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Eternal return

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Eternal return is a concept which posits that the universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...

 has been recurring, and will continue to recur, in a self-similar form an infinite
Infinity
Infinity is a concept in many fields, most predominantly mathematics and physics, that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity...

 number of times across infinite time or space. The concept initially inherent in Indian philosophy
Indian philosophy
India has a rich and diverse philosophical tradition dating back to ancient times. According to Radhakrishnan, the earlier Upanisads constitute "...the earliest philosophical compositions of the world."...

 was later found in ancient Egypt
Ancient Egypt
Ancient Egypt was an ancient civilization of Northeastern Africa, concentrated along the lower reaches of the Nile River in what is now the modern country of Egypt. Egyptian civilization coalesced around 3150 BC with the political unification of Upper and Lower Egypt under the first pharaoh...

, and was subsequently taken up by the Pythagoreans and Stoics. With the decline of antiquity
Classical antiquity
Classical antiquity is a broad term for a long period of cultural history centered on the Mediterranean Sea, comprising the interlocking civilizations of ancient Greece and ancient Rome, collectively known as the Greco-Roman world...

 and the spread of Christianity
Christianity
Christianity is a monotheistic religion based on the life and teachings of Jesus as presented in canonical gospels and other New Testament writings...

, the concept fell into disuse in the western world
Western world
The Western world, also known as the West and the Occident , is a term referring to the countries of Western Europe , the countries of the Americas, as well all countries of Northern and Central Europe, Australia and New Zealand...

, though Friedrich Nietzsche resurrected it as a thought experiment to argue for amor fati
Amor fati
Amor fati is a Latin phrase loosely translating to "love of fate" or "love of one's fate". It is used to describe an attitude in which one sees everything that happens in one's life, including suffering and loss, as good...

.

In addition, the philosophical concept of eternal recurrence was addressed by Arthur Schopenhauer
Arthur Schopenhauer
Arthur Schopenhauer was a German philosopher known for his pessimism and philosophical clarity. At age 25, he published his doctoral dissertation, On the Fourfold Root of the Principle of Sufficient Reason, which examined the four separate manifestations of reason in the phenomenal...

. It is a purely physical
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

 concept, involving no supernatural reincarnation
Reincarnation
Reincarnation best describes the concept where the soul or spirit, after the death of the body, is believed to return to live in a new human body, or, in some traditions, either as a human being, animal or plant...

, but the return of beings in the same bodies. Time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

 is viewed as being not linear
Linear
In mathematics, a linear map or function f is a function which satisfies the following two properties:* Additivity : f = f + f...

 but cyclical
Wheel of time
The Wheel of time or wheel of history is a concept found in several religious traditions and philosophies, notably religions of Indian origin such as Hinduism and Buddhism, which regard time as cyclical and consisting of repeating ages...

.

Premise


The basic premise proceeds from the assumption that the probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

 of a world coming into existence exactly like our own is finite. If either time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

 or space
Space
Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum...

 are infinite then mathematics tells us that our existence will recur an infinite number of times.

In 1871, Louis Auguste Blanqui
Louis Auguste Blanqui
Louis Auguste Blanqui was a French political activist, notable for the revolutionary theory of Blanquism, attributed to him....

, assuming a Newtonian cosmology where time and space are infinite proceeded to show that the eternal recurrence was a mathematical certainty. In the post-Einstein period, there are doubts that time or space is in fact infinite, but many models exist which provide the notion of spatial or temporal infinity required by the eternal return hypothesis.

The oscillatory universe model in physics could be provided as an example of how the universe cycles through the same events infinitely. Stephen Hawking
Stephen Hawking
Stephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...

's concept "arrow of time
Arrow of time
The arrow of time, or time’s arrow, is a term coined in 1927 by the British astronomer Arthur Eddington to describe the "one-way direction" or "asymmetry" of time...

", for example, discuss cosmology as proceeding up to a certain point, after which it undergoes a time reversal
Time reversal
Time reversal may refer to:* In physics, T-symmetry - the study of thermodynamics and the symmetry of certain physical laws where the concept of time is reversed — ie...

