However there is a different way of thinking about time. Imagine that the laws of our universe set a lower limit on the period of any recycling dynamical system that can serve as a clock. Recall that, owing to the irreversibility of time, and its intimate association with causation, the only way to establish a unit for measuring temporal durations is to build (either practically or as a thought experiment) a *machine* that, treated as a *system in isolation* , that is to say free of force fields or interactions with other systems, will recycle back to some initial state S at t= "0", *exactly* at some future time t="T". The structure of causation then assures that this system will recycle indefinitely in intervallic pulses T,2T,3T... unless its' isolation is broken by external forces.

To measure time one can, like John Harrison, set out to build a (magnificent) clock, or treat clocks in the abstract as causal loops allowed by the laws of nature. My suggestion is that one look for natural systems that function as clocks. Apart from rough approximations like the heart-beat, or the rotation of the earth about the sun, the best candidate for such a system embedded in nature is a photon of energy E, vibrating at a frequency ν, with E =hν.

There is obviously a close link between "uniformity" of causation in our universe and the regular pulsations of radiation. It shouldn't be difficult to demonstrate, from basic relativity theory, a connection between the constancy of the speed of light and the way that photonic vibrations function as the natural clocks of our universe.

In several articles of mine on the physics of time in Ferment Magazine (visit the folders of papersPhysics of Time , arguments are presented to show the following: if K is a collection of clocks, and μ the smallest period of any clock in K, then no algebraic combination of periods of other clocks in K, obtained by concatenating the inception and termination moments of these clocks, can create an effective clock mechanism that pulses at a period ν' strictly less than μ .

Yet a shortest period, or highest frequency, for all the radiation in the universe must exist. If photons were allowed to have infinitely or indefinitely large energies, then a number of impossible situations would result, including :

- The energy of such a photon would consume the whole universe.
- Its effective gravitational energy would cause all other objects to follow it into a massive Black Hole.

On the simple grounds of common sense, the assertion that there is an upper limit to the frequency of an isolated photon seems inevitable. Let this maximum frequency be ψ ; its inverse θ = 1/ψ becomes the shortest possible time period. θ then functions as the size of the minimum discrete time quantum for all clocks and for all measurable time intervals. Since time and energy are complements in quantum theory, and energy is emitted in discrete jumps, it is not surprising that time itself (in terms of what can be physically measured), would have a similar discrete character.

Positing a discrete time quantum ψ defined in terms of periods of constructible clocks, also provides a new way of looking at Heisenberg's Uncertainty Principle. The measurements on complementary variables that figure into the statement of this principle are taken to be both* simultaneous* and *instantaneous*. Relativity does not rule out the possibility of simultaneity for events occurring at the same location in space, or even in the same reference frame. It should come as no surprise, however, that the concept of an instantaneous measurement is inherently unsound in the quantum context. The discrete time quantum gives an explicit form to this objection.

What the Uncertainty Principle says is that the uncertainty in the *action* is greater than h, (or h/2π). The dimensions of action are mass, distance squared, and inverse time. If mass is taken to be a parameter, a precise measurement of time must produce a wide uncertainty in length; it doesn't matter whether one chooses to decompose the action into length and momentum, or energy and time, or if one speaks of the uncertainty in complementary measurements of distance and momentum, or of the time required to make an exact measurement of energy. If there are jumps in time (as measured by conceivable clocks), then there are jumps in causation, and these jumps must translate into uncertainties in measurement.