physics]] suggested that if you knew the position and motion of every object, you could predict the future perfectly. But the early twentieth century shattered this view. Experiments with atoms and light revealed that classical laws no longer applied. Energy was quantized, light sometimes behaved like a wave and sometimes like particles, and certainty gave way to probability.		For centuries, scientists saw the universe as a precise, predictable apparatus. Newtonian physics suggested that if you knew the position and motion of every object, you could predict the future perfectly. But the early twentieth century shattered this view. Experiments with atoms and light revealed that classical laws no longer applied. Energy was quantized, light sometimes behaved like a wave and sometimes like particles, and certainty gave way to probability.

	Quantum Mechanics emerged as a revolutionary framework, changing how we understand nature. Unlike classical physics, it does not give precise predictions. Instead, it provides probabilities, the propability of finding a particle in a particular place at a particular time. This uncertainty is not a flaw; it is the fundament of reality.		Quantum Mechanics emerged as a revolutionary framework, changing how we understand nature. Unlike classical physics, it does not give precise predictions. Instead, it provides probabilities, the propability of finding a particle in a particular place at a particular time. This uncertainty is not a flaw; it is the fundament of reality.

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	The word ''quantum'' is the neuter singular of the Latin interrogative adjective ''quantus'', meaning "how much". "Quanta", the neuter plural, short for "quanta of electricity" (electrons), was used in a 1902 article on the [[Physics:Quantum photoelectric effect\|photoelectric effect]] by [[Biography:Philipp Lenard\|Philipp Lenard]], who credited [[Biography:Hermann von Helmholtz\|Hermann von Helmholtz]] for using the word in the area of electricity. However, the word ''quantum'' in general was well known before 1900,<ref>E. Cobham Brewer 1810–1897. [http://www.bartleby.com/81/13830.html Dictionary of Phrase and Fable. 1898.] {{Web archive \|url=https://web.archive.org/web/20170630232946/http://www.bartleby.com/81/13830.html \|date=2017-06-30 }}</ref> e.g. ''quantum'' was used in E. A. Poe's Loss of Breath. It was often used by physicians, such as in the term ''quantum satis'', "the amount which is enough". Both Helmholtz and [[Biography:Julius von Mayer\|Julius von Mayer]] were physicians as well as physicists. Helmholtz used ''quantum'' with reference to heat in his article<ref>[http://www.ub.uni-heidelberg.de/helios/fachinfo/www/math/edd/helmholtz/R-Mayer.pdf E. Helmholtz, Robert Mayer's Priorität] {{Web archive \|url=https://web.archive.org/web/20150929101449/http://www.ub.uni-heidelberg.de/helios/fachinfo/www/math/edd/helmholtz/R-Mayer.pdf \|date=2015-09-29 }} </ref> on Mayer's work, and the word ''quantum'' can be found in the formulation of the first law of thermodynamics by Mayer in his letter<ref>{{cite web \|url=http://fs.math.uni-frankfurt.de/fsmath/misc/RobertMayer.html \|title=Heimatseite von Robert J. Mayer \|last=Herrmann \|first=Armin \|publisher=Weltreich der Physik, Gent-Verlag \|language=de \|date=1991\|url-status=bot: unknown \|archive-url=https://web.archive.org/web/19980209044633/http://fs.math.uni-frankfurt.de/fsmath/misc/RobertMayer.html \|archive-date=1998-02-09}}</ref> dated July 24, 1841.		