Fatalism

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Fatalism 

Destiny, painting by T. C. Gotch (1885–1886), Adelaide, Art Gallery of South Australia

Fatalism is a belief and philosophical doctrine which considers the entire universe as a deterministic system and stresses the subjugation of all events, actions, and behaviors to fate or destiny, which is commonly associated with the consequent attitude of resignation in the face of future events which are thought to be inevitable and outside of human control.

Definition

The term "fatalism" can refer to any of the following ideas:

• Broadly, any view according to which human beings are powerless to do anything other than what they actually do. Included in this is the belief that all events are decided by fate and are outside human control, hence humans have no power to influence the future or indeed the outcome of their own thoughts and actions.

More specifically:

• Theological fatalism, according to which free will is incompatible with the existence of an omniscient God who has foreknowledge of all future events. This is very similar to theological determinism.
• Logical fatalism, according to which propositions about the future which we take to currently be either true or false can only be true or false if future events are already determined.
• Causal determinism, which is usually treated as distinct from fatalism, on the grounds that it requires only the determination of each successive state in a system by that system's prior state, rather than the final state of a system being predetermined.
• The view that the appropriate reaction to the inevitability of some future event is acceptance or resignation, rather than resistance. For instance, 19th-century German philosopher Friedrich Nietzsche discusses what he calls "Turkish fatalism" (Türkenfatalismus) in his essay The Wanderer and His Shadow (1880), where he makes no distinction between the terms "fate" and "fatalism". This view is closer to everyday use of the word "fatalism" and parallels defeatism.

Religion

Throughout history, the belief that the entire universe is a deterministic system subject to the will of fate or destiny has been articulated in both Eastern and Western religions, philosophy, music, and literature.

The ancient Arabs that inhabited the Arabian Peninsula before the advent of Islam used to profess a widespread belief in fatalism (ḳadar) alongside a fearful consideration for the sky and the stars as divine beings, which they held to be ultimately responsible for every phenomenon that occurs on Earth and for the destiny of humankind. Accordingly, they shaped their entire lives in accordance with their interpretations of astral configurations and phenomena.

In the I Ching and philosophical Taoism, the ebb and flow of favorable and unfavorable conditions suggests the path of least resistance is effortless (see: Wu wei). In the philosophical schools of the Indian Subcontinent, the concept of karma deals with similar philosophical issues to the Western concept of determinism. Karma is understood as a spiritual mechanism which causes the eternal cycle of birth, death, and rebirth (saṃsāra). Karma, either positive or negative, accumulates according to an individual's actions throughout their life, and at their death determines the nature of their next life in the cycle of Saṃsāra. Most major religions originating in India hold this belief to some degree, most notably Hinduism, Jainism, Sikhism, and Buddhism.

The views on the interaction of karma and free will are numerous, and diverge from each other greatly. For example, in Sikhism, god's grace, gained through worship, can erase one's karmic debts, a belief which reconciles the principle of karma with a monotheistic god one must freely choose to worship. Jainists believe in a sort of compatibilism, in which the cycle of Saṃsara is a completely mechanistic process, occurring without any divine intervention. The Jains hold an atomic view of reality, in which particles of karma form the fundamental microscopic building material of the universe.

Ājīvika

In ancient India, the Ājīvika school of philosophy founded by Makkhali Gosāla (around 500 BCE), otherwise referred to as "Ājīvikism" in Western scholarship, upheld the Niyati ("Fate") doctrine of absolute fatalism or determinism, which negates the existence of free will and karma, and is therefore considered one of the nāstika or "heterodox" schools of Indian philosophy. The oldest descriptions of the Ājīvika fatalists and their founder Gosāla can be found both in the Buddhist and Jaina scriptures of ancient India. The predetermined fate of all sentient beings and the impossibility to achieve liberation (mokṣa) from the eternal cycle of birth, death, and rebirth (saṃsāra) was the major distinctive philosophical and metaphysical doctrine of this heterodox school of Indian philosophy, annoverated among the other Śramaṇa movements that emerged in India during the Second urbanization (600–200 BCE).

Buddhism

Main articles: Enlightenment in Buddhism and Two truths doctrine

Further information: Four stages of enlightenment, Sotāpanna, and Three marks of existence

Buddhist philosophy contains several concepts which some scholars describe as deterministic to various levels. However, the direct analysis of Buddhist metaphysics through the lens of determinism is difficult, due to the differences between European and Buddhist traditions of thought.

