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The distance and timing of the measurements can be chosen so as to make the interval between the two measurements spacelike, hence, any causal effect connecting the events would have to travel faster than light. According to the principles of special relativity, it is not possible for any information to travel between two such measuring events. It is not even possible to say which of the measurements came first. For two spacelike separated events  and  there are inertial frames in which  is first and others in which  is first. Therefore, the correlation between the two measurements cannot be explained as one measurement determining the other: different observers would disagree about the role of cause and effect.

The distance and timing of the measurements can be chosen so as to make the interval between the two measurements spacelike, hence, any causal effect connecting the events would have to travel faster than light. According to the principles of special relativity, it is not possible for any information to travel between two such measuring events. It is not even possible to say which of the measurements came first. For two spacelike separated events  and  there are inertial frames in which  is first and others in which  is first. Therefore, the correlation between the two measurements cannot be explained as one measurement determining the other: different observers would disagree about the role of cause and effect.

The counterintuitive predictions of quantum mechanics about strongly correlated systems were first discussed by [[Albert Einstein]] in 1935, in a joint paper with [[Boris Podolsky]] and [[Nathan Rosen]].<ref name="Einstein1935"/>

The counterintuitive predictions of quantum mechanics about strongly correlated systems were first discussed by [[Albert Einstein]] in 1935, in a joint paper with [[Boris Podolsky]] and [[Nathan Rosen]].<ref name="Einstein1935"/>

 

(In fact similar paradoxes can arise even without entanglement: the position of a single particle is spread out over space, and two widely separated detectors attempting to detect the particle in two different places must instantaneously attain appropriate correlation, so that they do not both detect the particle.)

(In fact similar paradoxes can arise even without entanglement: the position of a single particle is spread out over space, and two widely separated detectors attempting to detect the particle in two different places must instantaneously attain appropriate correlation, so that they do not both detect the particle.)

 

In this study, the three formulated the [[Einstein–Podolsky–Rosen paradox]] (EPR paradox), a [[thought experiment]] that attempted to show that [[quantum mechanics|quantum mechanical theory]] was [[Incompleteness of quantum physics|incomplete]]. They wrote: "We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete."<ref name="Einstein1935"/>

In this study, the three formulated the [[Einstein–Podolsky–Rosen paradox]] (EPR paradox), a [[thought experiment]] that attempted to show that [[quantum mechanics|quantum mechanical theory]] was [[Incompleteness of quantum physics|incomplete]]. They wrote: "We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete."<ref name="Einstein1935"/>

 

However, the three scientists did not coin the word ''entanglement'', nor did they generalize the special properties of the state they considered. Following the EPR paper, [[Erwin Schrödinger]] wrote a letter to Einstein in [[German language|German]] in which he used the word ''Verschränkung'' (translated by himself as ''entanglement'') "to describe the correlations between two particles that interact and then separate, as in the EPR experiment."<ref name=MK>Kumar, M., ''Quantum'', Icon Books, 2009, p. 313.</ref>

However, the three scientists did not coin the word ''entanglement'', nor did they generalize the special properties of the state they considered. Following the EPR paper, [[Erwin Schrödinger]] wrote a letter to Einstein in [[German language|German]] in which he used the word ''Verschränkung'' (translated by himself as ''entanglement'') "to describe the correlations between two particles that interact and then separate, as in the EPR experiment."<ref name=MK>Kumar, M., ''Quantum'', Icon Books, 2009, p. 313.</ref>

 

A possible resolution to the paradox is to assume that quantum theory is incomplete, and the result of measurements depends on predetermined "hidden variables".  The state of the particles being measured contains some hidden variables, whose values effectively determine, right from the moment of separation, what the outcomes of the spin measurements are going to be. This would mean that each particle carries all the required information with it, and nothing needs to be transmitted from one particle to the other at the time of measurement. Einstein and others (see the previous section) originally believed  this was the only way out of the paradox, and the accepted quantum mechanical description (with a random measurement outcome) must be incomplete.

