Christian socialism

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A variation of the hammer and sickle with the hammer replaced by a Christian cross, a widespread symbol of Christian socialism and, in particular, its sub-philosophy of Christian communism

Christian socialism is a religious and political philosophy that blends Christianity and socialism, endorsing left-wing politics and socialist economics on the basis of the Bible and the teachings of Jesus. Many Christian socialists believe capitalism to be idolatrous and rooted in the sin of greed. Christian socialists identify the cause of social inequality to be the greed that they associate with capitalism. Christian socialism became a major movement in the United Kingdom beginning in the 19th century. The Christian Socialist Movement, known as Christians on the Left since 2013, is one formal group.

According to the Encyclopedia Britannica Online, socialism is a "social and economic doctrine that calls for public rather than private ownership or control of property and natural resources. According to the socialist view, individuals do not live or work in isolation but live in cooperation with one another. Furthermore, everything that people produce is in some sense a social product, and everyone who contributes to the production of a good is entitled to a share in it. Society as a whole, therefore, should own or at least control property for the benefit of all its members. [...] Early Christian communities also practised the sharing of goods and labour, a simple form of socialism subsequently followed in certain forms of monasticism. Several monastic orders continue these practices today". The Christian socialist Hutterites believed in strict adherence to biblical principles, "church discipline" and practised a form of communism. The Hutterites "established in their communities a rigorous system of Ordnungen, which were codes of rules and regulations that governed all aspects of life and ensured a unified perspective. As an economic system, Christian communism was attractive to many of the peasants who supported social revolution in sixteenth century central Europe" such as the German Peasants' War and "Friedrich Engels thus came to view Anabaptists as proto-Communists".

Other earlier figures are also viewed as Christian socialists, such as the 19th-century writers Frederick Denison Maurice (The Kingdom of Christ, 1838), John Malcolm Forbes Ludlow (The Christian Socialist, 1850), John Ruskin (Unto This Last, 1862), Charles Kingsley (The Water-Babies, 1863), Thomas Hughes (Tom Brown's Schooldays, 1857), Frederick James Furnivall (co-creator of the Oxford English Dictionary), Adin Ballou (Practical Christian Socialism, 1854), and Francis Bellamy (a Baptist minister and the author of the United States' Pledge of Allegiance).

History

Biblical age

Elements that would form the basis of Christian socialism are found in the Old and New Testaments.

Old Testament

The Old Testament had divided perspectives on the issue of poverty. One part of the Jewish tradition held that poverty was judgment of God upon the wicked while viewing prosperity as a reward for the good, stating in the Proverbs 13:25 that "[t]he righteous have enough to satisfy their appetite, but the belly of the wicked is empty." However, there are other sections that instruct generosity to the "have nots" of society. The Torah instructs followers to treat neighbours equally and to be generous to have nots such as stating:

You shall not oppress your neighbour [...] but you shall love your neighbour as yourself: I am the Lord.

— Leviticus 19:13, 18

For the Lord your God is God of gods and Lord of lords, the great God, mighty and awesome, who shows no partiality and accepts no bribes. He defends the cause of the fatherless and the widow, and loves the foreigner residing among you, giving them food and clothing. And you are to love those who are foreigners, for you yourselves were foreigners in Egypt.

— Deuteronomy 10:17–19

When you reap in your harvest in the field, and have forgotten a sheaf in the field, you shall not go back to get it. [...] When you beat your olive trees, you shall not go over the boughs again. [...] When you gather the grapes of your vineyard, you shall not glean it afterward; it shall be for the sojourner, the fatherless and the widow. You shall remember that you were a slave in the land of Egypt; therefore I command you to do this.

— Deuteronomy 24:19–22

Some of the Psalms include many references to social justice for the poor:

Give justice to the weak and the fatherless; maintain the right of the afflicted and the destitute. Rescue the weak and the needy; deliver them from the hand of the wicked.

— Psalms 82 (81): 3, 4

Blessed is the man who fears the Lord, who greatly delights in his commandments! [...] He has distributed freely, he has given to the poor; his righteousness endures forever; his horn is exalted in honour.

— Psalms 112 (111): 1, 9

Amos emphasizes the need for "justice" and "righteousness" that is described as conduct that emphasizes love for those who are poor and to oppose oppression and injustice towards the poor. The prophet Isaiah, to whom is attributed the first thirty-nine chapters of the Book of Isaiah known as Proto-Isaiah, followed upon Amos' themes of justice and righteousness involving the poor as necessary for followers of God, denouncing those who do not do these things, stating:

Even though you make many prayers, I will not listen; your hands are full of blood. [...] [C]ease to do evil, learn to do good; seek justice, correct oppression; defend the fatherless, plead for the widow.

— Isaiah 1:15–17

The Book of Sirach, one of the Deuterocanonical or Apocryphal books of the Old Testament, denounces the pursuit of wealth, stating:

He who loves gold will not be justified, and he who pursues money will be led astray by it. Many have come to ruin because of gold, and their destruction has met them face to face. It is a stumbling block to those who are devoted to it, and every fool will be taken captive by it.

— Sirach 31: 5–7

New Testament

Jesus Expels the Moneylenders from the Temple by Giovanni Paolo Pannini, 1750

The teachings of Jesus are frequently described as socialist, especially by Christian socialists. Acts 4:32 records that in the early church in Jerusalem "[n]o one claimed that any of their possessions was their own", although the pattern would later disappear from church history except within monasticism. Christian socialism was one of the founding threads of the British Labour Party and is claimed to begin with the uprising of Wat Tyler and John Ball in the 14th century CE.

