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
A prominent 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:
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.clarification needed This model supposedly avoids the difficulties met by Abraham–Lorentz'swhich? and Dirac's approacheswhich? to the problem, and provides a natural explication of quantum decoherence.
Another model of quantised time was proposed by Sam Vaknin in his 1982 Ph.D. dissertation, titled "Time Asymmetry Revisited". He postulates the existence of a particle (chronon). In the proposed theory, time is the result of the interaction of chronons, very much as other forces in nature are the result of other particle interactions. Vaknin postulates the existence of various time quarks (up, down, colors, etc.) whose properties cancel each other and thus the arrow of time is derived (time asymmetry). The postulated particle (chronon) is not only an ideal clock, but also mediates time itself (analogous to the relationship between the Higgs boson and mass). In other words, what we call "time" is the interaction between chronons in a field. Chronons exchange between them a particle and thereby exert a force. "Events" are perturbations in the Time Field and they are distinct from chronon interactions. Chronon interactions (particle exchanges) in the Time Field generate "time" and "time asymmetry" as we observe them.78
Suchard's chronon is a purely geometric approach, complementing Vaknin's asymmetry and spinor-based approach. Equation (7) in Suchard's paper has a divergence component, that according to a possible interpretation (6.4), offers a way to achieve electro-gravity. A small correction is, however, that the coefficient of this term should be 2 and not 1 as it is in equation (7). The resulting postulated gravitational field resembles an electric dipole and offers elevation on the expense of the trajectories of far bodies of mass quite the same way ebb and tide take energy from the moon's trajectory. According to that assumption, the divergence term coincides with electric charges and therefore can explain the Dark Matter effect by a negligible excess of intra-galactic positive charges. The ordinary conservation law (8) is then replaced with a more general law (25) in the same paper “Upper Time Limit, Its Gradient Curvature, and Matter”.91011
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- Lévi 1927
- Yang 1947
- Margenau 1950
- Farias & Recami, p.11.
- Farias & Recami, p.18.
- Farias & Recami, p.11. Caldirola's original paper has a different formula due to not working in standard units.
- California Miramar University, available on Microfiche in UMI and from the Library of Congress http://catalog2.loc.gov/vwebv/holdingsInfo?searchId=115001&recPointer=0&recCount=25&searchType=1&bibId=3810279
- Vaknin S Time Asymmetry Re-Visited
- “Upper Time Limit, Its Gradient Curvature, and Matter” by Eytan H. Suchard (Journal of Modern Physics and Applications 2014, 2014:5) http://scik.org/index.php/jmpa/article/view/1317/640
- “Absolute Maximum Proper Time to an Initial Event, the Curvature of Its Gradient along Conflict Strings and Matter” by Eytan H. Suchard (Journal of Modern Physics Vol.4 No.6 (2013), Article ID:33086) http://www.scirp.org/journal/PaperInformation.aspx?PaperID=33086
- “Upper Time Limit, Its Gradient Curvature, and Matter” by Eytan H. Suchard
- 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". Lett. Nuovo Cim. 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 quant-ph.
- Albanese, Claudio; and Lawi, Stephan (2004). "Time Quantization and q-deformations". 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.
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