A chronon is a proposed quantum of time, that is, a discrete and indivisible "unit" of time as part of a hypothesis that proposes that time is not continuous.

Early work

While time is a continuous quantity in both standard quantum mechanics and general relativity, many physicists have suggested that a discrete model of time might work, especially when considering the combination of quantum mechanics with general relativity to produce a theory of quantum gravity. The term was introduced in this sense by Robert Lévi in 1927.[1] A quantum theory in which time is a quantum variable with a discrete spectrum, and which is nevertheless consistent with special relativity, was proposed by Chen Ning Yang in 1947.[2] Henry Margenau in 1950 suggested that the chronon might be the time for light to travel the classical radius of an electron.[3]

Work by Caldirola

A prominent model was introduced by Piero Caldirola in 1980. In Caldirola's model, one chronon corresponds to about 6.27×10−24
seconds for an electron.[4] This is much longer than the Planck time, which is only about 5.39×10−44
seconds. The Planck time is a theoretical lower-bound on the length of time that could exist between two connected events, but it is not a quantization of time itself since there is no requirement that the time between two events be separated by a discrete number of Planck times. For example, ordered pairs of events (A, B) and (B, C) could each be separated by slightly more than 1 Planck time: this would produce a measurement limit of 1 Planck time between A and B or B and C, but a limit of 3 Planck times between A and C. Additionally, the Planck time is a universal quantization of time itself, whereas the chronon is a quantization of the evolution in a system along its world line. Consequently, the value of the chronon, like other quantized observables in quantum mechanics, is a function of the system under consideration, particularly its boundary conditions.[5] The value for the chronon, θ0, is calculated from:


From this formula, it can be seen that the nature of the moving particle being considered must be specified since the value of the chronon depends on the particle's charge and mass.

Caldirola claims the chronon has important implications for quantum mechanics, in particular that it allows for a clear answer to the question of whether a free-falling charged particle does or does not emit radiation. This model supposedly avoids the difficulties met by Abraham–Lorentz's and Dirac's approaches to the problem, and provides a natural explication of quantum decoherence.

See also


  1. ^ Lévi 1927
  2. ^ Yang 1947
  3. ^ Margenau 1950
  4. ^ Farias & Recami, p.11.
  5. ^ Farias & Recami, p.18.
  6. ^ Farias & Recami, p.11. Caldirola's original paper has a different formula due to not working in standard units.


  • Lévi, Robert (1927). "Théorie de l'action universelle et discontinue". Journal de Physique et le Radium. 8 (4): 182–198. doi:10.1051/jphysrad:0192700804018200.
  • Margenau, Henry (1950). The Nature of Physical Reality. McGraw-Hill.
  • Yang, C N (1947). "On quantized space-time". Physical Review. 72 (9): 874. Bibcode:1947PhRv...72..874Y. doi:10.1103/PhysRev.72.874.
  • Caldirola, P. (1980). "The introduction of the chronon in the electron theory and a charged lepton mass formula". Lettere al Nuovo Cimento. 27 (8): 225–228. doi:10.1007/BF02750348.
  • Farias, Ruy A. H.; Recami, Erasmo (1997-06-27). "Introduction of a Quantum of Time ("chronon"), and its Consequences for Quantum Mechanics". arXiv:quant-ph/9706059.
  • Albanese, Claudio; Lawi, Stephan (2004). "Time Quantization and q-deformations" (PDF). Journal of Physics A. 37 (8): 2983–2987. arXiv:hep-th/0308190. Bibcode:2004JPhA...37.2983A. doi:10.1088/0305-4470/37/8/009. Retrieved 2006-07-31.

External links


An astrarium, also called a planetarium, is the mechanical representation of the cyclic nature of astronomical objects in one timepiece. It is an astronomical clock.

BPL (time service)

BPL is the call sign of the official long-wave time signal service of the People's Republic of China, operated by the Chinese Academy of Sciences, broadcasting on 100 kHz from CAS's National Time Service Center in Pucheng County, Shaanxi at 34°56′54″N 109°32′34″E, roughly 70 km northeast of Lintong, along with NTSC's short-wave time signal BPM on 2.5, 5.0, 10.0, and 15.0 MHz.

BPL broadcasts LORAN-C compatible format signal from 5:30 to 13:30 UTC, using an 800 kW transmitter covering a radius up to 3000 km.

Carl Gibeily

Carl Gibeily (IPA /ka:l ʤɪbeɪli/), born in 1966 in Lebanon, is a former Lebanese journalist for The Daily Star and The Gulf Online, and an author. His writing and articles often question the relationship between East and West, and also examine the complex political, social and psychological issues prevalent in the Middle East. For example, his article 'A global duality', examines the animosity held by the West towards the East, with their horror of 'weapons of mass destruction' and fears of an end to Western democracy. Gibeily has written three fictional novels: Pairing the Twain published in 1992 by The Book Guild; Blueprint for a Prophet, published in 1997 by Doubleday; and Greater than a Wall by Akkadia Press in 2017.