In the New Testament, Jesus identifies himself with the hungry, the poor, the sick, and the prisoners. Matthew 25:31–46 is a major component of Christianity and is considered the cornerstone of Christian socialism. Another key statement in the New Testament that is an important component of Christian socialism is Luke 10:25–37 that follows the statement "You shall love your neighbour as yourself" with the question "And who is my neighbour?" In the Parable of the Good Samaritan. Jesus gives the revolutionary response that the neighbour includes anyone in need, even people we might be expected to shun. The Samaritans were considered a heretical sect by Jews and neither would usually deal with the other.

Luke 6:20–21 shows Jesus narrating the Sermon on the Plain, stating: "Blessed are you poor, for yours is the kingdom of God. Blessed are you that hunger now, for you shall be satisfied." Christian socialists note that James the Just, the brother of Jesus, criticizes the rich intensely and in strong language in the Epistle of James:

Come now, you rich, weep and howl for the miseries that are coming upon you. Your riches have rotted and your garments are moth-eaten. Your gold and silver have rusted, and their rust will be evidence against you and will eat your flesh like fire. You have laid up for treasure for the last days. Behold, the wages of the labourers who mowed your fields, which you have kept back by fraud, cry out; and the cries of the harvesters have reached the ears of the Lord of hosts. You have lived on the earth in luxury and in pleasure; you have fattened your hearts in a day of slaughter.

— James 5:1–6

During the New Testament period and beyond, there is evidence that many Christian communities practised forms of sharing, redistribution and communism. Some of the Bible verses which inspired the communal economic arrangements of the Hutterites are found in the book of Acts:

All the believers were together and had everything in common. Selling their possessions and goods, they gave to anyone as he had need.

— Acts 2, 44–45

All the believers were one in heart and mind. No one claimed that any of his possessions were his own, but they shared everything they had.

— Acts 4, 32

There were no needy persons among them. For from time to time those who owned lands or houses sold them, brought the money from their sales and put it at the apostles' feet, and it was distributed to anyone as he had need.

— Acts 4, 34–35

Church Fathers age

Basil of Caesarea, the Father of the Eastern monks who became Bishop of Caesarea, established a complex around the church and monastery that included hostels, almshouses, and hospitals for infectious diseases. During the great famine of 368, Basil denounced against profiteers and the indifferent rich. Basil wrote a sermon on the Parable of the Rich Fool in which he states:

Who is the covetous man? One for whom plenty is not enough. Who is the defrauder? One who takes away what belongs to everyone. And are not you covetous, are you not a defrauder, when you keep for private use what you were given for distribution? When some one strips a man of his clothes we call him a thief. And one who might clothe the naked and does not—should not he be given the same name? The bread in your hoard belongs to the hungry; the cloak in your wardrobe belongs to the naked; the shoes you let rot belong to the barefoot; the money in your vaults belongs to the destitute. All you might help and do not—to all these you are doing wrong.

John Chrysostom declared his reasons for his attitude towards the rich and position of attitude towards wealth by stating:

I am often reproached for continually attacking the rich. Yes, because the rich are continually attacking the poor. But those I attack are not the rich as such, only those who misuse their wealth. I point out constantly that those I accuse are not the rich, but the rapacious; wealth is one thing, covetousness another. Learn to distinguish.

Early modern period

Main article: Diggers

During the English Civil War and the period of the Commonwealth of England (1642-1660), the Diggers espoused a political and economic theory rooted in Christianity that bears a strong resemblance to modern socialism, particularly its anarchist and communist strains.

19th century to present

In France Philippe Buchez began to characterize his philosophy as Christian socialism in the 1820s and 1830s. A variety of socialist perspectives emerged in 19th century Britain, beginning with John Ruskin.

John Ruskin

The influential Victorian art critic John Ruskin expounded theories about social justice in Unto This Last (1860). In it, he stated four goals that might be called "socialist" although Ruskin did not use the term.

1. "[T]raining schools for youth, established at government cost".
2. In connection with these schools, the government should establish "manufactories and workshops, for the production and sale of every necessary of life".
3. All unemployed people should be "set to work" or trained for work if needed or forced to work if necessary.
4. "[F]or the old and destitute, comfort and home should be provided".

Although Ruskin was not "an authentic Socialist in any of its various nineteenth-century meanings" as his only real contact with the Christian socialists came through the Working Men's College, he influenced later socialist thinking, especially William Morris.

Artists

The painters of the Pre-Raphaelite Brotherhood were influenced and sponsored by Ruskin. The artist William Morris was a leader of the Socialist League founded in December 1884.

Fabian Society

The Fabian Society was founded in 1884, with both Sydney and Beatrice Webb being among its leading members. The Fabians influenced members of the Bloomsbury Group and were important in the early history of the British Labour Party.

Episcopal Church Socialist League and the Church League for Industrial Democracy

Founded in 1911 by Vida Dutton Scudder, herself influenced by the Fabian Society, the Episcopal Church Socialist League and its successor the Church League for Industrial Democracy sought to ally Christian doctrine with the plight of the working class as a part of the larger social gospel movement that was taking hold of many urban churches across the United States in the early 20th century.

