corresponding counts accumulated Four separate subexperiments are conducted corresponding to the four terms in the test statistic S The settings a a b and b are generally in practice chosen to be ° ° and ° respectively — the Bell test angles — these being the ones for which the QM formula gives the greatest violation of the inequality For each selected value of a and b the numbers of coincidences in each category are recorded The experimental estimate for is then calculated as Once all the E s have been estimated an experimental estimate of S can be found If it is numerically greater than it has infringed the CHSH inequality and the experiment is declared to have supported the QM Quantum Mechanics prediction and ruled out all local hidden variable theories The CHSH paper lists many preconditions or reasonable and or presumable assumptions to derive the simplified theorem and formula For example for the method to be valid it has to be assumed that the detected pairs are a fair sample of those emitted In actual experiments detectors are never efficient so that only a sample of the emitted pairs are detected A subtle related requirement is that the hidden variables do not influence or determine detection probability in a way that would lead to different samples at each arm of the experiment Derivation of the CHSH inequality edit The original derivation will not be given here since it is not easy to follow and involves the assumption that the outcomes are all or never zero Bell s derivation is more general He effectively assumes the Objective Local Theory later used by Clauser and Horne Clauser It is assumed that any hidden variables associated with the detectors themselves are independent on the two sides and can be averaged out from the start Another derivation of interest is given in Clauser and Horne s paper in which they start from the CH inequality

It would appear from both these later derivations that the only assumptions really needed for the inequality itself as opposed to the method of estimation of the test statistic are that the distribution of the possible states of the source remains constant and the detectors on the two sides act independently Bell s derivation edit The following is based on page of Bell s Speakable and Unspeakable Bell the main change being to use the symbol E instead of P for the expected value of the quantum correlation This avoids any implication that the quantum correlation is itself a probability We start with the standard assumption of independence of the two sides enabling us to obtain the joint probabilities of pairs of outcomes by multiplying the separate probabilities for any selected value of the hidden variable is assumed to be drawn from a fixed distribution of possible states of the source the probability of the source being in the state for any particular trial being given by the density function the integral of which over the complete hidden variable space is We thus assume we can write where A and B are the average values of the outcomes Since the possible values of A and B are and it follows that Then if a a b and b are alternative settings for the detectors Taking absolute values of both sides and applying the triangle inequality to the right hand side we obtain We use the fact that and are both non negative to rewrite the right hand side of this as By this must be less than or equal to which using the fact that the integral of is is equal to which is equal to Putting this together with the left hand side we have which means that the left hand side is less than or equal to both and That is from which we obtain Bell s theorem is a no go theorem that draws an important distinction between quantum mechanics QM and the world as described by classical mechanics This theorem is named after John Stewart Bell In its simplest form Bell s theorem states No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics Cornell solid state physicist David Mermin has described the appraisals of the importance of Bell s theorem in the physics community as ranging from indifference to wild extravagance Lawrence Berkeley particle physicist Henry Stapp declared Bell s theorem is the most profound discovery of science Bell s theorem rules out local hidden variables as a viable explanation of quantum mechanics though it still leaves the door open for non local hidden variables Bell concluded In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements without changing the statistical predictions there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument however remote Moreover the signal involved must propagate instantaneously so that a theory could not be Lorentz invariant Bell summarized one of the least popular ways to address the theorem superdeterminism in a BBC Radio interview There is a way to escape the inference of superluminal speeds and spooky action at a distance But it involves absolute determinism in the universe the complete absence of free will Suppose the world is super deterministic with not just inanimate nature running on behind the scenes clockwork but with our behavior including our belief that we are free to choose to do one experiment rather than another absolutely predetermined including the decision by the experimenter to carry out one set of measurements rather than another the difficulty disappears There is no need for a faster than light signal to tell particle A what measurement has been carried out on particle B because the universe including particle A already knows what that measurement and its outcome will be Contents Historical background Overview Importance of the theorem Bell inequalities Original Bell s inequality CHSH inequality Local realism Derivation of CHSH inequality Bell inequalities are violated by quantum mechanical predictions Practical experiments testing Bell s theorem Two classes of Bell inequalities Practical challenges Metaphysical aspects Final remarks See also Pop Culture Notes References Further reading External links Historical background edit In the early s the philosophical implications of the current interpretations of quantum theory troubled many prominent physicists of the day including Albert Einstein In a well known paper Boris Podolsky and co authors Einstein and Nathan Rosen collectively EPR sought to demonstrate by the EPR paradox that QM was incomplete This provided hope that a more complete and less troubling theory might one day be discovered But that conclusion rested