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{{Short description|Scientific overview of
quantum mechanics}}
{{Quantum book backlink|Conceptual and interpretations}}
<br>
'''A Frivolous Approach to Quantum'''<br>
A popular scientific overview of [[Wikipedia:quantum|quantum]], its history, central concepts, and emerging technologies. Written in an informal style, the article covers principles such as [[Wikipedia:quantisation|quantisation]], [[Wikipedia:superposition|superposition]], and [[Wikipedia:quantum entanglement|quantum entanglement]], while linking them to both foundational experiments and modern applications. It covers Theory, History, Related equations, Related concepts, Applications, Interpretations and a [[Physics:Quantum A Walk Through the Universe#Quantum Cheat Sheet|'''Quantum Cheat Sheet''']].

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Big Bang Explosion
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== Theory ==

A quantum (plural quanta) is the smallest discrete unit of a physical property, such as energy, light, or angular momentum. For example, a [[Wikipedia:photon|photon]] is a quantum of light. This fundamental particle of electromagnetic radiation is the basic building block of light, which behaves as both a wave and a particle.<ref name="DOE2025">{{Cite journal |year=2025 |title=DOE Explains Quantum Mechanics|url=https://www.energy.gov/science/doe-explainsquantum-mechanics#:~:text=The%20particle%20portion%20of%20the,or%20light%2C%20is%20a%20photon.|journal=U.S. Department of Energy}}</ref>
[[File:Artistic impression of an atom 2c.jpg|thumb|Artistic impression of an atom 2c]]
[[File:Pexels-marcin-jozwiak-199600-14097222.jpg|thumb|Quantum artist impression]]
[[Wikipedia:Quantum physics|Quantum physics]] is the study of matter and energy at the most fundamental level. It aims to uncover the properties and behaviors of the very building blocks of nature. While many quantum experiments examine very small objects, such as electrons and photons, quantum phenomena are all around us, acting on every scale it is including [[Wikipedia:wave-particle duality|wave-particle duality]] and [[Wikipedia:Energy level|quantized energy levels]].

[[Physics:Quantum mechanics]] is the mathematical framework within quantum physics that provides the rules and equations to describe and predict the behavior of [[Wikipedia:quantum systems|quantum systems]]. It includes principles such as the [[Wikipedia:uncertainty principle|uncertainty principle]], [[Wikipedia:wavefunctions|wavefunctions]], and [[Wikipedia:superposition|superposition]].

In summary:
* Quantum = the smallest piece of a property.
* Quantum physics = the study of the behavior of these small pieces.
* Quantum mechanics = the set of rules and equations that describe how they behave.

Quantum Science consist of Quantum physics (QP) and Quantum mechanics (QM) describing the behaviour of matter and light at the atomic and subatomic scale.<ref name="Griffiths2018">{{cite book
| author = [[Wikipedia:David J. Griffiths|David J. Griffiths]] and Darrell F. Schroeter
| title = Introduction to Quantum Mechanics
| edition = 3rd
| publisher = Cambridge University Press
| location = Cambridge
| year = 2018
| isbn = 978-1-107-18963-8
}}</ref>
These phenomena underlie technologies such as [[Wikipedia:Semiconductor|semiconductors]], [[Wikipedia:Laser|lasers]], and [[Wikipedia:Solar cell|solar cells]], and form the basis of developing fields including [[Quantum computing|quantum computing]] and [[Wikipedia:Quantum sensor|quantum sensing]].<ref name="DowlingMilburn2003">{{cite journal
| authors = [[Wikipedia:Jonathan Dowling|Jonathan P. Dowling]] and [[Wikipedia:Gerard J. Milburn|Gerard J. Milburn]]
| title = Quantum technology: the second quantum revolution
| journal = Philosophical Transactions of the Royal Society A
| volume = 361
| issue = 1809
| pages = 1655–1674
| date = 2003-08-15
| doi = 10.1098/rsta.2003.1227
| bibcode = 2003RSPTA.361.1655D
| arxiv = quant-ph/0206091
| url = https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2003.1227
}}</ref>
Physicists have described quantum mechanics as both the most successful theory of nature and one of the most conceptually challenging, as its principles often conflict with intuitive human experience.<ref name="Jammer1966">{{cite book
| author = [[Wikipedia:Max Jammer|Max Jammer]]
| title = The Conceptual Development of Quantum Mechanics
| publisher = McGraw-Hill
| location = New York
| year = 1966
| url = https://archive.org/details/conceptualdevelo0000jamm
}}</ref>