A possible resolution to the paradox is to assume that quantum theory is incomplete, and the result of measurements depends on predetermined "hidden variables".  The state of the particles being measured contains some hidden variables, whose values effectively determine, right from the moment of separation, what the outcomes of the spin measurements are going to be. This would mean that each particle carries all the required information with it, and nothing needs to be transmitted from one particle to the other at the time of measurement. Einstein and others (see the previous section) originally believed  this was the only way out of the paradox, and the accepted quantum mechanical description (with a random measurement outcome) must be incomplete.

Schrödinger shortly thereafter published a seminal paper defining and discussing the notion of "entanglement." In the paper, he recognized the importance of the concept, and stated:<ref name="Schrödinger1935"/> "I would not call [entanglement] ''one'' but rather ''the'' characteristic trait of [[quantum mechanics]], the one that enforces its entire departure from [[Classical mechanics|classical]] lines of thought."

Schrödinger shortly thereafter published a seminal paper defining and discussing the notion of "entanglement." In the paper, he recognized the importance of the concept, and stated:<ref name="Schrödinger1935"/> "I would not call [entanglement] ''one'' but rather ''the'' characteristic trait of [[quantum mechanics]], the one that enforces its entire departure from [[Classical mechanics|classical]] lines of thought."

 

Local hidden variable theories fail, however, when measurements of the spin of entangled particles along different axes are considered. If a large number of pairs of such measurements are made (on a large number of pairs of entangled particles), then statistically, if the local realist or hidden variables view were correct, the results would always satisfy Bell's inequality. A number of experiments have shown in practice that Bell's inequality is not satisfied. However, prior to 2015, all of these had loophole problems that were considered the most important by the community of physicists. When measurements of the entangled particles are made in moving relativistic reference frames, in which each measurement (in its own relativistic time frame) occurs before the other, the measurement results remain correlated.

Local hidden variable theories fail, however, when measurements of the spin of entangled particles along different axes are considered. If a large number of pairs of such measurements are made (on a large number of pairs of entangled particles), then statistically, if the local realist or hidden variables view were correct, the results would always satisfy Bell's inequality. A number of experiments have shown in practice that Bell's inequality is not satisfied. However, prior to 2015, all of these had loophole problems that were considered the most important by the community of physicists. When measurements of the entangled particles are made in moving relativistic reference frames, in which each measurement (in its own relativistic time frame) occurs before the other, the measurement results remain correlated.

Like Einstein, Schrödinger was dissatisfied with the concept of entanglement, because it seemed to violate the speed limit on the transmission of information implicit in the [[theory of relativity]].<ref>Alisa Bokulich, Gregg Jaeger, ''Philosophy of Quantum Information and Entanglement'', Cambridge University Press, 2010, xv.</ref> Einstein later famously derided entanglement as "''spukhafte Fernwirkung''"<ref name="spukhafte">Letter from Einstein to Max Born, 3 March 1947; ''The Born-Einstein Letters; Correspondence between Albert Einstein and Max and Hedwig Born from 1916 to 1955'', Walker, New York, 1971. (cited in {{citation | title = Quantum Entanglement and Communication Complexity (1998) | journal = SIAM J. Comput. | volume = 30 | issue = 6 | citeseerx = 10.1.1.20.8324 | author = M. P. Hobson |pages=1829–1841 | display-authors = etal  | year = 1998 }})</ref> or "spooky [[Action at a distance (physics)|action at a distance]]."

Like Einstein, Schrödinger was dissatisfied with the concept of entanglement, because it seemed to violate the speed limit on the transmission of information implicit in the [[theory of relativity]].<ref>Alisa Bokulich, Gregg Jaeger, ''Philosophy of Quantum Information and Entanglement'', Cambridge University Press, 2010, xv.</ref> Einstein later famously derided entanglement as "''spukhafte Fernwirkung''"<ref name="spukhafte">Letter from Einstein to Max Born, 3 March 1947; ''The Born-Einstein Letters; Correspondence between Albert Einstein and Max and Hedwig Born from 1916 to 1955'', Walker, New York, 1971. (cited in {{citation | title = Quantum Entanglement and Communication Complexity (1998) | journal = SIAM J. Comput. | volume = 30 | issue = 6 | citeseerx = 10.1.1.20.8324 | author = M. P. Hobson |pages=1829–1841 | display-authors = etal  | year = 1998 }})</ref> or "spooky [[Action at a distance (physics)|action at a distance]]."