on the seemingly reasonable assumptions of locality and realism together called local realism or local hidden variables often interchangeably In the vernacular of Einstein locality meant no instantaneous spooky action at a distance realism meant the moon is there even when not being observed These assumptions were hotly debated in the physics community notably between Nobel laureates Einstein and Niels Bohr In his groundbreaking paper On the Einstein Podolsky Rosen paradox physicist John Stewart Bell presented an analogy based on spin measurements on pairs of entangled electrons to EPR s hypothetical paradox Using their reasoning he said a choice of measurement setting here should not affect the outcome of a measurement there and vice versa After providing a mathematical formulation of locality and realism based on this he showed specific cases where this would be inconsistent with the predictions of QM theory In experimental tests following Bell s example now using quantum entanglement of photons instead of electrons John Clauser and Stuart Freedman and Alain Aspect et al demonstrated that the predictions of QM are correct in this regard although relying on additional unverifiable assumptions that open loopholes for local realism In Oct Hensen and co workers reported that they performed a loophole free Bell test which might force one to reject at least one of the principles of locality realism or freedom the last leads to alternative superdeterministic theories citation needed Two of these logical possibilities non locality and non realism correspond to well developed interpretations of quantum mechanics and have many supporters this is not the case for the third logical possibility non freedom Conclusive experimental evidence of the violation of Bell s inequality would drastically reduce the class of acceptable deterministic theories but would not falsify absolute determinism which was described by Bell himself as not just inanimate nature running on behind the scenes clockwork but with our behaviour including our belief that we are free to choose to do one experiment rather than another absolutely predetermined However Bell himself considered absolute determinism an implausible solution Overview edit Figure Bell s theorem states that any physical theory that incorporates local realism cannot reproduce all the predictions of quantum mechanical theory Because numerous experiments agree with the predictions of quantum mechanical theory and show differences between correlations that could not be explained by local hidden variables the experimental results have been taken by many as refuting the concept of local realism as an explanation of the physical phenomena under test For a hidden variable theory if Bell s conditions are correct the results that agree with quantum mechanical theory appear to indicate superluminal effects in contradiction to the principle of locality These three key concepts – locality realism freedom – are highly technical and much debated In particular the concept of realism is now somewhat different from what it was in discussions in the s It is more precisely called counterfactual definiteness it means that we may think of outcomes of measurements that were not actually performed as being just as much part of reality as those that were made Locality is short for local relativistic causality Freedom refers to the physical possibility of determining settings on measurement devices independently of the internal state of the physical system being measured Illustration of Bell test for spin half particles such as electrons A source produces a singlet pair one particle is sent to one location and the other is sent to another location A measurement of the entangled property is performed at various angles at each location The scheme for measurements on photons looks very similar the quantum state is different but has very similar properties The theorem is usually proved by consideration of a quantum system of two entangled qubits The most common examples concern systems of particles that are entangled in spin or polarization Quantum mechanics allows predictions of correlations that would be observed if these two particles have their spin or polarization measured in different directions Bell showed that if a local hidden variable theory holds then these correlations would have to satisfy certain constraints called Bell inequalities However for the quantum correlations arising in the specific example considered those constraints are not satisfied hence the phenomenon being studied cannot be explained by a local hidden variables theory However there s a tentative explanation for this which is that entangled particles communicate through another dimension as shown in Figure Following the argument in the Einstein–Podolsky–Rosen EPR paradox paper but using the example of spin as in David Bohm s version of the EPR argument Bell considered an experiment in which there are a pair of spin one half particles formed somehow in the singlet spin state and moving freely in opposite directions The two particles travel away from each other to two distant locations at which measurements of spin are performed along axes that are independently chosen Each measurement yields a result of either spin up or spin down it means spin in the positive or negative direction of the chosen axis The probability of the same result being obtained at the two locations varies depending on the relative angles at which the two spin measurements are made and is strictly between zero and one for all relative angles other than perfectly parallel alignments ° or ° Bell s theorem is concerned with correlations defined in terms of averages taken over very many trials of the experiment The correlation of two binary variables is usually defined in quantum physics as the average of the products of the pairs of measurements Note that this is different from the usual definition of correlation in statistics The quantum physicist s correlation is the statistician s raw uncentered unnormalized product moment They are similar in that with either definition if the pairs of outcomes are always the same the correlation is if the pairs of outcomes are always opposite the correlation is and if the pairs of outcomes agree of the time then the correlation is The correlation is related in a simple way to the probability of equal outcomes namely it is equal to twice the probability of equal outcomes minus one