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Bell's theorem

Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measurement. "Local" here refers to the principle of locality, the idea that a particle can only be influenced by its immediate surroundings, and that interactions mediated by physical fields cannot propagate faster than the speed of light. "Hidden variables" are putative properties of quantum particles that are not included in quantum theory but nevertheless affect the outcome of experiments. In the words of physicist John Stewart Bell, for whom this family of results is named, "If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local."

The first such result was introduced by Bell in 1964, building upon the Einstein–Podolsky–Rosen paradox, which had called attention to the phenomenon of quantum entanglement. Bell deduced that if measurements are performed independently on the two separated particles of an entangled pair, then the assumption that the outcomes depend upon hidden variables within each half implies a mathematical constraint on how the outcomes on the two measurements are correlated. Such a constraint would later be named a Bell inequality. Bell then showed that quantum physics predicts correlations that violate this inequality. Multiple variations on Bell's theorem were put forward in the following years, using different assumptions and obtaining different Bell (or "Bell-type") inequalities.

The first rudimentary experiment designed to test Bell's theorem was performed in 1972 by John Clauser and Stuart Freedman. More advanced experiments, known collectively as Bell tests, have been performed many times since. Often, these experiments have had the goal of "closing loopholes", that is, ameliorating problems of experimental design or set-up that could in principle affect the validity of the findings of earlier Bell tests. Bell tests have consistently found that physical systems obey quantum mechanics and violate Bell inequalities; which is to say that the results of these experiments are incompatible with any local hidden-variable theory.

The exact nature of the assumptions required to prove a Bell-type constraint on correlations has been debated by physicists and by philosophers. While the significance of Bell's theorem is not in doubt, its full implications for the interpretation of quantum mechanics remain unresolved.

Theorem
There are many variations on the basic idea, some employing stronger mathematical assumptions than others. Significantly, Bell-type theorems do not refer to any particular theory of local hidden variables, but instead show that quantum physics violates general assumptions behind classical pictures of nature. The original theorem proved by Bell in 1964 is not the most amenable to experiment, and it is convenient to introduce the genre of Bell-type inequalities with a later example.

Hypothetical characters Alice and Bob stand in widely separated locations. Their colleague Victor prepares a pair of particles and sends one to Alice and the other to Bob. When Alice receives her particle, she chooses to perform one of two possible measurements (perhaps by flipping a coin to decide which). Denote these measurements by $$A_0$$ and $$A_1$$. Both $$A_0$$ and $$A_1$$ are binary measurements: the result of $$A_0$$ is either $$+1$$ or $$-1$$, and likewise for $$A_1$$. When Bob receives his particle, he chooses one of two measurements, $$B_0$$ and $$B_1$$, which are also both binary.

Suppose that each measurement reveals a property that the particle already possessed. For instance, if Alice chooses to measure $$A_0$$ and obtains the result $$+1$$, then the particle she received carried a value of $$+1$$ for a property $$a_0$$. Consider the combination$$a_0b_0 + a_0b_1 + a_1b_0-a_1b_1 = (a_0+a_1)b_0 + (a_0-a_1)b_1 \, .$$Because both $$a_0$$ and $$a_1$$ take the values $$\pm 1$$, then either $$a_0 = a_1$$ or $$a_0 = -a_1$$. In the former case, the quantity $$(a_0-a_1)b_1$$ must equal 0, while in the latter case, $$(a_0+a_1)b_0 = 0$$. So, one of the terms on the right-hand side of the above expression will vanish, and the other will equal $$\pm 2$$. Consequently, if the experiment is repeated over many trials, with Victor preparing new pairs of particles, the absolute value of the average of the combination $$a_0b_0 + a_0b_1 + a_1b_0-a_1b_1$$ across all the trials will be less than or equal to 2. No single trial can measure this quantity, because Alice and Bob can only choose one measurement each, but on the assumption that the underlying properties exist, the average value of the sum is just the sum of the averages for each term. Using angle brackets to denote averages$$| \langle A_0B_0 \rangle + \langle A_0B_1 \rangle + \langle A_1B_0 \rangle - \langle A_1B_1 \rangle | \leq 2 \, .$$ This is a Bell inequality, specifically, the CHSH inequality. Its derivation here depends upon two assumptions: first, that the underlying physical properties $$a_0, a_1, b_0,$$ and $$b_1$$ exist independently of being observed or measured (sometimes called the assumption of realism); and second, that Alice's choice of action cannot influence Bob's result or vice versa (often called the assumption of locality).

Quantum mechanics can violate the CHSH inequality, as follows. Victor prepares a pair of qubits which he describes by the Bell state $$|\psi\rangle = \frac{|0\rangle \otimes |1\rangle - |1\rangle \otimes |0\rangle}{\sqrt{2}} ,$$ where $$|0\rangle$$ and $$|1\rangle$$ are the eigenstates of one of the Pauli matrices, $$\sigma_z = \begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix}.$$ Victor then passes the first qubit to Alice and the second to Bob. Alice and Bob's choices of possible measurements are also defined in terms of the Pauli matrices. Alice measures either of the two observables $$\sigma_z$$ and $$\sigma_x$$: $$A_0 = \sigma_z,\ A_1 = \sigma_x = \begin{pmatrix}0 & 1 \\ 1 & 0 \end{pmatrix};$$ and Bob measures either of the two observables $$B_0 = -\frac{\sigma_x + \sigma_z}{\sqrt{2}},\ B_1 = \frac{\sigma_x - \sigma_z}{\sqrt{2}} .$$ Victor can calculate the quantum expectation values for pairs of these observables using the Born rule: $$\langle A_0 \otimes B_0 \rangle = \frac{1}{\sqrt{2}}, \langle A_0 \otimes B_1 \rangle = \frac{1}{\sqrt{2}}, \langle A_1 \otimes B_0 \rangle = \frac{1}{\sqrt{2}}, \langle A_1 \otimes B_1 \rangle = -\frac{1}{\sqrt{2}} \,. $$ While only one of these four measurements can be made in a single trial of the experiment, the sum $$\langle A_0 \otimes B_0 \rangle + \langle A_0 \otimes B_1 \rangle + \langle A_1 \otimes B_0 \rangle - \langle A_1 \otimes B_1 \rangle = 2\sqrt{2} $$ gives the sum of the average values that Victor expects to find across multiple trials. This value exceeds the classical upper bound of 2 that was deduced from the hypothesis of local hidden variables. The value $$2\sqrt{2}$$ is in fact the largest that quantum physics permits for this combination of expectation values, making it a Tsirelson bound.

The CHSH inequality can also be thought of as a game in which Alice and Bob try to coordinate their actions. Victor prepares two bits, $$x$$ and $$y$$, independently and at random. He sends bit $$x$$ to Alice and bit $$y$$ to Bob. Alice and Bob win if they return answer bits $$a$$ and $$b$$ to Victor, satisfying $$x y = a + b \mod 2 \, .$$ Or, equivalently, Alice and Bob win if the logical AND of $$x$$ and $$y$$ is the logical XOR of $$a$$ and $$b$$. Alice and Bob can agree upon any strategy they desire before the game, but they cannot communicate once the game begins. In any theory based on local hidden variables, Alice and Bob's probability of winning is no greater than $$3/4$$, regardless of what strategy they agree upon beforehand. However, if they share an entangled quantum state, their probability of winning can be as large as $$\frac{2+\sqrt{2}}{4} \approx 0.85 \, .$$

Bell (1964)
Bell's 1964 paper points out that under restricted conditions, local hidden-variable models can reproduce the predictions of quantum mechanics. He then demonstrates that this cannot hold true in general. Bell considers a refinement by David Bohm of the Einstein–Podolsky–Rosen (EPR) thought experiment. In this scenario, a pair of particles are formed together in such a way that they are described by a spin singlet state (which is an example of an entangled state). The particles then move apart in opposite directions. Each particle is measured by a Stern–Gerlach device, a measuring instrument that can be oriented in different directions and that reports one of two possible outcomes, representable by $$+1$$ and $$-1$$. The configuration of each measuring instrument is represented by a unit vector, and the quantum-mechanical prediction for the correlation between two detectors with settings $$\vec{a}$$ and $$\vec{b}$$ is $$P(\vec{a}, \vec{b}) = -\vec{a} \cdot \vec{b}.$$ In particular, if the orientation of the two detectors is the same ($$\vec{a} = \vec{b}$$), then the outcome of one measurement is certain to be the negative of the outcome of the other, giving $$P(\vec{a}, \vec{a}) = -1$$. And if the orientations of the two detectors are orthogonal ($$\vec{a} \cdot \vec{b} = 0$$), then the outcomes are uncorrelated, and $$P(\vec{a}, \vec{b}) = 0$$. Bell proves by example that these special cases can be explained in terms of hidden variables, then proceeds to show that the full range of possibilities involving intermediate angles cannot.

Bell posited that a local hidden-variable model for these correlations would explain them in terms of an integral over the possible values of some hidden parameter $$\lambda$$: $$P(\vec{a}, \vec{b}) = \int d\lambda\, \rho(\lambda) A(\vec{a}, \lambda) B(\vec{b}, \lambda),$$ where $$\rho(\lambda)$$ is a probability density function. The two functions $$A(\vec{a}, \lambda)$$ and $$B(\vec{b}, \lambda)$$ provide the responses of the two detectors given the orientation vectors and the hidden variable: $$A(\vec{a}, \lambda) = \pm 1, \, B(\vec{b}, \lambda) = \pm 1.$$ Crucially, the outcome of detector $$A$$ does not depend upon $$\vec{b}$$, and likewise the outcome of $$B$$ does not depend upon $$\vec{a}$$, because the two detectors are physically separated. Now we suppose that the experimenter has a choice of settings for the second detector: it can be set either to $$\vec{b}$$ or to $$\vec{c}$$. Bell proves that the difference in correlation between these two choices of detector setting must satisfy the inequality $$|P(\vec{a}, \vec{b}) - P(\vec{a}, \vec{c})| \leq 1 + P(\vec{b}, \vec{c}).$$ However, it is easy to find situations where quantum mechanics violates the Bell inequality. For example, let the vectors $$\vec{a}$$ and $$\vec{b}$$ be orthogonal, and let $$\vec{c}$$ lie in their plane at a 45° angle from both of them. Then $$P(\vec{a}, \vec{b}) = 0,$$ while $$P(\vec{a}, \vec{c}) = P(\vec{b}, \vec{c}) = -\frac{\sqrt{2}}{2},$$ but $$\frac{\sqrt{2}}{2} \nleq 1 - \frac{\sqrt{2}}{2}.$$ Therefore, there is no local hidden-variable model that can reproduce the predictions of quantum mechanics for all choices of $$\vec{a}$$, $$\vec{b}$$, and $$\vec{c}.$$ Experimental results contradict the classical curves and match the curve predicted by quantum mechanics as long as experimental shortcomings are accounted for.

