A chronon is a proposed quantum of time, that is, a discrete and indivisible "unit" of time as part of a theory that proposes that time is not continuous. 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.[1] Henry Margenau[2] suggested that the chronon might be the time for light to travel the classical radius of an electron. 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 C. N. Yang.[3]

One such model was introduced by Piero Caldirola in 1980. In Caldirola's model, one chronon corresponds to about 6.97×10−24
seconds for an electron.[4] This is much longer than the Planck time, another proposed unit for the quantization of time, which is only about 5.39×10-44
seconds. 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 and 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:

\theta_0=\frac{1}{6\pi\epsilon_0}\frac{e^2}{m_0c^3}\ [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 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. ^ Margenau 1950
  3. ^ Yang 1947
  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.