Measuring the spin of these entangled particles along anti parallel directions—i e along the same axis but in opposite directions the set of all results is perfectly correlated On the other hand if measurements are performed along parallel directions they always yield opposite results and the set of measurements shows perfect anti correlation Finally measurement at perpendicular directions has a chance of matching and the total set of measurements is uncorrelated These basic cases are illustrated in the table below Anti parallel Pair Pair Pair Pair … Pair n Alice ° … Bob ° … Correlation … n identical Parallel Pair Pair Pair Pair … Pair n Alice ° … Bob ° or ° … Correlation … n opposite Orthogonal Pair Pair Pair Pair … Pair n Alice ° … Bob ° or ° … Correlation … n identical opposite The best possible local realist imitation red for the quantum correlation of two spins in the singlet state blue insisting on perfect anti correlation at zero degrees perfect correlation at degrees Many other possibilities exist for the classical correlation subject to these side conditions but all are characterized by sharp peaks and valleys at degrees and none has more extreme values ± at degrees These values are marked by stars in the graph and are the values measured in a standard Bell CHSH type experiment QM allows local realism predicts ± or less With the measurements oriented at intermediate angles between these basic cases the existence of local hidden variables could agree with a linear dependence of the correlation in the angle but according to Bell s inequality see below could not agree with the dependence predicted by quantum mechanical theory namely that the correlation is the negative cosine of the angle Experimental results match the curve predicted by quantum mechanics Over the years Bell s theorem has undergone a wide variety of experimental tests However various common deficiencies in the testing of the theorem have been identified including the detection loophole and the communication loophole Over the years experiments have been gradually improved to better address these loopholes but no experiment to date has simultaneously fully addressed all of them However scientists generally expect that someone will conduct such an experiment in a few years and it is expected to confirm yet again quantum predictions For example Anthony Leggett has commented While no single existing experiment has simultaneously blocked all of the so called loopholes each one of those loopholes has been blocked in at least one experiment Thus to maintain a local hidden variable theory in the face of the existing experiments would appear to require belief in a very peculiar conspiracy of nature To date Bell s theorem is generally regarded as supported by a substantial


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body of evidence and there are few supporters of local hidden variables though the theorem is continually the subject of study criticism and refinement Importance of the theorem edit Bell s theorem derived in his seminal paper titled On the Einstein Podolsky Rosen paradox has been called on the assumption that the theory is correct the most profound in science Perhaps of equal importance is Bell s deliberate effort to encourage and bring legitimacy to work on the completeness issues which had fallen into disrepute Later in his life Bell expressed his hope that such work would continue to inspire those who suspect that what is proved by the impossibility proofs is lack of imagination The title of Bell s seminal article refers to the paper by Einstein Podolsky and Rosen that challenged the completeness of quantum mechanics In his paper Bell started from the same two assumptions as did EPR namely i reality that microscopic objects have real properties determining the outcomes of quantum mechanical measurements and ii locality that reality in one location is not influenced by measurements performed simultaneously at a distant location Bell was able to derive from those two assumptions an important result namely Bell s inequality The theoretical and later experimental violation of this inequality implies that at least one of the two assumptions must be false In two respects Bell s paper was a step forward compared to the EPR paper firstly it considered more hidden variables than merely the element of physical reality in the EPR paper and Bell s inequality was in part liable to be experimentally tested thus raising the possibility of testing the local realism hypothesis Limitations on such tests to date are noted below Whereas Bell s paper deals only with deterministic hidden variable theories Bell s theorem was later generalized to stochastic theories as well and it was also realised that the theorem is not so much about hidden variables as about the outcomes of measurements that could have been taken instead of the one actually taken Existence of these variables is called the assumption of realism or the assumption of counterfactual definiteness After the EPR paper quantum mechanics was in an unsatisfactory position either it was incomplete in the sense that it failed to account for some elements of physical reality or it violated the principle of a finite propagation speed of physical effects In a modified version of the EPR thought experiment two hypothetical observers now commonly referred to as Alice and Bob perform independent measurements of spin on a pair of electrons prepared at a source in a special state called a spin singlet state It is the conclusion of EPR that once Alice measures spin in one direction e g on the x axis Bob s measurement in that direction is determined with certainty as being the opposite outcome to that of Alice whereas immediately before Alice s measurement Bob s outcome was only statistically determined i e was only a probability not a certainty thus either the spin in each direction is an element of physical reality or the effects travel from Alice to Bob instantly In QM predictions are formulated in terms of probabilities — for example the probability that an electron will be detected in a particular place or the probability that its spin is up or down The idea persisted however that the electron in fact has a definite position and spin and that QM s weakness is its inability to predict those values precisely The possibility existed that some unknown theory such as a hidden variables theory might be able to predict those quantities exactly while at the