Bishop Spalding

In the November 1914 issue of The Christian Socialist, Episcopal bishop Franklin Spencer Spalding of Utah stated:

The Christian Church exists for the sole purpose of saving the human race. So far she has failed, but I think that Socialism shows her how she may succeed. It insists that men cannot be made right until the material conditions be made right. Although man cannot live by bread alone, he must have bread. Therefore, the Church must destroy a system of society which inevitably creates and perpetuates unequal and unfair conditions of life. These unequal and unfair conditions have been created by competition. Therefore competition must cease and cooperation take its place.

Christian anarchism

The Masses, 1917 political cartoon by socialist cartoonist Art Young

Although anarchists have traditionally been skeptical of or vehemently opposed to organized religion, some anarchists have provided religious interpretations and approaches to anarchism, including the idea that glorification of the state is a form of sinful idolatry.

Christian anarchists claim anarchism is inherent in Christianity and the Gospels, that it is grounded in the belief that there is only one source of authority to which Christians are ultimately answerable—the authority of God as embodied in the teachings of Jesus. It therefore rejects the idea that human governments have ultimate authority over human societies. Christian anarchists denounce the state, believing it is violent, deceitful and, when glorified, idolatrous.

The foundation of Christian anarchism is a rejection of violence, with Leo Tolstoy's The Kingdom of God Is Within You regarded as a key text. Tolstoy sought to separate Russian Orthodox Christianity—which was merged with the state—from what he believed was the true message of Jesus as contained in the Gospels, specifically in the Sermon on the Mount. Tolstoy takes the viewpoint that all governments who wage war, and churches who in turn support those governments, are an affront to the Christian principles of nonviolence and nonresistance. Although Tolstoy never actually used the term Christian anarchism in The Kingdom of God Is Within You, reviews of this book following its publication in 1894 appear to have coined the term. Christian anarchists hold that the "Reign of God" is the proper expression of the relationship between God and humanity. Under the "Reign of God", human relationships would be characterized by divided authority, servant leadership, and universal compassion—not by the hierarchical, authoritarian structures that are normally attributed to religious social order. Most Christian anarchists are pacifists who reject war and the use of violence. More than any other Bible source, the Sermon on the Mount is used as the basis for Christian anarchism. Leo Tolstoy's The Kingdom of God Is Within You is often regarded as a key text for modern Christian anarchism.

Critics of Christian anarchism include both Christians and anarchists. Christians often cite Romans 13 as evidence that the state should be obeyed while secular anarchists do not believe in any authority including God as per the slogan "no gods, no masters". Christian anarchists often believe Romans 13 is taken out of context, emphasizing that Revelation 13 and Isaiah 13, among other passages, are needed to fully understand Romans 13 text.

Christian democracy

The political movement of Christian democracy espouses some values of Christian socialism in the form of "economic justice" and "social welfare". It opposes an "individualist worldview" and approves state intervention in the economy in defence of "human dignity". On the other hand, because of its "close association with Roman Catholicism", Christian democracy differs from Christian socialism by its emphasis on "traditional church and family values", its defence of "private property" and by its opposition to "excessive intervention of the state".

Christian democratic parties under various names were formed in Europe and Latin America after World War II. Some became "a major political force".

Communism

Christian communism is a form of religious communism based on Christianity and the view that the teachings of Jesus compel Christians to support communism as the ideal social system. While there is no universal agreement on the exact date when Christian communism was founded, Christian communists assert that evidence from the Bible (Acts of the Apostles) suggests that the first Christians, including the apostles, established their own communist society in the years following Jesus' death and resurrection. Advocates of Christian communism argue that it was taught by Jesus and practised by the apostles themselves. Some independent historians confirm it.

Liberation theology

Liberation theology is a synthesis of Christian theology and socio-economic analyses, that emphasizes "social concern for the poor and political liberation for oppressed peoples." Beginning in the 1960s after the Second Vatican Council, liberation theology became the political praxis of Latin American theologians such as Gustavo Gutiérrez, Leonardo Boff and the Jesuits Juan Luis Segundo and Jon Sobrino, who popularized the phrase "preferential option for the poor". This expression was used first by Jesuit Fr. General Pedro Arrupe in 1968 and soon after this the World Synod of Catholic Bishops in 1971 chose as its theme "Justice in the World".

The Latin American context produced evangelical advocates of liberation theology such as Rubem Alves, José Míguez Bonino and C. René Padilla, who called for integral mission in the 1970s, emphasizing evangelism and social responsibility. Theologies of liberation have developed in other parts of the world such as black theology in the United States and South Africa, Palestinian liberation theology, Dalit theology in India and Minjung theology in South Korea.

Spiritualism and occultism

After 1848, utopian socialist ideas continued in new religious movements such as occultism and spiritualism. They were often marked by a heterodox Christian identity and a decidedly anti-materialist attitude.

In Catholicism

19th Century

In Catholicism, communism was strongly criticized in the 1878 papal encyclical Quod Apostolici Muneris by Pope Leo XIII as he believed that it led to state domination over the freedom of the individual and quelled proper religious worship, inherently turning the top hierarchical power over to the state instead of God. The labour movement in Ireland and the United States can trace its origins back to Roman Catholicism and the 1891 encyclical Rerum Novarum and the various subsequent encyclicals it spawned. The Starry Plough, a symbol associated with socialism in Ireland, was designed with an explicit reference to Catholicism in mind. The right to association such as the creation of and involvement in trade unions and co-operatives are regarded as a core part of Roman Catholic social teaching. The Knights of Saint Columbanus too can trace its origins back to Rerum novarum.