The EPR paper generated significant interest among physicists, which inspired much discussion about the foundations of quantum mechanics (perhaps most famously [[De Broglie–Bohm theory|Bohm's interpretation]] of quantum mechanics), but produced relatively little other published work. Despite the interest, the weak point in EPR's argument was not discovered until 1964, when [[John Stewart Bell]] proved that one of their key assumptions, the [[principle of locality]], as applied to the kind of hidden variables interpretation hoped for by EPR, was mathematically inconsistent with the predictions of quantum theory.

The EPR paper generated significant interest among physicists, which inspired much discussion about the foundations of quantum mechanics (perhaps most famously [[De Broglie–Bohm theory|Bohm's interpretation]] of quantum mechanics), but produced relatively little other published work. Despite the interest, the weak point in EPR's argument was not discovered until 1964, when [[John Stewart Bell]] proved that one of their key assumptions, the [[principle of locality]], as applied to the kind of hidden variables interpretation hoped for by EPR, was mathematically inconsistent with the predictions of quantum theory.

 

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Entanglement is required to preserve the Uncertainty principle, as seen in the EPR paradox. For example, say that a high energy photon decays into an electron / positron pair, and the position of the electron and the momentum of the positron are then measured. If we don't allow entanglement in the physical description of the pair, the position and momentum of each particle can still be deduced by reference to the conservation of momentum, violating the Uncertainty principle. Alternatively, if we require the uncertainty principle to hold true, and still disallow entanglement in the physical description of the pair, the uncertainty principle would allow violations in the law of conservation of momentum, because strong correlation in both position and momentum would be impossible (i.e., one would not be able to effectively deduce the position and momentum of the electron because they could not be highly correlated with both the position and momentum of the positron).-->

Entanglement is required to preserve the Uncertainty principle, as seen in the EPR paradox. For example, say that a high energy photon decays into an electron / positron pair, and the position of the electron and the momentum of the positron are then measured. If we don't allow entanglement in the physical description of the pair, the position and momentum of each particle can still be deduced by reference to the conservation of momentum, violating the Uncertainty principle. Alternatively, if we require the uncertainty principle to hold true, and still disallow entanglement in the physical description of the pair, the uncertainty principle would allow violations in the law of conservation of momentum, because strong correlation in both position and momentum would be impossible (i.e., one would not be able to effectively deduce the position and momentum of the electron because they could not be highly correlated with both the position and momentum of the positron).-->

纠缠是保持不确定性原理所必需的，如 EPR 悖论所示。例如，假设一个高能光子衰变成一个电子/正电子对，然后测量电子的位置和正电子的动量。如果我们在物理描述中不允许纠缠，那么每个粒子的位置和动量仍然可以通过参考动量守恒来推导，这违反了测不准原理。或者，如果我们要求不确定性原理保持真实，而仍然不允许在物理描述对的纠缠，不确定性原理将允许违反动量守恒定律，因为在位置和动量上强相关性是不可能的(也就是说，人们不能有效地推断电子的位置和动量，因为它们不能与正电子的位置和动量高度相关)。-->

纠缠是保持不确定性原理所必需的，如 EPR 悖论所示。例如，假设一个高能光子衰变成一个电子/正电子对，然后测量电子的位置和正电子的动量。如果我们在物理描述中不允许纠缠，那么每个粒子的位置和动量就可以通过参考动量守恒来推导，这就违反了测不准原理。或者，如果我们要求不确定性原理保持真实，而仍然不允许在物理上描述对的纠缠，不确定性原理将会违反动量守恒定律，因为在位置和动量上强相关性是不可能的(也就是说，人们不能有效地推断电子的位置和动量，因为它们不能与正电子的位置和动量高度相关)。-->