== Historical background ==
=== Early challenges to classical physics ===
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<gallery widths="75px" perrow="5" caption="Key figures in early quantum physics">
File:Max Planck by Hugo Erfurth 1938cr - restoration1.jpg|<small>Max Planck (1858–1947)</small>
File:Albert Einstein Head.jpg|<small>Albert Einstein (1879–1955)</small>
File:Niels Bohr.jpg|<small>Niels Bohr (1885–1962)</small>
File:Clinton Davisson.jpg|<small>Clinton Davisson (1881–1958)</small>
File:Germer Lester A2.jpg|<small>Lester Germer (1896–1971)</small>
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In the 19th century, classical physics described motion, gravity, and electromagnetism with high precision. Experiments such as [[Wikipedia:Thomas Young|Thomas Young]]’s 1801 [[Wikipedia:double-slit experiment|double-slit experiment]] supported the wave theory of light.<ref>{{Cite journal |last=Young |first=Thomas |year=1802 |title=The Bakerian Lecture: Experiments and Calculations Relative to Physical Optics |url=https://royalsocietypublishing.org/doi/10.1098/rstl.1802.0003 |journal=Philosophical Transactions of the Royal Society of London |volume=92 |pages=12–48 |doi=10.1098/rstl.1802.0003}}</ref> At the turn of the 20th century, several anomalies emerged. The [[Wikipedia:photoelectric effect|photoelectric effect]] demonstrated that increasing light intensity did not increase the [[Wikipedia:Kinetic energy|kinetic energy]] of emitted electrons as predicted by classical wave theory. In 1900, [[Wikipedia:Max Planck|Max Planck]] proposed that light is emitted in discrete packets, or quanta.<ref>{{Cite journal |last=Planck |first=Max |year=1901 |title=On the Law of Distribution of Energy in the Normal Spectrum |url=https://onlinelibrary.wiley.com/doi/10.1002/andp.19013090310 |journal=Annalen der Physik |volume=4 |pages=553–563 |doi=10.1002/andp.19013090310}}</ref> [[Wikipedia:Albert Einstein|Albert Einstein]] expanded this idea in 1905, introducing the concept of the photon.<ref>{{Cite journal |last=Einstein |first=Albert |year=1905 |title=On a Heuristic Viewpoint Concerning the Production and Transformation of Light |url=https://onlinelibrary.wiley.com/doi/10.1002/andp.19053220607 |journal=Annalen der Physik |volume=17 |pages=132–148 |doi=10.1002/andp.19053220607}}</ref>

[[Wikipedia:Niels Bohr|Niels Bohr]]’s 1913 atomic model explained electron behaviour in hydrogen but was limited for larger atoms and molecules. By 1927, [[Wikipedia:Clinton Davisson|Clinton Davisson]] and [[Wikipedia:Lester Germer|Lester Germer]] demonstrated electron diffraction, providing direct evidence of [[Wikipedia:wave–particle duality|wave–particle duality]]. <ref>{{Cite journal |last1=Davisson |first1=Clinton J. |last2=Germer |first2=Lester H. |year=1927 |title=Diffraction of Electrons by a Crystal of Nickel |url=https://journals.aps.org/pr/abstract/10.1103/PhysRev.30.705 |journal=Physical Review |volume=30 |issue=6 |pages=705–740 |doi=10.1103/PhysRev.30.705}}</ref>

== Related Equations and concepts ==
===Quantum tunneling===
[[File:Quantum tunnel effect and its application to the scanning tunneling microscope.ogv|Quantum tunnel effect and its application to the scanning tunneling microscope]]
In physics, '''quantum tunnelling''', '''barrier penetration''', or simply '''tunnelling''' is a [[Wikipedia:quantum mechanics|quantum mechanical]] phenomenon in which an object such as an electron or atom passes through a [[Wikipedia:potential barrier|potential energy barrier]] that, according to [[Wikipedia:classical mechanics|classical mechanics]], should not be passable due to the object not having sufficient energy to pass or surmount the barrier.