The word ''quantum'' is the neuter singular of the Latin interrogative adjective ''quantus'', meaning "how much". "Quanta", the neuter plural, short for "quanta of electricity" (electrons), was used in a 1902 article on the [[Physics:Quantum photoelectric effect\|photoelectric effect]] by [[Biography:Philipp Lenard\|Philipp Lenard]], who credited [[Biography:Hermann von Helmholtz\|Hermann von Helmholtz]] for using the word in the area of electricity. However, the word ''quantum'' in general was well known before 1900,<ref>E. Cobham Brewer 1810–1897. [http://www.bartleby.com/81/13830.html Dictionary of Phrase and Fable. 1898.] {{Web archive \|url=https://web.archive.org/web/20170630232946/http://www.bartleby.com/81/13830.html \|date=2017-06-30 }}</ref> e.g. ''quantum'' was used in E. A. Poe's Loss of Breath. It was often used by physicians, such as in the term ''quantum satis'', "the amount which is enough". Both Helmholtz and [[Biography:Julius von Mayer\|Julius von Mayer]] were physicians as well as physicists. Helmholtz used ''quantum'' with reference to heat in his article<ref>[http://www.ub.uni-heidelberg.de/helios/fachinfo/www/math/edd/helmholtz/R-Mayer.pdf E. Helmholtz, Robert Mayer's Priorität] {{Web archive \|url=https://web.archive.org/web/20150929101449/http://www.ub.uni-heidelberg.de/helios/fachinfo/www/math/edd/helmholtz/R-Mayer.pdf \|date=2015-09-29 }} </ref> on Mayer's work, and the word ''quantum'' can be found in the formulation of the first law of thermodynamics by Mayer in his letter<ref>{{cite web \|url=http://fs.math.uni-frankfurt.de/fsmath/misc/RobertMayer.html \|title=Heimatseite von Robert J. Mayer \|last=Herrmann \|first=Armin \|publisher=Weltreich der Physik, Gent-Verlag \|language=de \|date=1991\|url-status=bot: unknown \|archive-url=https://web.archive.org/web/19980209044633/http://fs.math.uni-frankfurt.de/fsmath/misc/RobertMayer.html \|archive-date=1998-02-09}}</ref> dated July 24, 1841.
	[[File:Max Planck (1858-1947).jpg\|thumb\|upright=1\|300px\|German Physicist]] and 1918 Nobel Prize for Physics recipient Max Planck (1858–1947)]]		[[File:Max Planck (1858-1947).jpg\|thumb\|upright=1\|300px\|German Physicist]] and 1918 Nobel Prize for Physics recipient Max Planck (1858–1947)]]
	In 1901, [[Biography:Max Planck\|Max Planck]] used ''quanta'' to mean "quanta of matter and electricity",<ref name="Planck1901">{{cite journal \|last = Planck \|first = M. \|year = 1901 \|title = Ueber die Elementarquanta der Materie und der Elektricität \|journal = ~~[[Physics:Annalen der Physik\|~~Annalen der Physik]] \|volume = 309 \|pages = 564–566 \|doi = 10.1002/andp.19013090311 \|bibcode = 1901AnP...309..564P \|issue = 3 \|language = de \|url = https://zenodo.org/record/1423997 \|access-date = 2019-09-16 \|archive-date = 2023-06-24 \|archive-url = https://web.archive.org/web/20230624230014/https://zenodo.org/record/1423997 \|url-status = live }}</ref> gas, and heat.<ref>{{cite journal \|last1=Planck \|first1=Max \|title=Ueber das thermodynamische Gleichgewicht von Gasgemengen \|journal=Annalen der Physik \|volume=255 \|pages=358–378 \|year=1883 \|doi=10.1002/andp.18832550612 \|bibcode=1883AnP...255..358P \|issue=6 \|language=de \|url=https://zenodo.org/record/1423794 \|access-date=2019-07-05 \|archive-date=2021-01-21 \|archive-url=https://web.archive.org/web/20210121222137/https://zenodo.org/record/1423794 \|url-status=live }}</ref> In 1905, in response to Planck's work and the experimental work of Lenard (who explained his results by using the term ''quanta of electricity''), [[Biography:Albert Einstein\|Albert Einstein]] suggested that [[Physics:Quantum electromagnetic field\|radiation]] existed in spatially localized packets which he called [[Physics:Quantum photon\|"quanta of light"]] ("''Lichtquanta''").