Chronon

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 standard quantum mechanics, 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.

One such model was introduced by P. Caldirola in 1980. In Caldirola's model, one chronon corresponds to about 2×10⁻²³ seconds. He 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.

Derivation of the Chronon Concept

The need for a Chronon comes about from the real physical limits to our universe, namely that nothing (not even space itself) can exist coherently smaller than the planck length. By imposing this limit on one half-wavelength of a beam of light and dividing by the speed of light one can obtain a maximum measurable frequency, and hence a minimum measurable period of time (1.078×10⁻⁴³ seconds). This time scale is too small to be noticeable on the space-time scale of humans, so the universe appears very continuous even though it is happening in discrete segments of time.

This concept becomes important on scales much smaller than the nucleus of an atom, and on much larger scales when a lot of mass is concentrated in a small space, like in a Gravastar or a Black Hole. The effects of Chronons may also become apparent as rapidly approaching observers moving through space can have their incoming light blue shifted up to this limit.

The Universe as a discrete-time system

The presence of a ‘smallest time’ in the universe means that time moves in discrete segments, and not continuously. However, since these segments are so small on the scale of human measurability, it is often a good approximation to assume time and space are continuous. The differences become apparent on extremely small length and time scales, and are therefore important for understanding quantum physics.

Discrete-time sampling theorem says that a discrete signal cannot contain higher frequencies than 1 cycle per 2 samples, where a cycle corresponds to a wave going from ‘high’ to ‘low’. In other words:

$f_{m}={\frac {1}{2T_{s}}}$

where f_m is the maximum possible frequency, and Ts is the period between each sample. In the case of our universe this sample period is the planck time, and that corresponds to a maximum measurable frequency of

$9.276\times 10^{42}{\mbox{ Hz}}$

Not to say that higher frequencies can't happen, only that we can't measure them with the limited ‘sampling rate’ of the universe.

So what happens to all of the higher frequencies? In discrete signal processing, if one tries to sample a continuous signal whose frequency content is too high, aliasing occurs. So instead of it being a high frequency, it appears as a low frequency. In effect, going past this frequency limit is the same as starting over at low frequencies again and moving up from there, with most of the original signal content lost in-between samples.

The relevance of this fact for the structure of the universe is not yet known, but it may have the power to explain several phenomenons in the world of quantum physics. For example, why space and time seem to become “fuzzy” around distances near the planck length, and times near the planck time (see quantum foam).

See also

• Quantum mechanics
• Particle physics
• Gravastar
• List of particles
• Elementary particle
• Theoretical physics

References

• Farias, Ruy A. H.; Recami, Erasmo (1997-06-27). "Introduction of a Quantum of Time ("chronon"), and its Consequences for Quantum Mechanics". arXiv. Retrieved 2006-07-31. {{cite journal}}: Cite journal requires |journal= (help)CS1 maint: multiple names: authors list (link)
• Albanese, Claudio (2004). "Time Quantization and q-deformations" (PDF). Journal of Physics A. 37. IoP: 2983–2987. doi:10.1088/0305-4470/37/8/009. Retrieved 2006-07-31. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)