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Reliable Clocks

Outline

EthnoPhysics began with the premise that we can understand time by describing what we see, hear, taste and feel.

Clocks are shown in this engraving from Diderot's Encyclopédie printed in Paris, 1768.
Horlogerie, Plate I, Encyclopédie, ou Dictionnaire Raisonné des Sciences, des Arts et des Métiers. Edited by Denis Diderot and Jean le Rond d’Alembert, Paris 1768. Photograph by D Dunlop.

But, according to Albert Einstein time is what a clock tells.1To be more precise, this quotation has been translated by Robert W. Lawson as “… we understand by the time of an event the reading (position of the hands) of that one of these clocks which is in the immediate vicinity (in space) of the event. In this manner a time-value is associated with every event which is essentially capable of observation.” From: Albert Einstein, Relativity the Special and the General Theory, page 24. Published by Methuen & Company, London 1936. So to make sense of time we are going to give some consideration to how a clock can be understood as a collection of sensations.

Over the next few pages we discuss temporal orientation as a binary description of thermal sensation. We also analyze how historical order is related to the temporal orientation. Einstein also taught us that time depends on some frame of reference, so we consider that too.

Ultimately clocks are mathematically modeled just like other particles. They are usually noted using the Greek letter  \mathbf{\Theta} . They are objectified from repetitive chains of events  \Psi written as

\Psi^{\mathbf{\Theta}} = \left( \mathsf{\Omega}_{1}, \, \mathsf{\Omega}_{2}, \, \mathsf{\Omega}_{3} \; \ldots \; \right)

where  \mathsf{\Omega} notes a repeated cycle. All clocks are supposedly made of quarks  \mathsf{q} so clock cycles are represented by collections of quarks

\mathsf{\Omega}^{\mathbf{\Theta}} = \left( \mathsf{q}_{1}, \, \mathsf{q}_{2}, \, \mathsf{q}_{3} \; \ldots \; \mathsf{q}_{N} \right)

Communally, some clocks are preferred for being exceptionally stable, cheap or accessible. Historical examples include seeing the daily movement of a sundial’s shadow, or hearing the routine ringing of a bell. Today, most practical clocks are terrestrial devices that have been calibrated for time-keeping consistency with their prehistoric forerunners, the solar clocks.

Reference Frames

Clocks are used to describe change. But for observations to be scientific, we also specify some standards for comparison. More exactly, let some well-known particle F be characterized by a chain of events noted as

\Psi^{\mathsf{F}} = \left( \mathsf{F}_{1}, \, \mathsf{F}_{2}, \, \mathsf{F}_{3} \; \ldots \; \mathsf{F}_{k} \; \ldots \; \right)

We might use this widely known sequence to provide a sort of background or context when reporting on the events of some other particle P. Then if P changes, the variation can be described relative to F. When we do this, we call F a frame of reference and presume that events of F and P are associated in pairs

\left\{ \mathsf{P}_{k}, \, \mathsf{F}_{k} \rule{0pt}{9px} \right\}

so that every report about P is at least implicitly accompanied by an observation of F. We may schematically describe P using the chain of events

\Psi^{\mathsf{P}} = \left( \mathsf{P}_{1}, \, \mathsf{P}_{2}, \, \mathsf{P}_{3} \; \ldots \; \mathsf{P}_{k} \; \ldots \; \right)

But if the description is expressed relative to a frame of reference, then events are explicitly described by the chain

\Psi^{\mathsf{P}} = \left( \; \left\{ \mathsf{P}_{1}, \mathsf{F}_{1} \right\},  \;  \left\{ \mathsf{P}_{2}, \mathsf{F}_{2} \right\} \;  \ldots \;  \left\{ \mathsf{P}_{k}, \mathsf{F}_{k} \right\}  \;  \ldots \; \rule{0px}{13px} \right)

Aside from being used to describe change, a reference frame is a compound quark like any other particle, and so it can be characterized by its quark coefficients. For example, we can use the angular momentum quantum number  \textsl{\textsf{J}} to describe F. Let the frame contain equal numbers of up and down seeds so that N^{ \mathsf{U}}  = N^{ \mathsf{D}}. Then

\textsl{\textsf{J}}^{ \, \mathsf{F}} \equiv \dfrac{ \, \left| \,  N^{\mathsf{U}} - N^{\mathsf{D}} \, \right| \, }{8} = 0