Tunnelling is a consequence of the [[Wikipedia:Matter wave|wave nature of matter]] and [[Wikipedia:quantum indeterminacy|quantum indeterminacy]]. The quantum [[Wikipedia:wave function|wave function]] describes the states of a particle or other [[Wikipedia:physical system|physical system]] and wave equations such as the [[Wikipedia:Schrödinger equation|Schrödinger equation]] describe their evolution. In a system with a short, narrow potential barrier, a small part of wavefunction can appear outside of the barrier representing a probability for tunnelling through the barrier.
[[File:Bound-states.svg|thumb|Bound-states]]

=== Schrödinger’s equation ===
In 1925–26, [[Wikipedia:Erwin Schrödinger|Erwin Schrödinger]] formulated the [[Schrödinger equation]], describing the probabilistic behaviour of quantum systems through the wavefunction (ψ). Debate persists on whether the wavefunction represents physical reality or knowledge of a system.<ref>{{Cite journal |last=Schrödinger |first=Erwin |year=1926 |title=Quantisation as an Eigenvalue Problem |url=https://onlinelibrary.wiley.com/doi/10.1002/andp.19263840404 |journal=Annalen der Physik |volume=384 |issue=4 |pages=361–376 |doi=10.1002/andp.19263840404}}</ref> The equation enables prediction of atomic and molecular structures and underpins [[Wikipedia:semiconductor|semiconductor]] physics.

=== Heisenberg Uncertainty Principle ===
[[File:The Heisenberg Uncertainty Principle with colors and diagram.jpg|thumb|100px]]
The Heisenberg uncertainty principle states that there is a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known. If the position of an electron is determined with great accuracy, the uncertainty in its momentum (and therefore its energy) increases, and vice versa. This principle is a basic to quantum mechanics.<ref name="Heisenberg1927">{{Cite journal |last=Heisenberg |first=Werner |year=1927 |title=Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik |url=https://link.springer.com/article/10.1007/BF01397280 |journal=Zeitschrift für Physik |volume=43 |issue=3–4 |pages=172–198 |doi=10.1007/BF01397280}}</ref>

[[File:Klein Gordon equation traveling wave plot5.gif|thumb]]
<br>

=== Klein–Gordon Equation ===
The Klein–Gordon equation is a relativistic wave equation that represented one of the earliest attempts to describe quantum particles. While it successfully incorporated the principles of [[special relativity]], it faced difficulties with the interpretation of probability density, which made it less suitable than the Schrödinger equation for describing certain quantum systems.

[[File:From flat band to cubic dispersion in a hbGNR by Vasil Saroka.gif|thumb]]
=== Dirac Equation ===
The [[Wikipedia:Dirac equation|Dirac equation]] is a relativistic quantum mechanical wave equation formulated as a relativistic generalization of the Schrödinger equation. It combines special relativity with quantum mechanics and involves only a single derivative with respect to both space and time. In the non-relativistic limit, the Dirac equation reduces to the Schrödinger equation. It also successfully predicted the existence of [[Wikipedia:antimatter|antimatter]].Energy bands of a half-bearded graphene nanoribbon subjected to an in-plane electric field in the continuum model based on a Dirac equation → ▶