Bell's 1964 theorem requires the possibility of perfect anti-correlations: the ability to make a probability-1 prediction about the result from the second detector, knowing the result from the first. This is related to the "EPR criterion of reality", a concept introduced in the 1935 paper by Einstein, Podolsky, and Rosen. This paper posits: "If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity."

GHZ–Mermin (1990)
Daniel Greenberger, Michael A. Horne, and Anton Zeilinger presented a four-particle thought experiment in 1990, which David Mermin then simplified to use only three particles. In this thought experiment, Victor generates a set of three spin-1/2 particles described by the quantum state $$|\psi\rangle = \frac{1}{\sqrt{2}}(|000\rangle - |111\rangle) \,, $$ where as above, $$|0\rangle$$ and $$|1\rangle$$ are the eigenvectors of the Pauli matrix $$\sigma_z$$. Victor then sends a particle each to Alice, Bob, and Charlie, who wait at widely separated locations. Alice measures either $$\sigma_x$$ or $$\sigma_y$$ on her particle, and so do Bob and Charlie. The result of each measurement is either $$+1$$ or $$-1$$. Applying the Born rule to the three-qubit state $$|\psi\rangle$$, Victor predicts that whenever the three measurements include one $$\sigma_x$$ and two $$\sigma_y$$'s, the product of the outcomes will always be $$+1$$. This follows because $$|\psi\rangle$$ is an eigenvector of $$\sigma_x \otimes \sigma_y \otimes \sigma_y$$ with eigenvalue $$+1$$, and likewise for $$\sigma_y \otimes \sigma_x \otimes \sigma_y$$ and $$\sigma_y \otimes \sigma_y \otimes \sigma_x$$. Therefore, knowing Alice's result for a $$\sigma_x$$ measurement and Bob's result for a $$\sigma_y$$ measurement, Victor can predict with probability 1 what result Charlie will return for a $$\sigma_y$$ measurement. According to the EPR criterion of reality, there would be an "element of reality" corresponding to the outcome of a $$\sigma_y$$ measurement upon Charlie's qubit. Indeed, this same logic applies to both measurements and all three qubits. Per the EPR criterion of reality, then, each particle contains an "instruction set" that determines the outcome of a $$\sigma_x$$ or $$\sigma_y$$ measurement upon it. The set of all three particles would then be described by the instruction set $$(a_x,a_y,b_x,b_y,c_x,c_y) \,, $$ with each entry being either $$-1$$ or $$+1$$, and each $$\sigma_x$$ or $$\sigma_y$$ measurement simply returning the appropriate value.

If Alice, Bob, and Charlie all perform the $$\sigma_x$$ measurement, then the product of their results would be $$a_x b_x c_x$$. This value can be deduced from $$(a_x b_y c_y) (a_y b_x c_y) (a_y b_y c_x) = a_x b_x c_x a_y^2 b_y^2 c_y^2 = a_x b_x c_x \,, $$ because the square of either $$-1$$ or $$+1$$ is $$1$$. Each factor in parentheses equals $$+1$$, so $$a_x b_x c_x = +1 \,, $$ and the product of Alice, Bob, and Charlie's results will be $$+1$$ with probability unity. But this is inconsistent with quantum physics: Victor can predict using the state $$|\psi\rangle$$ that the measurement $$\sigma_x \otimes \sigma_x \otimes \sigma_x$$ will instead yield $$-1$$ with probability unity.

This thought experiment can also be recast as a traditional Bell inequality or, equivalently, as a nonlocal game in the same spirit as the CHSH game. In it, Alice, Bob, and Charlie receive bits $$x,y,z$$ from Victor, promised to always have an even number of ones, that is, $$x\oplus y\oplus z = 0$$, and send him back bits $$a,b,c$$. They win the game if $$a,b,c$$ have an odd number of ones for all inputs except $$x=y=z=0$$, when they need to have an even number of ones. That is, they win the game iff $$a \oplus b \oplus c = x \lor y \lor z$$. With local hidden variables the highest probability of victory they can have is 3/4, whereas using the quantum strategy above they win it with certainty. This is an example of quantum pseudo-telepathy.

Kochen–Specker theorem (1967)
In quantum theory, orthonormal bases for a Hilbert space represent measurements that can be performed upon a system having that Hilbert space. Each vector in a basis represents a possible outcome of that measurement. Suppose that a hidden variable $$\lambda$$ exists, so that knowing the value of $$\lambda$$ would imply certainty about the outcome of any measurement. Given a value of $$\lambda$$, each measurement outcome — that is, each vector in the Hilbert space — is either impossible or guaranteed. A Kochen–Specker configuration is a finite set of vectors made of multiple interlocking bases, with the property that a vector in it will always be impossible when considered as belonging to one basis and guaranteed when taken as belonging to another. In other words, a Kochen–Specker configuration is an "uncolorable set" that demonstrates the inconsistency of assuming a hidden variable $$\lambda$$ can be controlling the measurement outcomes.

Free will theorem
The Kochen–Specker type of argument, using configurations of interlocking bases, can be combined with the idea of measuring entangled pairs that underlies Bell-type inequalities. This was noted beginning in the 1970s by Kochen, Heywood and Redhead, Stairs, and Brown and Svetlichny. As EPR pointed out, obtaining a measurement outcome on one half of an entangled pair implies certainty about the outcome of a corresponding measurement on the other half. The "EPR criterion of reality" posits that because the second half of the pair was not disturbed, that certainty must be due to a physical property belonging to it. In other words, by this criterion, a hidden variable $$\lambda$$ must exist within the second, as-yet unmeasured half of the pair. No contradiction arises if only one measurement on the first half is considered. However, if the observer has a choice of multiple possible measurements, and the vectors defining those measurements form a Kochen–Specker configuration, then some outcome on the second half will be simultaneously impossible and guaranteed.

This type of argument gained attention when an instance of it was advanced by John Conway and Simon Kochen under the name of the free will theorem. The Conway–Kochen theorem uses a pair of entangled qutrits and a Kochen–Specker configuration discovered by Asher Peres.

Quasiclassical entanglement
As Bell pointed out, some predictions of quantum mechanics can be replicated in local hidden-variable models, including special cases of correlations produced from entanglement. This topic has been studied systematically in the years since Bell's theorem. In 1989, Reinhard Werner introduced what are now called Werner states, joint quantum states for a pair of systems that yield EPR-type correlations but also admit a hidden-variable model. Werner states are bipartite quantum states that are invariant under unitaries of symmetric tensor-product form: $$\rho_{AB} = (U \otimes U) \rho_{AB} (U^\dagger \otimes U^\dagger).$$ In 2004, Robert Spekkens introduced a toy model that starts with the premise of local, discretized degrees of freedom and then imposes a "knowledge balance principle" that restricts how much an observer can know about those degrees of freedom, thereby making them into hidden variables. The allowed states of knowledge ("epistemic states") about the underlying variables ("ontic states") mimic some features of quantum states. Correlations in the toy model can emulate some aspects of entanglement, like monogamy, but by construction, the toy model can never violate a Bell inequality.

Background
The question of whether quantum mechanics can be "completed" by hidden variables dates to the early years of quantum theory. In his 1932 textbook on quantum mechanics, the Hungarian-born polymath John von Neumann presented what he claimed to be a proof that there could be no "hidden parameters". The validity and definitiveness of von Neumann's proof were questioned by Hans Reichenbach, in more detail by Grete Hermann, and possibly in conversation though not in print by Albert Einstein. (Simon Kochen and Ernst Specker rejected von Neumann's key assumption as early as 1961, but did not publish a criticism of it until 1967. )

Einstein argued persistently that quantum mechanics could not be a complete theory. His preferred argument relied on a principle of locality:
 * Consider a mechanical system constituted of two partial systems A and B which have interaction with each other only during limited time. Let the ψ function before their interaction be given. Then the Schrödinger equation will furnish the ψ function after their interaction has taken place. Let us now determine the physical condition of the partial system A as completely as possible by measurements. Then the quantum mechanics allows us to determine the ψ function of the partial system B from the measurements made, and from the ψ function of the total system. This determination, however, gives a result which depends upon which of the determining magnitudes specifying the condition of A has been measured (for instance coordinates or momenta). Since there can be only one physical condition of B after the interaction and which can reasonably not be considered as dependent on the particular measurement we perform on the system A separated from B it may be concluded that the ψ function is not unambiguously coordinated with the physical condition. This coordination of several ψ functions with the same physical condition of system B shows again that the ψ function cannot be interpreted as a (complete) description of a physical condition of a unit system.

The EPR thought experiment is similar, also considering two separated systems A and B described by a joint wave function. However, the EPR paper adds the idea later known as the EPR criterion of reality, according to which the ability to predict with probability 1 the outcome of a measurement upon B implies the existence of an "element of reality" within B.

In 1951, David Bohm proposed a variant of the EPR thought experiment in which the measurements have discrete ranges of possible outcomes, unlike the position and momentum measurements considered by EPR. The year before, Chien-Shiung Wu and Irving Shaknov had successfully measured polarizations of photons produced in entangled pairs, thereby making the Bohm version of the EPR thought experiment practically feasible.

By the late 1940s, the mathematician George Mackey had grown interested in the foundations of quantum physics, and in 1957 he drew up a list of postulates that he took to be a precise definition of quantum mechanics. Mackey conjectured that one of the postulates was redundant, and shortly thereafter, Andrew M. Gleason proved that it was indeed deducible from the other postulates. Gleason's theorem provided an argument that a broad class of hidden-variable theories are incompatible with quantum mechanics. More specifically, Gleason's theorem rules out hidden-variable models that are "noncontextual". Any hidden-variable model for quantum mechanics must, in order to avoid the implications of Gleason's theorem, involve hidden variables that are not properties belonging to the measured system alone but also dependent upon the external context in which the measurement is made. This type of dependence is often seen as contrived or undesirable; in some settings, it is inconsistent with special relativity. The Kochen–Specker theorem refines this statement by constructing a specific finite subset of rays on which no such probability measure can be defined.