One concept which is argued to support a hard determinism is the doctrine of dependent origination (pratītyasamutpāda) in the early Buddhist texts, which states that all phenomena (dharma) are necessarily caused by some other phenomenon, which it can be said to be dependent on, like links in a massive, never-ending chain; the basic principle is that all things (dharmas, phenomena, principles) arise in dependence upon other things, which means that they are fundamentally "empty" or devoid of any intrinsic, eternal essence and therefore are impermanent. In traditional Buddhist philosophy, this concept is used to explain the functioning of the eternal cycle of birth, death, and rebirth (saṃsāra); all thoughts and actions exert a karmic force that attaches to the individual's consciousness, which will manifest through reincarnation and results in future lives. In other words, righteous or unrighteous actions in one life will necessarily cause good or bad responses in another future life or more lives. The early Buddhist texts and later Tibetan Buddhist scriptures associate dependent arising with the fundamental Buddhist doctrines of emptiness (śūnyatā) and non-self (anattā).

Another Buddhist concept which many scholars perceive to be deterministic is the doctrine of non-self (anattā). In Buddhism, attaining enlightenment involves one realizing that neither in humans nor any other sentient beings is there a fundamental core of permanent being, identity, or personality which can be called the "soul", and that all sentient beings (including humans) are instead made of several, constantly changing factors which bind them to the eternal cycle of birth, death, and rebirth (saṃsāra). Sentient beings are composed of the five aggregates of existence (skandha): matter, sensation, perception, mental formations, and consciousness. In the Saṃyutta Nikāya of the Pāli Canon, the historical Buddha is recorded as saying that "just as the word 'chariot' exists on the basis of the aggregation of parts, even so the concept of 'being' exists when the five aggregates are available." The early Buddhist texts outline different ways in which dependent origination is a middle way between different sets of "extreme" views (such as "monist" and "pluralist" ontologies or materialist and dualist views of mind-body relation). In the Kaccānagotta Sutta of the Pāli Canon (SN 12.15, parallel at SA 301), the historical Buddha stated that "this world mostly relies on the dual notions of existence and non-existence" and then explains the right view as follows:

But when you truly see the origin of the world with right understanding, you won't have the notion of non-existence regarding the world. And when you truly see the cessation of the world with right understanding, you won't have the notion of existence regarding the world.

Some Western scholars argue that the concept of non-self necessarily disproves the ideas of free will and moral responsibility. If there is no autonomous self, in this view, and all events are necessarily and unchangeably caused by others, then no type of autonomy can be said to exist, moral or otherwise. However, other scholars disagree, claiming that the Buddhist conception of the universe allows for a form of compatibilism. Buddhism perceives reality occurring on two different levels: the ultimate reality, which can only be truly understood by the enlightened ones, and the illusory or false reality of the material world, which is considered to be "real" or "true" by those who are ignorant about the nature of metaphysical reality; i.e., those who still haven't achieved enlightenment. Therefore, Buddhism perceives free will as a notion belonging to the illusory belief in the unchanging self or personhood that pertains to the false reality of the material world, while concepts like non-self and dependent origination belong to the ultimate reality; the transition between the two can be truly understood, Buddhists claim, by one who has attained enlightenment.

Determinism and predeterminism

While the terms are sometimes used interchangeably, fatalism, determinism, and predeterminism are distinct, as each emphasizes a different aspect of the futility of human will or the foreordination of destiny. However, all these doctrines share common ground.

Determinists generally agree that human actions affect the future but that human action is itself determined by a causal chain of prior events. Their view does not accentuate a "submission" to fate or destiny, whereas fatalists stress an acceptance of future events as inevitable. Determinists believe the future is fixed specifically due to causality; fatalists and predeterminists believe that some or all aspects of the future are inescapable but, for fatalists, not necessarily due to causality.

Fatalism is a looser term than determinism. The presence of historical "indeterminisms" or chances, i.e. events that could not be predicted by sole knowledge of other events, is an idea still compatible with fatalism. Necessity (such as a law of nature) will happen just as inevitably as a chance—both can be imagined as sovereign. This idea has roots in Aristotle's work, "De interpretatione".

Theological fatalism is the thesis that infallible foreknowledge of a human act makes the act necessary and hence unfree. If there is a being who knows the entire future infallibly, then no human act is free. The early Islamic philosopher, Al Farabi, makes the case that if God does in fact know all human actions and choices, then Aristotle's original solution to this dilemma stands.

Idle argument

One famous ancient argument regarding fatalism was the so-called Idle Argument. It argues that if something is fated, then it would be pointless or futile to make any effort to bring it about. The Idle Argument was described by Origen and Cicero and it went like this:

• If it is fated for you to recover from this illness, then you will recover whether you call a doctor or not.
• Likewise, if you are fated not to recover, you will not do so whether you call a doctor or not.
• But either it is fated that you will recover from this illness, or it is fated that you will not recover.
• Therefore, it is futile to consult a doctor.

The Idle Argument was anticipated by Aristotle in his De Interpretatione chapter 9. The Stoics considered it to be a sophism and the Stoic Chrysippus attempted to refute it by pointing out that consulting the doctor would be as much fated as recovering. He seems to have introduced the idea that in cases like that at issue two events can be co-fated, so that one cannot occur without the other.