 (which, as a consequence of T-symmetry
T-symmetry
T Symmetry is the symmetry of physical laws under a time reversal transformation: T: t \mapsto -t.Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics.Time asymmetries...

, is thought to bring about a chaotic state due to entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...

). Hawking and J. Richard Gott
J. Richard Gott
John Richard Gott III is a professor of astrophysical sciences at Princeton University. He is known for developing and advocating two cosmological theories with the flavor of science fiction: Time travel and the Doomsday argument.- Exotic matter time travel theories :Paul Davies's bestseller How...

 have also proposed models by which a (or the) universe could undergo time travel
Time travel
Time travel is the concept of moving between different points in time in a manner analogous to moving between different points in space. Time travel could hypothetically involve moving backward in time to a moment earlier than the starting point, or forward to the future of that point without the...

, provided the balance between mass and energy created the appropriate cosmological geometry.

Multiverse hypotheses in physics describe models where space or time is infinite, although local universes with their own big bangs could be finite space-time bubbles.

Indian religions


The concept of cyclical patterns is very prominent in Indian religions, predominantly in Jainism
Jainism
Jainism is an Indian religion that prescribes a path of non-violence towards all living beings. Its philosophy and practice emphasize the necessity of self-effort to move the soul towards divine consciousness and liberation. Any soul that has conquered its own inner enemies and achieved the state...

 and inclusive of Hinduism
Hinduism
Hinduism is the predominant and indigenous religious tradition of the Indian Subcontinent. Hinduism is known to its followers as , amongst many other expressions...

 and Buddhism
Buddhism
Buddhism is a religion and philosophy encompassing a variety of traditions, beliefs and practices, largely based on teachings attributed to Siddhartha Gautama, commonly known as the Buddha . The Buddha lived and taught in the northeastern Indian subcontinent some time between the 6th and 4th...

 among others. The wheel of life
Bhavacakra
The bhavacakra is a symbolic representation of samsara found on the outside walls of Tibetan Buddhist temples and monasteries in the Indo-Tibet region...

 represents an endless cycle of birth, life, and death from which one seeks liberation. In Tantric Buddhism, a wheel of time
Wheel of time
The Wheel of time or wheel of history is a concept found in several religious traditions and philosophies, notably religions of Indian origin such as Hinduism and Buddhism, which regard time as cyclical and consisting of repeating ages...

 concept known as the Kalachakra
Kalachakra
Kalachakra is a Sanskrit term used in Tantric Buddhism that literally means "time-wheel" or "time-cycles".The spelling Kalacakra is also correct....

 expresses the idea of an endless cycle of existence and knowledge.

However it is to be noted that the cycle of life in Buddhism does not involve a soul passing from one body to another, but the karma of the deceased being carrying on to another being born. To get rid of this cycle the person should get rid of its karma through the attainment of enlightenment. (See: Rebirth (Buddhism)
Rebirth (Buddhism)
Rebirth in Buddhism is the doctrine that the evolving consciousness or stream of consciousness upon death , becomes one of the contributing causes for the arising of a new aggregation...

).

Classical antiquity


In ancient Egypt
Ancient Egypt
Ancient Egypt was an ancient civilization of Northeastern Africa, concentrated along the lower reaches of the Nile River in what is now the modern country of Egypt. Egyptian civilization coalesced around 3150 BC with the political unification of Upper and Lower Egypt under the first pharaoh...

, the scarab (or dung beetle
Dung beetle
Dung beetles are beetles that feed partly or exclusively on feces. All of these species belong to the superfamily Scarabaeoidea; most of them to the subfamilies Scarabaeinae and Aphodiinae of the family Scarabaeidae. This beetle can also be referred to as the scarab beetle. As most species of...

) was viewed as a sign of eternal renewal and reemergence of life, a reminder of the life to come. (See also "Atum
Atum
Atum, sometimes rendered as Atem or Tem, is an important deity in Egyptian mythology.- Name :Atum's name is thought to be derived from the word 'tem' which means to complete or finish. Thus he has been interpreted as being the 'complete one' and also the finisher of the world, which he returns to...

" and "Ma'at.")