same time also being in complete agreement with the probabilities predicted by QM If such a hidden variables theory exists then because the hidden variables are not described by QM the latter would be an incomplete theory Bell inequalities edit Bell inequalities concern measurements made by observers on pairs of particles that have interacted and then separated Assuming local realism certain constraints must hold on the relationships between the correlations between subsequent measurements of the particles under various possible measurement settings Original Bell s inequality edit The inequality that Bell derived can be written as where is the correlation between measurements of the spins of the pair of particles and a b and c refer to three arbitrary settings of the two analysers This inequality is however restricted in its application to the rather special case in which the outcomes on both sides of the experiment are always exactly anticorrelated whenever the analysers are parallel The advantage of restricting attention to this special case is the resulting simplicity of the derivation In experimental work the inequality is not very useful because it is hard if not impossible to create perfect anti correlation This simple form does have the virtue of being quite intuitive It is easily seen to be equivalent to the following elementary result from probability theory Consider three highly correlated and possibly biased coin flips X Y and Z with the property that X and Y give the same outcome both heads or both tails of the time Y and Z also give the same outcome of the time then X and Z must also yield the same outcome at least of the time The number of mismatches between X and Y plus the number of mismatches between Y and Z are together the maximum possible number of mismatches between X and Z a simple Boole–Fréchet inequality Imagine a pair of particles that can be measured at distant locations Suppose that the measurement devices have settings which are angles—e g the devices measure something called spin in some direction The experimenter chooses the directions one for each particle separately Suppose the measurement outcome is binary e g spin up spin down Suppose the two particles are perfectly anti correlated—in the sense that whenever both measured in the same direction one gets identically opposite outcomes when both measured in opposite directions they always give the same outcome The only way to imagine how this works is that both particles leave their common source with somehow the outcomes they will deliver when measured in any possible direction How else could particle know how to deliver the same answer as particle when measured in the same direction They don t know in advance how they are going to be measured The measurement on particle after switching its sign can be thought of as telling us what the same measurement on particle would have given Start with one setting exactly opposite to the other All the pairs of particles give the same outcome each pair is either both spin up or both spin down Now shift Alice s setting by one degree relative to Bob s They are now one degree off being exactly opposite to one another A small fraction of the pairs say f now give different outcomes If instead we had left Alice s setting unchanged but shifted Bob s by one degree in the opposite direction then again a fraction f of the pairs of particles turns out to give different outcomes Finally consider what happens when both shifts are implemented at the same time the two settings are now exactly two degrees away from being opposite to one another By the mismatch argument the chance of a mismatch at two degrees can t be more than twice the chance of a mismatch at one degree it cannot be more than f Compare this with the predictions from quantum mechanics for the singlet state For a small angle measured in radians the chance of a different outcome is approximately as explained by small angle approximation At two times this small angle the chance of a mismatch is therefore about times larger since But we just argued that it cannot be more than times as large This intuitive formulation is due to David Mermin The small angle limit is discussed in Bell s original article and therefore goes right back to the origin of the Bell inequalities CHSH inequality edit Main article CHSH inequality Generalizing Bell s original inequality John Clauser Michael Horne Abner Shimony and R A Holt introduced the CHSH inequality which puts classical limits on the set of four correlations in Alice and Bob s experiment without any assumption of perfect correlations or anti correlations at equal settings where denotes correlation in the quantum physicist s sense the expected value of the product of the two binary valued outcomes Making the special choice denoting and assuming perfect anti correlation at equal settings perfect correlation at opposite settings therefore and the CHSH inequality reduces to the original Bell inequality Nowadays is also often simply called the Bell inequality but sometimes more completely the Bell CHSH inequality Local realism edit To prove Bell s theorem via a derivation of the Bell CHSH inequality we first have to formalize local realism A common approach is the following There is a probability space and the observed outcomes by both Alice and Bob result by random sampling of the unknown hidden parameter The values observed by Alice or Bob are functions of the local detector settings and the hidden parameter only Thus there are functions A B S × { } such that The value observed by Alice with detector setting a is The value observed by Bob with detector setting b is Implicit in assumption above the hidden parameter space has a probability measure and the expectation of a random variable X on with respect to is written where for accessibility of notation we assume that the probability measure has a density that therefore is nonnegative and integrates to The hidden parameter is often thought of as being associated with source but it can just as well also contain components associated with the two measurement devices Derivation of CHSH inequality edit Given this formalization of what is meant by local realism or by a hidden variables theory the CHSH inequality can be derived as follows The subsequent derivation is clearer if we use the following abbreviated notation Thus each of these four quantities is ± and each depends on It follows that for any one of and is zero