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Wednesday, October 30, 2024

Apophatic theology

From Wikipedia, the free encyclopedia

The apophatic tradition is often, though not always, allied with the approach of mysticism, which aims at the vision of God, the perception of the divine reality beyond the realm of ordinary perception.

Etymology and definition

"Apophatic", Ancient Greek: ἀπόφασις (noun); from ἀπόφημι apophēmi, meaning 'to deny'. From Online Etymology Dictionary:

apophatic (adj.) "involving a mention of something one feigns to deny; involving knowledge obtained by negation", 1850, from Latinized form of Greek apophatikos, from apophasis "denial, negation", from apophanai "to speak off," from apo "off, away from" (see apo-) + phanai "to speak," related to pheme "voice," from PIE root *bha- (2) "to speak, tell, say."

Via negativa or via negationis (Latin), 'negative way' or 'by way of denial'. The negative way forms a pair together with the kataphatic or positive way. According to Deirdre Carabine,

Pseudo Dionysius describes the kataphatic or affirmative way to the divine as the "way of speech": that we can come to some understanding of the Transcendent by attributing all the perfections of the created order to God as its source. In this sense, we can say "God is Love", "God is Beauty", "God is Good".
The apophatic or negative way stresses God's absolute transcendence and unknowability in such a way that we cannot say anything about the divine essence because God is so totally beyond being. The dual concept of the immanence and transcendence of God can help us to understand the simultaneous truth of both "ways" to God: at the same time as God is immanent, God is also transcendent. At the same time as God is knowable, God is also unknowable. God cannot be thought of as one or the other only.

Origins and development

According to Fagenblat, "negative theology is as old as philosophy itself:" elements of it can be found in Plato's unwritten doctrines, while it is also present in Neo-Platonic, Gnostic and early Christian writers. A tendency to apophatic thought can also be found in Philo of Alexandria.

According to Carabine, "apophasis proper" in Greek thought starts with Neo-Platonism, with its speculations about the nature of the One, culminating in the works of Proclus. Carabine writes that there are two major points in the development of apophatic theology, namely the fusion of the Jewish tradition with Platonic philosophy in the writings of Philo, and the works of Pseudo-Dionysius the Areopagite, who infused Christian thought with Neo-Platonic ideas.

The Early Church Fathers were influenced by Philo, and Meredith even states that Philo "is the real founder of the apophatic tradition." Yet, it was with Pseudo-Dionysius the Areopagite and Maximus the Confessor, whose writings shaped both Hesychasm (the contemplative monastic tradition of the Eastern Orthodox Churches) and the mystical traditions of western Europe, that apophatic theology became a central element of Christian theology and contemplative practice.

Elijah's hearing of a "still, small voice" at 1 Kings 19:11-13 has been proposed as a Biblical example of apophatic prayer.

Greek philosophy

Pre-Socratic

For the ancient Greeks, knowledge of the gods was essential for proper worship. Poets had an important responsibility in this regard, and a central question was how knowledge of the Divine forms can be attained. Epiphany played an essential role in attaining this knowledge. Xenophanes (c. 570 – c. 475 BC) noted that the knowledge of the Divine forms is restrained by the human imagination, and Greek philosophers realized that this knowledge can only be mediated through myth and visual representations, which are culture-dependent.

According to Herodotus (484–425 BC), Homer and Hesiod (between 750 and 650 BC) taught the Greek the knowledge of the Divine bodies of the Gods. The ancient Greek poet Hesiod (between 750 and 650 BC) describes in his Theogony the birth of the gods and creation of the world, which became an "ur-text for programmatic, first-person epiphanic narratives in Greek literature," but also "explores the necessary limitations placed on human access to the divine." According to Platt, the statement of the Muses who grant Hesiod knowledge of the Gods "actually accords better with the logic of apophatic religious thought."

Parmenides (fl. late sixth or early fifth century BC), in his poem On Nature, gives an account of a revelation on two ways of inquiry. "The way of conviction" explores Being, true reality ("what-is"), which is "What is ungenerated and deathless,/whole and uniform, and still and perfect." "The way of opinion" is the world of appearances, in which one's sensory faculties lead to conceptions which are false and deceitful. His distinction between unchanging Truth and shifting opinion is reflected in Plato's allegory of the Cave. Together with the Biblical story of Moses's ascent of Mount Sinai, it is used by Gregory of Nyssa and Pseudo-Dionysius the Areopagite to give a Christian account of the ascent of the soul toward God. Cook notes that Parmenides' poem is a religious account of a mystical journey, akin to the mystery cults, giving a philosophical form to a religious outlook. Cook further notes that the philosopher's task is to "attempt through 'negative' thinking to tear themselves loose from all that frustrates their pursuit of wisdom."

Plato

Plato Silanion Musei Capitolini MC1377.

Plato (428/427 or 424/423 – 348/347 BC), "deciding for Parmenides against Heraclitus" and his theory of eternal change, had a strong influence on the development of apophatic thought.

Plato further explored Parmenides's idea of timeless truth in his dialogue Parmenides, which is a treatment of the eternal forms, Truth, Beauty and Goodness, which are the real aims for knowledge. The Theory of Forms is Plato's answer to the problem of how one fundamental reality or unchanging essence can admit of many changing phenomena, other than by dismissing them as being mere illusion.

In The Republic, Plato argues that the "real objects of knowledge are not the changing objects of the senses, but the immutable Forms," stating that the Form of the Good is the highest object of knowledge. His argument culminates in the Allegory of the Cave, in which he argues that humans are like prisoners in a cave, who can only see shadows of the Real, the Form of the Good. Humans are to be educated to search for knowledge, by turning away from their bodily desires toward higher contemplation, culminating in an intellectual understanding or apprehension of the Forms, c.q. the "first principles of all knowledge."

According to Cook, the Theory of Forms has a theological flavour, and had a strong influence on the ideas of his Neo-Platonist interpreters Proclus and Plotinus. The pursuit of Truth, Beauty and Goodness became a central element in the apophatic tradition, but nevertheless, according to Carabine "Plato himself cannot be regarded as the founder of the negative way." Carabine warns not to read later Neo-Platonic and Christian understandings into Plato, and notes that Plato did not identify his Forms with "one transcendent source," an identification which his later interpreters made.

Middle Platonism

Middle Platonism (1st century BC–3rd century AD) further investigated Plato's "Unwritten Doctrines," which drew on Pythagoras' first principles of the Monad and the Dyad (matter). Middle Platonism proposed a hierarchy of being, with God as its first principle at its top, identifying it with Plato's Form of the Good. An influential proponent of Middle Platonism was Philo (c. 25 BC–c. 50 AD), who employed Middle Platonic philosophy in his interpretation of the Hebrew scriptures, and asserted a strong influence on early Christianity. According to Craig D. Allert, "Philo made a monumental contribution to the creation of a vocabulary for use in negative statements about God." For Philo, God is undescribable, and he uses terms which emphasize God's transcendence.