== Other Related Concepts ==

[[File:schrodinger_equation.jpg|thumb|Schrodinger equation time dependent]]
[[File:Schrodinger equation time independent.jpg|thumb|Schrodinger equation time independent]]
The foundational equation of quantum mechanics is the '''Schrödinger equation''' It appears in two primary forms:
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<span style="font-size: 95%; font-style: italic; padding-right: 2em;">Time-dependent Schrödinger equation:</span><math>\displaystyle i \hbar \frac{\partial}{\partial t} \Psi(\mathbf{r}, t) = \hat{H} \Psi(\mathbf{r}, t)</math><br>
<span style="font-size: 95%; font-style: italic; padding-right: 2em;">Time-independent Schrödinger equation (eigenvalue form):</span><math>\displaystyle \hat{H} \psi(\mathbf{r}) = E \psi(\mathbf{r})</math>
</div>
[[Wikipedia:Hamiltonian (quantum mechanics)|Hamiltonian]]: The Hamiltonian symbol <math>\hat{H}</math> is a mathematical operator in quantum mechanics that corresponds to the total energy of a quantum system.<ref name="Griffiths2018" /><br> 
[[Wikipedia:Wave function|Wave function]]: The wave function (Ψ or ψ) is the central concept in the Schrödinger equation, representing the state of a quantum system. The squared magnitude, |Ψ|², gives the probability density of finding a particle in a given region.<ref name="Griffiths2018" /><br> 
[[Wikipedia:Eigenvalues and eigenvectors|Eigenvalue equation]]: The time-independent Schrödinger equation is an eigenvalue equation, in which the Hamiltonian operator acts on the wave function to yield the energy eigenvalue ''E''.<ref name="Griffiths2018" />

== Key concepts ==
== Measurement and uncertainty ==

[[File:Bundesarchiv Bild183-R57262, Werner Heisenberg.jpg|thumb|185px|Werner Heisenberg (1901-1976)]]
[[Wikipedia:Werner Heisenberg|Werner Heisenberg]]’s 1927 [[Wikipedia:uncertainty principle|uncertainty principle]] formalised the limitations of measuring quantum systems, in which observation itself alters the system. This led to probabilistic rather than deterministic outcomes.<ref name="Heisenberg1927" />
<ref name="Jammer1966" /><ref>{{Cite book |last=Messiah |first=Albert |title=Quantum Mechanics |publisher=North-Holland Publishing |year=1961 |isbn=978-0486784557 |volume=I}}</ref>

=== Superposition ===
[[File:Schrodingers cat.svg|thumb|upright=0.6|Schrödinger's cat.]]
Superposition refers to the ability of quantum systems to exist in unknown states simultaneously until measurement. Schrödinger illustrated the paradox with the 1935 [[Wikipedia:Schrödinger's cat|Schrödinger's cat]] thought experiment.<ref>{{Cite journal |last=Schrödinger |first=Erwin |year=1935 |title=Die gegenwärtige Situation in der Quantenmechanik |url=https://link.springer.com/article/10.1007/BF01491891 |journal=Naturwissenschaften |volume=23 |issue=48 |pages=807–812 |doi=10.1007/BF01491891}}</ref>
<ref name="Griffiths2018" /><ref>{{Cite book |last1=Greenstein |first1=George |title=The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics |last2=Zajonc |first2=Arthur |publisher=Jones and Bartlett |year=2005 |isbn=978-0763724702 |edition=2nd |location=Boston}}</ref>
[[File:SPDC figure.png |thumb|upright=0.6|Conceptual illustration of entanglement]]

=== Entanglement ===
[[Wikipedia:Quantum entanglement|Quantum entanglement]] occurs when two or more particles are in a shared quantum state, such that the measurement of one particle's property (e.g., spin, position, or momentum) almost instantly determines the corresponding property of the other particle(s), even at a distance between them. Einstein criticised this as "spooky action at a distance" in the [[Wikipedia:EPR paradox|EPR paradox]], but later experiments confirmed the effect.<ref>{{Cite journal |last=Bell |first=J. S. |year=1964 |title=On the Einstein Podolsky Rosen Paradox |url=https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195 |journal=Physics Physique Физика |volume=1 |issue=3 |pages=195–200 |doi=10.1103/PhysicsPhysiqueFizika.1.195}}</ref> Entanglement is now central to [[Wikipedia:quantum cryptography|quantum cryptography]] and related technologies.<ref>{{Cite journal |last1=Einstein |first1=Albert |last2=Podolsky |first2=Boris |last3=Rosen |first3=Nathan |year=1935 |title=Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? |url=https://journals.aps.org/pr/abstract/10.1103/PhysRev.47.777 |journal=Physical Review |volume=47 |issue=10 |pages=777–780 |doi=10.1103/PhysRev.47.777}}</ref>
<ref name="NielsenChuang2010">{{Cite book |last1=Nielsen |first1=Michael A. |title=Quantum Computation and Quantum Information |last2=Chuang |first2=Isaac L. |publisher=Cambridge University Press |year=2010 |isbn=978-1107002173 |edition=10th anniversary |location=Cambridge}}</ref>