and the other is ± From this it follows that and therefore At the heart of this derivation is a simple algebraic inequality concerning four variables which take the values ± only The CHSH inequality is seen to depend only on the following three key features of a local hidden variables theory realism alongside of the outcomes of actually performed measurements the outcomes of potentially performed measurements also exist at the same time locality the outcomes of measurements on Alice s particle don t depend on which measurement Bob chooses to perform on the other particle freedom Alice and Bob can indeed choose freely which measurements to perform The realism assumption is actually somewhat idealistic and Bell s theorem only proves non locality with respect to variables that only exist for metaphysical reasons However before the discovery of quantum mechanics both realism and locality were completely uncontroversial features of physical theories Bell inequalities are violated by quantum mechanical predictions edit The measurements performed by Alice and Bob are spin measurements on electrons Alice can choose between two detector settings labeled a and a these settings correspond to measurement of spin along the z or the x axis Bob can choose between two detector settings labeled b and b these correspond to measurement of spin along the z or x axis where the x z coordinate system is rotated ° relative to the x z coordinate system The spin observables are represented by the × self adjoint matrices These are the Pauli spin matrices normalized so that the corresponding eigenvalues are ± As is customary we use the bra–ket notation to denote the eigenvectors of Sx by Let be the spin singlet state for a pair of electrons discussed in the EPR paradox This is a specially constructed state described by the following vector in the tensor product Now let us apply the CHSH formalism to the measurements that can be performed by Alice and Bob The operators correspond to Bob s spin measurements along x and z Note that the A operators commute with the B operators so we can apply our calculation for the correlation In this case we can show that the CHSH inequality fails In fact a straightforward calculation shows that citation needed so that Bell s Theorem If the quantum mechanical formalism is correct then the system consisting of a pair of entangled electrons cannot satisfy the principle of local realism Note that v is indeed the upper bound for quantum mechanics called Tsirelson s bound The operators giving this maximal value are always isomorphic to the Pauli matrices Practical experiments testing Bell s theorem edit Scheme of a two channel Bell test The source S produces pairs of photons sent in opposite directions Each photon encounters a two channel polariser whose orientation a or b can be set by the experimenter Emerging signals from each channel are detected and coincidences of four types and counted by the coincidence monitor Main article Bell test experiments Experimental tests can determine whether the Bell inequalities required by local realism hold up to the empirical evidence Actually most experiments have been performed using polarization of photons rather than spin of electrons or other spin half particles The quantum state of the pair of entangled photons is not the singlet state and the correspondence between angles and outcomes is different from that in the spin half set up The polarization of a photon is measured in a pair of perpendicular directions Relative to a given orientation polarization is either vertical denoted by V or by or horizontal denoted by H or by The photon pairs are generated in the quantum state where and denotes the state of a single vertically or horizontally polarized photon respectively relative to a fixed and common reference direction for both particles When the polarization of both photons is measured in the same direction both give the same outcome perfect correlation When measured at directions making an angle degrees with one another the outcomes are completely random uncorrelated Measuring at directions at degrees to one another the two are perfectly anti correlated In general when the polarizers are at an angle to one another the correlation is cos So relative to the correlation function for the singlet state of spin half particles we have a positive rather than a negative cosine function and angles are halved the correlation is periodic with period p instead of p Bell s inequalities are tested by coincidence counts from a Bell test experiment such as the optical one shown in the diagram Pairs of particles are emitted as a result of a quantum process analysed with respect to some key property such as polarisation direction then detected The setting orientations of the analysers are selected by the experimenter Bell test experiments to date overwhelmingly violate Bell s inequality Two classes of Bell inequalities edit The fair sampling problem was faced openly in the s In early designs of their experiment Freedman and Clauser used fair sampling in the form of the Clauser–Horne–Shimony–Holt CHSH hypothesis However shortly afterwards Clauser and Horne made the important distinction between inhomogeneous IBI and homogeneous HBI Bell inequalities Testing an IBI requires that we compare certain coincidence rates in two separated detectors with the singles rates of the two detectors Nobody needed to perform the experiment because singles rates with all detectors in the s were at least ten times all the coincidence rates So taking into account this low detector efficiency the QM prediction actually satisfied the IBI To arrive at an experimental design in which the QM prediction violates IBI we require detectors whose efficiency exceeds for singlet states but have very low dark rate and short dead and resolving times This is now within reach Practical challenges edit Main article Loopholes in Bell test experiments Because at that time even the best detectors didn t detect a large fraction of all photons Clauser and Horne recognized that testing Bell s inequality required some extra assumptions They introduced the No Enhancement Hypothesis NEH