The ancient Mayans and Aztecs
Aztec calendar
The Aztec calendar is the calendar system that was used by the Aztecs as well as other Pre-Columbian peoples of central Mexico. It is one of the Mesoamerican calendars, sharing the basic structure of calendars from throughout ancient Mesoamerica....

 also took a cyclical view of time.

In ancient Greece
Ancient Greece
Ancient Greece is a civilization belonging to a period of Greek history that lasted from the Archaic period of the 8th to 6th centuries BC to the end of antiquity. Immediately following this period was the beginning of the Early Middle Ages and the Byzantine era. Included in Ancient Greece is the...

, the concept of eternal return was connected with Empedocles
Empedocles
Empedocles was a Greek pre-Socratic philosopher and a citizen of Agrigentum, a Greek city in Sicily. Empedocles' philosophy is best known for being the originator of the cosmogenic theory of the four Classical elements...

, Zeno of Citium
Zeno of Citium
Zeno of Citium was a Greek philosopher from Citium . Zeno was the founder of the Stoic school of philosophy, which he taught in Athens from about 300 BC. Based on the moral ideas of the Cynics, Stoicism laid great emphasis on goodness and peace of mind gained from living a life of virtue in...

, and Stoicism
Stoicism
Stoicism is a school of Hellenistic philosophy founded in Athens by Zeno of Citium in the early . The Stoics taught that destructive emotions resulted from errors in judgment, and that a sage, or person of "moral and intellectual perfection," would not suffer such emotions.Stoics were concerned...

.

Judaism


Judaism
Judaism
Judaism ) is the "religion, philosophy, and way of life" of the Jewish people...

 posits a creation "In the beginning" and a messianic "end of days," which mean Judaism has a linear, not a cyclical, view of time. But cyclical time and return are reflected in Jewish traditions such as: The history of the Jewish people is said to be repeating events in the lives of its biblical forefathers; people’s lives in the next world, or after death, are to some extent spiritual repetitions of what they did in this world; and some kabbalists wrote that time is composed of seven cycles, which repeat every seven thousand years (a view rejected by Isaac Luria
Isaac Luria
Isaac Luria , also called Yitzhak Ben Shlomo Ashkenazi acronym "The Ari" "Ari-Hakadosh", or "Arizal", meaning "The Lion", was a foremost rabbi and Jewish mystic in the community of Safed in the Galilee region of Ottoman Palestine...

). These concepts give events and human choices some of the eternal return’s infinite weight.

Renaissance



The symbol of the Ouroboros
Ouroboros
The Ouroboros is an ancient symbol depicting a serpent or dragon eating its own tail. The name originates from within Greek language; οὐρά meaning "tail" and βόρος meaning "eating", thus "he who eats the tail"....

, the snake
Snake
Snakes are elongate, legless, carnivorous reptiles of the suborder Serpentes that can be distinguished from legless lizards by their lack of eyelids and external ears. Like all squamates, snakes are ectothermic, amniote vertebrates covered in overlapping scales...

 or dragon
Dragon
A dragon is a legendary creature, typically with serpentine or reptilian traits, that feature in the myths of many cultures. There are two distinct cultural traditions of dragons: the European dragon, derived from European folk traditions and ultimately related to Greek and Middle Eastern...

 devouring its own tail, is the alchemical symbol par excellence of eternal recurrence, possibly borrowed from the Norse concept of Jörmungandr
Jörmungandr
In Norse mythology, Jörmungandr , mostly known as Jormungand, orJörmungand , or Midgard Serpent , or World Serpent, is a sea serpent, and the middle child of the giantess Angrboða and the god Loki...

 or the Midgard Serpent. The alchemist-physicians of the Renaissance and Reformation were aware of the idea of eternal recurrence; the physician-philosopher Sir Thomas Browne
Thomas Browne
Sir Thomas Browne was an English author of varied works which reveal his wide learning in diverse fields including medicine, religion, science and the esoteric....

 in his A Letter to a Friend
A Letter to a Friend
A Letter to a Friend , by the 17th century philosopher and physician Sir Thomas Browne is a medical treatise of case-histories and witty speculations upon the human condition.-External links:*...

 circa 1657 linked the Uroboros symbol with the idea of eternal return thus -

that the first day should make the last, that the Tail of the Snake should return into its Mouth precisely at that time, and they should wind up upon the day of their Nativity, is indeed a remarkable Coincidence, which tho Astrology hath taken witty pains to salve, yet hath it been very wary in making Predictions of it.

