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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.<ref>Lévi 1927</ref> 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.<ref>Yang 1947</ref> [[Henry Margenau]] in 1950 suggested that the chronon might be the time for light to travel the [[Classical electron radius|classical radius of an electron]].<ref>Margenau 1950</ref>

==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{{su|p=−24}} seconds for an [[electron]].<ref>Farias & Recami, p.11.</ref> This is much longer than the [[Planck time]], which is only about 5.39×10{{su|p=−44}} seconds.  The Planck time is a theoretical lower-bound on the length of time that could exist between two connected events{{citation needed|date=March 2019}}, 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.{{citation needed|date=July 2014}}  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.<ref>Farias & Recami, p.18.</ref> The value for the chronon, ''θ''<sub>0</sub>, is calculated from:

:<math>\theta_0=\frac{1}{6\pi\epsilon_0}\frac{e^2}{m_0c^3}\ </math><ref>Farias & Recami, p.11. Caldirola's original paper has a different formula due to not working in standard units.</ref>

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.{{clarify|date=February 2014}} This model supposedly avoids the difficulties met by Abraham–[[Hendrik Lorentz|Lorentz]]'s{{which|date=February 2014}} and [[Paul Dirac|Dirac]]'s approaches{{which|date=February 2014}} to the problem, and provides a natural explication of [[quantum decoherence]].<!--I assume these were Caldirola's claims, not merely the claims of some anonymous Wikipedia editor. I haven't checked them.-->

==See also==
*[[Elementary particle]]
*[[Gravastar]]
*[[List of particles]]
*[[Particle physics]]
*[[Theoretical physics]]

==Notes==
{{reflist}}

==References==
*{{cite journal
  | last =  Lévi
  | first = Robert
  | title = Théorie de l'action universelle et discontinue
  | journal = Journal de Physique et le Radium
  | volume = 8
  | pages = 182–198
  | year = 1927
  | doi =  10.1051/jphysrad:0192700804018200
  | issue =  4}}
*{{cite book
  | last =  Margenau
  | first = Henry
  | title = The Nature of Physical Reality
  | url =  https://archive.org/details/natureofphysical0000marg
  | url-access =  registration
  | publisher = McGraw-Hill
  | year = 1950}}
*{{cite journal
  | last =  Yang
  | first = C N
  | title = On quantized space-time
  | journal = Physical Review
  | volume = 72
  | pages = 874
  | year = 1947
  | doi =  10.1103/PhysRev.72.874|bibcode = 1947PhRv...72..874Y
  | issue =  9 }}
*{{cite journal
  | last = Caldirola
  | first = P.
  | title = The introduction of the chronon in the electron theory and a charged lepton mass formula
  | journal = Lettere al Nuovo Cimento
  | volume = 27
  | pages = 225–228
  | year = 1980
  | doi = 10.1007/BF02750348
  | issue = 8 }}
*{{cite arXiv
  |author1=Farias, Ruy A. H. |author2=Recami, Erasmo | title = Introduction of a Quantum of Time ("chronon"), and its Consequences for Quantum Mechanics
  | date = 1997-06-27
  | eprint = quant-ph/9706059
}}
*{{cite journal
  | last = Albanese
  | first = Claudio
  |author2=Lawi, Stephan
  | title = Time Quantization and q-deformations
  | journal = Journal of Physics A
  | volume = 37
  | pages = 2983–2987
  | year = 2004
  | url = http://eprints.imperial.ac.uk/bitstream/10044/1/48/1/Time%20Quantization%20and%20q.pdf
  | doi = 10.1088/0305-4470/37/8/009
  | accessdate = 2006-07-31 |arxiv = hep-th/0308190 |bibcode = 2004JPhA...37.2983A
  | issue = 8 }}

==External links==
*{{cite web|title=First Experimental Evidence That Time Is an Emergent Quantum Phenomenon|url=http://science.slashdot.org/story/13/10/23/129220/first-experimental-evidence-that-time-is-an-emergent-quantum-phenomenon|website=Slashdot|archiveurl=https://web.archive.org/web/20150325035225/http://science.slashdot.org/story/13/10/23/129220/first-experimental-evidence-that-time-is-an-emergent-quantum-phenomenon|archivedate=2015-03-25}}

{{Time Topics}}
{{Time measurement and standards}}

[[Category:Quantum gravity]]
[[Category:Units of time]]