A light signal originating in an atomic cascade for example has a certain probability of activating a detector Then if a polarizer is interposed between the cascade and the detector the detection probability cannot increase Given this assumption there is a Bell inequality between the coincidence rates with polarizers and coincidence rates without polarizers The experiment was performed by Freedman and Clauser who found that the Bell s inequality was violated So the no enhancement hypothesis cannot be true in a local hidden variables model While early experiments used atomic cascades later experiments have used parametric down conversion following a suggestion by Reid and Walls giving improved generation and detection properties As a result the most recent experiments with photons no longer suffer from the detection loophole see Bell test experiments This makes the photon the first experimental system for which all main experimental loopholes have been surmounted albeit presently only in separate experiments Giustina et al Bell violation using entangled photons without the fair sampling assumption Nature – B G Christensen et al Detection Loophole Free Test of Quantum Nonlocality and Applications arXiv Metaphysical aspects edit Most advocates of the hidden variables idea believe that experiments have ruled out local hidden variables They are ready to give up locality explaining the violation of Bell s inequality by means of a non local hidden variable theory in which the particles exchange information about their states This is the basis of the Bohm interpretation of quantum mechanics which requires that all particles in the universe be able to instantaneously exchange information with all others A experiment ruled out a large class of non Bohmian non local hidden variable theories If the hidden variables can communicate with each other faster than light Bell s inequality can easily be violated Once one particle is measured it can communicate the necessary correlations to the other particle Since in relativity the notion of simultaneity is not absolute this is unattractive One idea is to replace instantaneous communication with a process that travels backwards in time along the past light cone This is the idea behind a transactional interpretation of quantum mechanics which interprets the statistical emergence of a quantum history as a gradual coming to agreement between histories that go both forward and backward in time A few advocates of deterministic models have not given up on local hidden variables For example Gerard t Hooft has argued that the superdeterminism loophole cannot be dismissed A possible but not universally accepted solution is offered by the many worlds theory of quantum mechanics According to this not only is collapse of the wave function illusory but the apparent random branching of possible futures when quantum systems interact with the macroscopic world is also an illusion Measurement does not lead to a random choice of possible outcome rather the only ingredient of quantum mechanics is the unitary evolution of the wave function All possibilities co exist forever and the only reality is the quantum mechanical wave function According to this view two distant observers both split into superpositions when measuring a spin The Bell inequality violations are no longer counterintuitive because it is not clear which copy of the observer B will seen by observer A when they compare notes If reality includes all the different outcomes locality in physical space not outcome space places no restrictions on how the split observers can meet up This point underlines the fact that the argument that realism is incompatible with quantum mechanics and locality depends on a particular formalization of the concept of realism In its weakest form the assumption underpinning that particular formalization is called counterfactual definiteness This is the assumption that outcomes of measurements that are not performed are just as real as those of measurements that were performed Counterfactual definiteness is an uncontroversial property of all classical physical theories prior to quantum theory due to their determinism Many worlds interpretations are not only counterfactually indefinite but are also factually indefinite The results of all experiments even ones that have been performed are not uniquely determined If one chooses to reject counterfactual definiteness reality has been made smaller and there is no non locality problem On the other hand one is thereby introducing irreducible or intrinsic randomness into our picture of the world randomness that cannot be explained as merely the reflection of our ignorance of underlying variable physical quantities Non determinism becomes a fundamental property of nature Assuming counterfactual definiteness reality has been enlarged and there is a non locality problem On the other hand in the many worlds interpretation of quantum mechanics reality consists only of a deterministically evolving wave function and non locality is a non issue There have also been repeated claims that Bell s arguments are irrelevant because they depend on hidden assumptions that in fact are questionable—though none of these claims have ever achieved much support For example E T Jaynes claimed in that there are two hidden assumptions in Bell s theorem that could limit its generality According to him Bell interpreted conditional probability P X|Y as a causal inference i e Y exerted a causal inference on X in reality However P X|Y actually only means logical inference deduction Causes cannot travel faster than light or backward in time but deduction can Bell s inequality does not apply to some possible hidden variable theories It only applies to a certain class of local hidden variable theories In fact it might have just missed the kind of hidden variable theories that Einstein is most interested in However Richard D Gill has argued that Jaynes misunderstood Bell s analysis Gill points out that in the same conference volume in which Jaynes argues against Bell Jaynes confesses to being extremely impressed by a short proof by Steve Gull presented at the same conference that the singlet correlations could not be reproduced by a computer simulation of a local hidden variables theory According to Jaynes writing nearly years after Bell s landmark contributions it would probably take us another years to fully appreciate Gull s stunning result A recent flurry of activity about implications for determinism arose with the paper The Free Will Theorem which stated the response of a spin particle to a triple experiment is free—that is to say is not a function of properties of that part of the universe that is earlier than this response with respect to any given