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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. In simple language, a chronon is the smallest, discrete, non-decomposable unit of time.

In a one-dimensional model, a chronon is a time interval or period, while in an n-dimensional model it is a non-decomposable region in n-dimensional time. It is not easy to see how it could possibly be recast so as to postulate only a discrete spacetime (or even a merely dense one). For a set of instants to be dense, every instant not in the set must have a sequence of instants in the set that converge (get arbitrarily close) to it. For it to be a continuum, however, something more is required— that every set of instants earlier (later) than any given one should have a tight upper (lower) bound that is also an instant (see least upper bound property). It is continuity that enables modern mathematics to surmount the paradox of extension framed by the pre-Socratic eleatic Zeno—a paradox comprising the question of how a finite interval can be made up of dimensionless points or instants.[citation needed]

Early work

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While time is a continuous quantity in both standard quantum mechanics and general relativity, some 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

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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 may be postulated as a lower bound on the length of time that could exist between two connected events[citation needed], 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] 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 as[6]

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 that 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.[clarification needed] This model supposedly avoids the difficulties met by Abraham–Lorentz's[which?] and Dirac's approaches[which?] to the problem and provides a natural explication of quantum decoherence.

See also

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Notes

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References

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Chronon

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A chronon is a proposed quantum of time in , representing a discrete and indivisible fundamental that underlies the evolution of , particularly in extensions of non-relativistic . Introduced by Italian physicist Piero Caldirola in the 1970s, it posits that while time itself remains continuous, the dynamical responses of particles to forces occur in finite time intervals, addressing issues such as the stability of atomic states and from accelerated charges. For the , the chronon duration is derived from classical electrodynamics as τ0=2e23mec3≈6.27×10−24\tau_0 = \frac{2 e^2}{3 m_e c^3} \approx 6.27 \times 10^{-24} seconds, where ee is the , mem_e is the , and cc is the , reflecting the time scale associated with the particle's internal structure. Caldirola's framework incorporates the chronon into the , yielding discretized versions (retarded, symmetric, and advanced) that introduce non-unitary evolution and natural dissipation, such as friction and decoherence in . This leads to predictions like an upper limit for particles (Emax⁡=ℏ/τ0≈100E_{\max} = \hbar / \tau_0 \approx 100 MeV for electrons) and a spectrum of masses that closely match experimental values, for instance, the mass at approximately 105.7 MeV. The theory also resolves classical paradoxes, such as the absence of from uniformly accelerated charges in certain formulations, by treating particles as extended objects rather than point-like. Despite these implications, the chronon remains a speculative without direct experimental confirmation, as mainstream and relativity treat time as continuous. It has influenced discussions on quantized in approaches but is primarily explored in niche literature on foundational quantum issues. Ongoing theoretical work examines its compatibility with relativistic extensions and potential links to Planck-scale physics.

Definition and Fundamentals

Core Concept

The chronon is a proposed indivisible quantum of time, positing that while time itself flows continuously, the dynamical evolution of occurs in discrete steps rather than through changes. This hypothetical unit serves as the fundamental building block of temporal progression in certain theoretical frameworks of physics. In this quantized view, chronons define the smallest meaningful interval over which physical processes can occur, below which no further subdivision is physically significant. This discreteness mirrors the quantization seen in other domains, such as energy quanta exemplified by photons or action quanta in , providing a finite resolution to temporal dynamics. Unlike the universal Planck time, which represents a fixed scale derived from fundamental constants, the duration of a chronon is not constant but depends on the intrinsic properties of the particle involved, such as its and charge. For the , it is given by τ0=2e23mec3≈1.25×10−23\tau_0 = \frac{2 e^2}{3 m_e c^3} \approx 1.25 \times 10^{-23} seconds. Conceptually, the introduction of chronons aims to address infinities and inconsistencies in classical theories of the , such as infinite or losses for accelerating charged particles in the Lorentz-Dirac framework.

Relation to Planck Time

The Planck time, denoted tPt_P, represents a fundamental unit of time derived solely from three universal constants of nature: the reduced Planck constant ℏ\hbar, the GG, and the cc. It is given by the formula tP=ℏGc5,t_P = \sqrt{\frac{\hbar G}{c^5}},
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