Specifically, Bell demonstrated an upper limit, seen in [[Bell's inequality]], regarding the strength of correlations that can be produced in any theory obeying [[local realism]], and showed that quantum theory predicts violations of this limit for certain entangled systems.<ref>{{cite journal |author = J. S. Bell |title = On the Einstein-Poldolsky-Rosen paradox |journal = Physics Physique Физика |volume = 1 |issue = 3 |pages = 195–200 |year = 1964|doi = 10.1103/PhysicsPhysiqueFizika.1.195 |doi-access = free }}</ref> His inequality is experimentally testable, and there have been numerous [[Bell test experiments|relevant experiments]], starting with the pioneering work of [[Stuart Freedman]] and [[John Clauser]] in 1972<ref name="Clauser">{{cite journal|doi=10.1103/PhysRevLett.28.938|last1=Freedman|first1=Stuart J.|last2=Clauser|first2=John F.|title=Experimental Test of Local Hidden-Variable Theories|journal=Physical Review Letters |volume=28 |issue=14 |pages=938–941|year=1972 |bibcode=1972PhRvL..28..938F|url=https://escholarship.org/uc/item/2f18n5nk}}</ref> and [[Alain Aspect]]'s experiments in 1982.<ref>{{cite journal |author1=A. Aspect |author2=P. Grangier |author3=G. Roger  |name-list-style=amp |title = Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell's Inequalities |journal = Physical Review Letters |volume = 49 |issue = 2 |pages = 91–94 |year = 1982 |doi = 10.1103/PhysRevLett.49.91 |bibcode=1982PhRvL..49...91A|doi-access = free }}</ref> An early experimental breakthrough was due to Carl Kocher,<ref name="Kocher1"/><ref name="Kocherphd"/> who already in 1967 presented an apparatus in which two photons successively emitted from a calcium atom were shown to be entangled – the first case of entangled visible light. The two photons passed diametrically positioned parallel polarizers with higher probability than classically predicted but with correlations in quantitative agreement with quantum mechanical calculations. He also showed that the correlation varied only upon (as cosine square of) the angle between the polarizer settings<ref name="Kocherphd"/> and decreased exponentially with time lag between emitted photons.<ref name="Kocher2">{{cite journal | doi = 10.1016/0003-4916(71)90159-X | volume=65 | issue=1 | title=Time correlations in the detection of successively emitted photons | journal=Annals of Physics | pages=1–18 | last1 = Kocher | first1 = CA | year=1971| bibcode=1971AnPhy..65....1K }}</ref> Kocher’s apparatus, equipped with better polarizers, was used by Freedman and Clauser who could confirm the cosine square dependence and use it to demonstrate a violation of Bell’s inequality for a set of fixed angles.<ref name="Clauser"/> All these experiments have shown agreement with quantum mechanics rather than the principle of local realism.

Specifically, Bell demonstrated an upper limit, seen in [[Bell's inequality]], regarding the strength of correlations that can be produced in any theory obeying [[local realism]], and showed that quantum theory predicts violations of this limit for certain entangled systems.<ref>{{cite journal |author = J. S. Bell |title = On the Einstein-Poldolsky-Rosen paradox |journal = Physics Physique Физика |volume = 1 |issue = 3 |pages = 195–200 |year = 1964|doi = 10.1103/PhysicsPhysiqueFizika.1.195 |doi-access = free }}</ref> His inequality is experimentally testable, and there have been numerous [[Bell test experiments|relevant experiments]], starting with the pioneering work of [[Stuart Freedman]] and [[John Clauser]] in 1972<ref name="Clauser">{{cite journal|doi=10.1103/PhysRevLett.28.938|last1=Freedman|first1=Stuart J.|last2=Clauser|first2=John F.|title=Experimental Test of Local Hidden-Variable Theories|journal=Physical Review Letters |volume=28 |issue=14 |pages=938–941|year=1972 |bibcode=1972PhRvL..28..938F|url=https://escholarship.org/uc/item/2f18n5nk}}</ref> and [[Alain Aspect]]'s experiments in 1982.<ref>{{cite journal |author1=A. Aspect |author2=P. Grangier |author3=G. Roger  |name-list-style=amp |title = Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell's Inequalities |journal = Physical Review Letters |volume = 49 |issue = 2 |pages = 91–94 |year = 1982 |doi = 10.1103/PhysRevLett.49.91 |bibcode=1982PhRvL..49...91A|doi-access = free }}</ref> An early experimental breakthrough was due to Carl Kocher,<ref name="Kocher1"/><ref name="Kocherphd"/> who already in 1967 presented an apparatus in which two photons successively emitted from a calcium atom were shown to be entangled – the first case of entangled visible light. The two photons passed diametrically positioned parallel polarizers with higher probability than classically predicted but with correlations in quantitative agreement with quantum mechanical calculations. He also showed that the correlation varied only upon (as cosine square of) the angle between the polarizer settings<ref name="Kocherphd"/> and decreased exponentially with time lag between emitted photons.<ref name="Kocher2">{{cite journal | doi = 10.1016/0003-4916(71)90159-X | volume=65 | issue=1 | title=Time correlations in the detection of successively emitted photons | journal=Annals of Physics | pages=1–18 | last1 = Kocher | first1 = CA | year=1971| bibcode=1971AnPhy..65....1K }}</ref> Kocher’s apparatus, equipped with better polarizers, was used by Freedman and Clauser who could confirm the cosine square dependence and use it to demonstrate a violation of Bell’s inequality for a set of fixed angles.<ref name="Clauser"/> All these experiments have shown agreement with quantum mechanics rather than the principle of local realism.