inertial frame This theorem raised awareness of a tension between determinism fully governing an experiment on the one hand and Alice and Bob being free to choose any settings they like for their observations on the other The philosopher David Hodgson supports this theorem as showing that determinism is unscientific and that quantum mechanics allows observers at least in some instances the freedom to make observations of their choosing thereby leaving the door open for free will Final remarks edit The violations of Bell s inequalities due to quantum entanglement provide near definite demonstrations of something that was already strongly suspected that quantum physics cannot be represented by any version of the classical picture of physics Some earlier elements that had seemed incompatible with classical pictures included complementarity and wavefunction collapse The Bell violations show that no resolution of such issues can avoid the ultimate strangeness of quantum behavior The EPR paper pinpointed the unusual properties of the entangled states e g the above mentioned singlet state which is the foundation for present day applications of quantum physics such as quantum cryptography one application involves the measurement of quantum entanglement as a physical source of bits for Rabin s oblivious transfer protocol This non locality was originally supposed to be illusory because the standard interpretation could easily do away with action at a distance by simply assigning to each particle definite spin states for all possible spin directions The EPR argument was therefore these definite states exist therefore quantum theory is incomplete since they do not appear in the theory Bell s theorem showed that the entangledness prediction of quantum mechanics has a degree of non locality that cannot be explained away by any local theory In well defined Bell experiments see the paragraph on test experiments one can now falsify either quantum mechanics or Einstein s quasi classical assumptions currently many experiments of this kind have been performed and the experimental results support quantum mechanics though some point out that it is theoretically possible that detectors give a biased sample of photons so that until the relative number of unpaired photons is small enough the final word has not yet been spoken According to Marek Zukowski quoted in Science Magazine experimenters expect the first loophole free experiment to be done in five years According to one of the foremost experimentalists in this field Anton Zeilinger the goal of a loophole free experiment is very close and will be a major achievement According to Gregor Weihs University of Innsbruck and conducted a Bell test experiment at least four major experimental groups around the world are in the race to be first In Jason Gallicchio Andrew Friedman and David Kaiser published a paper in Physical Review letters proposing an experiment to close the free will loophole that uses light from quasars at opposite directions in the sky which have therefore not had any contact or communication since the Big Bang to decide on the settings of particle detectors As Kaiser explains it an experiment would go something like this A laboratory setup would consist of a particle generator such as a radioactive atom that emits pairs of entangled particles One detector measures a property of particle A while another detector does the same for particle B A split second after the particles are generated but just before the detectors are set scientists would use telescopic observations of distant quasars to determine which properties each detector will measure of a respective particle In other words quasar A determines the settings to detect particle A and quasar B sets the detector for particle B What is powerful about Bell s theorem is that it doesn t refer to any particular physical theory It shows that nature violates the most general assumptions behind classical pictures not just details of some particular models No combination of local deterministic and local random variables can reproduce the phenomena predicted by quantum mechanics and repeatedly observed in experiments See also edit Bell test experiments Bohr–Einstein debates on quantum mechanics CHSH Bell test Counterfactual definiteness Correlation does not imply causation Webcomics also known as online comics or Internet comics are comics published on a website While many are published exclusively on the web others are also published in magazines newspapers or in books Webcomics can be compared to self published print comics in that almost anyone can create their own webcomic and publish it Readership levels vary widely many are read only by the creator s immediate friends and family while some of the largest claim audiences well over one million readers Webcomics range from traditional comic strips and graphic novels to avant garde comics and cover many genres styles and subjects Only a select few are financially successful Contents Medium Styles Content Format Early webcomics Webcomics collectives Business Awards Webcomics in print Non anglophone webcomics Webtoon See also References External links Medium edit Many webcomics like Diesel Sweeties use non traditional art styles The themes of webcomics like Eric Millikin s have caused controversy There are several differences between webcomics and print comics With webcomics the restrictions of the traditional newspapers or magazines can be lifted allowing artists and writers to take advantage of the web s unique capabilities Styles edit The freedom webcomics provide allows artists to work in nontraditional styles Clip art or photo comics also known as fumetti are two types of webcomics that do not use traditional artwork A Softer World for example is made by overlaying photographs with strips of typewriter style text As in the constrained comics tradition a few webcomics such as Dinosaur Comics by Ryan North are created with most strips having art copied exactly from one or a handful of template comics and only the text changing Pixel art such as that created by Richard Stevens of Diesel Sweeties is similar to that of sprite comics but instead uses low resolution images created by the artist himself However it s very common for artists to use traditional styles and layouts similar to those published in newspapers or comic books Content edit Webcomics that are independently published are not subject to the content restrictions