Tsung-Dao Lee came close to deriving Bell's theorem in 1960. He considered events where two kaons were produced traveling in opposite directions, and came to the conclusion that hidden variables could not explain the correlations that could be obtained in such situations. However, complications arose due to the fact that kaons decay, and he did not go so far as to deduce a Bell-type inequality.

Bell's publications
Bell chose to publish his theorem in a comparatively obscure journal because it did not require page charges, in fact paying the authors who published there at the time. Because the journal did not provide free reprints of articles for the authors to distribute, however, Bell had to spend the money he received to buy copies that he could send to other physicists. While the articles printed in the journal themselves listed the publication's name simply as Physics, the covers carried the trilingual version Physics Physique Физика to reflect that it would print articles in English, French and Russian.

Prior to proving his 1964 result, Bell also proved a result equivalent to the Kochen–Specker theorem (hence the latter is sometimes also known as the Bell–Kochen–Specker or Bell–KS theorem). However, publication of this theorem was inadvertently delayed until 1966. In that paper, Bell argued that because an explanation of quantum phenomena in terms of hidden variables would require nonlocality, the EPR paradox "is resolved in the way which Einstein would have liked least."

Experiments

In 1967, the unusual title Physics Physique Физика caught the attention of John Clauser, who then discovered Bell's paper and began to consider how to perform a Bell test in the laboratory. Clauser and Stuart Freedman would go on to perform a Bell test in 1972. This was only a limited test, because the choice of detector settings was made before the photons had left the source. In 1982, Alain Aspect and collaborators performed the first Bell test to remove this limitation. This began a trend of progressively more stringent Bell tests. The GHZ thought experiment was implemented in practice, using entangled triplets of photons, in 2000. By 2002, testing the CHSH inequality was feasible in undergraduate laboratory courses.

In Bell tests, there may be problems of experimental design or set-up that affect the validity of the experimental findings. These problems are often referred to as "loopholes". The purpose of the experiment is to test whether nature can be described by local hidden-variable theory, which would contradict the predictions of quantum mechanics.

The most prevalent loopholes in real experiments are the detection and locality loopholes. The detection loophole is opened when a small fraction of the particles (usually photons) are detected in the experiment, making it possible to explain the data with local hidden variables by assuming that the detected particles are an unrepresentative sample. The locality loophole is opened when the detections are not done with a spacelike separation, making it possible for the result of one measurement to influence the other without contradicting relativity. In some experiments there may be additional defects that make local-hidden-variable explanations of Bell test violations possible.

Although both the locality and detection loopholes had been closed in different experiments, a long-standing challenge was to close both simultaneously in the same experiment. This was finally achieved in three experiments in 2015. Regarding these results, Alain Aspect writes that "no experiment ... can be said to be totally loophole-free," but he says the experiments "remove the last doubts that we should renounce" local hidden variables, and refers to examples of remaining loopholes as being "far fetched" and "foreign to the usual way of reasoning in physics."

These efforts to experimentally validate violations of the Bell inequalities would later result in Clauser, Aspect, and Anton Zeilinger being awarded the 2022 Nobel Prize in Physics.

Interpretations
Reactions to Bell's theorem have been many and varied. Maximilian Schlosshauer, Johannes Kofler, and Zeilinger write that Bell inequalities provide "a wonderful example of how we can have a rigorous theoretical result tested by numerous experiments, and yet disagree about the implications."

The Copenhagen interpretation
Copenhagen-type interpretations generally take the violation of Bell inequalities as grounds to reject the assumption often called counterfactual definiteness or "realism", which is not necessarily the same as abandoning realism in a broader philosophical sense. For example, Roland Omnès argues for the rejection of hidden variables and concludes that "quantum mechanics is probably as realistic as any theory of its scope and maturity ever will be". Likewise, Rudolf Peierls took the message of Bell's theorem to be that, because the premise of locality is physically reasonable, "hidden variables cannot be introduced without abandoning some of the results of quantum mechanics".

This is also the route taken by interpretations that descend from the Copenhagen tradition, such as consistent histories (often advertised as "Copenhagen done right"), as well as QBism.

Many-worlds interpretation of quantum mechanics
The Many-worlds interpretation, also known as the Everett interpretation, is dynamically local, meaning that it does not call for action at a distance, and deterministic, because it consists of the unitary part of quantum mechanics without collapse. It can generate correlations that violate a Bell inequality because it violates an implicit assumption by Bell that measurements have a single outcome. In fact, Bell's theorem can be proven in the Many-Worlds framework from the assumption that a measurement has a single outcome. Therefore, a violation of a Bell inequality can be interpreted as a demonstration that measurements have multiple outcomes.

The explanation it provides for the Bell correlations is that when Alice and Bob make their measurements, they split into local branches. From the point of view of each copy of Alice, there are multiple copies of Bob experiencing different results, so Bob cannot have a definite result, and the same is true from the point of view of each copy of Bob. They will obtain a mutually well-defined result only when their future light cones overlap. At this point we can say that the Bell correlation starts existing, but it was produced by a purely local mechanism. Therefore, the violation of a Bell inequality cannot be interpreted as a proof of non-locality.

Non-local hidden variables
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. One challenge for non-local hidden variable theories is to explain why this instantaneous communication can exist at the level of the hidden variables, but it cannot be used to send signals. A 2007 experiment ruled out a large class of non-Bohmian non-local hidden variable theories, though not Bohmian mechanics itself.

The transactional interpretation, which postulates waves traveling both backwards and forwards in time, is likewise non-local.

Superdeterminism
A necessary assumption to derive Bell's theorem is that the hidden variables are not correlated with the measurement settings. This assumption has been justified on the grounds that the experimenter has "free will" to choose the settings, and that it is necessary to do science in the first place. A (hypothetical) theory where the choice of measurement is necessarily correlated with the system being measured is known as superdeterministic.

A few advocates of deterministic models have not given up on local hidden variables. For example, Gerard 't Hooft has argued that superdeterminism cannot be dismissed.

title: Bell's theorem


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Mass (liturgy)

Mass is the main Eucharistic liturgical service in many forms of Western Christianity. The term Mass is commonly used in the Catholic Church, Western Rite Orthodoxy, Old Catholicism, and Independent Catholicism. The term is also used in some Lutheran churches, as well as in some Anglican churches, and on rare occasion by other Protestant churches.

Other Christian denominations may employ terms such as Divine Service or worship service (and often just "service"), rather than the word Mass. For the celebration of the Eucharist in Eastern Christianity, including Eastern Catholic Churches, other terms such as Divine Liturgy, Holy Qurbana, Holy Qurobo and Badarak (or Patarag) are typically used instead.

Etymology
The English noun Mass is derived from the Middle Latin missa. The Latin word was adopted in Old English as mæsse (via a Vulgar Latin form *messa), and was sometimes glossed as sendnes (i.e. 'a sending, dismission').

The Latin term missa itself was in use by the 6th century. It is most likely derived from the concluding formula Ite, missa est ("Go; the dismissal is made"); missa here is a Late Latin substantive corresponding to classical missio.

Historically, however, there have been other etymological explanations of the noun missa that claim not to derive from the formula ite, missa est. Fortescue (1910) cites older, "fanciful" etymological explanations, notably a latinization of Hebrew matzâh (מַצָּה) "unleavened bread; oblation", a derivation favoured in the 16th century by Reuchlin and Luther, or Greek μύησις "initiation", or even Germanic mese "assembly". The French historian Du Cange in 1678 reported "various opinions on the origin" of the noun missa "Mass", including the derivation from Hebrew matzah (Missah, id est, oblatio), here attributed to Caesar Baronius. The Hebrew derivation is learned speculation from 16th-century philology; medieval authorities did derive the noun missa from the verb mittere, but not in connection with the formula ite, missa est. Thus, De divinis officiis (9th century) explains the word as "a mittendo, quod nos mittat ad Deo" ("from 'sending', because it sends us towards God"), while Rupert of Deutz (early 12th century) derives it from a "dismissal" of the "enmities which had been between God and men" ("inimicitiarum quæ erant inter Deum et homines").

Order of the Mass
A distinction is made between texts that recur for every Mass celebration (ordinarium, ordinary), and texts that are sung depending on the occasion (proprium, proper).

Catholic Church
The Catholic Church sees the Mass or Eucharist as "the source and summit of the Christian life", to which the other sacraments are oriented. Remembered in the Mass are Jesus' life, Last Supper, and sacrificial death on the cross at Calvary. The ordained celebrant (priest or bishop) is understood to act in persona Christi, as he recalls the words and gestures of Jesus Christ at the Last Supper and leads the congregation in praise of God. The Mass is composed of two parts, the Liturgy of the Word and the Liturgy of the Eucharist.

Although similar in outward appearance to the Anglican Mass or Lutheran Mass, the Catholic Church distinguishes between its own Mass and theirs on the basis of what it views as the validity of the orders of their clergy, and as a result, does not ordinarily permit intercommunion between members of these Churches. In a 1993 letter to Bishop Johannes Hanselmann of the Evangelical Lutheran Church in Bavaria, Cardinal Ratzinger (later Pope Benedict XVI) affirmed that "a theology oriented to the concept of succession [of bishops], such as that which holds in the Catholic and in the Orthodox church, need not in any way deny the salvation-granting presence of the Lord [Heilschaffende Gegenwart des Herrn] in a Lutheran [evangelische] Lord's Supper". The Decree on Ecumenism, produced by Vatican II in 1964, records that the Catholic Church notes its understanding that when other faith groups (such as Lutherans, Anglicans, and Presbyterians) "commemorate His death and resurrection in the Lord's Supper, they profess that it signifies life in communion with Christ and look forward to His coming in glory".

Within the fixed structure outlined below, which is specific to the Roman Rite, the Scripture readings, the antiphons sung or recited during the entrance procession or at Communion, and certain other prayers vary each day according to the liturgical calendar.

Introductory rites

The priest enters, with a deacon if there is one, and altar servers (who may act as crucifer, candle-bearers and thurifer). The priest makes the sign of the cross with the people and formally greets them. Of the options offered for the Introductory Rites, that preferred by liturgists would bridge the praise of the opening hymn with the Glory to God which follows. The Kyrie eleison here has from early times been an acclamation of God's mercy. The Penitential Act instituted by the Council of Trent is also still permitted here, with the caution that it should not turn the congregation in upon itself during these rites which are aimed at uniting those gathered as one praiseful congregation. The Introductory Rites are brought to a close by the Collect Prayer.