An allusion to eternal recurrence also occurs at the conclusion of Browne's The Garden of Cyrus
The Garden of Cyrus
The Garden of Cyrus or The Quincunciall Lozenge, or Network Plantations of the Ancients, naturally, artificially, mystically considered is a Discourse written by Sir Thomas Browne. It was first published in 1658, along with its diptych companion, Urn-Burial...

-

All things began in order, so shall they end, and so shall they begin again;

Friedrich Nietzsche


The concept of "eternal recurrence" is central to the writings of Friedrich Nietzsche
Friedrich Nietzsche
Friedrich Wilhelm Nietzsche was a 19th-century German philosopher, poet, composer and classical philologist...

. As Heidegger points out in his lectures on Nietzsche, Nietzsche's first mention of eternal recurrence, in aphorism 341 of The Gay Science
The Gay Science
The Gay Science is a book written by Friedrich Nietzsche, first published in 1882 and followed by a second edition, which was published after the completion of Thus Spoke Zarathustra and Beyond Good and Evil, in 1887. This substantial expansion includes a fifth book and an appendix of songs...

(cited below), presents this concept as a hypothetical question
Thought experiment
A thought experiment or Gedankenexperiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences...

 rather than postulating it as a fact. According to Heidegger, it is the burden imposed by the question of eternal recurrence—whether or not such a thing could possibly be true—that is so significant in modern thought: "The way Nietzsche here patterns the first communication of the thought of the 'greatest burden' [of eternal recurrence] makes it clear that this 'thought of thoughts' is at the same time 'the most burdensome thought.' " The thought of eternal recurrence appears in a few of his works, in particular §285 and §341 of The Gay Science
The Gay Science
The Gay Science is a book written by Friedrich Nietzsche, first published in 1882 and followed by a second edition, which was published after the completion of Thus Spoke Zarathustra and Beyond Good and Evil, in 1887. This substantial expansion includes a fifth book and an appendix of songs...

and then in Thus Spoke Zarathustra
Thus Spoke Zarathustra
Thus Spoke Zarathustra: A Book for All and None is a philosophical novel by German philosopher Friedrich Nietzsche, composed in four parts between 1883 and 1885...

. It is also noted in a posthumous fragment. The origin of this thought is dated by Nietzsche himself, via posthumous fragments, to August 1881, at Sils-Maria
Sils im Engadin/Segl
Sils im Engadin/Segl is a municipality in the district of Maloja in the Swiss canton of Graubünden.-Name and coat of arms:The municipality's name is a combination of the German and Romansh names. Sils im Engadin is the German name while Segl is the Romansh. The coat of arms is Per fess Azure a...

. In Ecce Homo
Ecce Homo (book)
Ecce Homo: How One Becomes What One Is is the title of the last original book written by philosopher Friedrich Nietzsche before his final years of insanity that spanned until his death in 1900...

(1888), he wrote that he thought of the eternal return as the "fundamental conception" of Thus Spoke Zarathustra.

Several authors have pointed out other occurrences of this hypothesis in contemporary thought. Rudolf Steiner
Rudolf Steiner
Rudolf Joseph Lorenz Steiner was an Austrian philosopher, social reformer, architect, and esotericist. He gained initial recognition as a literary critic and cultural philosopher...

, who revised the first catalogue of Nietzsche's personal library in January 1896, pointed out that Nietzsche would have read something similar in Eugen Dühring
Eugen Dühring
Eugen Karl Dühring was a German philosopher and economist, a socialist who was a strong critic of Marxism.-Life and works:...