== Applications ==
Quantum mechanics underpins 20th-century technologies such as transistors, lasers, and magnetic resonance imaging. A "second quantum revolution" is under way, exploiting superposition and entanglement for new applications<ref name="Griffiths2018" /><ref name="DowlingMilburn2003" /><ref name="NielsenChuang2010" />
, including:
* Quantum computing: using [[qubit]]s for information processing.<ref name="NielsenChuang2010" /><ref>{{Cite journal |last=Preskill |first=John |year=2018 |title=Quantum Computing in the NISQ era and beyond |url=https://quantum-journal.org/papers/q-2018-08-06-79/ |journal=Quantum |volume=2 |pages=79 |doi=10.22331/q-2018-08-06-79}}</ref><ref>{{Cite conference |last=Shor |first=Peter W. |year=1994 |title=Algorithms for Quantum Computation: Discrete Logarithms and Factoring |url=https://ieeexplore.ieee.org/document/365700 |pages=124–134 |doi=10.1109/SFCS.1994.365700 |book-title=Proceedings 35th Annual Symposium on Foundations of Computer Science}}</ref>
* Quantum sensing: ultraprecise sensors, including devices capable of operating without [[Wikipedia:Global Positioning System|GPS]].<ref>{{Cite journal |last1=Degen |first1=Christian L. |last2=Reinhard |first2=Frank |last3=Cappellaro |first3=Paola |year=2017 |title=Quantum sensing |url=https://doi.org/10.1103/RevModPhys.89.035002 |journal=Reviews of Modern Physics |volume=89 |issue=3 |pages=035002 |doi=10.1103/RevModPhys.89.035002}}</ref><ref>{{Cite journal |last1=Pirandola |first1=Stefano |display-authors=et al. |year=2018 |title=Advances in quantum metrology|url=https://scholar.google.nl/scholar?q=Pirandola,+Stefano+(2018).+%22Advances+in+quantum+metrology%22.+Nature+Photonics&hl=nl&as_sdt=0&as_vis=1&oi=scholart |journal=Nature Photonics |volume=12 |pages=724–733 }}</ref><ref>{{Cite journal |last1=Komar |first1=Peter |display-authors=et al. |year=2014 |title=A quantum network of clocks |url=https://doi.org/10.1038/nphys3000 |journal=Nature Physics |volume=10 |pages=582–587 |doi=10.1038/nphys3000}}</ref>
* Quantum communication: secure communication enabled by entanglement.<ref name="NielsenChuang2010" /><ref>{{Cite conference |last1=Bennett |first1=Charles H. |last2=Brassard |first2=Gilles |year=1984 |title=Quantum Cryptography: Public Key Distribution and Coin Tossing |url=https://arxiv.org/abs/2003.06557 |location=Bangalore, India |pages=175–179 |book-title=Proceedings of IEEE International Conference on Computers, Systems and Signal Processing}}</ref><ref>{{Cite journal |last1=Gisin |first1=Nicolas |last2=Ribordy |first2=Gilles |last3=Tittel |first3=Wolfgang |last4=Zbinden |first4=Hugo |year=2002 |title=Quantum Cryptography |url=https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.74.145 |journal=Reviews of Modern Physics |volume=74 |issue=1 |pages=145–195 |doi=10.1103/RevModPhys.74.145}}</ref>
* Optical clocks: highly precise quantum timekeeping, including devices developed at the [[Wikipedia:University of Adelaide|University of Adelaide]].<ref name="Adelaide2025a">{{Cite web |date=2025-07-09 |title=Quantum clocks guarantee precise navigation |website=The University of Adelaide}}</ref><ref>{{Cite web |date=2025-07-07 |title=QuantX and University of Adelaide to advance and commercialise quantum clock and sensing technologies with Defence Trailblazer support |website=The University of Adelaide}}</ref><ref>{{Cite web |date=2024-05-29 |title=Portable Atomic Clocks |url=https://www.adelaide.edu.au/ipas/research-groups/precision-measurement-group/portable-atomic-clocks |website=The University of Adelaide}}</ref>