Liturgy of the Word
On Sundays and solemnities, three Scripture readings are given. On other days there are only two. If there are three readings, the first is from the Old Testament (a term wider than "Hebrew Scriptures", since it includes the Deuterocanonical Books), or the Acts of the Apostles during Eastertide. The first reading is followed by a psalm, recited or sung responsorially. The second reading is from the New Testament epistles, typically from one of the Pauline epistles. A Gospel acclamation is then sung as the Book of the Gospels is processed, sometimes with incense and candles, to the ambo; if not sung it may be omitted. The final reading and high point of the Liturgy of the Word is the proclamation of the Gospel by the deacon or priest. On all Sundays and Holy Days of Obligation, and preferably at all Masses, a homily or sermon that draws upon some aspect of the readings or the liturgy itself, is then given. The homily is preferably moral and hortatory. Finally, the Nicene Creed or, especially from Easter to Pentecost, the Apostles' Creed is professed on Sundays and solemnities, and the Universal Prayer or Prayer of the Faithful follows. The designation "of the faithful" comes from when catechumens did not remain for this prayer or for what follows.

Liturgy of the Eucharist

The Liturgy of the Eucharist begins with the preparation of the altar and gifts, while the collection may be taken. This concludes with the priest saying: "Pray, brethren, that my sacrifice and yours may be acceptable to God, the almighty Father." The congregation stands and responds: "May the Lord accept the sacrifice at your hands, for the praise and glory of His name, for our good, and the good of all His holy Church." The priest then pronounces the variable prayer over the gifts.

Then in dialogue with the faithful the priest brings to mind the meaning of "eucharist", to give thanks to God. A variable prayer of thanksgiving follows, concluding with the acclamation "Holy, Holy ....Heaven and earth are full of your glory. ...Blessed is he who comes in the name of the Lord. Hosanna in the highest." The anaphora, or more properly "Eucharistic Prayer", follows, The oldest of the anaphoras of the Roman Rite, fixed since the Council of Trent, is called the Roman Canon, with central elements dating to the fourth century. With the liturgical renewal following the Second Vatican Council, numerous other Eucharistic prayers have been composed, including four for children's Masses. Central to the Eucharist is the Institution Narrative, recalling the words and actions of Jesus at his Last Supper, which he told his disciples to do in remembrance of him. Then the congregation acclaims its belief in Christ's conquest over death, and their hope of eternal life. Since the early church an essential part of the Eucharistic prayer has been the epiclesis, the calling down of the Holy Spirit to sanctify our offering. The priest concludes with a doxology in praise of God's work, at which the people give their Amen to the whole Eucharistic prayer.

Communion rite

All together recite or sing the "Lord's Prayer" ("Pater Noster" or "Our Father"). The priest introduces it with a short phrase and follows it up with a prayer called the embolism, after which the people respond with another doxology. The sign of peace is exchanged and then the "Lamb of God" ("Agnus Dei" in Latin) litany is sung or recited while the priest breaks the host and places a piece in the main chalice; this is known as the rite of fraction and commingling.

The priest then displays the consecrated elements to the congregation, saying: "Behold the Lamb of God, behold him who takes away the sins of the world. Blessed are those called to the supper of the Lamb," to which all respond: "Lord, I am not worthy that you should enter under my roof, but only say the word and my soul shall be healed." Then Communion is given, often with lay ministers assisting with the consecrated wine. According to Catholic teaching, one should be in the state of grace, without mortal sin, to receive Communion. Singing by all the faithful during the Communion procession is encouraged "to express the communicants' union in spirit" from the bread that makes them one. A silent time for reflection follows, and then the variable concluding prayer of the Mass.

Concluding rite
The priest imparts a blessing over those present. The deacon or, in his absence, the priest himself then dismisses the people, choosing a formula by which the people are "sent forth" to spread the good news. The congregation responds: "Thanks be to God." A recessional hymn is sung by all, as the ministers process to the rear of the church.

Western Rite Orthodox Churches
Since most Eastern Orthodox Christians use the Byzantine Rite, most Eastern Orthodox Churches call their Eucharistic service "the Divine Liturgy." However, there are a number of parishes within the Eastern Orthodox Church which use an edited version of Latin liturgical rites. Most parishes use the "Divine Liturgy of St. Tikhon" which is a revision of the Anglican Book of Common Prayer, or "the Divine Liturgy of St. Gregory" which is derived from the Tridentine form of the Roman Rite Mass. These rubrics have been revised to reflect the doctrine and dogmas of the Eastern Orthodox Church. Therefore, the filioque clause has been removed, a fuller epiclesis has been added, and the use of leavened bread has been introduced.

Divine Liturgy of St. Gregory

 * The Preparation for Mass
 * Confiteor
 * Kyrie Eleison
 * Gloria in excelsis deo
 * Collect of the Day
 * Epistle
 * Gradual
 * Alleluia
 * Gospel
 * Sermon
 * Nicene-Constantinopolitan Creed
 * Offertory
 * Dialogue
 * Preface
 * Sanctus
 * Canon
 * Lord's Prayer
 * Fraction
 * Agnus Dei
 * Prayers before Communion
 * Holy Communion
 * Prayer of Thanksgiving
 * Dismissal
 * Blessing of the Faithful
 * Last Gospel

Anglicanism

In the Anglican tradition, Mass is one of many terms for the Eucharist. More frequently, the term used is either Holy Communion, Holy Eucharist, or the Lord's Supper. Occasionally the term used in Eastern churches, the Divine Liturgy, is also used. In the English-speaking Anglican world, the term used often identifies the Eucharistic theology of the person using it. "Mass" is frequently used by Anglo-Catholics.

Structure of the rite
The various Eucharistic liturgies used by national churches of the Anglican Communion have continuously evolved from the 1549 and 1552 editions of the Book of Common Prayer, both of which owed their form and contents chiefly to the work of Thomas Cranmer, who in about 1547 had rejected the medieval theology of the Mass. Although the 1549 rite retained the traditional sequence of the Mass, its underlying theology was Cranmer's and the four-day debate in the House of Lords during December 1548 makes it clear that this had already moved far beyond traditional Catholicism. In the 1552 revision, this was made clear by the restructuring of the elements of the rite while retaining nearly all the language so that it became, in the words of an Anglo-Catholic liturgical historian (Arthur Couratin) "a series of communion devotions; disembarrassed of the Mass with which they were temporarily associated in 1548 and 1549". Some rites, such as the 1637 Scottish rite and the 1789 rite in the United States, went back to the 1549 model. From the time of the Elizabethan Settlement in 1559 the services allowed for a certain variety of theological interpretation. Today's rites generally follow the same general five-part shape. Some or all of the following elements may be altered, transposed or absent depending on the rite, the liturgical season and use of the province or national church:

 * Gathering: Begins with a Trinitarian-based greeting or seasonal acclamation ("Blessed be God: Father, Son and Holy spirit. And Blessed be his kingdom, now and forever. Amen"). Then the Kyrie and a general confession and absolution follow. On Sundays outside Advent and Lent and on major festivals, the Gloria in Excelsis Deo is sung or said. The entrance rite then concludes with the collect of the day.
 * Proclaiming and Hearing the Word: Usually two to three readings of Scripture, one of which is always from the Gospels, plus a psalm (or portion thereof) or canticle between the lessons. This is followed by a sermon or homily; the recitation of one of the Creeds, viz., the Apostles' or Nicene, is done on Sundays and feasts.
 * The Prayers of the People: Quite varied in their form.
 * The Peace: The people stand and greet one another and exchange signs of God's peace in the name of the Lord. It functions as a bridge between the prayers, lessons, sermon and creeds to the Communion part of the Eucharist.
 * The Celebration of the Eucharist: The gifts of bread and wine are brought up, along with other gifts (such as money or food for a food bank, etc.), and an offertory prayer is recited. Following this, a Eucharistic Prayer (called "The Great Thanksgiving") is offered. This prayer consists of a dialogue (the Sursum Corda), a preface, the sanctus and benedictus, the Words of Institution, the Anamnesis, an Epiclesis, a petition for salvation, and a Doxology. The Lord's Prayer precedes the fraction (the breaking of the bread), followed by the Prayer of Humble Access or the Agnus Dei and the distribution of the sacred elements (the bread and wine).
 * Dismissal: There is a post-Communion prayer, which is a general prayer of thanksgiving. The service concludes with a Trinitarian blessing and the dismissal.

The liturgy is divided into two main parts: The Liturgy of the Word (Gathering, Proclaiming and Hearing the Word, Prayers of the People) and the Liturgy of the Eucharist (together with the Dismissal), but the entire liturgy itself is also properly referred to as the Holy Eucharist. The sequence of the liturgy is almost identical to the Roman Rite, except the Confession of Sin ends the Liturgy of the Word in the Anglican rites in North America, while in the Roman Rite (when used) and in Anglican rites in many jurisdictions the Confession is near the beginning of the service.

Special Masses
The Anglican tradition includes separate rites for nuptial, funeral, and votive Masses. The Eucharist is an integral part of many other sacramental services, including ordination and Confirmation.

Ceremonial
Some Anglo-Catholic parishes use Anglican versions of the Tridentine Missal, such as the English Missal, The Anglican Missal, or the American Missal, for the celebration of Mass, all of which are intended primarily for the celebration of the Eucharist, or use the order for the Eucharist in Common Worship arranged according to the traditional structure, and often with interpolations from the Roman Rite. In the Episcopal Church (United States), a traditional-language, Anglo-Catholic adaptation of the 1979 Book of Common Prayer has been published (An Anglican Service Book).

All of these books contain such features as meditations for the presiding celebrant(s) during the liturgy, and other material such as the rite for the blessing of palms on Palm Sunday, propers for special feast days, and instructions for proper ceremonial order. These books are used as a more expansively Catholic context in which to celebrate the liturgical use found in the Book of Common Prayer and related liturgical books. In England supplementary liturgical texts for the proper celebration of Festivals, Feast days and the seasons is provided in Common Worship; Times and Seasons (2013), Festivals (Common Worship: Services and Prayers for the Church of England) (2008) and Common Worship: Holy Week and Easter (2011).

These are often supplemented in Anglo-Catholic parishes by books specifying ceremonial actions, such as A Priest's Handbook by Dennis G. Michno, Ceremonies of the Eucharist by Howard E. Galley, Low Mass Ceremonial by C. P. A. Burnett, and Ritual Notes by E.C.R. Lamburn. Other guides to ceremonial include the General Instruction of the Roman Missal, Ceremonies of the Modern Roman Rite (Peter Elliott), Ceremonies of the Roman Rite Described (Adrian Fortescue), and The Parson's Handbook (Percy Dearmer). In Evangelical Anglican parishes, the rubrics detailed in the Book of Common Prayer are sometimes considered normative.