Logical fatalism and the argument from bivalence

Arguments for logical fatalism go back to antiquity. The argument from bivalence depends not on causation or physical circumstances but rather is based on logical truths and metaphysical necessity. There are numerous versions of this argument, including those by Aristotle and Richard Clyde Taylor.

The key idea of logical fatalism is that there exists necessarily true or false future describing propositions, or statements about what is going to happen in the future, and that there is something metaphysically necessary about the truth value of these statements. So, for example, if it is true today that tomorrow there will be a sea battle, then there cannot fail to be a sea battle tomorrow, since otherwise it would not be true today that such a battle will take place tomorrow.

There are two main forms of responses to logical fatalism. The first response is concerned with logical fatalism's reliance on the principle of bivalence, which says that a proposition is necessarily either true or false. If one wants to reject logical fatalism, one move to take is to reject that this principle applies to future describing propositions. Aristotle is famously attributed as making this move, though there are views that he does not. This response works well with an A-theory of time, which says that time is fundamentally tensed, and events can be classified as past, present, and perhaps, future. A-theory supports views of time that say that the future does not yet exist, like presentism. Relating to logical fatalism, If the future is considered to be undetermined, meaning that the truth value of a statement can only be determined once the event occurs, then the principle of bivalence can be rejected. However, the B-theory of time sees the past and future as being just as real as the present. On a B-theory of time, future facts do exist, and therefore the solution to reject the principle of bivalence on the grounds of undetermined future propositions does not work.

The second response can be attributed to William of Ockham, and is often called the Ockhamist Response. This response, essentially, challenges the idea that we cannot affect the past truth of future describing propositions. The truth value of propositions describing the future, then, may not be as metaphysically necessary as we think.

The argument for logical fatalism and its responses relate closely to the problem of future contingents. There are responses to this problem that allow one to also overcome logical fatalism. The third truth value view says that future contingents can have a third value which is beyond truth or falsity. The all-false view says that all future contingents are false.

Criticism

Semantic equivocation

One criticism comes from the novelist David Foster Wallace, who in a 1985 paper "Richard Taylor's Fatalism and the Semantics of Physical Modality" suggests that Richard Taylor reached his conclusion of fatalism only because his argument involved two different and inconsistent notions of impossibility. Wallace did not reject fatalism per se, as he wrote in his closing passage, "if Taylor and the fatalists want to force upon us a metaphysical conclusion, they must do metaphysics, not semantics. And this seems entirely appropriate." Willem deVries and Jay Garfield, both of whom were advisers on Wallace's thesis, expressed regret that Wallace never published his argument. In 2010, the thesis was, however, published posthumously as Time, Fate, and Language: An Essay on Free Will.

Time travel in fiction

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Time_travel_in_fiction

Poster for the 1960 film adaptation of H. G. Wells' 1895 novella The Time Machine

Spatial anomalies in fiction
Black holes in fiction • Portable hole • Teleportation in fiction • Wormholes in fiction • Stargate • Warp drive • Hyperspace • Time travel in fiction

Time travel is a common theme in fiction, mainly since the late 19th century, and has been depicted in a variety of media, such as literature, television, and film.

The concept of time travel by mechanical means was popularized in H. G. Wells' 1895 story, The Time Machine. In general, time travel stories focus on the consequences of traveling into the past or the future. The premise for these stories often involves changing history, either intentionally or by accident, and the ways by which altering the past changes the future and creates an altered present or future for the time traveler upon their return. In other instances, the premise is that the past cannot be changed or that the future is determined, and the protagonist's actions turn out to be inconsequential or intrinsic to events as they originally unfolded. Some stories focus solely on the paradoxes and alternate timelines that come with time travel, rather than time traveling. They often provide some sort of social commentary, as time travel provides a "necessary distancing effect" that allows science fiction to address contemporary issues in metaphorical ways.

Mechanisms

Further information: Time travel

Time travel in modern fiction is sometimes achieved by space and time warps, stemming from the scientific theory of general relativity. Stories from antiquity often featured time travel into the future through a time slip brought on by traveling or sleeping, in other cases, time travel into the past through supernatural means, for example brought on by angels or spirits.

Time slip

Main article: Time slip

A time slip is a plot device in fantasy and science fiction in which a person, or group of people, seem to travel through time by unknown means. The idea of a time slip has been used in 19th century fantasy, an early example being Washington Irving's 1819 Rip Van Winkle, where the mechanism of time travel is an extraordinarily long sleep. Mark Twain's 1889 A Connecticut Yankee in King Arthur's Court had considerable influence on later writers. The first novel to include both travel to the past and travel to the future and return to the present is the Charles Dickens 1843 novel A Christmas Carol.

