Part 1, which begins our examination of the question 'what is time?' can be viewed here.
Part 2 Some travels through time can be viewed  here.
Part 3 discussing language, sequence and order, can be viewed  here.

A Theory of Time Part 4 : Steno, Foucault and Allais

What, at the Most Fundamental Level, is a Clock?

A clock, as Gerhard Adam so astutely observes is a means by which any two observers can  connect their observations to a common frame of reference. In his terms it is an  independent source to which all adherents can relate their event.  To paraphrase the wording of biochemist Michael White: you can line up the causal chains detected by the observers, and you can see the similarities.

Any device, natural or artificial, which can generate a simple causal chain, can be used as a clock. The accuracy of any specific type of clock, in terms of lack of frequency drift, for example, can be assessed by overlaying sections of the chains which have been output by a number of such clocks.   Objectively, synchronising any two clocks is a process that can be reduced mathematically to the same paradigm as dendrochronology.   Time in the abstract is not necessary to the process:  it is simply a matter of pattern matching.

We humans agree on a shared causal chain model which we agree to call a clock. We compare our clocks in order to make sure that they march in step. But then we move from the particular to the general:
The clock paradigm works for us.
We can build mathematical models which replicate causal chains in a clock-like way.
Those mathematical models work for us in explaining cosmic scale and atomic scale events.
It follows that time must have a real existence.
This is a non sequiteur, from the Latin: it does not follow.
Other Types of Clock:  Rings, Layers and the LIFO Stack

Nicholas Steno came to geology from a backgound in anatomy and the scientific method. In 1666 he examined the head of a recently caught shark. He observed that the shark's tooth structure resembled certain rocks - glossopetrae - which were at that time being discussed in academia.   He deduced that the glossopetrae resembled shark's teeth simply because they were, in fact, shark's teeth.  Steno's studies of rock formations, and the glossopetrae finding, led him to deduce a theory about rock formations: layers on top of a set of strata conform to the shape of lower layers, therefore, the top layers must be youngest and the bottom layers must be oldest.  This is exactly the fundamental model of a LIFO stack.

The Steno Clock.

A proposed modification to Steno's law of superposition, for the purposes of this discussion:
Rock layers, where not upheaved by geological forces, are layed down as a LIFO stack, the last rock layer formed being the first to be eroded away by meteorological forces.

A plot of rock layer characteristics can be taken, and an attempt made to match that causal chain to rock layers anywhere else on Earth. This method, which I would call LIFO alignment, is one of the foundations of plate tectonics. Where such matching is inaccurate or infeasible, radiometric age dating is possible. But again, this process is but a pattern matching exercise - the causal chains of nuclear processes are matched. Time is not a necessary factor in the comparative measurement of the age of rocks. By means of such geochronolgy, it has been possible to show that widely separated geographic areas were once united in the Earth's history.

For an example of the methodology, see e.g. Geochronology of West Indonesia and its
implication on plate tectonics
, John A. Katili , referenced in Mataloko Geothermal Prospect

Erosion is the 'First Out' aspect of rock layers as a LIFO stack. Erosion has many causes, but water and CO2 seem to be the major players. The fact that water, especially as frost and as ice, can erode rock is widely known. The erosion of rock due to carbonic acid - dissolved CO2 is also widely known. Less widely studied is the erosion of rock by cavitation involving CO2.

Bite-Sized Time.

Like trees, teeth grow in layers. By counting the layers it is possible to established the age of a tree or a tooth. If the tooth coexists with other remains, it is possible to determine the creature's age at death. This is a pure counting process: in the determination of age, time is not a necessary factor.
For a paper on alternating tooth laminations see : Growth Layer Groups (GLGs) in the Teeth of an Adult Belukha Whale (Delphinapterus Leucas) Of Known Age: Evidence for Two Annual Layers, multiple authors.

And so the links are established between causal chains in trees, teeth and rocks, all can be used as clocks.
The Slinky

A slinky is a springy coil of wire, sold as a toy.  It is a useful demonstration of gravity and momentum.  Its wave-like motion when not constrained by gravity was demonstrated during a shuttle mission.  In its end over end motion the slinky has a fairly regular rhythm, and so may be considered as exhibiting a causal chain behaviour.  Hence, it may be categorised with clocks.  In addition, if the two ends of the slinky are painted different colours, its behaviour is a useful demonstration of a  LIFO stack in physics.
Foucault, Allais and the Metronome : a Brief  Introduction

The Mechanical Metronome

A metronome is any device which can produce a causal chain with insignificant drift, with usually an output as sound.  It is a clock with an emphasised tick.  It is brought in to the discussion to demonstrate a variant clock and its application, and to demonstrate an example of the inverted pendulum .  The inverted pendulum is important to later developments of this theory of time.

Foucault's Pendulum

Leon Foucault demonstrated an experiment using an extremely long wire with a large mass suspended at its end, in February 1851 in the Paris Observatory.  The Foucault Pendulum , during the course of the day, appears to change its path in relation to Earth.  This precession effect of the deviation is due to the Earth's rotation.  Descriptions of this pendulum's behaviour suggest that at the poles, the pendulum's path deviates across the ground at the same rate as the Earth's rotation, and that there is no deviation at the equator.
"The challenge is to explain the behavior of a Foucault pendulum that it is not located on either the poles or the equator."   Source
I would suggest that it is only by performing high-precision experiments at the poles and the equator that we may observe small perturbations so as to eliminate them from observations at other locations.

Maurice Allais

In 1954 the Nobel Laureate Maurice Allais was performing experiments on the Foucault pendulum when he noted an anomalous precession.  He noted another during the 1959 solar eclipse and wrote a report on this behaviour.  The effect, which has come to be known as the The Allais Effect is a matter of considerable controversy.
"Allais' pendulum experiments have never even been repeated, let alone improved upon, although Prof. Latham of Imperial College, London made a valiant effort around 1980. Yet the expense and effort involved would be quite trifling upon the general scale of modern physical research. We think that the main barriers have been informational and institutional. The fact that almost all Prof. Allais's original reports have remained (until now) in the French language has undoubtedly been an impediment. "

"unfortunately, we were not able to perform proper determinations during the solar eclipse which took place over Alaska on 14 October 2004 which (as is quite usual) preceded the lunar eclipse of 28 October by a fortnight - but the observations we made are interesting upon the anecdotal level. However, from about the start of November, we were able to conduct a number of twelve-hour runs which showed most interesting systematic disturbances of the pendulums, clearly not due to chance, which we have not as yet been able to explain;"
Nasa overview of the Allais effect
The Coriolis Effect, explained towards the foot of the page on this educational site must be considered in any discussion of the Foucault pendulum and the Allais effect.

I will suspend the discussion here.  There is much room for comments before I move on to a deeper investigation into the nature of time.

Recommended Further Reading:

A review of conventional explanations of anomalous observations during solar eclipses -
Chris P. Duif

The discussion of Foucault, Allais and the Inverted Pendulum
will be developed further in 'A Theory of Time Part 5'.