20th century

Leo XIII's opinions on socialism were moderated in an encyclical issued by Pope Pius XI on 15 May 1931 Quadragesimo anno, wherein Pius describes the major dangers for human freedom and dignity arising from unrestrained capitalism and totalitarian communism. Pius XI called upon true socialism to distance itself from totalitarian communism as a matter of clarity and also as a matter of principle. Communists were accused of attempting to overthrow all existing civil society. It was argued that Christian socialism, if allied to communism, was deemed to be an oxymoron because of this. Pius XI famously wrote at the time that "no one can be at the same time a good Catholic and a true socialist". Nonetheless, prominent Catholic socialists did exist during Pope Pius XI's era such as Dorothy Day in the United States (though she later advocated distributism) and Father Michael O'Flanagan (who was suspended for his beliefs) in Ireland. Pius XI also clarified that a Catholic was free to vote for the Labour Party, the British affiliate of the Socialist International. Later, in 1937, Pius XI rejected atheistic communism in an encyclical entitled Divini Redemptoris as "a system full of errors and sophisms", with a "pseudo-ideal of justice, equality, and fraternity" and "a certain false mysticism", and contrasted it with a humane society (civitas humana).

In 1949, Pope Pius XII issued the Decree against Communism, which declared Catholics who professed Communist doctrine to be excommunicated as apostates from the Christian faith.

In 1959, on the question of whether Catholics could "associate themselves with the communists and support them with their course of action", a response from the Holy Office under Pope John XXIII replied "No". On May 15 1961, John XXIII promulgated the encyclical Mater et magistra, which reaffirmed the Church's anti-socialist stances. John XIII wrote

Pope Pius XI further emphasized the fundamental opposition between Communism and Christianity, and made it clear that no Catholic could subscribe even to moderate Socialism. The reason is that Socialism is founded on a doctrine of human society which is bounded by time and takes no account of any objective other than that of material well-being. Since, therefore, it proposes a form of social organization which aims solely at production, it places too severe a restraint on human liberty, at the same time flouting the true notion of social authority.

In 1971, Pope Paul VI wrote the Apostolic Letter Octogesima Adveniens, stating: "Too often Christians attracted by socialism tend to idealize it in terms which, apart from anything else, are very general: a will for justice, solidarity and equality. They refuse to recognize the limitations of the historical socialist movements, which remain conditioned by the ideologies from which they originated."

Pope John Paul II attacked socialism in his 1991 encyclical Centesimus annus, writing:

[t]he fundamental error of socialism is anthropological in nature. Socialism considers the individual person simply as an element, a molecule within the social organism, so that the good of the individual is completely subordinated to the functioning of the socio-economic mechanism. Socialism likewise maintains that the good of the individual can be realized without reference to his free choice, to the unique and exclusive responsibility which he exercises in the face of good or evil. Man is thus reduced to a series of social relationships, and the concept of the person as the autonomous subject of moral decision disappears, the very subject whose decisions build the social order. From this mistaken conception of the person there arise both a distortion of law, which defines the sphere of the exercise of freedom, and an opposition to private property. A person who is deprived of something he can call "his own", and of the possibility of earning a living through his own initiative, comes to depend on the social machine and on those who control it. This makes it much more difficult for him to recognize his dignity as a person, and hinders progress towards the building up of an authentic human community.

The 1992 Catechism of the Catholic Church, also promulgated by Pope John Paul II, condemns socialism in paragraph 2425, stating:

The Church has rejected the totalitarian and atheistic ideologies associated in modem times with "communism" or "socialism." She has likewise refused to accept, in the practice of "capitalism," individualism and the absolute primacy of the law of the marketplace over human labor. Regulating the economy solely by centralized planning perverts the basis of social bonds; regulating it solely by the law of the marketplace fails social justice, for "there are many human needs which cannot be satisfied by the market." Reasonable regulation of the marketplace and economic initiatives, in keeping with a just hierarchy of values and a view to the common good, is to be commended.

21st Century

In 2004, Pope Benedict XVI addressed the Italian Senate, declaring that "[i]n many respects democratic socialism was and is close to Catholic social doctrine; in any case, it contributed toward the formation of a social consciousness". In 2007, Benedict XVI attacked Karl Marx is his encycical Spe Salvi, stating that "[w]ith the victory of the revolution, though, Marx's fundamental error also became evident. He showed precisely how to overthrow the existing order, but he did not say how matters should proceed thereafter...He forgot that freedom always remains also freedom for evil. He thought that once the economy had been put right, everything would automatically be put right. His real error is materialism: man, in fact, is not merely the product of economic conditions, and it is not possible to redeem him purely from the outside by creating a favourable economic environment."

Pope Francis has shown some sympathy to socialist causes, with claims that the world economy is "[f]undamental terrorism, against all of Humanity" and that "[i]f anything, it is the communists who think like Christians. Christ spoke of a society where the poor, the weak and the marginalized have the right to decide." When later questioned on whether or not he is a communist, Francis responded "As for whether or not I’m a communist: I am sure that I have not said anything more than what the Church’s social doctrine teaches…maybe the impression of being a little more “of the left” has been given, but that would be a misinterpretation" and that "Marxist ideology is wrong."

More recently, movements such as liberation theology have argued for the compatibility of socialism and Catholicism. António Guterres, a practicing Catholic and current Secretary-General of the United Nations is the immediate past President of the Socialist International.

In Calvinism

In France, the birthplace of Calvinism, the Christianisme Social (Social Christianity) movement emerged from the preaching of Tommy Fallot in the 1870s. Early on, the movement focused on such issues as illiteracy and alcoholism amongst the poor. After the First World War, Social Christianity moved in two directions: towards pacifism and towards ecumenism.