Neo-Platonism

Neo-Platonism was a mystical or contemplative form of Platonism, which "developed outside the mainstream of Academic Platonism." It started with the writings of Plotinus (204/5–270 AD), and ended with the closing of the Platonic Academy by Emperor Justinian in 529 AD, when the pagan traditions were ousted. It is a product of Hellenistic syncretism, which developed due to the crossover between Greek thought and the Jewish scriptures, and also gave birth to Gnosticism. Proclus of Athens (*412–485 C.E.) played a crucial role in the transmission of Platonic philosophy from antiquity to the Middle Ages., serving as head or ‘successor’ (diadochos, sc. of Plato) of the Platonic ‘Academy’ for over 50 years. His student Pseudo-Dionysius had a far-stretching Neo-Platonic influence on Christianity and Christian mysticism.

Plotinus

Plotinus, 204/5–270 AD.

Plotinus (204/5–270 AD) was the founder of Neo-Platonism. In the Neo-Platonic philosophy of Plotinus and Proclus, the first principle became even more elevated as a radical unity, which was presented as an unknowable Absolute. For Plotinus, the One is the first principle, from which everything else emanates. He took it from Plato's writings, identifying the Good of the Republic, as the cause of the other Forms, with the One of the first hypothesis of the second part of the Parmenides. For Plotinus, the One precedes the Forms, and "is beyond Mind and indeed beyond Being." From the One comes the Intellect, which contains all the Forms. The One is the principle of Being, while the Forms are the principle of the essence of beings, and the intelligibility which can recognize them as such. Plotinus's third principle is Soul, the desire for objects external to itself. The highest satisfaction of desire is the contemplation of the One, which unites all existents "as a single, all-pervasive reality."

The One is radically simple, and does not even have self-knowledge, since self-knowledge would imply multiplicity. Nevertheless, Plotinus does urge for a search for the Absolute, turning inward and becoming aware of the "presence of the intellect in the human soul," initiating an ascent of the soul by abstraction or "taking away," culminating in a sudden appearance of the One. In the Enneads Plotinus writes:

Our thought cannot grasp the One as long as any other image remains active in the soul [...] To this end, you must set free your soul from all outward things and turn wholly within yourself, with no more leaning to what lies outside, and lay your mind bare of ideal forms, as before of the objects of sense, and forget even yourself, and so come within sight of that One.

Carabine notes that Plotinus' apophasis is not just a mental exercise, an acknowledgement of the unknowability of the One, but a means to ecstasis and an ascent to "the unapproachable light that is God." Pao-Shen Ho, investigating what are Plotinus' methods for reaching henosis, concludes that "Plotinus' mystical teaching is made up of two practices only, namely philosophy and negative theology." According to Moore, Plotinus appeals to the "non-discursive, intuitive faculty of the soul," by "calling for a sort of prayer, an invocation of the deity, that will permit the soul to lift itself up to the unmediated, direct, and intimate contemplation of that which exceeds it (V.1.6)." Pao-Shen Ho further notes that "for Plotinus, mystical experience is irreducible to philosophical arguments." The argumentation about henosis is preceded by the actual experience of it, and can only be understood when henosis has been attained. Ho further notes that Plotinus's writings have a didactic flavour, aiming to "bring his own soul and the souls of others by way of Intellect to union with the One." As such, the Enneads as a spiritual or ascetic teaching device, akin to The Cloud of Unknowing, demonstrating the methods of philosophical and apophatic inquiry. Ultimately, this leads to silence and the abandonment of all intellectual inquiry, leaving contemplation and unity.

Proclus

Proclus (412–485) introduced the terminology used in apophatic and cataphatic theology. He did this in the second book of his Platonic Theology, arguing that Plato states that the One can be revealed "through analogy," and that "through negations [dia ton apophaseon] its transcendence over everything can be shown." For Proclus, apophatic and cataphatic theology form a contemplatory pair, with the apophatic approach corresponding to the manifestation of the world from the One, and cataphatic theology corresponding to the return to the One. The analogies are affirmations which direct us toward the One, while the negations underlie the confirmations, being closer to the One. According to Luz, Proclus also attracted students from other faiths, including the Samaritan Marinus. Luz notes that "Marinus' Samaritan origins with its Abrahamic notion of a single ineffable Name of God (יהוה‎) should also have been in many ways compatible with the school's ineffable and apophatic divine principle."

Christianity

Engraving of Otto van Veen (1660), who negatively describes God as Quod oculus non vidit, nec auris audivit (Vulgate), "What no eye has seen, nor ear heard" (1 Corinthians 2:9).

Apostolic Age

The Book of Revelation 8:1 mentions "the silence of the perpetual choir in heaven." According to Dan Merkur:

The silence of the perpetual choir in heaven had mystical connotations, because silence attends the disappearance of plurality during experiences of mystical oneness. The term "silence" also alludes to the "still small voice" (1 Kings 19:12) whose revelation to Elijah on Mount Horeb rejected visionary imagery by affirming a negative theology.

Early Church Fathers

The Early Church Fathers were influenced by Philo[4] (c. 25 BC – 50 AD), who saw Moses as "the model of human virtue and Sinai as the archetype of man's ascent into the 'luminous darkness' of God." His interpretation of Moses was followed by Clement of Alexandria, Origen, the Cappadocian Fathers, Pseudo-Dionysius, and Maximus the Confessor.

God's appearance to Moses in the burning bush was often elaborated on by the Early Church Fathers, especially Gregory of Nyssa (c. 335 – 395), realizing the fundamental unknowability of God; an exegesis which continued in the medieval mystical tradition. Their response is that, although God is unknowable, Jesus as person can be followed, since "following Christ is the human way of seeing God."

Clement of Alexandria (c. 150 – 215) was an early proponent of apophatic theology. Clement holds that God is unknowable, although God's unknowability, concerns only his essence, not his energies, or powers. According to R.A. Baker, in Clement's writings the term theoria develops further from a mere intellectual "seeing" toward a spiritual form of contemplation. Clement's apophatic theology or philosophy is closely related to this kind of theoria and the "mystic vision of the soul." For Clement, God is transcendent and immanent. According to Baker, Clement's apophaticism is mainly driven not by Biblical texts, but by the Platonic tradition. His conception of an ineffable God is a synthesis of Plato and Philo, as seen from a Biblical perspective. According to Osborne, it is a synthesis in a Biblical framework; according to Baker, while the Platonic tradition accounts for the negative approach, the Biblical tradition accounts for the positive approach. Theoria and abstraction is the means to conceive of this ineffable God; it is preceded by dispassion.

According to Tertullian (c. 155c. 240):

[T]hat which is infinite is known only to itself. This it is which gives some notion of God, while yet beyond all our conceptions – our very incapacity of fully grasping Him affords us the idea of what He really is. He is presented to our minds in His transcendent greatness, as at once known and unknown.