of book publishers or newspaper syndicates enjoying an artistic freedom similar to underground and alternative comics Some webcomics stretch the boundaries of taste taking advantage of the fact that internet censorship is virtually nonexistent in countries like the United States The content of webcomics can still cause problems such as Leisure Town artist Tristan Farnon s legal trouble after creating a homoerotic Dilbert parody or the Catholic League s protest of artist Eric Millikin s blasphemous treatment of Jesus Format edit Scott McCloud one of the first advocates of webcomics has pioneered the idea of the infinite canvas where rather than being confined to normal print dimensions artists are free to spread out in any direction indefinitely with their comics Other webcomics such as Charley Parker s Argon Zark or the work of political cartoonist Mark Fiore incorporate animations or even interactive elements into their comics However the format and style of many if not most webcomics is still similar to that of traditional newspaper comic strips like Peanuts consisting of three or four panels Similar to comic books manga and graphic novels other webcomics come in a page form rather than a strip form and tend to focus more on story than gags Webcomic creators often publish print collections when their archive consists of a significant number of strips artists who create webcomics in nonstandard formats may experience difficulties to come up with an adequate page layout Early webcomics edit The first online comic was Eric Millikin s Witches and Stitches an unauthorized Wizard of Oz parody comic which was published on CompuServe in It was followed by T H E Fox a furry comic strip by Joe Ekaitis which was published on CompuServe and Quantum Link in Other online comics followed in the early s Hans Bjordahl s college themed comic strip Where the Buffalo Roam was published on FTP and usenet in and David Farley s single panel gag cartoon Doctor Fun was published on the web in September Stafford Huyler s stick figure comic NetBoy began publishing on the web in the summer of and NetComics Weekly from Finnish Comics Society was started in mid Among the longest running webcomics some of which are still being published are Rogues of Clwyd Rhan a Dutch comic that started in November The Polymer City Chronicles March Art Comics Daily March Argon Zark June Kevin and Kell September Slow Wave November and Eric Millikin Fall The term webcomics was used as early as April The late s saw the number of webcomics increase dramatically In Goats appeared in April followed by Sluggy Freelance in August Roomies in September Piled Higher and Deeper in October User Friendly in November The webcomics Pokey the Penguin Penny Arcade Jerkcity and PvP began a year later in Webcomics collectives edit In March Bebe Williams launched the webcomics portal Art Comics Daily an online gallery of several webcomics In March Chris Crosby Crosby s mother Teri and Darren Bleuel founded the webcomics portal Keenspot In July Austin Osueke launched eigoMANGA a web portal that published original online manga webmanga Within this year eigoMANGA brought comic book industry attention to webcomics after being featured in many comic book web magazine articles and later appearing in the March issue of Wizard Magazine In the subscription webcomics site Cool Beans World was launched after a high profile publicity campaign including extensive print advertising It won Internet Magazine s Site of the Month award in October Contributors included amongst others UK based comic book creators Pat Mills Simon Bisley John Bolton and Kevin O Neill and the author Clive Barker Serialised content included Scarlet Traces and Marshal Law In March Shannon Denton and Patrick Coyle launched Komikwerks com serving free strips from comics and animation professionals The site launched with titles including Steve Conley s Astounding Space Thrills Jason Kruse s The World of Quest and Bernie Wrightson s The Nightmare Expeditions On March Joey Manley founded Modern Tales offering subscription based webcomics The Modern Tales spin off serializer followed in October then came girlamatic and Graphic Smash in March and September respectively By webcomics hosting had become a business in its own right with sites such as The Rampage Network and Webcomics Nation While comic strip syndicates had been present online since the mid s traditional comic book publishers such as Marvel Comics and Slave Labour Graphics did not begin making serious digital efforts until and DC Comics launched its web comic imprint Zuda Comics in October The site featured user submitted comics in a competition for a professional contract to produce web comics In July it was announced that DC was closing down Zuda Business edit Only a few webcomics such as xkcd are financially successful Further information List of professional webcomic artists A growing number of artists make a full time living from their businesses and intellectual property among them Mike Krahulik and Jerry Holkins of Penny Arcade Pete Abrams of Sluggy Freelance and Randall Munroe of xkcd Comics online can generate revenue from many sources including advertising original art sales merchandising print collections subscription fees and reader donations These methods are not dissimilar to avenues of income available to traditional artists Awards edit Main article List of webcomic awards Many webcomics artists have received honors for their work In Gene Luen Yang s graphic novel American Born Chinese originally published as a webcomic on Modern Tales was the first graphic novel to be nominated for a National Book Award Don Hertzfeldt s animated film based on his webcomics Everything Will Be OK won the Sundance Film Festival Jury Award in Short Filmmaking a prize rarely bestowed on an animated film Many traditionally print comics focused organizations have added award categories for comics published on the web The Eagle Awards established a Favorite Web based Comic category in and the Ignatz Awards followed the next year by introducing an Outstanding Online Comic category in After having nominated webcomics in several of their traditional print comics categories the Eisner Awards began awarding comics in the Best Digital Comic category in In the Harvey Awards established a Best Online Comics Work category and in the Shuster Awards began an Outstanding Canadian Web Comic Creator Award In the National Cartoonists Society