Hence within the movement emerged conscientious objectors such as Jacques Martin, Philo Vernier and Henri Roser, economists pursuing policies that reflected cooperation and solidarity (such as Bernard Lavergne and Georges Lasserre), and theologians such as Paul Ricoeur. One of the pastors in the movement, Jacques Kaltenbach, was also to have a formative influence on André Trocmé.

Under the Vichy regime which had seen the emergence of other forms of witness, particularly the support of internees in the camps and aiding Jews to escape, the movement was reborn to tackle the problems of a changing world. It expressed a Christian socialism, more or less in line with the beginning of a new political left. Political activism was very broad and included the denunciation of torture, East–West debate on European integration and taking a stance on the process of decolonization. It facilitated meetings between employers, managers and trade unionists to discern a new economic order.

After the events of May 68, Calvinism in France became much more left-wing in its orientation. One doctrinal text produced in this period, Church and Authorities, was described as Marxist in its orientation. Churches now seized for themselves the political and social issues to tackle, such as nuclear power and justice for the Third World.

In the early 2000s, the Social Christianity movement temporarily discontinued and its journal Other Times ceased to be published. However, the movement was relaunched on 10 June 2010 with a petition signed by over 240 people and now maintains an active presence with its own website.

Economically, Most Calvinists have supported capitalism and have been in the vanguard of promoting market capitalism and have produced many of France's leading entrepreneurs. With regard to politics and social issues however, they are very much socialists. Three of France's post-war prime ministers have been Calvinists, despite Protestants only making up two percent of the population. Two of these prime ministers have been socialists.

In Australia, the academic Roland Boer has attempted to synthesize Calvinism and Marxism. He has stated that "it became clear to me that within Christianity there is a strong tradition of political and theological radicalism, which I continued to explore personally. Reformed or Calvinist theology did not seem to sit easily with that interest, so I spent many a long year rejecting that tradition, only to realise later that Calvin himself was torn between the radical potential of elements in the Bible and his own conservative preferences".

In Wales, Calvinistic Methodism is the largest non-conformist religion. Its beginnings may be traced to Griffith Jones (1684–1761), of Llanddowror, Carmarthenshire, whose sympathy for the poor led him to set on foot a system of circulating charity schools for the education of children. However, until the nineteenth century, the prevailing thought amongst Welsh non-conformists was that "it would be wiser if the churches limited their activities to those of the altar and not to meddle at all with the state and social questions". This stemmed partly from the traditional nonconformist belief in the separation of church and state.

In his influential sermon Y Ddwy Alwedigaeth (The Two Vocations), Emrys ap Iwan challenged this passive pietism: "We must not think, like the old Methodists, Puritans and some Catholics, that we can only seek Godliness outside our earthly vocation." He condemned those Christians who limited godliness to directly religious matters such as Sabbath observance and personal devotion. He declared that all earthly things, including language and culture, have some kind of divine origin.

Many of the founders of the Welsh nationalist social-democratic party, Plaid Cymru were also devout Calvinists, including John Edward Daniel. Daniel was the theologian credited for bringing neo-orthodoxy to Wales. Daniel argued that God did not create man as an isolated individual but as a social being.

The second generation of Plaid Cymru leaders included R. Tudur Jones. His political stance, combined with Calvinist doctrine, created an integrated vision that was significant to the religious life of Christian Wales in the later half of the 20th century. Jones argued that the "state should be a servant, to preserve order and to allow men to live the good life".

Today, many Calvinist socialists in Wales support same-sex marriage on the grounds that it delivers marriage equality in the eyes of the state while still allowing churches to follow their own conscience, thus upholding the traditional Protestant belief in separation of church and state.

The Calvinist tradition in Plaid Cymru has also influenced its non-violent approach. According to Rhys Llwyd, "[t]he ideal is no fist violence, no verbal violence, and no heart violence. [...] Christians [...] point to the New Testament example of Jesus Christ clearing the temple. Here there is no suggestion of violence against people; rather the tables are turned as a symbolic act. The life and teaching of Jesus Christ were seen as the foundations of nonviolent direct action [for Plaid Cymru members] [...] loving their enemies on the one hand, but not compromising on what they saw as an issue of moral rightness". Plaid Cymru continues to see itself as very much part of the Christian pacifist tradition.

Criticism

In Rendering Unto Caesar, Lawrence Reed, president emeritus of the libertarian-leaning Foundation for Economic Education, writes that Jesus was not a socialist in that he promoted voluntary giving and charity rather than the mandatory taking by government (taxes). Conservative Evangelical Christian Johnnie Moore Jr., Professor of Religion at Liberty University, a "bastion of the Christian right" in American politics, writing on the homepage of Fox News Radio's Todd Starnes, claimed that Jesus was a capitalist. Traditionalist conservative Bryan Fischer of the American Family Association, a Christian fundamentalist organization in the United States, also claimed that Jesus was a capitalist who advocated "voluntary redistribution of wealth".

Charles Haddon Spurgeon was critical of socialist doctrines, and warned that those who seek socialism "may soon have too much of it". Specifically, he regarded collectivist Christianity as inferior to faith on an individual level. He said that "I would not have you exchange the gold of individual Christianity for the base metal of Christian socialism".