Lutheranism

In the Book of Concord, Article XXIV ("Of the Mass") of the Augsburg Confession (1530) begins thus: "Falsely are our churches accused of abolishing the Mass; for the Mass is retained among us, and celebrated with the highest reverence. We do not abolish the Mass but religiously keep and defend it. [...] We keep the traditional liturgical form. [...] In our churches Mass is celebrated every Sunday and on other holy days, when the sacrament is offered to those who wish for it after they have been examined and absolved (Article XXIV)."

Martin Luther rejected parts of the Roman Rite Mass, specifically the Canon of the Mass, which, as he argued, did not conform with. That verse contrasts the Old Testament priests, who needed to make a sacrifice for sins on a regular basis, with the single priest Christ, who offers his body only once as a sacrifice. The theme is carried out also in, , and. Luther composed as a replacement a revised Latin-language rite, Formula missae, in 1523, and the vernacular Deutsche Messe in 1526.

Scandinavian, Finnish, and some English speaking Lutherans, use the term "Mass" for their Eucharistic service, but in most German and English-speaking churches, the terms "Divine Service", "Holy Communion, or "the Holy Eucharist" are used.

Lutheran churches often celebrate the Eucharist each Sunday, if not at every worship service. This aligns with Luther's preference and the Lutheran confessions. Also, eucharistic ministers take the sacramental elements to the sick in hospitals and nursing homes. The practice of weekly Communion is increasingly the norm again in most Lutheran parishes throughout the world. The bishops and pastors of the larger Lutheran bodies have strongly encouraged this restoration of the weekly Mass.

Methodism
The celebration of the "Mass" in Methodist churches, commonly known as the Service of the Table, is based on The Sunday Service of 1784, a revision of the liturgy of the 1662 Book of Common Prayer authorized by John Wesley. The use of the term "Mass" is very rare in Methodism. The terms "Holy Communion", "Lord's Supper", and to a lesser extent "Eucharist" are far more typical.

The celebrant of a Methodist Eucharist must be an ordained or licensed minister. In the Free Methodist Church, the liturgy of the Eucharist, as provided in its Book of Discipline, is outlined as follows: Methodist services of worship, post-1992, reflect the ecumenical movement and Liturgical Movement, particularly the Methodist Mass, largely the work of theologian Donald C. Lacy.
 * The Invitation: You who truly and earnestly repent of your sins, who live in love and peace with your neighbors and who intend to lead a new life, following the commandments of God and walking in His holy ways, draw near with faith, and take this holy sacrament to your comfort; and humbly kneeling, make your honest confession to Almighty God.
 * General Confession
 * Lord's Prayer
 * Affirmation of Faith
 * Collect
 * Sanctus
 * Gloria Patri
 * Prayer of Humble Access
 * Prayer of Consecration of the Elements
 * Benediction

Calendrical usage
The English suffix  (equivalent to modern English "Mass") can label certain prominent (originally religious) feasts or seasons based on a traditional liturgical year. For example:
 * Candlemas
 * Childermas
 * Christmas

 * Johnmas
 * Lammas

 * Martinmas
 * Michelmas

title: Mass (liturgy)


text:
Framing error

Framing error can refer to the following:
 * General form of a framing error is the result of starting to read a sequence of data at the wrong point.
 * In serial communications, a framing error is the result of reading a data frame – a string of symbols which are grouped in blocks – at the wrong starting point. The symbols are bits and the blocks are bytes, ten bits in asynchronous transmission and eight in synchronous. A framing error in an asynchronous stream usually recovers quickly, but a framing error in a synchronous stream produces gibberish at the end of the packet. Framing errors can be detected with parity bits.
 * In genetics, a framing error (also called a frameshift or a frameshift mutation) is a mutation that inserts or deletes a single nucleotide from a DNA sequence. Due to the triplet nature of gene expression, the insertion/deletion can disrupt the grouping of the codons, resulting in a completely different translation from the original.
 * In psychology, the framing effect (psychology) is an example of cognitive bias in which people react to a particular choice in different ways depending on how it is presented. Cognitive errors as a result of this bias are commonly called framing errors.

title: Framing error


text:
List of major opera composers

This list provides a guide to opera composers, as determined by their presence on a majority of compiled lists of significant opera composers. (See the "Lists Consulted" section for full details.) The composers run from Jacopo Peri, who wrote the first ever opera in late 16th century Italy, to John Adams, one of the leading figures in the contemporary operatic world. The brief accompanying notes offer an explanation as to why each composer has been considered major. Also included is a section about major women opera composers, compiled from the same lists. For an introduction to operatic history, see opera. The organisation of the list is by birthdate.

1550–1699

 * Jacopo Peri (1561–1633) Florentine who composed both the first opera ever, Dafne (1598), and the first surviving opera, Euridice (1600).
 * Claudio Monteverdi (1567–1643) Generally regarded as the first major opera composer. In Orfeo (1607) he blended Peri's experiments in opera with the lavish spectacle of the intermedi. Later, in Venice in the 1640s, he helped make opera a commercially viable form with Il ritorno d'Ulisse in patria and L'incoronazione di Poppea, one of the earliest operas in the present-day operatic repertoire.
 * Francesco Cavalli (1602–1676) Amongst the most important of Monteverdi's successors, Cavalli was a major force in spreading opera throughout Italy and also helped introduce it to France. His Giasone was " the most popular opera of the 17th century".
 * Jean-Baptiste Lully (1632–1687) In close collaboration with the librettist Philippe Quinault, Lully founded the tradition of tragédie en musique, combining singing, dance and visual spectacle, which would remain the most prestigious French operatic genre for almost a hundred years. Cadmus et Hermione (1673) is often regarded as the first example of French opera.
 * Henry Purcell (1659–1695) First English operatic composer of significance. His masterwork is Dido and Aeneas.
 * Alessandro Scarlatti (1660–1725) Key figure in the development of opera seria, Scarlatti claimed to have composed over 100 operas, of which La Griselda is a notable example.
 * Jean-Philippe Rameau (1683–1764) Most important French opera composer of the 18th century. Following in the genre established by Lully, he endowed his works with a great richness of invention. Rameau's musical daring provoked great controversy in his day, but he was an important influence on Gluck.
 * Johann Christoph Pepusch (1667–1752) Arranger of the first English ballad opera, the biting political satire, The Beggar's Opera.
 * George Frideric Handel (1685–1759) Handel's opera serie set the standard in his day. Handel composed a series of over 30 operas.

1700–1799

 * Giovanni Battista Pergolesi (1710–1736) Though Pergolesi also composed opera serias, his most influential work was the short opera buffa, La serva padrona.
 * Christoph Willibald Gluck (1714–1787) Was a key figure in the transformation of Baroque into Classical opera, paving the way for Mozart, though his influence stretched much further into the 19th century, with both Berlioz and Wagner acknowledging their debt to him. In his reform operas from Orfeo ed Euridice onwards, he sought to throw off the formal conventions of opera seria and write music of "beautiful simplicity" (his own words).
 * Joseph Haydn (1732–1809) Haydn wrote nineteen operas including several comic operas and singspiels.
 * Giovanni Paisiello (1740–1816) Italian composer who wrote the first opera to include Beaumarchais' character Figaro as a main character, as well as writing a substantial number of other operas, some of them in St. Petersburg.
 * André Grétry (1741–1813) Liège (present day Belgian) composer crucial to the development of French opéra comique, whose simplicity of musical style and sophisticated dramaturgy were immensely popular, as well as linking pre-revolutionary rococo comedy to the later romantic style.
 * Domenico Cimarosa (1749–1801) Italian composer most famous for the opera buffa, Il matrimonio segreto, which forms a bridge between the comedies of Mozart and Rossini.
 * Wolfgang Amadeus Mozart (1756–1791) Mozart's series of comic collaborations (The Marriage of Figaro, Don Giovanni, and Così fan tutte) with Lorenzo Da Ponte are among the most popular operas in the repertoire today, along with his Singspiel The Magic Flute.
 * Antonio Salieri (1750–1825) Italian composer who was a major contributor to and shaper of Viennese musical life from 1770 to 1820, he also composed successful operas in Italy and Paris, and won admiration from German operagoers as a composer who, in the words of one contemporary critic, ‘could bind all the power of German music to the sweet Italian style’. His opera Europa riconosciuta was composed for the inauguration of La Scala. Among his other most successful operas were Les Danaïdes, Axur, re d'Ormus (the Italian version of French Tarare) and Falstaff.
 * Luigi Cherubini (1760–1842) Follower of Gluck, Cherubini's most famous opera is Médée. The title role has proved a challenge to sopranos (including Maria Callas) since its premiere in 1797.
 * Ludwig van Beethoven (1770–1827) Wrote only one opera, Fidelio, a tale of freedom from political oppression, which has become one of the major German language operas.
 * Gaspare Spontini (1774–1851) Though Italian, Spontini is best known for his work in France during the Napoleonic era. His masterpiece La vestale influenced Bellini and Berlioz.
 * Daniel Auber (1782–1871) French composer celebrated for high-spirited opéra comiques such as Fra Diavolo and Le domino noir. His grand opera La muette de Portici attained unexpected political influence when a performance in Brussels in 1830 sparked off a revolution which led to the creation of Belgium.
 * Carl Maria von Weber (1786–1826) Founded German Romantic opera in order to challenge the dominance of Italian bel canto. Master of orchestral colour and atmosphere, Weber was never well served by his librettists, and only one of his works, Der Freischütz, is performed with any frequency. Though he died young, his influence on later German composers, especially Wagner, was immense.
 * Giacomo Meyerbeer (1791–1864) The archetypal composer of French grand opera, Meyerbeer's huge extravaganzas such as Les Huguenots and Le prophète were immensely popular in their day.
 * Gioachino Rossini (1792–1868) Links bel canto with grand opera. His immortal Barber of Seville was the only one of his operas that was continuously performed into the 20th century, but his serious operas, such as Semiramide and Ermione, are recognised as masterpieces now that singers with appropriate technique are again available to perform them. Guillaume Tell, his swan-song, has a vast sweep only equalled in the 19th century by the later works of Verdi, Mussorgsky and Wagner.
 * Heinrich Marschner (1795–1861) German composer who was the most important exponent of German Romantic opera in the generation between Weber and Wagner. His most successful operas were Hans Heiling, Der Vampyr and Der Templer und die Jüdin.
 * Gaetano Donizetti (1797–1848) Along with Rossini and Bellini, Donizetti is generally acknowledged as one of the masters of the bel canto style. His masterwork is generally cited as being Lucia di Lammermoor.
 * Fromental Halévy (1799–1862) Along with Meyerbeer, the best known composer of French grand opera, Halévy's key work is La Juive, a story of religious intolerance set in 15th century Switzerland.