Saint Cyril of Jerusalem (313–386), in his Catechetical Homilies, states:

For we explain not what God is but candidly confess that we have not exact knowledge concerning Him. For in what concerns God to confess our ignorance is the best knowledge.

Filippo Lippi, Vision of St. Augustine, c. 1465, tempera, Hermitage Museum, Saint Petersburg.

Augustine of Hippo (354–430) defined God aliud, aliud valde, meaning 'other, completely other', in Confessions 7.10.16, wrote Si [enim] comprehendis, non est Deus, meaning 'if you understand [something], it is not God', in Sermo 117.3.5 (PL 38, 663), and a famous legend tells that, while walking along the Mediterranean shoreline meditating on the mystery of the Trinity, he met a child who with a seashell (or a little pail) was trying to pour the whole sea into a small hole dug in the sand. Augustine told him that it was impossible to enclose the immensity of the sea in such a small opening, and the child replied that it was equally impossible to try to understand the infinity of God within the limited confines of the human mind.

The Chalcedonian Christological dogma

The Christological dogma, formulated by the Fourth Ecumenical Council held in Chalcedon in 451, is based on dyophysitism and hypostatic union, concepts used to describe the union of humanity and divinity in a single hypostasis, or individual existence, that of Jesus Christ. This remains transcendent to mankind's rational categories, a mystery which has to be guarded by apophatic language, as it is a personal union of a singularly unique kind.

Pseudo-Dionysius the Areopagite

Apophatic theology found its most influential expression in the works of Pseudo-Dionysius the Areopagite (late 5th to early 6th century), a student of Proclus (412–485) who combined a Christian worldview with Neo-Platonic ideas. He is a constant factor in the contemplative tradition of the eastern Orthodox Churches, and from the 9th century onwards his writings also had a strong impact on western mysticism.

Dionysius the Areopagite was a pseudonym, taken from Acts of the Apostles chapter 17, in which Paul gives a missionary speech to the court of the Areopagus in Athens. In Acts 17:23 Paul makes a reference to an altar-inscription, dedicated to the Unknown God, "a safety measure honoring foreign gods still unknown to the Hellenistic world." For Paul, Jesus Christ is this unknown God, and as a result of Paul's speech Dionysius the Areopagite converts to Christianity. Yet, according to Stang, for Pseudo-Dionysius the Areopagite Athens is also the place of Neo-Platonic wisdom, and the term "unknown God" is a reversal of Paul's preaching toward an integration of Christianity with Neo-Platonism, and the union with the "unknown God."

According to Corrigan and Harrington, "Dionysius' central concern is how a triune God [...] who is utterly unknowable, unrestricted being, beyond individual substances, beyond even goodness, can become manifest to, in, and through the whole of creation in order to bring back all things to the hidden darkness of their source." Drawing on Neo-Platonism, Pseudo-Dionysius described human ascent to divinity as a process of purgation, illumination and union. Another Neo-Platonic influence was his description of the cosmos as a series of hierarchies, which overcome the distance between God and humans.

Eastern Orthodox Christianity

In Orthodox Christianity, apophatic theology is taught as superior to cataphatic theology. The fourth-century Cappadocian Fathers stated a belief in the existence of God, but an existence unlike that of everything else: everything else that exists was created, but the Creator transcends this existence, is uncreated. The essence of God is completely unknowable; mankind can acquire an incomplete knowledge of God in his attributes (propria), positive and negative, by reflecting upon and participating in his self-revelatory operations (energeiai). Gregory of Nyssa (c. 335c. 395), John Chrysostom (c. 349–407), and Basil the Great (329–379) emphasized the importance of negative theology to an orthodox understanding of God. John of Damascus (c. 675/676–749) employed negative theology when he wrote that positive statements about God reveal "not the nature, but the things around the nature."

Maximus the Confessor (580–622) took over Pseudo-Dionysius' ideas, and had a strong influence on the theology and contemplative practices of the Eastern Orthodox Churches. Gregory Palamas (1296–1359) formulated the definite theology of Hesychasm, the Eastern Orthodox practices of contemplative prayer and theosis, "deification."

Influential 20th-century Orthodox theologians include the Neo-Palamist writers Vladimir Lossky, John Meyendorff, John S. Romanides, and Georges Florovsky. Lossky argues, based on his reading of Dionysius and Maximus Confessor, that positive theology is always inferior to negative theology, which is a step along the way to the superior knowledge attained by negation. This is expressed in the idea that mysticism is the expression of dogmatic theology par excellence.

According to Lossky, outside of directly revealed knowledge through Scripture and Sacred Tradition, such as the Trinitarian nature of God, God in his essence is beyond the limits of what human beings (or even angels) can understand. He is transcendent in essence (ousia). Further knowledge must be sought in a direct experience of God or his indestructible energies through theoria (vision of God). According to Aristotle Papanikolaou, in Eastern Christianity, God is immanent in his hypostasis or existences.

Western Christianity

In The Creation of Adam painted by Michelangelo (c. 1508–1512), the two index fingers are separated by a small gap (34 inch (1.9 cm)): some scholars think that it represents the unattainability of divine perfection by man.

Negative theology has a place in the Western Christian tradition as well. The 9th-century theologian John Scotus Erigena wrote:

We do not know what God is. God Himself does not know what He is because He is not anything [i.e., "not any created thing"]. Literally God is not, because He transcends being.

When he says "He is not anything" and "God is not", Scotus does not mean that there is no God, but that God cannot be said to exist in the way that creation exists, i.e. that God is uncreated. He is using apophatic language to emphasise that God is "other".

Theologians like Meister Eckhart and John of the Cross exemplify some aspects of or tendencies towards the apophatic tradition in the West. The medieval work, The Cloud of Unknowing and John of the Cross' Dark Night of the Soul are particularly well known. In 1215 apophatism became the official position of the Catholic Church, which, on the basis of Scripture and church tradition, during the Fourth Lateran Council formulated the following dogma:

Between Creator and creature no similitude can be expressed without implying an even greater dissimilitude.

The via eminentiae

Thomas Aquinas was born ten years later (1225–1274) and, although in his Summa Theologiae he quotes Pseudo-Dionysius 1,760 times, stating that "Now, because we cannot know what God is, but rather what He is not, we have no means for considering how God is, but rather how He is not" and leaving the work unfinished because it was like "straw" compared to what had been revealed to him, his reading in a neo-Aristotelian key of the conciliar declaration overthrew its meaning inaugurating the "analogical way" as tertium between via negativa and via positiva: the via eminentiae. In this way, the believers see what attributes are common between them and God, as well as the unique, not human, properly divine and not understandable way in respect of which God possesses that attributes.

According to Adrian Langdon:

The distinction between univocal, equivocal, and analogous language and relations corresponds to the distinction between the via positiva, via negativa, and via eminentiae. In Thomas Aquinas, for example, the via positiva undergirds the discussion of univocity, the via negativa the equivocal, and the via eminentiae the final defense of analogy.