Time slip is one of the main plot devices of time travel stories, another being a time machine. The difference is that in time slip stories, the protagonist typically has no control and no understanding of the process (which is often never explained at all) and is either left marooned in a past or future time and must make the best of it, or is eventually returned by a process as unpredictable and uncontrolled as the journey out. The plot device is also popular in children's literature. The 2011 film, Midnight in Paris similarly presents time travel as occurring without explanation, as the director "eschews a 'realist' internal logic that might explain the time travel, while also foregoing experimental time Distortion techniques, in favor of straightforward editing and a fantastical narrative set-up".

Time portal

A time portal or a time gate is a doorway in time, employed in various fiction genres, especially science fiction and fantasy, to transport characters to the past or future. They differ from time machines in being a permanent or semi-permanent fixture, often linking specific points in time. An influential example of such a work is the short story, "By His Bootstraps", by Robert A. Heinlein, which features a time gate built by aliens and plays with some of the inherent paradoxes that would be caused by time travel.

Communication from the future

In literature, communication from the future is a plot device in some science fiction and fantasy stories. Forrest J. Ackerman noted in his 1973 anthology of the best fiction of the year that "the theme of getting hold of tomorrow's newspaper is a recurrent one". An early example of this device can be found in H. G. Wells's 1932 short story "The Queer Story of Brownlow's Newspaper", which tells the tale of a man who receives such a paper from 40 years in the future. The 1944 film It Happened Tomorrow also employs this device, with the protagonist receiving the next day's newspaper from an elderly colleague (who is possibly a ghost). Ackerman's anthology also highlights a 1972 short story by Robert Silverberg, "What We Learned from this Morning's Newspaper". In that story, a block of homeowners wake to discover that on November 22, they have received The New York Times for the coming December 1. As characters learn of future events affecting them through a newspaper delivered a week early, the ultimate effect is that this "so upsets the future that spacetime is destroyed".^[1]: 165 The television series Early Edition, similar to the film It Happened Tomorrow, also revolved around a character who daily received the next day's newspaper, and sought to change some event therein forecast to happen.

A newspaper from the future can be a fictional edition of a real newspaper, or an entirely fictional newspaper. John Buchan's 1932 novel The Gap in the Curtain, is similarly premised on a group of people being enabled to see, for a moment, an item in The Times newspaper from one year in the future. During the Swedish general election of 2006, the Swedish liberal party used election posters which looked like news items, called Framtidens nyheter ("News of the future"), featuring a future Sweden that had become what the party wanted.

A communication from the future raises questions about the ability of humans to control their destiny. The visual novel Steins;Gate features characters sending short text messages backwards in time to avert disaster, only to find their problems are exacerbated due to not knowing how individuals in the past will actually utilize the information.

Precognition

Precognition has been explored as a form of time travel in fiction. Author J. B. Priestley wrote of it both in fiction and non-fiction, analysing testimonials of precognition and other "temporal anomalies" in his book Man and Time. His books include time travel to the future through dreaming, which upon waking up results in memories from the future. Such memories, he writes, may also lead to the feeling of déjà vu, that the present events have already been experienced, and are now being re-experienced. Infallible precognition, which describes the future as it truly is, may lead to causal loops, one form of which is explored in Newcomb's paradox. The film 12 Monkeys heavily deals with themes of predestination and the Cassandra complex, where the protagonist who travels back in time explains that he can't change the past.

The protagonist of the short story Story of Your Life, later adapted into the film, Arrival, experiences life as a superimposition of the present and the totality of her life, future included, as a consequence of learning an alien language. The mental faculty is speculation based on the Sapir–Whorf hypothesis.

Time loop

Main article: Time loop

A "time loop" or "temporal loop" is a plot device in which periods of time are repeated and re-experienced by the characters, and there is often some hope of breaking out of the cycle of repetition. Time loops are sometimes referred to as causal loops, but these two concepts are distinct. Although similar, causal loops are unchanging and self-originating, whereas time loops are constantly resetting. In a time loop when a certain condition is met, such as a death of a character or a clock reaching a certain time, the loop starts again, with one or more characters retaining the memories from the previous loop. Stories with time loops commonly center on the character learning from each successive loop through time.

Experiencing time in reverse

In some media, certain characters are presented as moving through time backwards. This is a very old concept, with some accounts asserting that English mythological figure Merlin lived backwards, and appeared to be able to prophesy the future because for him it was a memory. This tradition has been reflected in certain modern fictional accounts of the character. In the Piers Anthony book Bearing an Hourglass, the second of eight books in the Incarnations of Immortality series, the character of Norton becomes the incarnation of Time and continues his life living backwards in time. The 2016 film Doctor Strange has the character use the Time Stone, one of the Infinity Stones in the Marvel Cinematic Universe, to reverse time, experiencing time backwards while so doing.