1800–1849

 * Vincenzo Bellini (1801–1835) On account of such works as Norma and I puritani, Bellini is recognised as one of the leading composers of the bel canto style of opera.
 * Hector Berlioz (1803–1869) Berlioz's attempts to carve out an operatic career for himself were thwarted by an unimaginative musical establishment. Nevertheless, he managed to produce Benvenuto Cellini, Béatrice et Bénédict and his masterpiece, the epic Les Troyens,. Berlioz's dramatic legend, La damnation de Faust, has also been staged as an opera in recent years.
 * Mikhail Glinka (1804–1857) Founded the Russian operatic tradition with his historical drama A Life for the Tsar and his fairy tale piece Ruslan and Lyudmila.
 * Michael William Balfe (1808–1870) Irish composer, his opera The Bohemian Girl is notable for its Arline's aria Gipsy Girl's Dream.
 * Ambroise Thomas (1811–1896) French composer noted for the operas Mignon and Hamlet.
 * George Alexander Macfarren (1813–1887) English composer noted for the operas Robin Hood and Helvellyn.
 * Richard Wagner (1813–1883) Wagner revolutionised opera. In a series of "music dramas" such as Tristan und Isolde, Parsifal, and most of all his epic tetralogy Der Ring des Nibelungen, Wagner abolished the traditional distinction between recitative and aria and pioneered a new through-composed style of opera.
 * Giuseppe Verdi (1813–1901) Had a long composing career, during which his compositional style kept evolving. Among his most famous works are Nabucco, Rigoletto, Il Trovatore, La traviata, Don Carlos, Aida, and Otello.
 * Charles Gounod (1818–1893) Wrote lyrical operas on literary themes, including Roméo et Juliette and Mireille. His Faust still holds the stage today, in spite of criticisms of its "Victorianism".

 * Jacques Offenbach (1819–1880) Founder of French operetta and a prolific composer of pieces which achieved tremendous success with Parisian audiences for their catchy melodies and satirical bite such as La Vie parisienne and Orpheus in the Underworld. At the time of his death, Offenbach was working on a more serious opera, The Tales of Hoffmann.
 * Bedřich Smetana (1824–1884) Established Czech national opera with such historical epics as Dalibor. His folk comedy The Bartered Bride has entered the international repertory.
 * Alexander Borodin (1833–1887) A "weekend composer" who spent 17 years working on a single opera, Prince Igor, which now forms a key part of the Russian repertory.
 * Camille Saint-Saëns (1835–1921). French composer of around a dozen operas of which one, the Biblical Samson et Delila, is still performed.
 * Léo Delibes (1836–1891) French composer, whose Lakmé is notable for its Flower Duet and as a vehicle for coloratura sopranos.
 * Georges Bizet (1838–1875) Bizet's masterwork Carmen is a staple of the repertoire of opera houses the world over. At the time of its premiere, the controversial plot scandalised both critics and the public.
 * Modest Mussorgsky (1839–1881) Mussorgsky completed only one opera, but Boris Godunov proved to be inspiration for generations of Russian composers on account of its uniquely nationalist character.
 * Pyotr Ilyich Tchaikovsky (1840–1893) Tchaikovsky's international fame as an opera composer mainly rests on two works, Eugene Onegin and The Queen of Spades. Less interested in cultivating a uniquely Russian style than his contemporary Mussorgsky, Tchaikovsky also shows the influence of Mozart, bel canto and Bizet's Carmen in these pieces.
 * Emmanuel Chabrier (1841–1894) Had ambitions to write grand operas in the Wagnerian vein, but is now most celebrated for lighter pieces, such as L'étoile and Le roi malgré lui, which were greatly admired by Ravel and Poulenc.
 * Antonín Dvořák (1841–1904) Leading Czech opera composer between Smetana and Janáček. His Rusalka, based on the Undine legend, is his most popular work internationally.
 * Jules Massenet (1842–1912) Arguably the most representative French opera composer of his era (the Belle Époque), Massenet was a prolific and versatile writer whose works cover a wide variety of themes. His popularity faded somewhat after the First World War, but Werther and Manon still make regular appearances in the opera house.
 * Arthur Sullivan (1842–1900) English composer who is best known for his series of 14 operatic collaborations with the dramatist W. S. Gilbert, including such enduring works as H.M.S. Pinafore, The Pirates of Penzance and The Mikado.
 * Nikolai Rimsky-Korsakov (1844–1908) Russian composer who wrote colourful operas on legendary and historical subjects.

1850–1899

 * Leoš Janáček (1854–1928) Janáček's first mature opera (Jenůfa) blended folksong-like melodies and an emphasis on natural speech-rhythms à la Mussorgsky with a character-driven plot of some intensity; his later works became increasingly terse, with recurrent melodic fragments, lyrical outbursts and unconventional orchestration serving a diverse collection of source-material – just a few bars of these operas can instantly be identified as his.
 * Ruggero Leoncavallo (1857–1919) Italian composer associated with verismo. His Pagliacci is a staple of the operatic repertoire and is usually given alongside Mascagni's Cavalleria rusticana.
 * Giacomo Puccini (1858–1924) The only true successor to Giuseppe Verdi in Italian opera, Puccini's Tosca, La bohème and Madama Butterfly are among the most popular and well-recognised in the repertoire today.
 * Gustave Charpentier (1860–1956) French composer famous for a single opera, Louise, set in a working class district of Paris.
 * Claude Debussy (1862–1918) Like Beethoven, Debussy finished only one opera, but his setting of Maeterlinck's Symbolist play Pelléas et Mélisande is a key work in 20th century music drama. In many ways an "anti-opera", Pelléas contained little of the conventional singing or action audiences at the première had come to expect, but Debussy used his subtle orchestration to create an elusive, dream-like atmosphere, which still has the power to fascinate listeners today.
 * Pietro Mascagni (1863–1945) Italian composer, famous above all for Cavalleria rusticana, usually given in a double-bill with Leoncavallo's Pagliacci.
 * Richard Strauss (1864–1949) Strauss was one of very few opera composers in the early years of the 20th century to accept and conquer the challenge laid down by the scale and radical nature of Wagner's innovative works. He composed several operas that remain extremely popular today, including Salome, Elektra, and Der Rosenkavalier.
 * Hans Pfitzner (1869–1949) A follower of Wagner, Pfitzner is best known for the opera Palestrina which explores the debate between tradition and innovation in music.
 * Arnold Schoenberg (1874–1951) A leading Modernist composer and the deviser of the twelve-tone system, Schoenberg began his operatic career with the Expressionist monodrama Erwartung. His major opera Moses und Aron was left unfinished at his death.
 * Maurice Ravel (1875–1937) Wrote two short, but innovative, operas: L'enfant et les sortilèges, set in the world of childhood, and the Spanish-flavoured L'heure espagnole.
 * Franz Schreker (1878–1934) Austrian composer associated with Expressionism, Schreker once rivalled Richard Strauss in popularity but, as a Jew, he fell foul of the Nazis. His operas include Der ferne Klang and Die Gezeichneten.
 * Béla Bartók (1881–1945) Wrote only one opera, Duke Bluebeard's Castle, a key piece in 20th century music theatre and the only Hungarian work with a secure place in the international operatic repertoire.
 * Igor Stravinsky (1882–1971) After composing the Rimsky-Korsakov-inspired The Nightingale and the near-operas Renard and The Soldier's Tale, Stravinsky bucked 20th century trends by composing a "number" opera, The Rake's Progress, using diatonicism.
 * Alban Berg (1885–1935) Because of their atonal music which uses tonal conventions harkening back to late romanticism and tragic libretti, Berg's masterworks Wozzeck and Lulu have stayed in the repertory and assumed increased popularity after his death.
 * Sergei Prokofiev (1891–1953) Major modern composer in the Russian tradition, Prokofiev produced operas on a wide variety of subjects, from the comic fairy-tale The Love for Three Oranges, to the dark and occult The Fiery Angel and the epic War and Peace. Like Shostakovich, Prokofiev suffered under the Soviet artistic regime, but his work has recently been championed by conductors such as Valery Gergiev.
 * Paul Hindemith (1895–1963) German composer who came to prominence in the years following World War I. His key opera Mathis der Maler, dealing with the problems of an artist in a time of crisis, has been seen as an allegory of Hindemith's situation during the Third Reich.
 * George Gershwin (1898–1937) Owes his place in the standard operatic repertoire to Porgy and Bess.

1900–present

 * William Walton (1902–1983) Walton's major opera is Troilus and Cressida.
 * Michael Tippett (1905–1998) Probably the most famous British composer to follow in the wake of Benjamin Britten, Tippett wrote operas exploring metaphysical and social themes. They include The Midsummer Marriage and The Knot Garden.
 * Dmitri Shostakovich (1906–1975) Shostakovich's most famous opera, Lady Macbeth of the Mtsensk District, a violent love story set in provincial Russia, scandalised Soviet authorities. He later produced a revised version, Katerina Ismailova. Nevertheless, the original became one of the most performed operatic works of the 20th century.
 * Samuel Barber (1910–1981) American who composed two major operas, Vanessa and Antony and Cleopatra.
 * Gian Carlo Menotti (1911–2007) Italian American composer, particularly famous for the Christmas piece Amahl and the Night Visitors, the first opera to be written specifically for television.
 * Benjamin Britten (1913–1976) One of the handful of British opera composers to reach international acclaim, and one of the extremely few composers of 20th century operas that stayed in the standard repertory after their premieres. These operas include his masterworks Peter Grimes, A Midsummer Night's Dream, and The Turn of the Screw.
 * Hans Werner Henze (1926–2012) One of the most widely performed post-World War II opera composers, Henze's works include The Bassarids and Elegy for Young Lovers.
 * Peter Maxwell Davies (1934–2016) A British modernist of the "Manchester school", Davies wrote many stage works, including Taverner and The Martyrdom of St Magnus.
 * Philip Glass (born 1937) A leading American composer of the minimalist school, Glass first came to fame with the opera Einstein on the Beach, a collaboration with the theatre director Robert Wilson. Many stage works (including Akhnaten and The Voyage) followed.
 * John Adams (born 1947) Like Glass, Adams started as a minimalist. His operas dealing with contemporary subjects, Nixon in China and The Death of Klinghoffer, have gained critical acclaim and provoked political controversy.