According to Catholic Encyclopedia, the Doctor Angelicus and the scholastici declare that:

God is not absolutely unknowable, and yet it is true that we cannot define Him adequately. But we can conceive and name Him in an "analogical way". The perfections manifested by creatures are in God, not merely nominally (equivoce) but really and positively, since He is their source. Yet, they are not in Him as they are in the creature, with a mere difference of degree, nor even with a mere specific or generic difference (univoce), for there is no common concept including the finite and the Infinite. They are really in Him in a supereminent manner (eminenter) which is wholly incommensurable with their mode of being in creatures. We can conceive and express these perfections only by an analogy; not by an analogy of proportion, for this analogy rests on a participation in a common concept, and, as already said, there is no element common to the finite and the Infinite; but by an analogy of proportionality.

Since then Thomism has played a decisive role in resizing the negative or apophatic tradition of the magisterium.

20th century

Herman Dooyeweerd

Apophatic statements are still crucial to many modern theologians, restarting in the 1800s by Søren Kierkegaard (see his concept of the infinite qualitative distinction) up to Rudolf Otto, Karl Barth (see their idea of "Wholly Other", i.e. ganz Andere or totaliter aliter), the Ludwig Wittgenstein of the Tractatus, and Martin Heidegger after his Kehre.

C. S. Lewis, in his book Miracles (1947), advocates the use of negative theology when first thinking about God, in order to cleanse one's mind of misconceptions. He goes on to advocate refilling the mind with the truth about God, untainted by mythology, bad analogies or false mind-pictures.

The mid-20th century Dutch philosopher Herman Dooyeweerd, who is often associated with a neo-Calvinistic tradition, provides a philosophical foundation for understanding the impossibility of absolutely knowing God, and yet the possibility of truly knowing something of God. Dooyeweerd made a sharp distinction between theoretical and pre-theoretical attitudes of thought. He argues that most of the discussion of knowledge of God presupposes theoretical knowledge, which involves reflection and attempts to define and discuss. Theoretical knowing, for Dooyeweerd, is never absolute, always depends on religious presuppositions, and cannot grasp either God or the law side. Pre-theoretical knowing, on the other hand, is intimate engagement, exhibits a diverse range of aspects, and can grasp at least the law side. According to Dooyeweerd, knowledge of God, as God wishes to reveal it, is pre-theoretical, immediate and intuitive, never theoretical in nature. The philosopher Leo Strauss considered that the Bible, for example, should be treated as pre-theoretical (everyday) rather than theoretical in what it contains.

Ivan Illich (1926–2002), the historian and social critic, can be read as an apophatic theologian, according to a longtime collaborator, Lee Hoinacki, in a paper presented in memory of Illich, called "Why Philia?"

21st century

Karen Armstrong, in her book The Case for God (2009), notices a recovery of apophatic theology in postmodern theology.

Philosopher and literary scholar William Franke, particularly in his 2007 two-volume collection On What Cannot Be Said and his 2014 monograph A Philosophy of the Unsayable, puts forth that negative theology's exploration and performance of language's limitations is not simply one current among many in religious thought, but is "a kind of perennial counter-philosophy to the philosophy of Logos" that persistently challenges central tenets of Western thought throughout its history. For Franke, literature demonstrates the "infinitely open" nature of language which negative theology and related forms of philosophical thought seek to draw attention to. Franke therefore argues that literature, philosophy, and theology begin to bleed into one another as they approach what he frames as the "apophatic" side of Western thought.

Islam

Various traditions and schools in Islam (see Islamic schools and branches) draw on sundry theologies in approaching God in Islam (Allah, Arabic الله) or the ultimate reality. "Negative theology" involves the use of تَعْطِيل, ta'tīl, defined as 'setting aside', 'canceling out', 'negation', or 'nullification'. The followers of the Mu'tazili school of Kalam, the spread of which is often attributed to Wasil ibn Ata, are often called the Mu'aṭṭilah ('cancelers' or 'negators'), a description, sometimes employed derogatorily, deriving from the school's descriptions of the Islamic God.

Rajab ʿAlī Tabrīzī, an Iranian and Shi'ite philosopher and mystic of the 17th century, is credited with instilling an apophatic theology in a generation of philosophers and theologians whose influence extended into the Qajar period. Mulla Rajab affirmed the completely unknowable, unqualifiable, and attributeless nature of God and upheld a general view concerning God's attributes which can only be negatively 'affirmed' (that is, by affirmingly negating all that is not God about God).

Shia Islam largely adopts "negative theology". In the words of the Persian Ismaili missionary, Abu Yaqub al-Sijistani: "There does not exist a tanzíh ["transcendence"] more brilliant and more splendid than that by which we establish the absolute transcendence of our Originator through the use of these phrases in which a negative and a negative of a negative apply to the thing denied."

Literalists completely reject and condemn any negation that would clash with the wording of the Islamic Scriptures or with the narratives ascribed to the Islamic Prophet. They therefore hold that descriptors and qualifiers that occur in the Qur'ān and in the canonized religious traditions, even if seeming or sounding humanlike such as "hand", "finger, or "foot", are to be wholly affirmed as attributes of God (not limbs).

Many Sunnites, like the Ash'aris and Maturidis, adhere to some middle path or synthesis between negation and anthropomorphism, though the kind of each combination of negation and affirmation varies greatly.

Judaism

Maimonides, 1138–1204 AD.

Maimonides (1135/1138–1204) was "the most influential medieval Jewish exponent of the via negativa." Maimonides – along with Samuel ibn Tibbon – draws on Bahya ibn Paquda, who shows that our inability to describe God is related to the fact of his absolute unity. God, as the entity which is "truly One" (האחד האמת), must be free of properties and is thus unlike anything else and indescribable. In The Guide for the Perplexed, Maimonides states:

God's existence is absolute and it includes no composition and we comprehend only the fact that He exists, not His essence. Consequently it is a false assumption to hold that He has any positive attribute [...] still less has He accidents (מקרה), which could be described by an attribute. Hence it is clear that He has no positive attribute however, the negative attributes are necessary to direct the mind to the truths which we must believe [...] When we say of this being, that it exists, we mean that its non-existence is impossible; it is living — it is not dead; [...] it is the first — its existence is not due to any cause; it has power, wisdom, and will — it is not feeble or ignorant; He is One — there are not more Gods than one [...] Every attribute predicated of God denotes either the quality of an action, or, when the attribute is intended to convey some idea of the Divine Being itself — and not of His actions — the negation of the opposite.

According to Rabbi Yosef Wineberg, Maimonides stated that "[God] is knowledge," and saw his essence, being, and knowledge as completely one, "a perfect unity and not a composite at all." Wineberg quotes Maimonides as stating:

This [form of unity] wherein G‑d's knowledge and so on is one with G‑d Himself is beyond the capacity of the mouth to express, beyond the capacity of the ear to hear, and beyond the capacity of the heart of man to apprehend clearly.