In the film Tenet, characters time travel without jumping back, but by experiencing past reality in reverse, and at the same speed, after going through a 'turnstile' device and until they revert to normal time flow by going through such a device again. In the meantime, two versions of the time traveller coexist (and must not meet, lest they mutually destruct): the one that had been 'traveling forward' (existing normally) until entering a turnstile and the one traveling backward from the turnstile. The laws of thermodynamics are reversed for time traveling people and objects, so that for example backward travel requires the use of a respirator. Objects left behind by time travellers obey 'reverse thermodynamics;' for example, bullets shot or even simply deposited while traveling backward fly back into (forward traveling) guns.

Themes

Time paradox

Further information: Temporal paradox

The idea of changing the past is logically contradictory, creating situations like the grandfather paradox, where time travellers go back in time and change the past in a way that affects their future in a way that could be seen as paradoxical or illogical, such as by killing their grandparents. The engineer Paul J. Nahin states that "even though the consensus today is that the past cannot be changed, science fiction writers have used the idea of changing the past for good story effect". Time travel to the past and precognition without the ability to change events may result in causal loops.

The possibility of characters changing the past gave rise to the idea of "time police", people who prevent such changes from occurring by engaging in time travel to reverse the changes.

Alternative future, history, timelines, and dimensions

See also: Parallel universes in fiction, Future history, and Alternate history

An alternative future or alternate future is a possible future that never comes to pass, typically when someone travels into the past and alters it so that the events of the alternative future cannot occur or when a communication from the future to the past effected a change that alters the future. Alternative histories may exist "side by side", with the time traveller arriving at different dimensions as he changes time.

Butterfly effect

See also: Butterfly effect in popular culture

The butterfly effect is the notion that small events can have large, widespread consequences. The term describes events observed in chaos theory where a very small change in initial conditions has vastly different results. The term was coined by mathematician Edward Lorenz years after the phenomenon was first described.

The butterfly effect has found its way into popular imagination. For example, in Ray Bradbury's 1952 short story A Sound of Thunder, the killing of an insect millions of years in the past drastically changes the world and in the 2004 film The Butterfly Effect, the protagonist's small changes to his past results in extreme consequences.

Time tourism

A "distinct subgenre" of stories explore time travel as a means of tourism, with travelers curious to visit periods or events such as the Victorian Era or the Crucifixion of Christ, or to meet historical figures such as Abraham Lincoln or Ludwig van Beethoven. This theme can be addressed from two or three directions. An early example of present-day tourists travelling back to the past is Ray Bradbury's 1952 A Sound of Thunder, in which the protagonists are big game hunters who travel to the distant past to hunt dinosaurs. An early example of another type, in which tourists from the future visit the present, is Catherine L. Moore and Henry Kuttner's 1946 Vintage Season. The final type in which there are people time-traveling to the future is experienced in the second book of Douglas Adams' The Hitchhiker's Guide to the Galaxy series, The Restaurant at the End of the Universe, which, as the title indicates, includes a restaurant that exists at the end of the universe. In the restaurant, people time-traveling from all over the space-time continuum (especially the rich) came to the restaurant to view the explosion of the universe put on repeat.

Time war

See also: Category:Temporal war fiction

The Encyclopedia of Science Fiction describes a time war as a fictional war that is "fought across time, usually with each side knowingly using time travel ... to establish the ascendancy of one or another version of history". Time wars are also known as "change wars" and "temporal wars". Examples include Clifford D. Simak's 1951 Time and Again, Russell T. Davies' 2005 revival of Doctor Who, Barrington J. Bayley's 1974 The Fall of Chronopolis, Matthew Costello's 1990 Time of the Fox, and the central premise of Star Trek: Enterprise.

Ghost story

Researcher Barbara Bronlow wrote that traditional ghost stories are in effect an early form of time travel, since they depict living people of the present interacting with (dead) people of the past. She noted as an instance that Christopher Marlow's Doctor Faustus called up Helen of Troy and met her arising from her grave.

Caesium standard

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Caesium_standard 

A caesium atomic fountain used as part of an atomic clock

The caesium standard is a primary frequency standard in which the photon absorption by transitions between the two hyperfine ground states of caesium-133 atoms is used to control the output frequency. The first caesium clock was built by Louis Essen in 1955 at the National Physical Laboratory in the UK and promoted worldwide by Gernot M. R. Winkler of the United States Naval Observatory.

Caesium atomic clocks are one of the most accurate time and frequency standards, and serve as the primary standard for the definition of the second in the International System of Units (SI), the modern metric system. By definition, radiation produced by the transition between the two hyperfine ground states of caesium-133 (in the absence of external influences such as the Earth's magnetic field) has a frequency, Δν_Cs, of exactly 9192631770 Hz. That value was chosen so that the caesium second equaled, to the limit of measuring ability in 1960 when it was adopted, the existing standard ephemeris second based on the Earth's orbit around the Sun. Because no other measurement involving time had been as precise, the effect of the change was less than the experimental uncertainty of all existing measurements.

