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Alternative approaches to quantization of time are seldom discussed in modern scientific literature. I would like to offer a subject for discussion at your Web site, which might be interesting.
Let us confine ourselves to the assumption that time is a phenomenon and factor of variability.
Any object ages. This provision is fixed in the second low of thermodynamics. Naturally, this law is based on statistical categories and has no formal basis at the quantum level.
However, the increment of entropy is somehow or other connected with quantum processes. It is possible to make an attempt to examine the transition of the object from one (quantium) state to a subsequent one.
It is interesting to view the application of this task in relation to the microcosm. The idea is that the wave function gets rearranged at the moment of reduction only. While the wave function remain the same, it is possible to consider the microparticle's intrinsic time as suspended, the particle "does not age" in this time interval.
This hypothesis makes it possible to handle the phenomenon of time and gravitation quantization. If we deem the reduction as an "event", then we may assume that quantization take place according to the following scheme: event - space -next event - other space configuration, etc. The self local time of quantum object is considered, it is logical to assume, that to it there corresponds self local spatial configuration.
This model enables us to view the difficulties of quantum mechanics from a quite unusual point of view. I believe that the puzzle of the so-called "Action at a distance" is concluding in the quantization of gravitation. In EPR paradox, a pair of microparticles that are separated in space will be correlated only till their space-time continuum undergoes changes. Meanwhile their intrinsic time "is suspended".
The interpretation of the Dirac equation with reference to this model was offered. An assumption was made stating that such approach makes it possible to reveal the uniform mechanism for realization of "the time arrow" and the increasing entropy.
The similar approach has offered Yu. S. Vladimirov (the Moscow State university) in papers about binary systems of complex relations. Its theory offers an expedient of the description of microparticles at transition from one quantum state to the following, without use of the aprioristic space and time. Thus, the stream of time and space arise only at a macroscopical level as effect of numerous quantum transitions.Attachment #1: report_Silin.pdf