Friedmann–Lemaître–Robertson–Walker metric

From Wikipedia, the free encyclopedia

The Friedmann–Lemaître–Robertson–Walker (FLRW; /ˈfriːdmən ləˈmɛtrə ... /) metric is an exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe that is path-connected, but not necessarily simply connected. The general form of the metric follows from the geometric properties of homogeneity and isotropy; Einstein's field equations are only needed to derive the scale factor of the universe as a function of time. Depending on geographical or historical preferences, the set of the four scientists – Alexander Friedmann, Georges Lemaître, Howard P. Robertson and Arthur Geoffrey Walker – are customarily grouped as Friedmann or Friedmann–Robertson–Walker (FRW) or Robertson–Walker (RW) or Friedmann–Lemaître (FL). This model is sometimes called the Standard Model of modern cosmology, although such a description is also associated with the further developed Lambda-CDM model. The FLRW model was developed independently by the named authors in the 1920s and 1930s.

General metric

The FLRW metric starts with the assumption of homogeneity and isotropy of space. It also assumes that the spatial component of the metric can be time-dependent. The generic metric which meets these conditions is

${\displaystyle -c^{2}\mathrm {d} \tau ^{2}=-c^{2}\mathrm {d} t^{2}+{a(t)}^{2}\mathrm {d} \mathbf {\Sigma } ^{2}}$

where ${\displaystyle \mathbf {\Sigma } }$ ranges over a 3-dimensional space of uniform curvature, that is, elliptical space, Euclidean space, or hyperbolic space. It is normally written as a function of three spatial coordinates, but there are several conventions for doing so, detailed below. ${\displaystyle \mathrm {d} \mathbf {\Sigma } }$ does not depend on t — all of the time dependence is in the function a(t), known as the "scale factor".

Reduced-circumference polar coordinates

In reduced-circumference polar coordinates the spatial metric has the form

${\displaystyle \mathrm {d} \mathbf {\Sigma } ^{2}={\frac {\mathrm {d} r^{2}}{1-kr^{2}}}+r^{2}\mathrm {d} \mathbf {\Omega } ^{2},\quad {\text{where }}\mathrm {d} \mathbf {\Omega } ^{2}=\mathrm {d} \theta ^{2}+\sin ^{2}\theta \,\mathrm {d} \phi ^{2}.}$

k is a constant representing the curvature of the space. There are two common unit conventions:

• k may be taken to have units of length⁻², in which case r has units of length and a(t) is unitless. k is then the Gaussian curvature of the space at the time when a(t) = 1. r is sometimes called the reduced circumference because it is equal to the measured circumference of a circle (at that value of r), centered at the origin, divided by 2π (like the r of Schwarzschild coordinates). Where appropriate, a(t) is often chosen to equal 1 in the present cosmological era, so that ${\displaystyle \mathrm {d} \mathbf {\Sigma } }$ measures comoving distance.
• Alternatively, k may be taken to belong to the set {−1,0,+1} (for negative, zero, and positive curvature respectively). Then r is unitless and a(t) has units of length. When k = ±1, a(t) is the radius of curvature of the space, and may also be written R(t).

A disadvantage of reduced circumference coordinates is that they cover only half of the 3-sphere in the case of positive curvature—circumferences beyond that point begin to decrease, leading to degeneracy. (This is not a problem if space is elliptical, i.e. a 3-sphere with opposite points identified.)

Hyperspherical coordinates

In hyperspherical or curvature-normalized coordinates the coordinate r is proportional to radial distance; this gives

${\displaystyle \mathrm {d} \mathbf {\Sigma } ^{2}=\mathrm {d} r^{2}+S_{k}(r)^{2}\,\mathrm {d} \mathbf {\Omega } ^{2}}$

where ${\displaystyle \mathrm {d} \mathbf {\Omega } }$ is as before and

${\displaystyle S_{k}(r)={\begin{cases}{\sqrt {k}}^{\,-1}\sin(r{\sqrt {k}}),&k>0\\r,&k=0\\{\sqrt {|k|}}^{\,-1}\sinh(r{\sqrt {|k|}}),&k<0.\end{cases}}}$

As before, there are two common unit conventions:

• k may be taken to have units of length⁻², in which case r has units of length and a(t) is unitless. k is then the Gaussian curvature of the space at the time when a(t) = 1. Where appropriate, a(t) is often chosen to equal 1 in the present cosmological era, so that ${\displaystyle \mathrm {d} \mathbf {\Sigma } }$ measures comoving distance.
• Alternatively, as before, k may be taken to belong to the set {−1,0,+1} (for negative, zero, and positive curvature respectively). Then r is unitless and a(t) has units of length. When k = ±1, a(t) is the radius of curvature of the space, and may also be written R(t). Note that when k = +1, r is essentially a third angle along with θ and φ. The letter χ may be used instead of r.

Though it is usually defined piecewise as above, S is an analytic function of both k and r. It can also be written as a power series

${\displaystyle S_{k}(r)=\sum _{n=0}^{\infty }{\frac {(-1)^{n}k^{n}r^{2n+1}}{(2n+1)!}}=r-{\frac {kr^{3}}{6}}+{\frac {k^{2}r^{5}}{120}}-\cdots }$

or as

${\displaystyle S_{k}(r)=r\;\mathrm {sinc} \,(r{\sqrt {k}}),}$

where sinc is the unnormalized sinc function and ${\displaystyle {\sqrt {k}}}$ is one of the imaginary, zero or real square roots of k. These definitions are valid for all k.