According to Fagenblat, it is only in the modern period that negative theology really gains importance in Jewish thought. Yeshayahu Leibowitz (1903–1994) was a prominent modern exponent of Jewish negative theology. According to Leibowitz, a person's faith is their commitment to obey God, meaning God's commandments, and this has nothing to do with a person's image of God. This must be so because Leibowitz thought that God cannot be described, that God's understanding is not man's understanding, and thus all the questions asked of God are out of place.

Jacques Derrida

The work of Jewish philosopher Jacques Derrida, and in particular his critical method called deconstruction, has frequently been compared to negative theology, and led to renewed interest in apophaticism in the late 20th century, even among continental philosophers and literary scholars who may not have otherwise have been particularly invested in theological issues. Conversely, the perception that deconstruction resembled or essentially was a form of secular negative theology also – according to Derrida himself – took the form of an accusation from his critics, implicitly positing both negative theology and deconstruction as being elaborate ways of saying nothing of any substance or importance. However, Derrida strongly repudiated this comparison for much of his career, arguing that any resemblance between his thought and apophaticism is purely superficial. Derrida argued that the aims of negative theology – to demonstrate the ultimate, incomprehensible, transcendent reality of God – are a form of ontotheology which runs fundamentally counter to deconstruction's aim of purging Western thought of its pervasive metaphysics of presence.

Later in his career, such in as his essay "Sauf le nom", Derrida comes to see apophatic theology as potentially but not necessarily a means through which the intractable inadequacies of language and the ontological difficulties which proceed from them can brought to our attention and explored:

There is one apophasis that can in effect respond to, correspond to, correspond with the most insatiable desire of God, according to the history and the event of its manifestation or the secret of its non-manifestation. The other apophasis, the other voice, can remain readily foreign to all desire, in any case to every anthropotheomorphic form of desire.

Scholars such as Stephen Shakespeare have noted that – despite Derrida's pervasive concern with many aspects of Jewish theology and identity – his writing on negative theology draws almost exclusively on Christian writing and couches the topic in the language of Christianity generally. Derrida's thought in general, but in particular his later writing on negative theology, was highly influential in the development of the Weak Theology movement, and of postmodern theology as a whole.

David Wood and Robert Bernasconi have highlighted how Derrida explains what deconstruction is in an overwhelmingly negative, "apophatic" fashion.

Indian parallels

Adi Shankara, 788–820 AD.

Early Indian philosophical works which have apophatic themes include the Principal Upanishads (800 BC to the start of the common era) and the Brahma Sutras (from 450 BC and 200 AD). An expression of negative theology is found in the Brihadaranyaka Upanishad, where Brahman is described as "neti neti" or "neither this, nor that". Further use of apophatic theology is found in the Brahma Sutras, which state:

Whenever we deny something unreal, it is in reference to something real.

Buddhist philosophy has also strongly advocated the way of negation, beginning with the Buddha's own theory of anatta (not-atman, not-self) which denies any truly existent and unchanging essence of a person. Madhyamaka is a Buddhist philosophical school founded by Nagarjuna (2nd–3rd century AD), which is based on a four-fold negation of all assertions and concepts and promotes the theory of emptiness (shunyata). Apophatic assertions are also an important feature of Mahayana sutras, especially the prajñaparamita genre. These currents of negative theology are visible in all forms of Buddhism.

Apophatic movements in medieval Hindu philosophy are visible in the works of Shankara (8th century), a philosopher of Advaita Vedanta (non-dualism), and Bhartṛhari (5th century), a grammarian. While Shankara holds that the transcendent noumenon, Brahman, is realized by the means of negation of every phenomenon including language, Bhartṛhari theorizes that language has both phenomenal and noumenal dimensions, the latter of which manifests Brahman.

In Advaita, Brahman is defined as being Nirguna or without qualities. Anything imaginable or conceivable is not deemed to be the ultimate reality. The Taittiriya hymn speaks of Brahman as "one where the mind does not reach". Yet the Hindu scriptures often speak of Brahman's positive aspect. For instance, Brahman is often equated with bliss. These contradictory descriptions of Brahman are used to show that the attributes of Brahman are similar to ones experienced by mortals, but not the same.

Negative theology also figures in the Buddhist and Hindu polemics. The arguments go something like this – Is Brahman an object of experience? If so, how do you convey this experience to others who have not had a similar experience? The only way possible is to relate this unique experience to common experiences while explicitly negating their sameness.

Bahá'í Faith

Bahá'í's believe that God is an ultimately unknowable being (see God in the Baháʼí Faith) and Bahá'í writings state that "there can be no tie of direct intercourse to bind the one true God with His creation, and no resemblance whatever can exist between the transient and the Eternal, the contingent and the Absolute."

According to the Bahá'í Faith, the only way to grow nearer to God is to gain knowledge of the Manifestation of God, who is a reflection of God's reality in a similar way to how a mirror reflects an image of the sun. Stephen Lambden has written a paper entitled, The Background and Centrality of Apophatic Theology in Bábí and Bahá'í Scripture and Ian Kluge has also looked into the Apophatic Theology and the Baha'i faith in the second part of his paper, Neoplatonism and the Bahá'í Writings.

Apophatic theology and atheism

Even though the via negativa essentially rejects theological understanding in and of itself as a path to God, some have sought to make it into an intellectual exercise, by describing God only in terms of what God is not. One problem noted with this approach is that there seems to be no fixed basis on deciding what God is not, unless the Divine is understood as an abstract experience of full aliveness unique to each individual consciousness, and universally, the perfect goodness applicable to the whole field of reality. Apophatic theology is often accused of being a version of atheism or agnosticism, since it cannot say truly that God exists. "The comparison is crude, however, for conventional atheism treats the existence of God as a predicate that can be denied ("God is nonexistent"), whereas negative theology denies that God has predicates". "God or the Divine is" without being able to attribute qualities about "what He is" would be the prerequisite of positive theology in negative theology that distinguishes theism from atheism. "Negative theology is a complement to, not the enemy of, positive theology". Since religious experience—or consciousness of the holy or sacred, is not reducible to other kinds of human experience, an abstract understanding of religious experience cannot be used as evidence or proof that religious discourse or praxis can have no meaning or value. In apophatic theology, the negation of theisms in the via negativa also requires the negation of their correlative atheisms if the dialectical method it employs is to maintain integrity.

Tuesday, October 29, 2024

Conservation of energy

From Wikipedia, the free encyclopedia
 
The law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time. In the case of a closed system the principle says that the total amount of energy within the system can only be changed through energy entering or leaving the system. Energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another. For instance, chemical energy is converted to kinetic energy when a stick of dynamite explodes. If one adds up all forms of energy that were released in the explosion, such as the kinetic energy and potential energy of the pieces, as well as heat and sound, one will get the exact decrease of chemical energy in the combustion of the dynamite.