While the second is the only base unit to be explicitly defined in terms of the caesium standard, the majority of SI units have definitions that mention either the second, or other units defined using the second. Consequently, every base unit except the mole and every named derived unit except the coulomb, gray, sievert, radian, and steradian have values that are implicitly at least partially defined by the properties of the caesium-133 hyperfine transition radiation. And of these, all but the mole, the coulomb, and the dimensionless radian and steradian are implicitly defined by the general properties of electromagnetic radiation.

Technical details

The official definition of the second was first given by the BIPM at the 13th General Conference on Weights and Measures in 1967 as: "The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom." At its 1997 meeting the BIPM added to the previous definition the following specification: "This definition refers to a caesium atom at rest at a temperature of 0 K."

The BIPM restated this definition in its 26th conference (2018), "The second is defined by taking the fixed numerical value of the caesium frequency ∆νCs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s⁻¹."

The meaning of the preceding definition is as follows. The caesium atom has a ground state electron state with configuration [Xe] 6s¹ and, consequently, atomic term symbol ²S_1/2. This means that there is one unpaired electron and the total electron spin of the atom is 1/2. Moreover, the nucleus of caesium-133 has a nuclear spin equal to 7/2. The simultaneous presence of electron spin and nuclear spin leads, by a mechanism called hyperfine interaction, to a (small) splitting of all energy levels into two sub-levels. One of the sub-levels corresponds to the electron and nuclear spin being parallel (i.e., pointing in the same direction), leading to a total spin F equal to F = 7/2 + 1/2 = 4; the other sub-level corresponds to anti-parallel electron and nuclear spin (i.e., pointing in opposite directions), leading to a total spin F = 7/2 − 1/2 = 3. In the caesium atom it so happens that the sub-level lowest in energy is the one with F = 3, while the F = 4 sub-level lies energetically slightly above. When the atom is irradiated with electromagnetic radiation having an energy corresponding to the energetic difference between the two sub-levels the radiation is absorbed and the atom is excited, going from the F = 3 sub-level to the F = 4 one. After some time the atom will re-emit the radiation and return to its F = 3 ground state. From the definition of the second it follows that the radiation in question has a frequency of exactly 9.19263177 GHz, corresponding to a wavelength of about 3.26 cm and therefore belonging to the microwave range.

Note that a common confusion involves the conversion from angular frequency (${\displaystyle \omega }$) to frequency (${\displaystyle f}$), or vice versa. Angular frequencies are conventionally given as s⁻¹ in scientific literature, but here the units implicitly mean radians per second. In contrast, the unit Hz should be interpreted as cycles per second. The conversion formula is ${\displaystyle \omega =2\pi f}$, which implies that 1 Hz corresponds to an angular frequency of approximately 6.28 radians per second (or 6.28 s⁻¹ where radians is omitted for brevity by convention).

Parameters and significance in the second and other SI units

Suppose the caesium standard has the parameters:

• Velocity: c
• Energy/frequency: h
• Time period: Δt_Cs
• Frequency: Δν_Cs
• Wavelength: Δλ_Cs
• Photon energy: ΔE_Cs
• Photon mass equivalent: ΔM_Cs

Time and frequency

The first set of units defined using the caesium standard were those relating to time, with the second being defined in 1967 as "the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom" meaning that:

• 1 second, s, = 9,192,631,770 Δt_Cs
• 1 hertz, Hz, = 1/s = ⁠Δν_Cs/9,192,631,770⁠
• 1 becquerel, Bq, = 1 nuclear decay/s = ⁠1/9,192,631,770⁠ nuclear decays/Δt_Cs

This also linked the definitions of the derived units relating to force and energy (see below) and of the ampere, whose definition at the time made reference to the newton, to the caesium standard. Before 1967 the SI units of time and frequency were defined using the tropical year and before 1960 by the length of the mean solar day

Length

In 1983, the meter was, indirectly, defined in terms of the caesium standard with the formal definition "The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. This implied:

• 1 metre, m, = ⁠c s/299,792,458⁠ = ⁠9,192,631,770/299,792,458⁠ c Δt_Cs = ⁠9,192,631,770/299,792,458⁠ Δλ_Cs
• 1 radian, rad, = 1 m/m = Δλ_Cs/Δλ_Cs = 1 (dimensionless unit of angle)
• 1 steradian, sr, = 1 m²/m² = Δλ_Cs²/Δλ_Cs² = 1 (dimensionless unit of solid angle)

Between 1960 and 1983, the metre had been defined by the wavelength of a different transition frequency associated with the krypton-86 atom. This had a much higher frequency and shorter wavelength than the caesium standard, falling inside the visible spectrum. The first definition, used between 1889 and 1960, was by the international prototype meter.