Female opera composers
A number of reasons, including the high cost of production and high status of opera, have been suggested to explain the relatively few women who have been composers of opera, and no woman composer met the criteria for inclusion above. However, some experts in our sample disagreed, and named either or both of the women below as comparable to those already listed:

 * Francesca Caccini (18 September 1587 – after 1641) Italian composer, singer, lutenist, poet, and music teacher of the early Baroque era. She was also known by the nickname "La Cecchina", given to her by the Florentines and probably a diminutive of "Francesca". She was the daughter of Giulio Caccini. Her only surviving stage work, La liberazione di Ruggiero, is widely considered the oldest opera by a woman composer.
 * Dame Ethel Smyth (1858–1944) Perhaps most famous for her work for the suffragettes; however, she also wrote several operas of note, including The Wreckers.
 * Judith Weir (born 1954) Began composing full-length operas in 1987 with A Night at the Chinese Opera.

 * Shafiga Akhundova (21 January 1924 – 26 July 2013) was a prominent Azerbaijani composer, the first professional female author of an opera in the East and People’s Artist of Azerbaijan.

 * Svitlana Azarova (born 1976) Commissioned by the Royal Danish Opera to write Momo and the Time Thieves, which premiered in 2017.

Other notable women opera composers include Peggy Glanville-Hicks, Lori Laitman, Missy Mazzoli, Rachel Portman, and Olga Neuwirth.

Lists consulted
This list was compiled by consulting ten lists of great opera composers, created by recognized authorities in the field of opera, and selecting all of the composers who appeared on at least six of these (i.e. all composers on a majority of the lists). Judith Weir appears on four of the ten lists consulted, more than any other female composer in the sample. The lists used were:

 * 1) Composers mentioned in Nicholas Kenyon's introduction to the Viking Opera Guide (1993 edition) ISBN 0-670-81292-7.
 * 2) "The Standard Repertoire of Grand Opera 1607–1969", a list included in Norman Davies's Europe: a History (OUP, 1996; paperback edition Pimlico, 1997) ISBN 0-7126-6633-8.
 * 3) Composers mentioned in the chronology by Mary Ann Smart in The Oxford Illustrated History of Opera (OUP, 1994) ISBN 0-19-816282-0.
 * 4) "A Bird's Eye View of the World's Chief Opera Composers" in The Oxford Companion to Music by Percy Scholes (10th edition revised by John Owen Ward, 1970). ISBN 0-19-311306-6.
 * 5) Composers with recordings included in The Penguin Guide to Opera on Compact Discs  ed. Greenfield, March and Layton (1993 edition) ISBN 0-14-046957-5.
 * 6) The New Kobbe's Opera Book, ed. Lord Harewood (1997 edition) ISBN 0-399-14332-7.
 * 7)  by Matthew Boyden. (2002 edition) ISBN 1-85828-749-9.
 * 1) Composers with recordings included in The Penguin Guide to Opera on Compact Discs  ed. Greenfield, March and Layton (1993 edition) ISBN 0-14-046957-5.
 * 2) The New Kobbe's Opera Book, ed. Lord Harewood (1997 edition) ISBN 0-399-14332-7.
 * 3)  by Matthew Boyden. (2002 edition) ISBN 1-85828-749-9.

Note:
 * The composers included in all 10 lists cited are: Berg, Britten, Donizetti, Gluck, Handel, Monteverdi, Mozart, Puccini, Rameau, Rossini, Richard Strauss, Verdi, and Wagner.
 * The composers included in nine of the lists are: Bellini, Berlioz, Bizet, Glinka, Gounod, Lully, Massenet, Mussorgsky, and Tchaikovsky.
 * The composers included in eight of the lists are: Adams, Debussy, Glass, Henze, Janáček, Leoncavallo, Menotti, Meyerbeer, Pergolesi, Purcell, Rimsky-Korsakov, Schoenberg, Smetana, Thomas (Ambroise), Tippett, and Weber.
 * The composers included in seven of the lists are: Auber, Beethoven, Borodin, Cavalli, Cherubini, Cimarosa, Delibes, Hindemith, Mascagni, Offenbach, Prokofiev, Ravel, Saint-Saëns, Shostakovich, and Gustave Charpentier.
 * The composers included in six of the lists are: Barber, Bartók, Chabrier, Peter Maxwell Davies, Dvořák, Gay and Pepusch, Gershwin, Halévy, Peri, Pfitzner, Scarlatti, Schreker, Spontini, Stravinsky, Walton.
 * Judith Weir was included in four lists; Dame Ethel Smyth in two.

title: List of major opera composers


text:
Aniara

Aniara (Aniara: en revy om människan i tid och rum ) is a book-length epic science fiction poem written by Swedish Nobel laureate Harry Martinson from 1953 to 1956. It narrates the tragedy of a large passenger spacecraft carrying a cargo of colonists escaping destruction on Earth veering off course, leaving the Solar System and entering into an existential struggle. The style is symbolic, sweeping and innovative for its time, with creative use of neologisms to suggest the science fictional setting. It was published in its final form on 13October 1956.

Aniara has been translated to around twenty languages. It was adapted into an opera in 1959 and a Swedish feature film in 2018.

Aniara, published in October 1956, was met with public interest and enthusiasm from literary critics and readers. The work was praised for its lyrical storytelling, profound thought, and its portrayal of human greatness turning into humiliation and powerlessness. Aniara has influenced other works of science fiction, such as Tau Zero (1970) by Poul Anderson and A Fire Upon the Deep (1992) by Vernor Vinge. The poem has become a landmark literary work and is often used as the basis for planetarium shows in Sweden. In 2019, the extrasolar planet HD 102956 b was named after Isagel, a character from the story, and its star was named Aniara.

Title
In a 1997 Swedish edition of Aniara, literary scholar Johan Wrede writes that the neologism “Aniara” is Harry Martinson's own invention. Martinson came up with the word years before writing the work while reading astronomer Arthur Eddington, then giving it the meaning as the "name for the space in which the atoms move". Others have submitted additional theories as to the origin of the word. A preface to a 2005 Italian edition claims that the title comes from ancient Greek ἀνιαρός, "sad, despairing", plus special resonances that the sound "a" had for Martinson. Another theory makes up the word "Aniara" from the chemical symbols Ni (Nickel) and Ar (Argon) and the negative prefix "a-", and interprets this as the ship being untethered to both earth (Nickel being abundant in the Earth's core) and sky (Argon being abundant in the Earth's atmosphere). Martinson himself is said (by Tord Hall, longtime friend) to have been fond of this interpretation.

Interpretation
According to Ott and Broman, Aniara is an effort to "[mediate] between science and poetry, between the wish to understand and the difficulty to comprehend". Martinson translates scientific imagery into the poem: for example, the "curved space" from Albert Einstein's general theory of relativity is likely an inspiration for Martinson's description of the cosmos as "a bowl of glass", according to the Nobel Prize Foundation. Martinson also said he was influenced by Paul Dirac.

The poem
The poem consists of 103 cantos, each relating the tragedy of a large passenger spacecraft originally bound for Mars with a cargo of colonists from the ravaged Earth. After an accident, the ship is ejected from the Solar System and into an existential struggle.

"We listen daily to the sonic coins provided every one of us and played through the Finger-singer worn on the left hand. We trade coins of diverse denominations: and all of them play all that they contain and though a dyma 1 scarcely weighs one grain it plays out like a cricket on each hand blanching here in this distraction-land."

The first 29 cantos of Aniara had previously been published in Martinson's collection Cikada (1953), under the title Sången om Doris och Mima (The Song of Doris and Mima), relating the departure from Earth, the accidental near-collision with an asteroid (incidentally named Hondo, another name for the main Japanese isle where Hiroshima is situated) and ejection from the solar system, the first few years of increasing despair and distractions of the passengers, until news is received of the destruction of their home port, and perhaps of Earth itself. According to Martinson, he dictated the initial cycle as in a fever after a troubling dream, affected by the Cold War and the Soviet suppression of the 1956 Hungarian revolution; in another recounting, he said the first 29 cantos were said to be inspired by his observation of the Andromeda Galaxy.

A major theme is that of art, symbolised by the semi-mystical machinery of the Mima, who relieves the ennui of crew and passengers with scenes of far-off times and places, and whose operator is also the sometimes naïve main narrator. The rooms of Mima, according to Martinson, represent different kinds of life styles or forms of consciousness. The accumulated destruction the Mima witnesses impels her to destroy herself in despair, to which she, the machine, is finally moved by the white tears of the granite melted by the phototurb which annihilates their home port, the great city of Dorisburg. Without the succour of the Mima, the erstwhile colonists seek distraction in sensual orgies, memories of their own and earlier lives, low comedy, religious cults, observations of strange astronomical phenomena, empty entertainments, science, routine tasks, brutal totalitarianism, and in all kinds of human endeavour, but ultimately cannot face the emptiness outside and inside.

The poems are metrical and mostly rhymed, using both traditional and individual forms, several alluding to a wide range of Swedish and Nordic poetry, such as the Finnish Kalevala.

Translations
Aniara has been translated to around twenty languages including French, German, Italian, Danish, Finnish, Norwegian, Czech, Russian, Spanish, Japanese, Chinese, Arabic, Hebrew, English, and Esperanto.

English translations
Aniara was translated into English as Aniara, A Review of Man in Time and Space by Hugh MacDiarmid and E. Harley Schubert in 1963. It was translated again into English by Stephen Klass and Leif Sjöberg for a 1999 edition. Neither edition is in print.

Geoffrey O'Brien, writing for the New York Review of Books, compares the two editions and finds the recent Klass Sjöberg edition more faithful to "Martinson's formal schemes" while considering the MacDiarmid Schubert edition "more persuasive" as English poetry. Burns Singer wrote of the original translation "it may well prove a seminal volume in the history of English letters" in Times Literary Supplement.

Reception
The publication of Aniara in October 1956 was met with much public interest and was enthusiastically received by many Swedish literary critics and readers. Reviewing it in Expressen in 1956, Bo Strömstedt wrote: "it is a fabulous story, and Harry Martinson tells it with an ingenuity – in substance and in words – that is also quite fabulous; even though most of the songs are written in the same iambic verse, the book never becomes monotonous." "Harry Martinson has not only written a breathtakingly lyrical science fiction story; he has also (...) created a gigantic "Paradise lost", an epic about how human greatness is turned into humiliation and powerlessness".