<ref name="Einstein1905">{{cite journal \|last = Einstein \|first = A. \|author-link = Albert Einstein \|year = 1905 \|title = Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt \|url = http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1905_17_132-148.pdf \|journal = ~~[[Physics:Annalen der Physik\|~~Annalen der Physik]] \|volume = 17 \|pages = 132–148 \|doi = 10.1002/andp.19053220607 \|bibcode = 1905AnP...322..132E \|issue = 6 \|language = de \|doi-access = free \|access-date = 2010-08-26 \|archive-date = 2015-09-24 \|archive-url = https://web.archive.org/web/20150924072915/http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1905_17_132-148.pdf \|url-status = live }}. A partial [https://en.wikisource.org/?curid=59468 English translation] {{Webarchive \|url=https://web.archive.org/web/20210121022128/https://en.wikisource.org/?curid=59468 \|date=2021-01-21 }} is available from [[Wikisource]].</ref>		In 1901, [[Biography:Max Planck\|Max Planck]] used ''quanta'' to mean "quanta of matter and electricity",<ref name="Planck1901">{{cite journal \|last = Planck \|first = M. \|year = 1901 \|title = Ueber die Elementarquanta der Materie und der Elektricität \|journal = Annalen der Physik \|volume = 309 \|pages = 564–566 \|doi = 10.1002/andp.19013090311 \|bibcode = 1901AnP...309..564P \|issue = 3 \|language = de \|url = https://zenodo.org/record/1423997 \|access-date = 2019-09-16 \|archive-date = 2023-06-24 \|archive-url = https://web.archive.org/web/20230624230014/https://zenodo.org/record/1423997 \|url-status = live }}</ref> gas, and heat.<ref>{{cite journal \|last1=Planck \|first1=Max \|title=Ueber das thermodynamische Gleichgewicht von Gasgemengen \|journal=Annalen der Physik \|volume=255 \|pages=358–378 \|year=1883 \|doi=10.1002/andp.18832550612 \|bibcode=1883AnP...255..358P \|issue=6 \|language=de \|url=https://zenodo.org/record/1423794 \|access-date=2019-07-05 \|archive-date=2021-01-21 \|archive-url=https://web.archive.org/web/20210121222137/https://zenodo.org/record/1423794 \|url-status=live }}</ref> In 1905, in response to Planck's work and the experimental work of Lenard (who explained his results by using the term ''quanta of electricity''), [[Biography:Albert Einstein\|Albert Einstein]] suggested that [[Physics:Quantum electromagnetic field\|radiation]] existed in spatially localized packets which he called [[Physics:Quantum photon\|"quanta of light"]] ("''Lichtquanta''").<ref name="Einstein1905">{{cite journal \|last = Einstein \|first = A. \|author-link = Albert Einstein \|year = 1905 \|title = Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt \|url = http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1905_17_132-148.pdf \|journal = Annalen der Physik \|volume = 17 \|pages = 132–148 \|doi = 10.1002/andp.19053220607 \|bibcode = 1905AnP...322..132E \|issue = 6 \|language = de \|doi-access = free \|access-date = 2010-08-26 \|archive-date = 2015-09-24 \|archive-url = https://web.archive.org/web/20150924072915/http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1905_17_132-148.pdf \|url-status = live }}. A partial [https://en.wikisource.org/?curid=59468 English translation] {{Webarchive \|url=https://web.archive.org/web/20210121022128/https://en.wikisource.org/?curid=59468 \|date=2021-01-21 }} is available from Wikisource.</ref>

