The choice of mathematical model of the time parameter plays a central role in all theories. If we think of time as continuous, then we can formulate concepts of velocity and acceleration, fundamental to most modern theories of the universe. On the other hand, if time is discontinuous or discrete, we will have different mathematical structures, such as difference equations rather than differential equations.

Particle decays

Many so-called ‘elementary’ particles are unstable, decaying into two or more other particles. Usually there is a characteristic timescale for each type of decay. The measurement of these decay lifetimes is a fundamental weapon in the validation of modern particle theories, as these usually give predictions for such lifetimes. Normally, particle decay lifetimes are modelled in terms of time dependent decaying exponentials of the form e~^{rt}, where Г is the theoretical lifetime being investigated. Although this seems simple and straightforward, the architecture associated with particle decay experiments is actually complicated and very different to the simplistic Block Universe architecture usually assumed to faithfully model the universe. Such exponentials represent data acquired from many repetitions of a decay, with measurements taken at the end of each run, each of which has its own stopping time. It was pointed out by Misra and Sudarshen that decay experiments involved several different architectures that depend on the type of questions asked by the observers of the decay processes being investigated [Misra & Sudarshan, 1977]. A spectacular demonstration of this is in the class of experiments demonstrating the so-called ‘Quantum Zeno’ effect [Itano et al., 1990], where the observational protocol (specific techniques of measurement) imposes an architecture in which an otherwise unstable SUO appears to be stable. Such experiments can be discussed using discrete time rather than continuous time [Jaroszkiewicz, 2008b].