In experiments in 2012 and 2013, polarization correlation was created between photons that never coexisted in time. The authors claimed that this result was achieved by entanglement swapping between two pairs of entangled photons after measuring the polarization of one photon of the early pair, and that it proves that quantum non-locality applies not only to space but also to time.

In experiments in 2012 and 2013, polarization correlation was created between photons that never coexisted in time. The authors claimed that this result was achieved by entanglement swapping between two pairs of entangled photons after measuring the polarization of one photon of the early pair, and that it proves that quantum non-locality applies not only to space but also to time.

In three independent experiments in 2013 it was shown that classically communicated separable quantum states can be used to carry entangled states. The first loophole-free Bell test was held in TU Delft in 2015 confirming the violation of Bell inequality.

In three independent experiments in 2013 it was shown that classically communicated separable quantum states can be used to carry entangled states. The first loophole-free Bell test was held in TU Delft in 2015 confirming the violation of Bell inequality.

In August 2014, Brazilian researcher Gabriela Barreto Lemos and team were able to "take pictures" of objects using photons that had not interacted with the subjects, but were entangled with photons that did interact with such objects. Lemos, from the University of Vienna, is confident that this new quantum imaging technique could find application where low light imaging is imperative, in fields like biological or medical imaging.

In August 2014, Brazilian researcher Gabriela Barreto Lemos and team were able to "take pictures" of objects using photons that had not interacted with the subjects, but were entangled with photons that did interact with such objects. Lemos, from the University of Vienna, is confident that this new quantum imaging technique could find application where low light imaging is imperative, in fields like biological or medical imaging.

== Concept ==

== Concept 概念==

In 2015, Markus Greiner's group at Harvard performed a direct measurement of Renyi entanglement in a system of ultracold bosonic atoms.

In 2015, Markus Greiner's group at Harvard performed a direct measurement of Renyi entanglement in a system of ultracold bosonic atoms.

=== Meaning of entanglement ===

=== Meaning of entanglement纠缠的意义 ===

From 2016 various companies like IBM, Microsoft etc. have successfully created quantum computers and allowed developers and tech enthusiasts to openly experiment with concepts of quantum mechanics including quantum entanglement.

From 2016 various companies like IBM, Microsoft etc. have successfully created quantum computers and allowed developers and tech enthusiasts to openly experiment with concepts of quantum mechanics including quantum entanglement.

An entangled system is defined to be one whose [[quantum state]] cannot be factored as a product of states of its local constituents; that is to say, they are not individual particles but are an inseparable whole. In entanglement, one constituent cannot be fully described without considering the other(s). The state of a composite system is always expressible as a sum, or [[quantum superposition|superposition]], of products of states of local constituents; it is entangled if this sum necessarily has more than one term.

An entangled system is defined to be one whose [[quantum state]] cannot be factored as a product of states of its local constituents; that is to say, they are not individual particles but are an inseparable whole. In entanglement, one constituent cannot be fully described without considering the other(s). The state of a composite system is always expressible as a sum, or [[quantum superposition|superposition]], of products of states of local constituents; it is entangled if this sum necessarily has more than one term.