	The concept of quantization of radiation was discovered in 1900 by [[Biography:Max Planck\|Max Planck]], who had been trying to understand the emission of radiation from heated objects, known as [[Physics:Quantum black-body radiation\|black-body radiation]]. By assuming that energy can be absorbed or released only in tiny, differential, discrete packets (which he called "bundles", or "energy elements"),<ref>{{cite journal \|author=Max Planck \|title=Ueber das Gesetz der Energieverteilung im Normalspectrum (On the Law of Distribution of Energy in the Normal Spectrum) \|url=http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html \|journal=Annalen der Physik \|volume= 309 \|doi=10.1002/andp.19013090310 \|page=553 \|year=1901 \|archive-url = https://web.archive.org/web/20080418002757/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html \|archive-date = 2008-04-18 \|bibcode = 1901AnP...309..553P \|issue=3 \|doi-access=free }}</ref> Planck accounted for certain objects changing color when heated.<ref>Brown, T., LeMay, H., Bursten, B. (2008). ''Chemistry: The Central Science'' Upper Saddle River, New Jersey: Pearson Education {{ISBN\|0-13-600617-5}}</ref> On December 14, 1900, Planck reported his [[Physics:Quantum black-body radiation\|findings]] to the German Physical Society, and introduced the idea of quantizat[[Physics:Quantum black-body radiation\|findings]]ion for the first time as a part of his research on black-body radiation.<ref>{{cite journal \|last1=Klein \|first1=Martin J. \|title=Max Planck and the beginnings of the quantum theory \|journal=Archive for History of Exact Sciences \|volume=1 \|pages=459–479 \|year=1961 \|doi=10.1007/BF00327765 \|issue=5\|s2cid=121189755 }}</ref> As a result of his experiments, Planck deduced the numerical value of ''h'', known as the [[Physics:Quantum Planck constant\|Planck constant]], and reported more precise values for the unit of electrical charge and the Avogadro–Loschmidt number, the number of real molecules in a mole, to the German Physical Society. After his theory was validated, Planck was awarded the Nobel Prize in Physics for his discovery in 1918.		The concept of quantization of radiation was discovered in 1900 by [[Biography:Max Planck\|Max Planck]], who had been trying to understand the emission of radiation from heated objects, known as [[Physics:Quantum black-body radiation\|black-body radiation]]. By assuming that energy can be absorbed or released only in tiny, differential, discrete packets (which he called "bundles", or "energy elements"),<ref>{{cite journal \|author=Max Planck \|title=Ueber das Gesetz der Energieverteilung im Normalspectrum (On the Law of Distribution of Energy in the Normal Spectrum) \|url=http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html \|journal=Annalen der Physik \|volume= 309 \|doi=10.1002/andp.19013090310 \|page=553 \|year=1901 \|archive-url = https://web.archive.org/web/20080418002757/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html \|archive-date = 2008-04-18 \|bibcode = 1901AnP...309..553P \|issue=3 \|doi-access=free }}</ref> Planck accounted for certain objects changing color when heated.<ref>Brown, T., LeMay, H., Bursten, B. (2008). ''Chemistry: The Central Science'' Upper Saddle River, New Jersey: Pearson Education {{ISBN\|0-13-600617-5}}</ref> On December 14, 1900, Planck reported his [[Physics:Quantum black-body radiation\|findings]] to the German Physical Society, and introduced the idea of quantizat[[Physics:Quantum black-body radiation\|findings]]ion for the first time as a part of his research on black-body radiation.<ref>{{cite journal \|last1=Klein \|first1=Martin J. \|title=Max Planck and the beginnings of the quantum theory \|journal=Archive for History of Exact Sciences \|volume=1 \|pages=459–479 \|year=1961 \|doi=10.1007/BF00327765 \|issue=5\|s2cid=121189755 }}</ref> As a result of his experiments, Planck deduced the numerical value of ''h'', known as the [[Physics:Quantum Planck constant\|Planck constant]], and reported more precise values for the unit of electrical charge and the Avogadro–Loschmidt number, the number of real molecules in a mole, to the German Physical Society. After his theory was validated, Planck was awarded the Nobel Prize in Physics for his discovery in 1918.
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	[[File:Quantum superposition.svg\|thumb\|Quantum Superposition and Probability Density]]		[[File:Quantum superposition.svg\|thumb\|Quantum Superposition and Probability Density]]
	* [[Physics:Quantum superposition\|'''Superposition:''']] A quantum particle can exist in several different states simultaneously. Schrödinger captured this strangeness with his famous thought experiment: a cat sealed in a box, tied to a random quantum event. Until the box is opened and observed, the cat is, in a very real quantum sense, both alive and dead at the same time. This dramatically illustrates how quantum logic defies our everyday intuition.		* [[Physics:Quantum superposition\|'''Superposition:''']] A quantum particle can exist in several different states simultaneously. Schrödinger captured this strangeness with his famous thought experiment: a cat sealed in a box, tied to a random quantum event. Until the box is opened and observed, the cat is, in a very real quantum sense, both alive and dead at the same time. This dramatically illustrates how quantum logic defies our everyday intuition.
	[[File:~~Entanglement filtering via anti-parity time (APT) symmetry~~.png\|thumb\|Entanglement via (APT)]]		[[File:Quantum_book1_basics_yellow.png\|thumb\|Entanglement via (APT)]]