Australian research institutions, including the University of Sydney, the University of Queensland, and the University of Adelaide, are noted contributors to international quantum research.<ref name="Monro">{{Cite web |last=Monro |first=Tanya |title=Quantum technologies for defence |url=https://www.dst.defence.gov.au/staff/professor-tanya-monro-ac |website=Defence Science and Technology Group}}</ref>

== Interpretations ==
While quantum mechanics is experimentally well verified, its interpretation remains contested. Some physicists view the wavefunction as an element of physical reality, while others regard it as a tool for predicting measurement outcomes.<ref name="Zeilinger">{{Cite web |last=Zeilinger |first=Anton |date=2022-12-08 |title=Quantum mechanics and the nature of reality |url=https://www.nobelprize.org/prizes/physics/2022/zeilinger/lecture/ |website=NobelPrize.org}}</ref>
==See also==
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}
{{Quantum mechanics}}
* [[Wikipedia:Qubit|Qubit]]
* [[Wikipedia:History of quantum mechanics|History of quantum mechanics]]
* [[Wikipedia:Wave–particle duality|Wave–particle duality]]
* [[Schrödinger equation]]
* [[Wikipedia:Quantum entanglement|Quantum entanglement]]
* [[Quantum computing]]
* [[Wikipedia:List of equations in quantum mechanics|List of equations in quantum mechanics]]

= Quantum Cheat Sheet =

== Quantum ==
A quantum (plural quanta) is the smallest discrete unit of a physical property, such as energy or light. For example, light comes in tiny packets called photons, each of which is a quantum of light.

== Quantum Physics ==
Quantum physics is the branch of science that studies the behavior of matter and energy at very small scales, such as atoms and subatomic particles. It explores phenomena where classical physics does not apply.

== Quantum Mechanics ==
Quantum mechanics is the mathematical framework and set of rules used to describe and predict the behavior of particles in the quantum world. It includes concepts such as wavefunctions, superposition, and the uncertainty principle.

== Real-Life Examples ==
*Smartphones and Computers: Modern electronics rely on quantum mechanics to function. Transistors work because electrons follow quantum rules, such as tunneling and discrete energy levels.
*Lasers: Lasers are based on photons, which are quanta of light. Controlling how atoms release these photons creates a focused beam.
*MRI Scanners: MRI machines use quantum properties of particle spins to create detailed images of the body.

== Weird Quantum Effects ==
*Superposition: Particles can exist in multiple states at once, like an electron spinning both "up" and "down" until measured.
*Entanglement: Two particles can become linked so that the state of one instantly affects the other, even at large distances.

== Quantum Computers ==
Quantum computers use the strange rules of quantum mechanics to solve complex problems faster than classical computers.

*Superposition: Qubits can be in multiple states (0 and 1) at once, allowing the computer to try many possibilities in parallel.
*Entanglement: Entangled qubits work together instantly, enabling faster computation on certain problems.

=== Real-World Applications ===
*Drug Discovery: Quantum computers can simulate molecules to discover new medicines faster.
*Finance: They can model millions of financial scenarios in parallel, helping with risk analysis.
*Cybersecurity: Quantum computers can break some current encryption methods or create ultra-secure quantum-based encryption.

== Summary ==
* Quantum = smallest piece of a property.
* Quantum physics = the study of the tiny.
* Quantum mechanics = the rulebook describing how the tiny pieces behave.
* Quantum computers = devices that use these rules to solve problems classical computers cannot handle efficiently.
=References=
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{{Reflist}}
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{{Author|Harold Foppele}}


{{Sourceattribution|Quantum A Walk Through the Universe|1}}

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