Classically, conservation of energy was distinct from conservation of mass. However, special relativity shows that mass is related to energy and vice versa by , the equation representing mass–energy equivalence, and science now takes the view that mass-energy as a whole is conserved. Theoretically, this implies that any object with mass can itself be converted to pure energy, and vice versa. However, this is believed to be possible only under the most extreme of physical conditions, such as likely existed in the universe very shortly after the Big Bang or when black holes emit Hawking radiation.

Given the stationary-action principle, conservation of energy can be rigorously proven by Noether's theorem as a consequence of continuous time translation symmetry; that is, from the fact that the laws of physics do not change over time.

A consequence of the law of conservation of energy is that a perpetual motion machine of the first kind cannot exist; that is to say, no system without an external energy supply can deliver an unlimited amount of energy to its surroundings. Depending on the definition of energy, conservation of energy can arguably be violated by general relativity on the cosmological scale.

History

Ancient philosophers as far back as Thales of Miletus c. 550 BCE had inklings of the conservation of some underlying substance of which everything is made. However, there is no particular reason to identify their theories with what we know today as "mass-energy" (for example, Thales thought it was water). Empedocles (490–430 BCE) wrote that in his universal system, composed of four roots (earth, air, water, fire), "nothing comes to be or perishes"; instead, these elements suffer continual rearrangement. Epicurus (c. 350 BCE) on the other hand believed everything in the universe to be composed of indivisible units of matter—the ancient precursor to 'atoms'—and he too had some idea of the necessity of conservation, stating that "the sum total of things was always such as it is now, and such it will ever remain."

In 1605, the Flemish scientist Simon Stevin was able to solve a number of problems in statics based on the principle that perpetual motion was impossible.

In 1639, Galileo published his analysis of several situations—including the celebrated "interrupted pendulum"—which can be described (in modern language) as conservatively converting potential energy to kinetic energy and back again. Essentially, he pointed out that the height a moving body rises is equal to the height from which it falls, and used this observation to infer the idea of inertia. The remarkable aspect of this observation is that the height to which a moving body ascends on a frictionless surface does not depend on the shape of the surface.

In 1669, Christiaan Huygens published his laws of collision. Among the quantities he listed as being invariant before and after the collision of bodies were both the sum of their linear momenta as well as the sum of their kinetic energies. However, the difference between elastic and inelastic collision was not understood at the time. This led to the dispute among later researchers as to which of these conserved quantities was the more fundamental. In his Horologium Oscillatorium, he gave a much clearer statement regarding the height of ascent of a moving body, and connected this idea with the impossibility of perpetual motion. Huygens's study of the dynamics of pendulum motion was based on a single principle: that the center of gravity of a heavy object cannot lift itself.

Gottfried Leibniz

Between 1676 and 1689, Gottfried Leibniz first attempted a mathematical formulation of the kind of energy that is associated with motion (kinetic energy). Using Huygens's work on collision, Leibniz noticed that in many mechanical systems (of several masses mi, each with velocity vi),

was conserved so long as the masses did not interact. He called this quantity the vis viva or living force of the system. The principle represents an accurate statement of the approximate conservation of kinetic energy in situations where there is no friction. Many physicists at that time, including Isaac Newton, held that the conservation of momentum, which holds even in systems with friction, as defined by the momentum:

was the conserved vis viva. It was later shown that both quantities are conserved simultaneously given the proper conditions, such as in an elastic collision.

In 1687, Isaac Newton published his Principia, which set out his laws of motion. It was organized around the concept of force and momentum. However, the researchers were quick to recognize that the principles set out in the book, while fine for point masses, were not sufficient to tackle the motions of rigid and fluid bodies. Some other principles were also required.

By the 1690s, Leibniz was arguing that conservation of vis viva and conservation of momentum undermined the then-popular philosophical doctrine of interactionist dualism. (During the 19th century, when conservation of energy was better understood, Leibniz's basic argument would gain widespread acceptance. Some modern scholars continue to champion specifically conservation-based attacks on dualism, while others subsume the argument into a more general argument about causal closure.)

Daniel Bernoulli

The law of conservation of vis viva was championed by the father and son duo, Johann and Daniel Bernoulli. The former enunciated the principle of virtual work as used in statics in its full generality in 1715, while the latter based his Hydrodynamica, published in 1738, on this single vis viva conservation principle. Daniel's study of loss of vis viva of flowing water led him to formulate the Bernoulli's principle, which asserts the loss to be proportional to the change in hydrodynamic pressure. Daniel also formulated the notion of work and efficiency for hydraulic machines; and he gave a kinetic theory of gases, and linked the kinetic energy of gas molecules with the temperature of the gas.

This focus on the vis viva by the continental physicists eventually led to the discovery of stationarity principles governing mechanics, such as the D'Alembert's principle, Lagrangian, and Hamiltonian formulations of mechanics.

Emilie du Chatelet

Émilie du Châtelet (1706–1749) proposed and tested the hypothesis of the conservation of total energy, as distinct from momentum. Inspired by the theories of Gottfried Leibniz, she repeated and publicized an experiment originally devised by Willem 's Gravesande in 1722 in which balls were dropped from different heights into a sheet of soft clay. Each ball's kinetic energy—as indicated by the quantity of material displaced—was shown to be proportional to the square of the velocity. The deformation of the clay was found to be directly proportional to the height from which the balls were dropped, equal to the initial potential energy. Some earlier workers, including Newton and Voltaire, had believed that "energy" was not distinct from momentum and therefore proportional to velocity. According to this understanding, the deformation of the clay should have been proportional to the square root of the height from which the balls were dropped. In classical physics, the correct formula is , where is the kinetic energy of an object, its mass and its speed. On this basis, du Châtelet proposed that energy must always have the same dimensions in any form, which is necessary to be able to consider it in different forms (kinetic, potential, heat, ...).

Engineers such as John Smeaton, Peter Ewart, Carl Holtzmann [de; ar], Gustave-Adolphe Hirn, and Marc Seguin recognized that conservation of momentum alone was not adequate for practical calculation and made use of Leibniz's principle. The principle was also championed by some chemists such as William Hyde Wollaston. Academics such as John Playfair were quick to point out that kinetic energy is clearly not conserved. This is obvious to a modern analysis based on the second law of thermodynamics, but in the 18th and 19th centuries, the fate of the lost energy was still unknown.

Gradually it came to be suspected that the heat inevitably generated by motion under friction was another form of vis viva. In 1783, Antoine Lavoisier and Pierre-Simon Laplace reviewed the two competing theories of vis viva and caloric theory. Count Rumford's 1798 observations of heat generation during the boring of cannons added more weight to the view that mechanical motion could be converted into heat and (that it was important) that the conversion was quantitative and could be predicted (allowing for a universal conversion constant between kinetic energy and heat). Vis viva then started to be known as energy, after the term was first used in that sense by Thomas Young in 1807.