	* [[Physics:Quantum entanglement\|'''Quantum entanglement''':]] Two or more particles can become linked so that the state of one influences the other, even at a distance. Einstein called this “spooky action at a distance.” Experiments have confirmed it, as the basis of quantum computing and secure communication.<br><br>		* [[Physics:Quantum entanglement\|'''Quantum entanglement''':]] Two or more particles can become linked so that the state of one influences the other, even at a distance. Einstein called this “spooky action at a distance.” Experiments have confirmed it, as the basis of quantum computing and secure communication.<br><br>

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	{{Author\|Harold Foppele}}		{{Author\|Harold Foppele}}

	{{Sourceattribution\|Quantum basics\|1}}		{{Sourceattribution\|Physics:Quantum basics\|1}}

Harold: /* Canonical quantum gravity */

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Canonical quantum gravity

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	== Canonical quantum gravity ==		== Canonical quantum gravity ==
	[[File:Quantum gravity combination.png\|1000px\|center]]		[[File:Quantum gravity combination.png\|1000px\|center]]
	In physics, '''canonical quantum gravity''' is an attempt to quantize the canonical formulation of general relativity (or '''canonical gravity'''). It is a [[Physics:Quantum Hamiltonian\|Hamiltonian]] formulation of [[Biography:Albert Einstein\|Einstein]]'s [[Physics:Quantum gravity\|general theory of relativity]]. The basic theory was outlined by [[Biography:Bryce DeWitt\|Bryce DeWitt]]{{ref\|dewitt}} in a seminal 1967 paper, and based on earlier work by Peter G. Bergmann{{ref\|bergmann}} using the so-called [[Physics:Quantum methods/quantization\|canonical quantization]] techniques for constrained Hamiltonian systems invented by [[Biography:Paul Dirac\|Paul Dirac]].{{ref\|dirac}} Dirac's approach allows the quantization of systems that include gauge symmetries using Hamiltonian techniques in a fixed [[Physics:Quantum gauge theory\|gauge choice]]. Newer approaches based in part on the work of DeWitt and Dirac include the [[~~Astronomy~~:~~Hartle–Hawking state~~\|Hartle–Hawking state]], [[Physics:~~Regge calculus~~\|Regge calculus]], the [[Physics:Quantum basics#Cosmology\|Wheeler–DeWitt equation]] and [[Physics:Quantum gravity\|loop quantum gravity]].		In physics, '''canonical quantum gravity''' is an attempt to quantize the canonical formulation of general relativity (or '''canonical gravity'''). It is a [[Physics:Quantum Hamiltonian\|Hamiltonian]] formulation of [[Biography:Albert Einstein\|Einstein]]'s [[Physics:Quantum gravity\|general theory of relativity]]. The basic theory was outlined by [[Biography:Bryce DeWitt\|Bryce DeWitt]]{{ref\|dewitt}} in a seminal 1967 paper, and based on earlier work by Peter G. Bergmann{{ref\|bergmann}} using the so-called [[Physics:Quantum methods/quantization\|canonical quantization]] techniques for constrained Hamiltonian systems invented by [[Biography:Paul Dirac\|Paul Dirac]].{{ref\|dirac}} Dirac's approach allows the quantization of systems that include gauge symmetries using Hamiltonian techniques in a fixed [[Physics:Quantum gauge theory\|gauge choice]]. Newer approaches based in part on the work of DeWitt and Dirac include the [[Physics:Quantum basics#Cosmology\|Hartle–Hawking state]], [[Physics:Quantum gravity\|Regge calculus]], the [[Physics:Quantum basics#Cosmology\|Wheeler–DeWitt equation]] and [[Physics:Quantum gravity\|loop quantum gravity]].

	== Core concepts and introduction to the quantum world ==		== Core concepts and introduction to the quantum world ==

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	{{Short description\|Learning project introducing the quantum concept and the fundamental principles of quantum mechanics, from quantization to quantum technologies}}		{{Short description\|Learning project introducing the quantum concept and the fundamental principles of quantum mechanics, from quantization to quantum technologies}}

	{{Quantum book backlink\|Foundations}}		{{Quantum book backlink\|Foundations}}
	{{Quantum article nav\|next=Physics:Quantum photoelectric effect\|next label=Photoelectric effect}}		{{Quantum article nav\|next=Physics:Quantum photoelectric effect\|next label=Photoelectric effect}}

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	{{Short description\|Learning project introducing the quantum concept and the fundamental principles of quantum mechanics, from quantization to quantum technologies}}		{{Short description\|Learning project introducing the quantum concept and the fundamental principles of quantum mechanics, from quantization to quantum technologies}}