Chronometry (from Greek χρόνος chronos, "time" and μέτρον metron, "measure") is the science of the measurement of time, or timekeeping. Chronometry applies to electronic devices, while horology refers to mechanical devices.

It should not to be confused with chronology, the science of locating events in time, which often relies upon it.

Common year

A common year is a calendar year with 365 days, as distinguished from a leap year, which has 366. More generally, a common year is one without intercalation. The Gregorian calendar, (like the earlier Julian calendar), employs both common years and leap years to keep the calendar aligned with the tropical year, which does not contain an exact number of days.

The common year of 365 days has 52 weeks and one day, hence a common year always begins and ends on the same day of the week (for example, January 1 and December 31 fell on a Sunday in 2017) and the year following a common year will start on the subsequent day of the week. In common years, February has four weeks, so March will begin on the same day of the week. November will also begin on this day.

In the Gregorian calendar, 303 of every 400 years are common years. By comparison, in the Julian calendar, 300 out of every 400 years are common years, and in the Revised Julian calendar (used by Greece) 682 out of every 900 years are common years.


HD2IOA is the callsign of a time signal radio station operated by the Navy of Ecuador. The station is located at Guayaquil, Ecuador and transmits in the HF band on 3.81 and 7.6 MHz.The transmission is in AM mode with only the lower sideband (part of the time H3E and the rest H2B/H2D) and consists of 780 Hz tone pulses repeated every ten seconds and voice announcements in Spanish.

While sometimes this station is described as defunct, reception reports of this station on 3.81 MHz appear regularly at the Utility DX Forum.

How the Self Controls Its Brain

How the Self Controls Its Brain is a book by Sir John Eccles, proposing a theory of philosophical dualism, and offering a justification of how there can be mind-brain action without violating the principle of the conservation of energy. The model was developed jointly with the nuclear physicist Friedrich Beck in the period 1991-1992.Eccles called the fundamental neural units of the cerebral cortex "dendrons", which are cylindrical bundles of neurons arranged vertically in the six outer layers or laminae of the cortex, each cylinder being about 60 micrometres in diameter. Eccles proposed that each of the 40 million dendrons is linked with a mental unit, or "psychon", representing a unitary conscious experience. In willed actions and thought, psychons act on dendrons and, for a moment, increase the probability of the firing of selected neurons through quantum tunneling effect in synaptic exocytosis, while in perception the reverse process takes place.

Previous mention of the "psychon"

The earliest prior use of the word "psychon" with a similar meaningof an "element of consciousness" is in the book "Concerning Fluctuating and Inaudible Sounds" by K. Dunlap in 1908.

The most popular prior use is in Robert Heinlein's short story Gulf, wherein a character refers to the fastest speed of thought possible as "one psychon per chronon".

Intercalation (timekeeping)

Intercalation or embolism in timekeeping is the insertion of a leap day, week, or month into some calendar years to make the calendar follow the seasons or moon phases. Lunisolar calendars may require intercalations of both days and months.


The minute is a unit of time or angle. As a unit of time, the minute is most of times equal to ​1⁄60 (the first sexagesimal fraction) of an hour, or 60 seconds. In the UTC time standard, a minute on rare occasions has 61 seconds, a consequence of leap seconds (there is a provision to insert a negative leap second, which would result in a 59-second minute, but this has never happened in more than 40 years under this system). As a unit of angle, the minute of arc is equal to ​1⁄60 of a degree, or 60 seconds (of arc). Although not an SI unit for either time or angle, the minute is accepted for use with SI units for both. The SI symbols for minute or minutes are min for time measurement, and the prime symbol after a number, e.g. 5′, for angle measurement. The prime is also sometimes used informally to denote minutes of time.

Planck time

In quantum mechanics, the Planck time (tP) is the unit of time in the system of natural units known as Planck units. A Planck time unit is the time required for light to travel a distance of 1 Planck length in a vacuum, which is a time interval of approximately 5.39 × 10 −44 s. The unit is named after Max Planck, who was the first to propose it.

The Planck time is defined as:


ħ = ​h2π is the reduced Planck constant (sometimes h is used instead of ħ in the definition)
G = gravitational constant
c = speed of light in vacuum

Using the known values of the constants, the approximate equivalent value in terms of the SI unit, the second, is

where the two digits between parentheses denote the standard error of the approximated value.

Quantum Break

Quantum Break is a science fiction action-adventure third-person shooter video game developed by Remedy Entertainment and published by Microsoft Studios. The game was released worldwide for Microsoft Windows and Xbox One in April 2016. The game centers on Jack Joyce, granted time manipulation powers after a failed time-machine experiment, as he comes into conflict with former friend Paul Serene over how to deal with an apocalyptic "End of Time". In addition, the game includes platform game elements in less action-oriented segments. There are also "junction points" that affect the game's outcome. The game features episodes of an integrated live-action television show, featuring the actors of the characters. The characters interact with the player's choices, displaying the results of the decisions made.