Gaspard-Gustave Coriolis

The recalibration of vis viva to

which can be understood as converting kinetic energy to work, was largely the result of Gaspard-Gustave Coriolis and Jean-Victor Poncelet over the period 1819–1839. The former called the quantity quantité de travail (quantity of work) and the latter, travail mécanique (mechanical work), and both championed its use in engineering calculations.

In the paper Über die Natur der Wärme (German "On the Nature of Heat/Warmth"), published in the Zeitschrift für Physik in 1837, Karl Friedrich Mohr gave one of the earliest general statements of the doctrine of the conservation of energy: "besides the 54 known chemical elements there is in the physical world one agent only, and this is called Kraft [energy or work]. It may appear, according to circumstances, as motion, chemical affinity, cohesion, electricity, light and magnetism; and from any one of these forms it can be transformed into any of the others."

Mechanical equivalent of heat

A key stage in the development of the modern conservation principle was the demonstration of the mechanical equivalent of heat. The caloric theory maintained that heat could neither be created nor destroyed, whereas conservation of energy entails the contrary principle that heat and mechanical work are interchangeable.

In the middle of the eighteenth century, Mikhail Lomonosov, a Russian scientist, postulated his corpusculo-kinetic theory of heat, which rejected the idea of a caloric. Through the results of empirical studies, Lomonosov came to the conclusion that heat was not transferred through the particles of the caloric fluid.

In 1798, Count Rumford (Benjamin Thompson) performed measurements of the frictional heat generated in boring cannons and developed the idea that heat is a form of kinetic energy; his measurements refuted caloric theory, but were imprecise enough to leave room for doubt.

James Prescott Joule

The mechanical equivalence principle was first stated in its modern form by the German surgeon Julius Robert von Mayer in 1842. Mayer reached his conclusion on a voyage to the Dutch East Indies, where he found that his patients' blood was a deeper red because they were consuming less oxygen, and therefore less energy, to maintain their body temperature in the hotter climate. He discovered that heat and mechanical work were both forms of energy, and in 1845, after improving his knowledge of physics, he published a monograph that stated a quantitative relationship between them.

Joule's apparatus for measuring the mechanical equivalent of heat. A descending weight attached to a string causes a paddle immersed in water to rotate.

Meanwhile, in 1843, James Prescott Joule independently discovered the mechanical equivalent in a series of experiments. In one of them, now called the "Joule apparatus", a descending weight attached to a string caused a paddle immersed in water to rotate. He showed that the gravitational potential energy lost by the weight in descending was equal to the internal energy gained by the water through friction with the paddle.

Over the period 1840–1843, similar work was carried out by engineer Ludwig A. Colding, although it was little known outside his native Denmark.

Both Joule's and Mayer's work suffered from resistance and neglect but it was Joule's that eventually drew the wider recognition.

In 1844, the Welsh scientist William Robert Grove postulated a relationship between mechanics, heat, light, electricity, and magnetism by treating them all as manifestations of a single "force" (energy in modern terms). In 1846, Grove published his theories in his book The Correlation of Physical Forces. In 1847, drawing on the earlier work of Joule, Sadi Carnot, and Émile Clapeyron, Hermann von Helmholtz arrived at conclusions similar to Grove's and published his theories in his book Über die Erhaltung der Kraft (On the Conservation of Force, 1847). The general modern acceptance of the principle stems from this publication.

In 1850, the Scottish mathematician William Rankine first used the phrase the law of the conservation of energy for the principle.

In 1877, Peter Guthrie Tait claimed that the principle originated with Sir Isaac Newton, based on a creative reading of propositions 40 and 41 of the Philosophiae Naturalis Principia Mathematica. This is now regarded as an example of Whig history.

Mass–energy equivalence

Matter is composed of atoms and what makes up atoms. Matter has intrinsic or rest mass. In the limited range of recognized experience of the nineteenth century, it was found that such rest mass is conserved. Einstein's 1905 theory of special relativity showed that rest mass corresponds to an equivalent amount of rest energy. This means that rest mass can be converted to or from equivalent amounts of (non-material) forms of energy, for example, kinetic energy, potential energy, and electromagnetic radiant energy. When this happens, as recognized in twentieth-century experience, rest mass is not conserved, unlike the total mass or total energy. All forms of energy contribute to the total mass and total energy.

For example, an electron and a positron each have rest mass. They can perish together, converting their combined rest energy into photons which have electromagnetic radiant energy but no rest mass. If this occurs within an isolated system that does not release the photons or their energy into the external surroundings, then neither the total mass nor the total energy of the system will change. The produced electromagnetic radiant energy contributes just as much to the inertia (and to any weight) of the system as did the rest mass of the electron and positron before their demise. Likewise, non-material forms of energy can perish into matter, which has rest mass.

Thus, conservation of energy (total, including material or rest energy) and conservation of mass (total, not just rest) are one (equivalent) law. In the 18th century, these had appeared as two seemingly-distinct laws.

Conservation of energy in beta decay

The discovery in 1911 that electrons emitted in beta decay have a continuous rather than a discrete spectrum appeared to contradict conservation of energy, under the then-current assumption that beta decay is the simple emission of an electron from a nucleus. This problem was eventually resolved in 1933 by Enrico Fermi who proposed the correct description of beta-decay as the emission of both an electron and an antineutrino, which carries away the apparently missing energy.

First law of thermodynamics

For a closed thermodynamic system, the first law of thermodynamics may be stated as:

, or equivalently,

where is the quantity of energy added to the system by a heating process, is the quantity of energy lost by the system due to work done by the system on its surroundings, and is the change in the internal energy of the system.

The δ's before the heat and work terms are used to indicate that they describe an increment of energy which is to be interpreted somewhat differently than the increment of internal energy (see Inexact differential). Work and heat refer to kinds of process which add or subtract energy to or from a system, while the internal energy is a property of a particular state of the system when it is in unchanging thermodynamic equilibrium. Thus the term "heat energy" for means "that amount of energy added as a result of heating" rather than referring to a particular form of energy. Likewise, the term "work energy" for means "that amount of energy lost as a result of work". Thus one can state the amount of internal energy possessed by a thermodynamic system that one knows is presently in a given state, but one cannot tell, just from knowledge of the given present state, how much energy has in the past flowed into or out of the system as a result of its being heated or cooled, nor as a result of work being performed on or by the system.

Entropy is a function of the state of a system which tells of limitations of the possibility of conversion of heat into work.

For a simple compressible system, the work performed by the system may be written:

where is the pressure and is a small change in the volume of the system, each of which are system variables. In the fictive case in which the process is idealized and infinitely slow, so as to be called quasi-static, and regarded as reversible, the heat being transferred from a source with temperature infinitesimally above the system temperature, the heat energy may be written

where is the temperature and is a small change in the entropy of the system. Temperature and entropy are variables of the state of a system.