	{{Quantum book backlink\|Foundations}}		{{Quantum book backlink\|Foundations}}
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	The word ''quantum'' is the neuter singular of the Latin interrogative adjective ''quantus'', meaning "how much". "Quanta", the neuter plural, short for "quanta of electricity" (electrons), was used in a 1902 article on the [[Physics:Quantum photoelectric effect\|photoelectric effect]] by [[Biography:Philipp Lenard\|Philipp Lenard]], who credited [[Biography:Hermann von Helmholtz\|Hermann von Helmholtz]] for using the word in the area of electricity. However, the word ''quantum'' in general was well known before 1900,<ref>E. Cobham Brewer 1810–1897. [http://www.bartleby.com/81/13830.html Dictionary of Phrase and Fable. 1898.] {{Web archive \|url=https://web.archive.org/web/20170630232946/http://www.bartleby.com/81/13830.html \|date=2017-06-30 }}</ref> e.g. ''quantum'' was used in E. A. Poe's Loss of Breath. It was often used by physicians, such as in the term ''quantum satis'', "the amount which is enough". Both Helmholtz and [[Biography:Julius von Mayer\|Julius von Mayer]] were physicians as well as physicists. Helmholtz used ''quantum'' with reference to heat in his article<ref>[http://www.ub.uni-heidelberg.de/helios/fachinfo/www/math/edd/helmholtz/R-Mayer.pdf E. Helmholtz, Robert Mayer's Priorität] {{Web archive \|url=https://web.archive.org/web/20150929101449/http://www.ub.uni-heidelberg.de/helios/fachinfo/www/math/edd/helmholtz/R-Mayer.pdf \|date=2015-09-29 }} </ref> on Mayer's work, and the word ''quantum'' can be found in the formulation of the first law of thermodynamics by Mayer in his letter<ref>{{cite web \|url=http://fs.math.uni-frankfurt.de/fsmath/misc/RobertMayer.html \|title=Heimatseite von Robert J. Mayer \|last=Herrmann \|first=Armin \|publisher=Weltreich der Physik, Gent-Verlag \|language=de \|date=1991\|url-status=bot: unknown \|archive-url=https://web.archive.org/web/19980209044633/http://fs.math.uni-frankfurt.de/fsmath/misc/RobertMayer.html \|archive-date=1998-02-09}}</ref> dated July 24, 1841.		The word ''quantum'' is the neuter singular of the Latin interrogative adjective ''quantus'', meaning "how much". "Quanta", the neuter plural, short for "quanta of electricity" (electrons), was used in a 1902 article on the [[Physics:Quantum photoelectric effect\|photoelectric effect]] by [[Biography:Philipp Lenard\|Philipp Lenard]], who credited [[Biography:Hermann von Helmholtz\|Hermann von Helmholtz]] for using the word in the area of electricity. However, the word ''quantum'' in general was well known before 1900,<ref>E. Cobham Brewer 1810–1897. [http://www.bartleby.com/81/13830.html Dictionary of Phrase and Fable. 1898.] {{Web archive \|url=https://web.archive.org/web/20170630232946/http://www.bartleby.com/81/13830.html \|date=2017-06-30 }}</ref> e.g. ''quantum'' was used in E. A. Poe's Loss of Breath. It was often used by physicians, such as in the term ''quantum satis'', "the amount which is enough". Both Helmholtz and [[Biography:Julius von Mayer\|Julius von Mayer]] were physicians as well as physicists. Helmholtz used ''quantum'' with reference to heat in his article<ref>[http://www.ub.uni-heidelberg.de/helios/fachinfo/www/math/edd/helmholtz/R-Mayer.pdf E. Helmholtz, Robert Mayer's Priorität] {{Web archive \|url=https://web.archive.org/web/20150929101449/http://www.ub.uni-heidelberg.de/helios/fachinfo/www/math/edd/helmholtz/R-Mayer.pdf \|date=2015-09-29 }} </ref> on Mayer's work, and the word ''quantum'' can be found in the formulation of the first law of thermodynamics by Mayer in his letter<ref>{{cite web \|url=http://fs.math.uni-frankfurt.de/fsmath/misc/RobertMayer.html \|title=Heimatseite von Robert J. Mayer \|last=Herrmann \|first=Armin \|publisher=Weltreich der Physik, Gent-Verlag \|language=de \|date=1991\|url-status=bot: unknown \|archive-url=https://web.archive.org/web/19980209044633/http://fs.math.uni-frankfurt.de/fsmath/misc/RobertMayer.html \|archive-date=1998-02-09}}</ref> dated July 24, 1841.
	[[File:Max Planck (1858-1947).jpg\|thumb\|upright=1\|300px\|German Physicist]] and 1918 Nobel Prize for Physics recipient Max Planck (1858–1947)]]		[[File:Max Planck (1858-1947).jpg\|thumb\|upright=1\|300px\|German Physicist]] and 1918 Nobel Prize for Physics recipient Max Planck (1858–1947)]]