The well-known American science fiction writer, Theodore Sturgeon, in reviewing a 1964 American edition for a genre audience, stated that "Martinson's achievement here is an inexpressible, immeasurable sadness. [It] [t]ranscends panic and terror and even despair [and] leaves you in the quiet immensities, with the feeling that you have spent time, and have been permanently tinted, by and with an impersonal larger-than-God force."

Writing a guest review for The New York Times, D. Bruce Lockerbie suggested that with Aniara Martinson had, along with C. S. Lewis, "found that an interplanetary setting, light years removed from mundanity" supplied "the esthetic distance necessary for truly profound thought."

The poem has also been reviewed more recently. In a 2015 review, James Nicoll writes "Martinson’s creative approach to astronomy and related matters gives the work an misleadingly archaic feel." M. A. Orthofer finds in 2018, the poem "a product of its times, but even as aspects may no longer seem as current, it holds up well in its bleak vision." In his 2019 overview of Martinson's works in the New York Review of Books, Geoffrey O'Brien concludes "Aniara is an epic of extinction, conceived at a moment when extinction had begun to seem not only possible but perhaps imminent."

Legacy
Aniara has had an influence on later works of science fiction, such as Tau Zero by Danish-American writer Poul Anderson.

In the 2004 centennial celebration of the birth of Harry Martinson, the Martinson Society characterized Aniara as an "epic poem about the spaceship in which we flee the destruction of the earth, the spaceship that drifts off course into an endless universe", and considered the poem to have achieved becoming a legend in their own right, one of the myths people are familiar with without necessarily knowing who created them.

In December 2019, the extrasolar planet HD 102956 b was named after a character aboard the spacecraft, the pilot Isagel, as part of the IAU NameExoWorlds project. The exoplanet's star was named Aniara.

Adaptations
An opera by Karl-Birger Blomdahl also called Aniara premiered in 1959 with a libretto by Erik Lindegren based on Martinson's poem; it was staged in Stockholm, Hamburg, Brussels and Darmstadt, and later in Gothenburg and Malmö. A performance by the Royal Swedish Opera at the Edinburgh International Festival was broadcast on the BBC Third Programme in Sept 1959.

Aniara (1960), a Swedish TV film directed by Arne Arnbom, written by Erik Lindegren and Harry Martinson, and starring Margareta Hallin, Elisabeth Söderström, Erik Sædén and Arne Tyrén. The music was composed by Karl-Birger Blomdahl.

The BBC Third Programme broadcast an English translation, read over five nights, in November 1962.

In Martinsons home country of Sweden, Aniara has commonly been used as the basis of planetarium shows, the first one set up in 1988 by Björn Stenholm using music by Dmitrij Shostakovich in the planetarium then housed in what is now the Old Observatory in Lund, Sweden. An English-language show premiered during the International Planetarium Society conference in Salt Lake City, Utah in 1992.

Tommy Körberg headlined 31 songs from Aniara, a stage concert first set up in Olofström, Sweden in 1997.

The fourth album from the Swedish progressive metal band Seventh Wonder called The Great Escape (2010) is based on Aniara, the title track last 30:21 minutes and relates all the poem from beginning to end.

Swedish musician Kleerup released an album based on Aniara in 2012.

A melding of Aniara and Beethoven's opera Fidelio was staged by the Opéra de Lyon under the direction of American artist Gary Hill in 2013.

Aniara, a 2018 Swedish feature film by directors Pella Kågerman and Hugo Lilja, starring Emelie Jonsson, premiered at the Toronto International Film Festival that year. Also in 2018, artist Fia Backstrom made the installation  A Vaudeville on Mankind in Time and Space, using Aniara as its point of origin.

Aniara: Fragments of Time and Space, a choral theatre work with The Crossing, Helsinki’s Klockriketeatern, and composer Robert Maggio was performed in 2019."

title: Aniara


text:
The Brothers Johnson

The Brothers Johnson were an American funk and R&B band consisting of the American brothers George ("Lightnin' Licks") and Louis E. Johnson ("Thunder Thumbs"). They achieved their greatest success from the mid-1970s to early 1980s, with three singles topping the R&B charts ("I'll Be Good to You", "Strawberry Letter 23", and "Stomp!").

Formation
Guitarist/vocalist George and bassist/vocalist Louis formed the band Johnson Three Plus One with older brother Tommy and their cousin Alex Weir while attending school in Los Angeles, California. When they became professionals, the band backed such touring R&B acts as Bobby Womack and the Supremes. George and Louis Johnson later joined Billy Preston's band and wrote selections for his albums Music Is My Life and The Kids & Me before leaving his group in 1973. In 1976, the Brothers covered the Beatles' song, "Hey Jude", for the musical documentary All This and World War II.

Quincy Jones hired them to play on his LP Mellow Madness, and recorded four of their songs, including "Is It Love That We're Missin'?" and "Just a Taste of Me".

After touring with various artists including Bobby Womack and Billy Preston, they were hired by Quincy Jones for a tour in Japan and produced their debut album Look Out for #1, released in March 1976, which went to number 9 on the U.S. Billboard chart. Their Right on Time album was released in May 1977 and reached number 13 on the Billboard Hot 200. Blam!! came out in August 1978 and reached number 7 on the Billboard 200.

Two of the band's songs were featured on the soundtrack of the 1976 film Mother, Jugs & Speed and one on the 1997 film Jackie Brown. The instrumental track "Thunder Thumbs and Lightnin' Licks" refers to the brothers' nicknames. "Get the Funk Out Ma Face" was cowritten with Quincy Jones.

Their popular album Light Up the Night was released in March 1980 and rose to #5 on the Billboard 200. It was number 46 on the "Top 100 LPs of 1980" list in Rolling Stone. The brothers self-produced the subsequent album, Winners; released in July 1981, it only reached #48 on the Billboard 200.

Among their most popular songs are "I'll Be Good to You" (Billboard Hot 100 #3 in 1976) which prominently featured Syreeta Wright, "Strawberry Letter 23" (Hot 100 #5 in 1977, originally recorded by Shuggie Otis), "Ain't We Funkin' Now" (1978), and "Stomp!" (Hot 100 #7 and Hot Dance Music/Club Play #1 in 1980). Their styles include funk, and R&B ballads. Each album also included at least one instrumental cut that would either be considered light jazz ("Tomorrow", 1976; "Q", 1977; "Streetwave", 1978; "Smilin' On Ya", 1980; "Tokyo", 1984) or funk ("Thunder Thumbs & Lightnin' Licks", 1976; "Brother Man", 1977; "Mista' Cool", 1978; "Celebrations", 1980).

1982 split
The duo split up in 1982 to pursue separate projects.

Louis' solo work
Louis Johnson recorded a gospel music album in 1981 with his own group Passage, which included his then-wife Valerie Johnson and former Brothers Johnson percussionist/singer Richard Heath. He played bass on Michael Jackson's Thriller. In 1985 he recorded a single, "Kinky", on Capitol Records; it appears on his Evolution album which was exclusively released in Europe that year. Louis then made 3 instructional videotapes for the Starlicks video-distribution company in which he shared his bass-playing skills. The first was released in 1985. He then settled down to enjoy family life with his wife and son, but by 1988 his then-manager Diane Taren talked him into going back into the recording studio. He started his bass academy during the 1990s and gave workshop clinics via his own Website. Louis Johnson died on May 21, 2015, age 60. His last performance was in 2013.

Tommy Johnson left the group and had a 29-year career with the LAFD.

George's solo work
George Johnson released one single in 1985, "Back Against the Wall", on Quincy Jones' own Qwest label. A complete album (recorded but unreleased) came from that session, as George confirmed when he and Louis were interviewed around 1987/88 for Blues & Soul Magazine in the United Kingdom (see link below). George also delivered guitar work for Steve Arrington's album Dancing in the Key of Life (1985) and had ad-libbed vocals on the track "Think Back And Remember" from the Galaxian album by the Jeff Lorber Fusion, released in 1981 on Arista Records.

Various 1980s reunions and other projects
In 1984 the brothers reunited in the recording studio. The resulting Leon Sylvers-produced LP, Out of Control, did not equal their past success, but it did garner them another R&B hit with "You Keep Me Coming Back". They teamed up again in 1988 to record Kickin', the title track of which ("Kick It to the Curb") was a collaboration with their then-neighbor Irene Cara. Although "Kick It to the Curb" became a minor hit, the album's success was even more limited.

Between the two albums, both George and Louis released their aforementioned solo material and also appeared on Street Shadows, an album by keyboardist/arranger David Diggs, who had provided horn and string arrangements for Winners, Blast!, and Louis' Passage. "Last Night", Streets opening track showcases George's bass-guitar playing. He previously showed his bass skills on tracks like "Teaser" from Winners and "The Great Awakening" from Blast, the same way Louis shows his guitar skills on the duo's various compositions.

Also during this time, the band's song "Tomorrow" (originally an instrumental on the B-side of "Get the Funk Out Ma Face") was recorded with vocals by Tevin Campbell for Quincy Jones' Back on the Block release in 1989. This album also included Jones' hit remake of the Brothers Johnson's "I'll Be Good to You", featuring Ray Charles and Chaka Khan.

Besides the brothers' brief appearance in Japan around 1994 and George guest-appearing at a Graham Central Station concert in Japan (including a released double-CD), the duo launched an expanded US tour in 2002 which got positive, wide exposure. It was visited by many fans and various artists in the entertainment business. Along with a website and discussion-forum, online visitors could share their experiences of the shows by wandering through the Land of Ladies and reliving Funkadelia's heyday. A few years later, a combi-release of live-CD + DVD was released under the name Strawberry Letter 23: Live.

In 2006, Louis gave a duo-show with a drummer on the Poetry in Motion 1 Festival in Maryland. In late 2007 George performed with his own band at a Detroit festival, including a persona called Sir Nose. These days George performs with a special band, an initiative of Michael Henderson that includes Adina Howard, Cherrelle, Ray Parker Jr., and others.

Louis Johnson was found dead at his home in Las Vegas, May 21, 2015. The cause of death was gastrointestinal bleeding of the esophagus.

In 2022, the brothers' song "Ain't We Funkin' Now" was sampled in singer Harry Styles' song 'Daydreaming" from his third album Harry's House.

Live albums

 * Strawberry Letter 23: Live (2004, Goldenlane)

Videography

 * 1977 – Right on Time
 * 1980 – Stomp
 * 1981 – The Real Thing
 * 1988 – Kick It to the Curb

title: The Brothers Johnson