's Courses on philosophy (1875), which Nietzsche readily criticized. Lou Andreas-Salomé
Lou Andreas-Salomé
Lou Andreas-Salomé was a Russian-born psychoanalyst and author. Her diverse intellectual interests led to friendships with a broad array of distinguished western luminaries, including Nietzsche, Wagner, Freud, and Rilke.- Early years :Lou Salomé was born in St...

 pointed out that Nietzsche referred to ancient cyclical conceptions of time, in particular by the Pythagoreans
Pythagoreanism
Pythagoreanism was the system of esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics. Pythagoreanism originated in the 5th century BCE and greatly influenced Platonism...

, in the Untimely Meditations. Henri Lichtenberger and Charles Andler have pinpointed three works contemporary to Nietzsche which carried on the same hypothesis: J.G. Vogt, Die Kraft. Eine real-monistische Weltanschauung (1878), Auguste Blanqui, L'éternité par les astres (1872) and Gustave Le Bon
Gustave Le Bon
Gustave Le Bon was a French social psychologist, sociologist, and amateur physicist...

, L'homme et les sociétés (1881). Walter Benjamin
Walter Benjamin
Walter Bendix Schönflies Benjamin was a German-Jewish intellectual, who functioned variously as a literary critic, philosopher, sociologist, translator, radio broadcaster and essayist...

 juxtaposes Blanqui and Nietzsche's discussion of eternal recurrence in his unfinished, monumental work The Arcades Project. However, Gustave Le Bon is not quoted anywhere in Nietzsche's manuscripts; and Auguste Blanqui was named only in 1883. Vogt's work, on the other hand, was read by Nietzsche during this summer of 1881 in Sils-Maria. Blanqui is mentioned by Albert Lange in his Geschichte des Materialismus
Geschichte des Materialismus
Geschichte des Materialismus und Kritik seiner Bedeutung in der Gegenwart is a philosophical work by Friedrich Albert Lange, originally written in German and published in October 1865 . Lange vastly extended the second edition published in two volumes in 1873–75...

(History of Materialism), a book closely read by Nietzsche.
The eternal recurrence is also mentioned in passing by the Devil in Part Four, Book XI, Chapter 9 of Dostoevsky's The Brothers Karamazov
The Brothers Karamazov
The Brothers Karamazov is the final novel by the Russian author Fyodor Dostoyevsky. Dostoyevsky spent nearly two years writing The Brothers Karamazov, which was published as a serial in The Russian Messenger and completed in November 1880...

, which is another possible source that Nietzsche may have been drawing upon.

Walter Kaufmann suggests that Nietzsche may have encountered this idea in the works of Heinrich Heine
Heinrich Heine
Christian Johann Heinrich Heine was one of the most significant German poets of the 19th century. He was also a journalist, essayist, and literary critic. He is best known outside Germany for his early lyric poetry, which was set to music in the form of Lieder by composers such as Robert Schumann...

, who once wrote:

[T]ime is infinite, but the things in time, the concrete bodies, are finite. They may indeed disperse into the smallest particles; but these particles, the atoms, have their determinate numbers, and the numbers of the configurations which, all of themselves, are formed out of them is also determinate. Now, however long a time may pass, according to the eternal laws governing the combinations of this eternal play of repetition, all configurations which have previously existed on this earth must yet meet, attract, repulse, kiss, and corrupt each other again...


Nietzsche calls the idea "horrifying and paralyzing", and says that its burden is the "heaviest weight" ("das schwerste Gewicht") imaginable. The wish for the eternal return of all events would mark the ultimate affirmation of life:

What, if some day or night a demon were to steal after you into your loneliest loneliness and say to you: 'This life as you now live it and have lived it, you will have to live once more and innumerable times more' ... Would you not throw yourself down and gnash your teeth and curse the demon who spoke thus? Or have you once experienced a tremendous moment when you would have answered him: 'You are a god and never have I heard anything more divine.' [The Gay Science
The Gay Science
The Gay Science is a book written by Friedrich Nietzsche, first published in 1882 and followed by a second edition, which was published after the completion of Thus Spoke Zarathustra and Beyond Good and Evil, in 1887. This substantial expansion includes a fifth book and an appendix of songs...