	In 1901, [[Biography:Max Planck\|Max Planck]] used ''quanta'' to mean "quanta of matter and electricity",<ref name="Planck1901">{{cite journal \|last = Planck \|first = M. \|year = 1901 \|title = Ueber die Elementarquanta der Materie und der Elektricität \|journal = ~~[[Physics:Annalen der Physik\|~~Annalen der Physik]] \|volume = 309 \|pages = 564–566 \|doi = 10.1002/andp.19013090311 \|bibcode = 1901AnP...309..564P \|issue = 3 \|language = de \|url = https://zenodo.org/record/1423997 \|access-date = 2019-09-16 \|archive-date = 2023-06-24 \|archive-url = https://web.archive.org/web/20230624230014/https://zenodo.org/record/1423997 \|url-status = live }}</ref> gas, and heat.<ref>{{cite journal \|last1=Planck \|first1=Max \|title=Ueber das thermodynamische Gleichgewicht von Gasgemengen \|journal=Annalen der Physik \|volume=255 \|pages=358–378 \|year=1883 \|doi=10.1002/andp.18832550612 \|bibcode=1883AnP...255..358P \|issue=6 \|language=de \|url=https://zenodo.org/record/1423794 \|access-date=2019-07-05 \|archive-date=2021-01-21 \|archive-url=https://web.archive.org/web/20210121222137/https://zenodo.org/record/1423794 \|url-status=live }}</ref> In 1905, in response to Planck's work and the experimental work of Lenard (who explained his results by using the term ''quanta of electricity''), [[Biography:Albert Einstein\|Albert Einstein]] suggested that [[Physics:Quantum electromagnetic field\|radiation]] existed in spatially localized packets which he called [[Physics:Quantum photon\|"quanta of light"]] ("''Lichtquanta''").<ref name="Einstein1905">{{cite journal \|last = Einstein \|first = A. \|author-link = Albert Einstein \|year = 1905 \|title = Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt \|url = http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1905_17_132-148.pdf \|journal = ~~[[Physics:Annalen der Physik\|~~Annalen der Physik]] \|volume = 17 \|pages = 132–148 \|doi = 10.1002/andp.19053220607 \|bibcode = 1905AnP...322..132E \|issue = 6 \|language = de \|doi-access = free \|access-date = 2010-08-26 \|archive-date = 2015-09-24 \|archive-url = https://web.archive.org/web/20150924072915/http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1905_17_132-148.pdf \|url-status = live }}. A partial [https://en.wikisource.org/?curid=59468 English translation] {{Webarchive \|url=https://web.archive.org/web/20210121022128/https://en.wikisource.org/?curid=59468 \|date=2021-01-21 }} is available from [[Wikisource]].</ref>		In 1901, [[Biography:Max Planck\|Max Planck]] used ''quanta'' to mean "quanta of matter and electricity",<ref name="Planck1901">{{cite journal \|last = Planck \|first = M. \|year = 1901 \|title = Ueber die Elementarquanta der Materie und der Elektricität \|journal = Annalen der Physik \|volume = 309 \|pages = 564–566 \|doi = 10.1002/andp.19013090311 \|bibcode = 1901AnP...309..564P \|issue = 3 \|language = de \|url = https://zenodo.org/record/1423997 \|access-date = 2019-09-16 \|archive-date = 2023-06-24 \|archive-url = https://web.archive.org/web/20230624230014/https://zenodo.org/record/1423997 \|url-status = live }}</ref> gas, and heat.<ref>{{cite journal \|last1=Planck \|first1=Max \|title=Ueber das thermodynamische Gleichgewicht von Gasgemengen \|journal=Annalen der Physik \|volume=255 \|pages=358–378 \|year=1883 \|doi=10.1002/andp.18832550612 \|bibcode=1883AnP...255..358P \|issue=6 \|language=de \|url=https://zenodo.org/record/1423794 \|access-date=2019-07-05 \|archive-date=2021-01-21 \|archive-url=https://web.archive.org/web/20210121222137/https://zenodo.org/record/1423794 \|url-status=live }}</ref> In 1905, in response to Planck's work and the experimental work of Lenard (who explained his results by using the term ''quanta of electricity''), [[Biography:Albert Einstein\|Albert Einstein]] suggested that [[Physics:Quantum electromagnetic field\|radiation]] existed in spatially localized packets which he called [[Physics:Quantum photon\|"quanta of light"]] ("''Lichtquanta''").<ref name="Einstein1905">{{cite journal \|last = Einstein \|first = A. \|author-link = Albert Einstein \|year = 1905 \|title = Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt \|url = http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1905_17_132-148.pdf \|journal = Annalen der Physik \|volume = 17 \|pages = 132–148 \|doi = 10.1002/andp.19053220607 \|bibcode = 1905AnP...322..132E \|issue = 6 \|language = de \|doi-access = free \|access-date = 2010-08-26 \|archive-date = 2015-09-24 \|archive-url = https://web.archive.org/web/20150924072915/http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1905_17_132-148.pdf \|url-status = live }}. A partial [https://en.wikisource.org/?curid=59468 English translation] {{Webarchive \|url=https://web.archive.org/web/20210121022128/https://en.wikisource.org/?curid=59468 \|date=2021-01-21 }} is available from Wikisource.</ref>