Cartesian coordinates

When k = 0 one may write simply

${\displaystyle \mathrm {d} \mathbf {\Sigma } ^{2}=\mathrm {d} x^{2}+\mathrm {d} y^{2}+\mathrm {d} z^{2}.}$

This can be extended to k ≠ 0 by defining

${\displaystyle x=r\cos \theta \,}$,

${\displaystyle y=r\sin \theta \cos \phi \,}$, and

${\displaystyle z=r\sin \theta \sin \phi \,}$,

where r is one of the radial coordinates defined above, but this is rare.

Curvature

Cartesian coordinates

In flat ${\displaystyle (k=0)}$ FLRW space using Cartesian coordinates, the surviving components of the Ricci tensor are

${\displaystyle R_{tt}=-3{\frac {\ddot {a}}{a}},\quad R_{xx}=R_{yy}=R_{zz}=c^{-2}(a{\ddot {a}}+2{\dot {a}}^{2})}$

and the Ricci scalar is

${\displaystyle R=6c^{-2}\left({\frac {{\ddot {a}}(t)}{a(t)}}+{\frac {{\dot {a}}^{2}(t)}{a^{2}(t)}}\right).}$

Spherical coordinates

In more general FLRW space using spherical coordinates (called "reduced-circumference polar coordinates" above), the surviving components of the Ricci tensor are

${\displaystyle R_{tt}=-3{\frac {\ddot {a}}{a}},}$

${\displaystyle R_{rr}={\frac {c^{-2}(a(t){\ddot {a}}(t)+2{\dot {a}}^{2}(t))+2k}{1-kr^{2}}}}$

${\displaystyle R_{\theta \theta }=r^{2}(c^{-2}(a(t){\ddot {a}}(t)+2{\dot {a}}^{2}(t))+2k)}$

${\displaystyle R_{\phi \phi }=r^{2}(c^{-2}(a(t){\ddot {a}}(t)+2{\dot {a}}^{2}(t))+2k)\sin ^{2}(\theta )}$

and the Ricci scalar is

${\displaystyle R=6\left({\frac {{\ddot {a}}(t)}{c^{2}a(t)}}+{\frac {{\dot {a}}^{2}(t)}{c^{2}a^{2}(t)}}+{\frac {k}{a^{2}(t)}}\right).}$

Solutions

Main article: Friedmann equations

Einstein's field equations are not used in deriving the general form for the metric: it follows from the geometric properties of homogeneity and isotropy. However, determining the time evolution of ${\displaystyle a(t)}$ does require Einstein's field equations together with a way of calculating the density, ${\displaystyle \rho (t),}$ such as a cosmological equation of state.

This metric has an analytic solution to Einstein's field equations ${\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\frac {8\pi G}{c^{4}}}T_{\mu \nu }}$ giving the Friedmann equations when the energy–momentum tensor is similarly assumed to be isotropic and homogeneous. The resulting equations are:

${\displaystyle \left({\frac {\dot {a}}{a}}\right)^{2}+{\frac {kc^{2}}{a^{2}}}-{\frac {\Lambda c^{2}}{3}}={\frac {8\pi G}{3}}\rho }$

${\displaystyle 2{\frac {\ddot {a}}{a}}+\left({\frac {\dot {a}}{a}}\right)^{2}+{\frac {kc^{2}}{a^{2}}}-\Lambda c^{2}=-{\frac {8\pi G}{c^{2}}}p.}$

These equations are the basis of the standard Big Bang cosmological model including the current ΛCDM model. Because the FLRW model assumes homogeneity, some popular accounts mistakenly assert that the Big Bang model cannot account for the observed lumpiness of the universe. In a strictly FLRW model, there are no clusters of galaxies, stars or people, since these are objects much denser than a typical part of the universe. Nonetheless, the FLRW model is used as a first approximation for the evolution of the real, lumpy universe because it is simple to calculate, and models which calculate the lumpiness in the universe are added onto the FLRW models as extensions. Most cosmologists agree that the observable universe is well approximated by an almost FLRW model, i.e., a model which follows the FLRW metric apart from primordial density fluctuations. As of 2003, the theoretical implications of the various extensions to the FLRW model appear to be well understood, and the goal is to make these consistent with observations from COBE and WMAP.

If the spacetime is multiply connected, then each event will be represented by more than one tuple of coordinates.

Interpretation

The pair of equations given above is equivalent to the following pair of equations

${\displaystyle {\dot {\rho }}=-3{\frac {\dot {a}}{a}}\left(\rho +{\frac {p}{c^{2}}}\right)}$

${\displaystyle {\frac {\ddot {a}}{a}}=-{\frac {4\pi G}{3}}\left(\rho +{\frac {3p}{c^{2}}}\right)+{\frac {\Lambda c^{2}}{3}}}$

with ${\displaystyle k}$, the spatial curvature index, serving as a constant of integration for the first equation.

The first equation can be derived also from thermodynamical considerations and is equivalent to the first law of thermodynamics, assuming the expansion of the universe is an adiabatic process (which is implicitly assumed in the derivation of the Friedmann–Lemaître–Robertson–Walker metric).

The second equation states that both the energy density and the pressure cause the expansion rate of the universe ${\displaystyle {\dot {a}}}$ to decrease, i.e., both cause a deceleration in the expansion of the universe. This is a consequence of gravitation, with pressure playing a similar role to that of energy (or mass) density, according to the principles of general relativity. The cosmological constant, on the other hand, causes an acceleration in the expansion of the universe.