, §341]


To comprehend eternal recurrence in his thought, and to not merely come to peace with it but to embrace it, requires amor fati
Amor fati
Amor fati is a Latin phrase loosely translating to "love of fate" or "love of one's fate". It is used to describe an attitude in which one sees everything that happens in one's life, including suffering and loss, as good...

, "love of fate":

My formula for human greatness is amor fati: that one wants to have nothing different, not forward, not backward, not in all eternity. Not merely to bear the necessary, still less to conceal it--all idealism is mendaciousness before the necessary--but to love it.


In Carl Jung's seminar on Thus Spoke Zarathustra
Thus Spoke Zarathustra
Thus Spoke Zarathustra: A Book for All and None is a philosophical novel by German philosopher Friedrich Nietzsche, composed in four parts between 1883 and 1885...

, Jung claims that the dwarf states the idea of the Eternal Return before Zarathustra finishes his argument of the Eternal Return when the dwarf says, "'Everything straight lies,' murmured the dwarf disdainfully. 'All truth is crooked, time itself is a circle.'" However, Zarathustra rebuffs the dwarf in the following paragraph, warning him against over-simplifications.

A late 1880s comment by Nietzsche, "In an infinite period of time, every possible combination would at some time be attained," has been cited to argue that Nietzsche dropped his plans to try to scientifically prove the theory because he realized that if he would have to eventually repeat life as it is, his presumption of infinite time means "he" would also have to "repeat" life differently, since every configuration of atoms and events will occur. Instead, according to this interpretation of Nietzsche, he continued to propound the doctrine for its psychological and philosophical import.

Poincaré recurrence theorem


Related to the concept of eternal return is the Poincaré recurrence theorem
Poincaré recurrence theorem
In mathematics, the Poincaré recurrence theorem states that certain systems will, after a sufficiently long time, return to a state very close to the initial state. The Poincaré recurrence time is the length of time elapsed until the recurrence. The result applies to physical systems in which...

 in mathematics. It states that a system whose dynamics are volume-preserving and which is confined to a finite spatial volume will, after a sufficiently long time, return to an arbitrarily small neighborhood of its initial state. "A sufficiently long time" could be much longer than the predicted lifetime of the observable universe (see 1 E19 s and more).

Modern cosmology


The oscillating universe theory - that the universe will end in a collapse or 'big crunch
Big Crunch
In physical cosmology, the Big Crunch is one possible scenario for the ultimate fate of the universe, in which the metric expansion of space eventually reverses and the universe recollapses, ultimately ending as a black hole singularity.- Overview :...

' followed by another big bang
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

, and so on - dates from 1930. Theoretical physicist Peter Lynds
Peter Lynds
Peter Lynds is a New Zealander who first drew attention in 2003 with the publication of a physics paper about time, mechanics and Zeno's paradoxes....

 suggested a model of eternal recurrence in a 2006 paper. Others have approached the question of eternal recurrence from a physics perspective in different ways, including a hypothesis based on the transactional interpretation
Transactional interpretation
The transactional interpretation of quantum mechanics describes quantum interactions in terms of a standing wave formed by retarded and advanced waves. It was first proposed in 1986 by John G...

 of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

. Other cosmologists such as Massachusetts Institute of Technology
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...

 professor Max Tegmark
Max Tegmark
Max Tegmark is a Swedish-American cosmologist. Tegmark is a professor at the Massachusetts Institute of Technology and belongs to the scientific directorate of the Foundational Questions Institute.-Early life:...

 suggests that if space is sufficiently large and uniform, or infinite as some theories suggest, then identical instances of the history of Earth's entire Hubble volume
Hubble volume
In cosmology, the Hubble volume, or Hubble sphere, is the region of the Universe surrounding an observer beyond which objects recede from the observer at a rate greater than the speed of light, due to the expansion of the Universe....

 occur every so often, simply by chance. Tegmark calculates that our nearest so-called doppelgänger
Doppelgänger
In fiction and folklore, a doppelgänger is a paranormal double of a living person, typically representing evil or misfortune...