	The concept of quantization of radiation was discovered in 1900 by [[Biography:Max Planck\|Max Planck]], who had been trying to understand the emission of radiation from heated objects, known as [[Physics:Quantum black-body radiation\|black-body radiation]]. By assuming that energy can be absorbed or released only in tiny, differential, discrete packets (which he called "bundles", or "energy elements"),<ref>{{cite journal \|author=Max Planck \|title=Ueber das Gesetz der Energieverteilung im Normalspectrum (On the Law of Distribution of Energy in the Normal Spectrum) \|url=http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html \|journal=Annalen der Physik \|volume= 309 \|doi=10.1002/andp.19013090310 \|page=553 \|year=1901 \|archive-url = https://web.archive.org/web/20080418002757/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html \|archive-date = 2008-04-18 \|bibcode = 1901AnP...309..553P \|issue=3 \|doi-access=free }}</ref> Planck accounted for certain objects changing color when heated.<ref>Brown, T., LeMay, H., Bursten, B. (2008). ''Chemistry: The Central Science'' Upper Saddle River, New Jersey: Pearson Education {{ISBN\|0-13-600617-5}}</ref> On December 14, 1900, Planck reported his [[Physics:Quantum black-body radiation\|findings]] to the German Physical Society, and introduced the idea of quantizat[[Physics:Quantum black-body radiation\|findings]]ion for the first time as a part of his research on black-body radiation.<ref>{{cite journal \|last1=Klein \|first1=Martin J. \|title=Max Planck and the beginnings of the quantum theory \|journal=Archive for History of Exact Sciences \|volume=1 \|pages=459–479 \|year=1961 \|doi=10.1007/BF00327765 \|issue=5\|s2cid=121189755 }}</ref> As a result of his experiments, Planck deduced the numerical value of ''h'', known as the [[Physics:Quantum Planck constant\|Planck constant]], and reported more precise values for the unit of electrical charge and the Avogadro–Loschmidt number, the number of real molecules in a mole, to the German Physical Society. After his theory was validated, Planck was awarded the Nobel Prize in Physics for his discovery in 1918.		The concept of quantization of radiation was discovered in 1900 by [[Biography:Max Planck\|Max Planck]], who had been trying to understand the emission of radiation from heated objects, known as [[Physics:Quantum black-body radiation\|black-body radiation]]. By assuming that energy can be absorbed or released only in tiny, differential, discrete packets (which he called "bundles", or "energy elements"),<ref>{{cite journal \|author=Max Planck \|title=Ueber das Gesetz der Energieverteilung im Normalspectrum (On the Law of Distribution of Energy in the Normal Spectrum) \|url=http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html \|journal=Annalen der Physik \|volume= 309 \|doi=10.1002/andp.19013090310 \|page=553 \|year=1901 \|archive-url = https://web.archive.org/web/20080418002757/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Planck-1901/Planck-1901.html \|archive-date = 2008-04-18 \|bibcode = 1901AnP...309..553P \|issue=3 \|doi-access=free }}</ref> Planck accounted for certain objects changing color when heated.<ref>Brown, T., LeMay, H., Bursten, B. (2008). ''Chemistry: The Central Science'' Upper Saddle River, New Jersey: Pearson Education {{ISBN\|0-13-600617-5}}</ref> On December 14, 1900, Planck reported his [[Physics:Quantum black-body radiation\|findings]] to the German Physical Society, and introduced the idea of quantizat[[Physics:Quantum black-body radiation\|findings]]ion for the first time as a part of his research on black-body radiation.<ref>{{cite journal \|last1=Klein \|first1=Martin J. \|title=Max Planck and the beginnings of the quantum theory \|journal=Archive for History of Exact Sciences \|volume=1 \|pages=459–479 \|year=1961 \|doi=10.1007/BF00327765 \|issue=5\|s2cid=121189755 }}</ref> As a result of his experiments, Planck deduced the numerical value of ''h'', known as the [[Physics:Quantum Planck constant\|Planck constant]], and reported more precise values for the unit of electrical charge and the Avogadro–Loschmidt number, the number of real molecules in a mole, to the German Physical Society. After his theory was validated, Planck was awarded the Nobel Prize in Physics for his discovery in 1918.
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	[[File:Quantum superposition.svg\|thumb\|Quantum Superposition and Probability Density]]		[[File:Quantum superposition.svg\|thumb\|Quantum Superposition and Probability Density]]
	* [[Physics:Quantum superposition\|'''Superposition:''']] A quantum particle can exist in several different states simultaneously. Schrödinger captured this strangeness with his famous thought experiment: a cat sealed in a box, tied to a random quantum event. Until the box is opened and observed, the cat is, in a very real quantum sense, both alive and dead at the same time. This dramatically illustrates how quantum logic defies our everyday intuition.		* [[Physics:Quantum superposition\|'''Superposition:''']] A quantum particle can exist in several different states simultaneously. Schrödinger captured this strangeness with his famous thought experiment: a cat sealed in a box, tied to a random quantum event. Until the box is opened and observed, the cat is, in a very real quantum sense, both alive and dead at the same time. This dramatically illustrates how quantum logic defies our everyday intuition.
	[[File:~~Entanglement filtering via anti-parity time (APT) symmetry~~.png\|thumb\|Entanglement via (APT)]]		[[File:Quantum_book1_basics_yellow.png\|thumb\|Entanglement via (APT)]]

	* [[Physics:Quantum entanglement\|'''Quantum entanglement''':]] Two or more particles can become linked so that the state of one influences the other, even at a distance. Einstein called this “spooky action at a distance.” Experiments have confirmed it, as the basis of quantum computing and secure communication.<br><br>		* [[Physics:Quantum entanglement\|'''Quantum entanglement''':]] Two or more particles can become linked so that the state of one influences the other, even at a distance. Einstein called this “spooky action at a distance.” Experiments have confirmed it, as the basis of quantum computing and secure communication.<br><br>