 

Quantum [[physical system|systems]] can become entangled through various types of interactions. For some ways in which entanglement may be achieved for experimental purposes, see the section below on [[#Methods of creating entanglement|methods]]. Entanglement is broken when the entangled particles [[quantum decoherence|decohere]] through interaction with the environment; for example, when a measurement is made.<ref name="Peres1993">Asher Peres, ''[[Quantum Theory: Concepts and Methods]]'', Kluwer, 1993; {{ISBN|0-7923-2549-4}} p. 115.</ref>

Quantum [[physical system|systems]] can become entangled through various types of interactions. For some ways in which entanglement may be achieved for experimental purposes, see the section below on [[#Methods of creating entanglement|methods]]. Entanglement is broken when the entangled particles [[quantum decoherence|decohere]] through interaction with the environment; for example, when a measurement is made.<ref name="Peres1993">Asher Peres, ''[[Quantum Theory: Concepts and Methods]]'', Kluwer, 1993; {{ISBN|0-7923-2549-4}} p. 115.</ref>

There have been suggestions to look at the concept of time as an emergent phenomenon that is a side effect of quantum entanglement.

There have been suggestions to look at the concept of time as an emergent phenomenon that is a side effect of quantum entanglement.

In other words, time is an entanglement phenomenon, which places all equal clock readings (of correctly prepared clocks, or of any objects usable as clocks) into the same history. This was first fully theorized by Don Page and William Wootters in 1983.

In other words, time is an entanglement phenomenon, which places all equal clock readings (of correctly prepared clocks, or of any objects usable as clocks) into the same history. This was first fully theorized by Don Page and William Wootters in 1983.

As an example of entanglement: a [[subatomic particle]] [[Particle decay|decays]] into an entangled pair of other particles. The decay events obey the various [[conservation laws]], and as a result, the measurement outcomes of one daughter particle must be highly correlated with the measurement outcomes of the other daughter particle (so that the total momenta, angular momenta, energy, and so forth remains roughly the same before and after this process). For instance, a [[Spin (physics)|spin]]-zero particle could decay into a pair of spin-½ particles. Since the total spin before and after this decay must be zero (conservation of angular momentum), whenever the first particle is measured to be [[Spin (physics)#Direction|spin up]] on some axis, the other, when measured on the same axis, is always found to be [[Spin (physics)#Direction|spin down]]. (This is called the spin anti-correlated case; and if the prior probabilities for measuring each spin are equal, the pair is said to be in the [[singlet state]].)

As an example of entanglement: a [[subatomic particle]] [[Particle decay|decays]] into an entangled pair of other particles. The decay events obey the various [[conservation laws]], and as a result, the measurement outcomes of one daughter particle must be highly correlated with the measurement outcomes of the other daughter particle (so that the total momenta, angular momenta, energy, and so forth remains roughly the same before and after this process). For instance, a [[Spin (physics)|spin]]-zero particle could decay into a pair of spin-½ particles. Since the total spin before and after this decay must be zero (conservation of angular momentum), whenever the first particle is measured to be [[Spin (physics)#Direction|spin up]] on some axis, the other, when measured on the same axis, is always found to be [[Spin (physics)#Direction|spin down]]. (This is called the spin anti-correlated case; and if the prior probabilities for measuring each spin are equal, the pair is said to be in the [[singlet state]].)

 

The Wheeler–DeWitt equation that combines general relativity and quantum mechanics – by leaving out time altogether – was introduced in the 1960s and it was taken up again in 1983, when Page and Wootters made a solution based on quantum entanglement. Page and Wootters argued that entanglement can be used to measure time.

The Wheeler–DeWitt equation that combines general relativity and quantum mechanics – by leaving out time altogether – was introduced in the 1960s and it was taken up again in 1983, when Page and Wootters made a solution based on quantum entanglement. Page and Wootters argued that entanglement can be used to measure time.

The special property of entanglement can be better observed if we separate the said two particles. Let's put one of them in the White House in Washington and the other in Buckingham Palace (think about this as a thought experiment, not an actual one). Now, if we measure a particular characteristic of one of these particles (say, for example, spin), get a result, and then measure the other particle using the same criterion (spin along the same axis), we find that the result of the measurement of the second particle will match (in a complementary sense) the result of the measurement of the first particle, in that they will be opposite in their values.