Mass, energy, and force

Following the 2019 revision of the SI, electromagnetic radiation, in general, was explicitly defined to have the exact parameters:

• c = 299,792,458 m/s
• h = 6.62607015×10⁻³⁴ J s

The caesium-133 hyperfine transition radiation was explicitly defined to have frequency:

• Δν_Cs = 9,192,631,770 Hz

Though the above values for c and Δν_Cs were already obviously implicit in the definitions of the metre and second. Together they imply:

• Δt_Cs = ⁠1/Δν_Cs⁠ = ⁠s/9,192,631,770⁠
• Δλ_Cs = c Δt_Cs = ⁠299,792,458/9,192,631,770⁠ m
• ΔE_Cs = h Δν_Cs = 9,192,631,770 Hz × 6.62607015×10⁻³⁴ J s = 6.09110229711386655×10⁻²⁴ J
• ΔM_Cs = ⁠ΔE_Cs/c²⁠ = ⁠6.09110229711386655×10⁻²⁴ J/89,875,517,873,681,764 m²/s²⁠ = ⁠6.09110229711386655/8.9875517873681764×10⁴⁰⁠ kg

Notably, the wavelength has a fairly human-sized value of about 3.26 centimetres and the photon energy is surprisingly close to the average molecular kinetic energy per degree of freedom per kelvin. From these it follows that:

• 1 kilogram, kg, = ⁠8.9875517873681764×10⁴⁰/6.09110229711386655⁠ ΔM_Cs
• 1 joule, J, = ⁠10²⁴/6.09110229711386655⁠ ΔE_Cs
• 1 watt, W, = 1 J/s = ⁠10¹⁴/5.59932604907689089550702935⁠ ΔE_Cs Δν_Cs
• 1 newton, N, = 1 J/m = ⁠2.99792458×10²²/5.59932604907689089550702935⁠ ΔE_Cs/Δλ_Cs
• 1 pascal, Pa, = 1 N/m² = ⁠2.6944002417373989539335912×10¹⁹/4.73168129737820913189287698892486811451620615⁠ ΔE_Cs/Δλ_Cs³
• 1 gray, Gy, = 1 J/kg = ⁠1/89,875,517,873,681,764⁠ ΔE_Cs/ΔM_Cs = ⁠c²/89,875,517,873,681,764⁠
• 1 sievert, Sv, = the ionizing radiation dose equivalent to 1 gray of gamma rays

Prior to the revision, between 1889 and 2019, the family of metric (and later SI) units relating to mass, force, and energy were somewhat notoriously defined by the mass of the International Prototype of the Kilogram (IPK), a specific object stored at the headquarters of the International Bureau of Weights and Measures in Paris, meaning that any change to the mass of that object would have resulted in a change to the size of the kilogram and of the many other units whose value at the time depended on that of the kilogram.

Temperature

From 1954 to 2019, the SI temperature scales were defined using the triple point of water and absolute zero. The 2019 revision replaced these with an assigned value for the Boltzmann constant, k, of 1.380649×10⁻²³ J/K, implying:

• 1 kelvin, K, = 1.380649×10⁻²³ J/2 per degree of freedom = ⁠1.380649×10⁻²³ × 10²⁴/2/6.09110229711386655⁠ ΔE_Cs per degree of freedom = ⁠1.380649/1.21822045942277331⁠ ΔE_Cs per degree of freedom
• Temperature in degrees Celsius, °C, = temperature in kelvins − 273.15 = ⁠1.21822045942277331 × kinetic energy per degree of freedom − 377.12427435 ΔE_Cs/1.380649 ΔE_Cs⁠

Amount of substance

The mole is an extremely large number of "elementary entities" (i.e. atoms, molecules, ions, etc). From 1969 to 2019, this number was 0.012 × the mass ratio between the IPK and a carbon 12 atom. The 2019 revision simplified this by assigning the Avogadro constant the exact value 6.02214076×10²³ elementary entities per mole, thus, uniquely among the base units, the mole maintained its independence from the caesium standard:

• 1 mole, mol, = 6.02214076×10²³ elementary entities
• 1 katal, kat, = 1 mol/s = ⁠6.02214076×10¹⁴/9.19263177⁠ elementary entities/Δt_Cs

Electromagnetic units

Prior to the revision, the ampere was defined as the current needed to produce a force between 2 parallel wires 1 m apart of 0.2 μN per meter. The 2019 revision replaced this definition by giving the charge on the electron, e, the exact value 1.602176634×10⁻¹⁹ coulombs. Somewhat incongruously, the coulomb is still considered a derived unit and the ampere a base unit, rather than vice versa. In any case, this convention entailed the following exact relationships between the SI electromagnetic units, elementary charge, and the caesium-133 hyperfine transition radiation:

• 1 coulomb, C, = ⁠10¹⁹/1.602176634⁠ e
• 1 ampere, or amp, A, = 1 C/s = ⁠10⁹/1.472821982686006218⁠ e Δν_Cs
• 1 volt, V, = 1 J/C = ⁠1.602176634×10⁵/6.09110229711386655⁠ ΔE_Cs/e
• 1 farad, F, = 1 C/V = ⁠6.09110229711386655×10¹⁴/2.566969966535569956⁠ e²/ΔE_Cs
• 1 ohm, Ω, = 1 V/A = ⁠2.359720966701071721258310212×10⁻⁴/6.09110229711386655⁠ ΔE_Cs/Δν_Cs e² = ⁠2.359720966701071721258310212×10⁻⁴/6.09110229711386655⁠ h/e²
• 1 siemens, S, = 1/Ω = ⁠6.09110229711386655×10⁴/2.359720966701071721258310212⁠ e²/h
• 1 weber, Wb, = 1 V s = ⁠1.602176634×10¹⁵/6.62607015⁠ ΔE_Cs Δt_Cs/e = ⁠1.602176634×10¹⁵/6.62607015⁠ h/e
• 1 tesla, T, = 1 Wb/m² = ⁠1.43996454705862285832702376×10¹²/5.59932604907689089550702935⁠ ΔE_Cs Δt_Cs/e Δλ_Cs² = ⁠1.43996454705862285832702376×10¹²/5.59932604907689089550702935⁠ E/e c Δλ_Cs
• 1 henry, H, = Ω s = ⁠2.359720966701071721258310212×10⁶/6.62607015⁠ h Δt_Cs/e²

Optical units

From 1967 to 1979 the SI optical units, lumen, lux, and candela are defined using the incandescent glow of platinum at its melting point. After 1979, the candela was defined as the luminous intensity of a monochromatic visible light source of frequency 540 THz (i.e ⁠6000/1.02140353⁠ that of the caesium standard) and radiant intensity ⁠1/683⁠ watts per steradian. This linked the definition of the candela to the caesium standard and, until 2019, to the IPK. Unlike the units relating to mass, energy, temperature, amount of substance, and electromagnetism, the optical units were not massively redefined in 2019, though they were indirectly affected since their values depend on that of the watt, and hence of the kilogram. The frequency used to define the optical units has the parameters:

• Frequency: 540 THz
• Time period: ⁠50/27⁠ fs
• Wavelength: ⁠14.9896229/27⁠ μm
• Photon energy: 5.4×10¹⁴ Hz × 6.62607015×10⁻³⁴ J s = 3.578077881×10⁻¹⁹ J
• luminous efficacy, K_CD, = 683 lm/W
• luminous energy per photon, ${\displaystyle Q_{\mathrm{v}}}$, = 3.578077881×10⁻¹⁹ J × 683 lm/W = 2.443827192723×10⁻¹⁶ lm s

This implies:

• 1 lumen, lm, = ⁠10⁶/2.246520349221536260971⁠ ${\displaystyle Q_{\mathrm{v}}}$ Δν_Cs
• 1 candela, cd, = 1 lm/sr = ⁠10⁶/2.246520349221536260971⁠ ${\displaystyle Q_{\mathrm{v}}}$ Δν_Cs/sr
• 1 lux, lx, = 1 lm/m² = ⁠8.9875517873681764×10²/1.898410313566852566340456048807087002459⁠ ${\displaystyle Q_{\mathrm{v}}}$ Δν_Cs/Δλ_Cs²

Summary

The parameters of the caesium-133 hyperfine transition radiation expressed exactly in SI units are:

• Frequency = 9,192,631,770 Hz
• Time period = ⁠1/9,192,631,770⁠ s
• Wavelength = ⁠299,792,458/9,192,631,770⁠ m
• Photon energy = 6.09110229711386655×10⁻²⁴ J
• Photon mass equivalent = ⁠6.09110229711386655×10⁻⁴⁰/8.9875517873681764⁠ kg

If the seven base units of the SI are expressed explicitly in terms of the SI defining constants, they are:

• 1 second = ⁠9,192,631,770/Δν_Cs⁠
• 1 metre = ⁠9,192,631,770/299,792,458⁠ c/Δν_Cs
• 1 kilogram = ⁠8.9875517873681764×10⁴⁰/6.09110229711386655⁠ h Δν_Cs/c²
• 1 ampere = ⁠10⁹/1.472821982686006218⁠ e Δν_Cs
• 1 kelvin = ⁠13.80649/6.09110229711386655⁠ h Δν_Cs/k
• 1 mole = 6.02214076×10²³ elementary entities
• 1 candela = ⁠10¹¹/3.82433969151951648163130104605⁠ h Δν_Cs² K_CD/sr

Ultimately, 6 of the 7 base units (all but the dimensionless mole) notably have values that depend on that of Δν_Cs, which appears far more often than any of the other defining constants. However, the derived unit of one coulomb, which is an ampere-second, is a dimensionful unit defined purely in terms of the elementary charge and hence is independent of Δν_Cs.