, is 1010115 meters away from us (a double exponential function larger than a googolplex). In principle, it would be impossible to scientifically verify an identical Hubble volume. However, it does follow as a fairly straightforward consequence from otherwise unrelated scientific observations and theories. Tegmark suggests that statistical analyses exploiting the anthropic principle
Anthropic principle
In astrophysics and cosmology, the anthropic principle is the philosophical argument that observations of the physical Universe must be compatible with the conscious life that observes it. Some proponents of the argument reason that it explains why the Universe has the age and the fundamental...

 provide an opportunity to test multiverse
Multiverse
The multiverse is the hypothetical set of multiple possible universes that together comprise all of reality.Multiverse may also refer to:-In fiction:* Multiverse , the fictional multiverse used by DC Comics...

 theories in some cases. Generally, science would consider a multiverse theory that posits neither a common point of causation, nor the possibility of interaction between universes, to be an ideal speculation. However, it is a fundamental assumption of cosmology that the universe continues to exist beyond the scope of the observable universe
Observable universe
In Big Bang cosmology, the observable universe consists of the galaxies and other matter that we can in principle observe from Earth in the present day, because light from those objects has had time to reach us since the beginning of the cosmological expansion...

, and that the distribution of matter is everywhere the same at such a large scale (see cosmological principle
Cosmological Principle
In modern physical cosmology, the cosmological principle is the working assumption that observers on Earth do not occupy an unusual or privileged location within the universe as a whole, judged as observers of the physical phenomena produced by uniform and universal laws of physics...

).

Arguments against eternal return


Nietzsche scholar Walter Kaufmann has described an argument originally put forward by Georg Simmel
Georg Simmel
Georg Simmel was a major German sociologist, philosopher, and critic.Simmel was one of the first generation of German sociologists: his neo-Kantian approach laid the foundations for sociological antipositivism, asking 'What is society?' in a direct allusion to Kant's question 'What is nature?',...

, which rebuts the claim that a finite number of states must repeat within an infinite amount of time:

Even if there were exceedingly few things in a finite space in an infinite time, they would not have to repeat in the same configurations. Suppose there were three wheels of equal size, rotating on the same axis, one point marked on the circumference of each wheel, and these three points lined up in one straight line. If the second wheel rotated twice as fast as the first, and if the speed of the third wheel was 1/π of the speed of the first, the initial line-up would never recur.

See also


  • Cyclical pattern
  • Endless knot
    Endless knot
    The endless knot or eternal knot is a symbolic knot and one of the Eight Auspicious Symbols. It is an important cultural marker in places significantly influenced by Tibetan Buddhism such as Tibet, Mongolia, Tuva, Kalmykia, and Buryatia...

  • Ergodic theory
    Ergodic theory
    Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics....

  • Eternal Return (Eliade)
    Eternal return (Eliade)
    The "Eternal return" is, according to the theories of religious historian Mircea Eliade, a belief, expressed in religious behavior, in the ability to return to the mythical age, to become contemporary with the events described in one's myths...

  • Eternalism (philosophy of time)
  • Historic recurrence
    Historic recurrence
    Historic recurrence is the repetition of similar events in history. In the extreme, the concept hypothetically assumes the form of the Doctrine of Eternal Recurrence, which has been written about in various forms since antiquity and was described in the 19th century by Heinrich Heine and Friedrich...

  • Infinite loop
    Infinite loop
    An infinite loop is a sequence of instructions in a computer program which loops endlessly, either due to the loop having no terminating condition, having one that can never be met, or one that causes the loop to start over...

  • Mandala
    Mandala
    Maṇḍala is a Sanskrit word that means "circle". In the Buddhist and Hindu religious traditions their sacred art often takes a mandala form. The basic form of most Hindu and Buddhist mandalas is a square with four gates containing a circle with a center point...

  • Möbius strip
    Möbius strip
    The Möbius strip or Möbius band is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being non-orientable. It can be realized as a ruled surface...

  • Nikolay Danilevsky
  • Ourobouros
  • Poincaré recurrence theorem
    Poincaré recurrence theorem
    In mathematics, the Poincaré recurrence theorem states that certain systems will, after a sufficiently long time, return to a state very close to the initial state. The Poincaré recurrence time is the length of time elapsed until the recurrence. The result applies to physical systems in which...

  • Universal Function