The special property of entanglement can be better observed if we separate the said two particles. Let's put one of them in the White House in Washington and the other in Buckingham Palace (think about this as a thought experiment, not an actual one). Now, if we measure a particular characteristic of one of these particles (say, for example, spin), get a result, and then measure the other particle using the same criterion (spin along the same axis), we find that the result of the measurement of the second particle will match (in a complementary sense) the result of the measurement of the first particle, in that they will be opposite in their values.

 

In 2013, at the Istituto Nazionale di Ricerca Metrologica (INRIM) in Turin, Italy, researchers performed the first experimental test of Page and Wootters' ideas. Their result has been interpreted to confirm that time is an emergent phenomenon for internal observers but absent for external observers of the universe just as the Wheeler-DeWitt equation predicts. The approach to entanglement would be from the perspective of the causal arrow of time, with the assumption that the cause of the measurement of one particle determines the effect of the result of the other particle's measurement.

In 2013, at the Istituto Nazionale di Ricerca Metrologica (INRIM) in Turin, Italy, researchers performed the first experimental test of Page and Wootters' ideas. Their result has been interpreted to confirm that time is an emergent phenomenon for internal observers but absent for external observers of the universe just as the Wheeler-DeWitt equation predicts. The approach to entanglement would be from the perspective of the causal arrow of time, with the assumption that the cause of the measurement of one particle determines the effect of the result of the other particle's measurement.

2013年，在意大利都灵的国家理查尔卡计量研究所(INRIM) ，研究人员对佩奇和伍特的想法进行了首次实验测试。他们的结果被解释为证实了对于内部观察者来说时间是一种涌现的现象，但正如惠勒-德威特方程所预测的那样，对于宇宙的外部观察者来说时间是不存在的。纠缠的方法是从因果时间箭头的角度出发，假设一个粒子被测量的原因决定了另一个粒子测量结果的影响。

2013年，在意大利都灵的国家理查尔卡计量研究所(INRIM) ，研究人员对佩奇和伍特的想法进行了首次实验测试。他们的结果被解释为证实了对于内部观察者来说时间是一种涌现的现象，但正如惠勒-德威特方程所预测的那样，对于宇宙的外部观察者来说时间是不存在的。纠缠的方法是从因果时间箭头的角度出发，假设一个粒子被测量的原因决定了另一个粒子测量结果的效应。

The above result may or may not be perceived as surprising. A classical system would display the same property, and a [[hidden variable theory]] (see below) would certainly be required to do so, based on conservation of angular momentum in classical and quantum mechanics alike. The difference is that a classical system has definite values for all the observables all along, while the quantum system does not. In a sense to be discussed below, the quantum system considered here seems to acquire a probability distribution for the outcome of a measurement of the spin along any axis of the other particle upon measurement of the first particle. This probability distribution is in general different from what it would be without measurement of the first particle. This may certainly be perceived as surprising in the case of spatially separated entangled particles.

The above result may or may not be perceived as surprising. A classical system would display the same property, and a [[hidden variable theory]] (see below) would certainly be required to do so, based on conservation of angular momentum in classical and quantum mechanics alike. The difference is that a classical system has definite values for all the observables all along, while the quantum system does not. In a sense to be discussed below, the quantum system considered here seems to acquire a probability distribution for the outcome of a measurement of the spin along any axis of the other particle upon measurement of the first particle. This probability distribution is in general different from what it would be without measurement of the first particle. This may certainly be perceived as surprising in the case of spatially separated entangled particles.

 

===Paradox矛盾===

===Paradox===

 

Based on AdS/CFT correspondence, Mark Van Raamsdonk suggested that spacetime arises as an emergent phenomenon of the quantum degrees of freedom that are entangled and live in the boundary of the space-time. Induced gravity can emerge from the entanglement first law.

Based on AdS/CFT correspondence, Mark Van Raamsdonk suggested that spacetime arises as an emergent phenomenon of the quantum degrees of freedom that are entangled and live in the boundary of the space-time. Induced gravity can emerge from the entanglement first law.