The game originally was envisioned as a sequel to Remedy's previous game, Alan Wake. The game's focus was shifted to time travel, as Microsoft wanted a new intellectual property with interactive storytelling. The team consulted scientists while creating the fictional science in this game. While the video game portion was developed internally by Remedy and directed by studio veteran Sam Lake, the TV side of the game was developed by Lifeboat Productions and directed by Ben Ketai. Shawn Ashmore, Aidan Gillen and Lance Reddick portrayed important roles in the game. The game uses a new engine developed by Remedy, the Northlight engine, and a technology called Digital Molecular Matter.

The game was announced in mid-2013 and was set to release in 2015, but its release was delayed to avoid competition with other Xbox One exclusives. It received a positive reception, with critics praising the game's graphics, gameplay, presentation, and story. Critics had mixed opinions regarding the platforming elements, the convergence of video game and television, and the overall quality of the TV show. The Windows 10 version was criticized for its technical issues. Quantum Break was the best-selling new intellectual property published by Microsoft since the launch of Xbox One.

Rascal (video game)

Rascal is a platform game developed by Traveller's Tales and published by Psygnosis exclusively for the PlayStation. The main character and several enemies were designed by Jim Henson's Creature Shop.

Sam Vaknin

Shmuel "Sam" Vaknin (born April 21, 1961) is an Israeli writer. He is the author of Malignant Self Love: Narcissism Revisited (2001), has been the editor-in-chief of the former website Global Politician, and runs a private website about narcissistic personality disorder (NPD). He has also postulated a theory on chronons and time asymmetry.

Tempus fugit

Tempus fugit is a Latin phrase, usually translated into English as "time flies". The expression comes from line 284 of book 3 of Virgil's Georgics, where it appears as fugit inreparabile tempus: "it escapes, irretrievable time". The phrase is used in both its Latin and English forms as a proverb that "time's a-wasting". Tempus fugit, however, is typically employed as an admonition against sloth and procrastination (cf. carpe diem) rather than a motto in favor of licentiousness (cf. "gather ye rosebuds while ye may"); the English form is often merely descriptive: "time flies like the wind", "time flies when you're having fun".

The phrase's full appearance in the Georgics is:

The phrase is a common motto, particularly on sundials and clocks.

Term (time)

A term is a period of duration, time or occurrence, in relation to an event. To differentiate an interval or duration, common phrases are used to distinguish the observance of length are near-term or short-term, medium-term or mid-term and long-term.

It is also used as part of a calendar year, especially one of the three parts of an academic term and working year in the United Kingdom: Michaelmas term, Hilary term / Lent term or Trinity term / Easter term, the equivalent to the American semester. In America there is a midterm election held in the middle of the four-year presidential term, there are also academic midterm exams.

In economics, it is the period required for economic agents to reallocate resources, and generally reestablish equilibrium. The actual length of this period, usually numbered in years or decades, varies widely depending on circumstantial context. During the long term, all factors are variable.

In finance or financial operations of borrowing and investing, what is considered long-term is usually above 3 years, with medium-term usually between 1 and 3 years and short-term usually under 1 year. It is also used in some countries to indicate a fixed term investment such as a term deposit.

In law, the term of a contract is the duration for which it is to remain in effect (not to be confused with the meaning of "term" that denotes any provision of a contract). A fixed-term contract is one concluded for a pre-defined time.

Tomorrow (time)

Tomorrow is a temporal construct of the relative future; literally of the day after the current day (today), or figuratively of future periods or times. Tomorrow is usually considered just beyond the present and counter to yesterday. It is important in time perception because it is the first direction the arrow of time takes humans on Earth.


Wa-Tor is a population dynamics simulation devised by Alexander Keewatin Dewdney and presented in the December 1984 issue of Scientific American in a five-page article entitled "Computer Recreations: Sharks and fish wage an ecological war on the toroidal planet Wa-Tor".

(T)he planet Wa-Tor ... is shaped like a torus, or doughnut, and is entirely covered with water. The two dominant denizens of Wa-Tor are sharks and fish ...

Wa-Tor is usually implemented as a two-dimensional grid with three colours, one for fish, one for sharks and one for empty water. If a creature moves past the edge of the grid, it reappears on the opposite side. The sharks are predatory and eat the fish. Both sharks and fish live, move, reproduce and die in Wa-Tor according to the simple rules defined below. From these simple rules, complex emergent behavior can be seen to arise.


YVTO is the callsign of the official time signal from the Juan Manuel Cagigal Naval Observatory in Caracas, Venezuela. The content of YVTO's signal, which is a continuous 1 kW amplitude modulated carrier wave at 5.000 MHz, is much simpler than that broadcast by some of the other time signal stations around the world, such as WWV.

The methods of time transmission from YVTO are very limited. The broadcast employs no form of digital time code. The time of day is given in Venezuelan Standard Time (VET), and is only sent using Spanish language voice announcements. YVTO also transmits 100 ms-long beeps of 1000 Hz every second, except for thirty seconds past the minute. The top of the minute is marked by a 0.5 second 800 Hz tone.The station previously broadcast on 6,100 MHz but appears to have changed to the current frequency by 1990.

Yesterday (time)

Yesterday is a temporal construct of the relative past; literally of the day before the current day (today), or figuratively of earlier periods or times, often but not always within living memory.

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