Cosmological constant

The cosmological constant term can be omitted if we make the following replacements

${\displaystyle \rho \rightarrow \rho +{\frac {\Lambda c^{2}}{8\pi G}}}$

${\displaystyle p\rightarrow p-{\frac {\Lambda c^{4}}{8\pi G}}.}$

Therefore, the cosmological constant can be interpreted as arising from a form of energy which has negative pressure, equal in magnitude to its (positive) energy density:

${\displaystyle p=-\rho c^{2}.\,}$

Such form of energy—a generalization of the notion of a cosmological constant—is known as dark energy.

In fact, in order to get a term which causes an acceleration of the universe expansion, it is enough to have a scalar field which satisfies

${\displaystyle p<-{\frac {\rho c^{2}}{3}}.\,}$

Such a field is sometimes called quintessence.

Newtonian interpretation

This is due to McCrea and Milne, although sometimes incorrectly ascribed to Friedmann. The Friedmann equations are equivalent to this pair of equations:

${\displaystyle -a^{3}{\dot {\rho }}=3a^{2}{\dot {a}}\rho +{\frac {3a^{2}p{\dot {a}}}{c^{2}}}\,}$

${\displaystyle {\frac {{\dot {a}}^{2}}{2}}-{\frac {G{\frac {4\pi a^{3}}{3}}\rho }{a}}=-{\frac {kc^{2}}{2}}\,.}$

The first equation says that the decrease in the mass contained in a fixed cube (whose side is momentarily a) is the amount which leaves through the sides due to the expansion of the universe plus the mass equivalent of the work done by pressure against the material being expelled. This is the conservation of mass–energy (first law of thermodynamics) contained within a part of the universe.

The second equation says that the kinetic energy (seen from the origin) of a particle of unit mass moving with the expansion plus its (negative) gravitational potential energy (relative to the mass contained in the sphere of matter closer to the origin) is equal to a constant related to the curvature of the universe. In other words, the energy (relative to the origin) of a co-moving particle in free-fall is conserved. General relativity merely adds a connection between the spatial curvature of the universe and the energy of such a particle: positive total energy implies negative curvature and negative total energy implies positive curvature.

The cosmological constant term is assumed to be treated as dark energy and thus merged into the density and pressure terms.

During the Planck epoch, one cannot neglect quantum effects. So they may cause a deviation from the Friedmann equations.

Name and history

The Soviet mathematician Alexander Friedmann first derived the main results of the FLRW model in 1922 and 1924. Although the prestigious physics journal Zeitschrift für Physik published his work, it remained relatively unnoticed by his contemporaries. Friedmann was in direct communication with Albert Einstein, who, on behalf of Zeitschrift für Physik, acted as the scientific referee of Friedmann's work. Eventually Einstein acknowledged the correctness of Friedmann's calculations, but failed to appreciate the physical significance of Friedmann's predictions.

Friedmann died in 1925. In 1927, Georges Lemaître, a Belgian priest, astronomer and periodic professor of physics at the Catholic University of Leuven, arrived independently at results similar to those of Friedmann and published them in the Annales de la Société Scientifique de Bruxelles (Annals of the Scientific Society of Brussels). In the face of the observational evidence for the expansion of the universe obtained by Edwin Hubble in the late 1920s, Lemaître's results were noticed in particular by Arthur Eddington, and in 1930–31 Lemaître's paper was translated into English and published in the Monthly Notices of the Royal Astronomical Society.

Howard P. Robertson from the US and Arthur Geoffrey Walker from the UK explored the problem further during the 1930s. In 1935 Robertson and Walker rigorously proved that the FLRW metric is the only one on a spacetime that is spatially homogeneous and isotropic (as noted above, this is a geometric result and is not tied specifically to the equations of general relativity, which were always assumed by Friedmann and Lemaître).

This solution, often called the Robertson–Walker metric since they proved its generic properties, is different from the dynamical "Friedmann–Lemaître" models, which are specific solutions for a(t) which assume that the only contributions to stress–energy are cold matter ("dust"), radiation, and a cosmological constant.

Einstein's radius of the universe

Einstein's radius of the universe is the radius of curvature of space of Einstein's universe, a long-abandoned static model that was supposed to represent our universe in idealized form. Putting

${\displaystyle {\dot {a}}={\ddot {a}}=0}$

in the Friedmann equation, the radius of curvature of space of this universe (Einstein's radius) is

${\displaystyle R_{E}=c/{\sqrt {4\pi G\rho }}}$,

where ${\displaystyle c}$ is the speed of light, ${\displaystyle G}$ is the Newtonian gravitational constant, and ${\displaystyle \rho }$ is the density of space of this universe. The numerical value of Einstein's radius is of the order of 10¹⁰ light years.

Evidence

By combining the observation data from some experiments such as WMAP and Planck with theoretical results of Ehlers–Geren–Sachs theorem and its generalization, astrophysicists now agree that the universe is almost homogeneous and isotropic (when averaged over a very large scale) and thus nearly a FLRW spacetime. That being said, attempts to confirm the purely kinematic interpretation of the Cosmic Microwave Background (CMB) dipole through studies of radio galaxies  and quasars show disagreement in the magnitude. Taken at face value, these observations are at odds with the Universe being described by the FLRW metric. Moreover, one can argue that there is a maximum value to the Hubble constant within an FLRW cosmology tolerated by current observations, ${\displaystyle H_{0}=71\pm 1}$ km/s/Mpc, and depending on how local determinations converge, this may point to an explanation beyond the FLRW metric. Such speculations aside, it should be stressed that the FLRW metric is a valid first approximation for the Universe.