If an open system (in which mass may be exchanged with the environment) has several walls such that the mass transfer is through rigid walls separate from the heat and work transfers, then the first law may be written as

where is the added mass of species and is the corresponding enthalpy per unit mass. Note that generally in this case, as matter carries its own entropy. Instead, , where is the entropy per unit mass of type , from which we recover the fundamental thermodynamic relation

because the chemical potential is the partial molar Gibbs free energy of species and the Gibbs free energy .

Noether's theorem

Emmy Noether (1882-1935) was an influential mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics.

The conservation of energy is a common feature in many physical theories. From a mathematical point of view it is understood as a consequence of Noether's theorem, developed by Emmy Noether in 1915 and first published in 1918. In any physical theory that obeys the stationary-action principle, the theorem states that every continuous symmetry has an associated conserved quantity; if the theory's symmetry is time invariance, then the conserved quantity is called "energy". The energy conservation law is a consequence of the shift symmetry of time; energy conservation is implied by the empirical fact that the laws of physics do not change with time itself. Philosophically this can be stated as "nothing depends on time per se". In other words, if the physical system is invariant under the continuous symmetry of time translation, then its energy (which is the canonical conjugate quantity to time) is conserved. Conversely, systems that are not invariant under shifts in time (e.g. systems with time-dependent potential energy) do not exhibit conservation of energy – unless we consider them to exchange energy with another, external system so that the theory of the enlarged system becomes time-invariant again. Conservation of energy for finite systems is valid in physical theories such as special relativity and quantum theory (including QED) in the flat space-time.

Special relativity

With the discovery of special relativity by Henri Poincaré and Albert Einstein, the energy was proposed to be a component of an energy-momentum 4-vector. Each of the four components (one of energy and three of momentum) of this vector is separately conserved across time, in any closed system, as seen from any given inertial reference frame. Also conserved is the vector length (Minkowski norm), which is the rest mass for single particles, and the invariant mass for systems of particles (where momenta and energy are separately summed before the length is calculated).

The relativistic energy of a single massive particle contains a term related to its rest mass in addition to its kinetic energy of motion. In the limit of zero kinetic energy (or equivalently in the rest frame) of a massive particle, or else in the center of momentum frame for objects or systems which retain kinetic energy, the total energy of a particle or object (including internal kinetic energy in systems) is proportional to the rest mass or invariant mass, as described by the equation .

Thus, the rule of conservation of energy over time in special relativity continues to hold, so long as the reference frame of the observer is unchanged. This applies to the total energy of systems, although different observers disagree as to the energy value. Also conserved, and invariant to all observers, is the invariant mass, which is the minimal system mass and energy that can be seen by any observer, and which is defined by the energy–momentum relation.

General relativity

General relativity introduces new phenomena. In an expanding universe, photons spontaneously redshift and tethers spontaneously gain tension; if vacuum energy is positive, the total vacuum energy of the universe appears to spontaneously increase as the volume of space increases. Some scholars claim that energy is no longer meaningfully conserved in any identifiable form.

John Baez's view is that energy–momentum conservation is not well-defined except in certain special cases. Energy-momentum is typically expressed with the aid of a stress–energy–momentum pseudotensor. However, since pseudotensors are not tensors, they do not transform cleanly between reference frames. If the metric under consideration is static (that is, does not change with time) or asymptotically flat (that is, at an infinite distance away spacetime looks empty), then energy conservation holds without major pitfalls. In practice, some metrics, notably the Friedmann–Lemaître–Robertson–Walker metric that appears to govern the universe, do not satisfy these constraints and energy conservation is not well defined. Besides being dependent on the coordinate system, pseudotensor energy is dependent on the type of pseudotensor in use; for example, the energy exterior to a Kerr–Newman black hole is twice as large when calculated from Møller's pseudotensor as it is when calculated using the Einstein pseudotensor.

For asymptotically flat universes, Einstein and others salvage conservation of energy by introducing a specific global gravitational potential energy that cancels out mass-energy changes triggered by spacetime expansion or contraction. This global energy has no well-defined density and cannot technically be applied to a non-asymptotically flat universe; however, for practical purposes this can be finessed, and so by this view, energy is conserved in our universe. Alan Guth stated that the universe might be "the ultimate free lunch", and theorized that, when accounting for gravitational potential energy, the net energy of the Universe is zero.

Quantum theory

In quantum mechanics, the energy of a quantum system is described by a self-adjoint (or Hermitian) operator called the Hamiltonian, which acts on the Hilbert space (or a space of wave functions) of the system. If the Hamiltonian is a time-independent operator, emergence probability of the measurement result does not change in time over the evolution of the system. Thus the expectation value of energy is also time independent. The local energy conservation in quantum field theory is ensured by the quantum Noether's theorem for the energy-momentum tensor operator. Thus energy is conserved by the normal unitary evolution of a quantum system.

However, when the non-unitary Born rule is applied, the system's energy is measured with an energy that can be below or above the expectation value, if the system was not in an energy eigenstate. (For macroscopic systems, this effect is usually too small to measure.) The disposition of this energy gap is not well-understood; most physicists believe that the energy is transferred to or from the macroscopic environment in the course of the measurement process, while others believe that the observable energy is only conserved "on average". No experiment has been confirmed as definitive evidence of violations of the conservation of energy principle in quantum mechanics, but that does not rule out that some newer experiments, as proposed, may find evidence of violations of the conservation of energy principle in quantum mechanics.

Status

In the context of perpetual motion machines such as the Orbo, Professor Eric Ash has argued at the BBC: "Denying [conservation of energy] would undermine not just little bits of science - the whole edifice would be no more. All of the technology on which we built the modern world would lie in ruins". It is because of conservation of energy that "we know - without having to examine details of a particular device - that Orbo cannot work."

Energy conservation has been a foundational physical principle for about two hundred years. From the point of view of modern general relativity, the lab environment can be well approximated by Minkowski spacetime, where energy is exactly conserved. The entire Earth can be well approximated by the Schwarzschild metric, where again energy is exactly conserved. Given all the experimental evidence, any new theory (such as quantum gravity), in order to be successful, will have to explain why energy has appeared to always be exactly conserved in terrestrial experiments. In some speculative theories, corrections to quantum mechanics are too small to be detected at anywhere near the current TeV level accessible through particle accelerators. Doubly special relativity models may argue for a breakdown in energy-momentum conservation for sufficiently energetic particles; such models are constrained by observations that cosmic rays appear to travel for billions of years without displaying anomalous non-conservation behavior. Some interpretations of quantum mechanics claim that observed energy tends to increase when the Born rule is applied due to localization of the wave function. If true, objects could be expected to spontaneously heat up; thus, such models are constrained by observations of large, cool astronomical objects as well as the observation of (often supercooled) laboratory experiments.

Milton A. Rothman wrote that the law of conservation of energy has been verified by nuclear physics experiments to an accuracy of one part in a thousand million million (1015). He then defines its precision as "perfect for all practical purposes".

Introduction to entropy

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