And so by definition F is a non-rotating frame of reference. This specification does not appeal to some vague spatial framework like the distant stars. But it still uses a celestial body, the Sun, as a reference sensation to define rotating seeds. It avoids several hundred years of inconclusive analysis about rotating buckets.2Isaac Newton, Mathematical Principles of Natural Philosophy, page 10. Translated by Andrew Motte and Florian Cajori. University of California Press, 1946., 3Ernst Mach, The Science of Mechanics, second edition page 231. Translated by Thomas J. McCormack. The Open Court Publishing Company, Chicago 1902. And it eschews many experimentally inaccessible assertions concerning Mach’s principle .

Temporal Orientation

Let P be some particle characterized by its quark coefficients N. Recall that these coefficients present N^{\mathsf{T}} as the total number of top quarks plus top anti-quarks in P. So N^{\mathsf{T}} is also the number of top seeds in P. Similarly N^{\mathsf{B}} marks the number of bottom seeds, N^{\mathsf{S}} notes the number of strange seeds and N^{\mathsf{C}} indicates the number of charmed seeds. Taken together, these quantities describe the distribution of baryonic seeds in P. They are combined to define the temporal orientation as

\delta_{t} \equiv \begin{cases} +1 & \mathsf{\text{if}} \; \; \; N^{\mathsf{T}} + N^{\mathsf{C}} > N^{\mathsf{B}} + N^{\mathsf{S}} \\ \; \; 0 & \mathsf{\text{if}} \; \; \; N^{\mathsf{T}} + N^{\mathsf{C}} = N^{\mathsf{B}} + N^{\mathsf{S}} \\ -1 & \mathsf{\text{if}} \; \; \; N^{\mathsf{T}} + N^{\mathsf{C}} < N^{\mathsf{B}} + N^{\mathsf{S}} \end{cases}

This number  \delta_{t} is used in the next few articles to assign a time of occurrence to P’s events. It is compared with reference sensations to establish a relationship between the numerical order assigned to events, and the order that they occur in history.

Temporal orientation is a binary description of thermal sensations like those shown in this icon.

Sensory interpretation: Top seeds and charmed seeds are objectified from warm and burning thermal sensations. Whereas bottom seeds and strange seeds are defined from cool and freezing thermal feelings. So the number  \delta_{t} is a binary report that collectively describes all thermal sensations. If  \delta_{t} = 0 then we say that P is tepid.

Thus, the temporal orientation notes if a compound sensation is overall hotter or colder than tepid. So  \delta_{t} is a crude indication of whether the temperature of a particle is higher or lower than average.

Upcoming pages go into more detail, but here is a preview of how  \delta_{t} is relevant for establishing a collective understanding time’s direction. First, particles with the same temporal orientation satisfy a condition for being thermally similar. Then, two similar particles would interact with a tepid particle in the same way; both would experience either a warming process, or a cooling process. But not one of each. Next we consider how this agreement allows for the logical development of historically ordered events.

Temporal orientation is a binary description of quantized sensation like those shown by these beads from Borneo.
Baby Carrier panel, Bahau people. Borneo 20th century, 30 x 29 cm. Photograph by D Dunlop.

Historical Order

Earthiness is illustrated by this planet icon for the sensation of touching the earth.

Our knowledge of time’s arrow comes from the ordinary run of human affairs. So for EthnoPhysics, the direction of time is derived from the historical record of human events; our collective experience, as recorded in the newspapers. Arbitrary sequences of events can be compared with such mundane proceedings, and a binary description of their relationship made as follows.

The historical record is introduced via the reference sensation of touching the Earth. And the very common human experience of keeping in touch with some selection of terrestrial events is assumed to provide an ordered set of sensations that we note by  \Psi^{\mathsf{Earth}}. Consider comparing these terrestrial-events with another chain-of-events associated with particle P, written as

\Psi^{\mathsf{P}} = \left( \mathsf{P}_{1}, \, \mathsf{P}_{ 2}, \, \mathsf{P}_{ 3} \; \ldots \; \mathsf{P}_{k} \; \ldots \; \right)

Make the comparison using  \delta_{t} their temporal orientation. Then we define   \epsilon_{t} as the direction-of-time for P’s events

 \epsilon_{t}^{\, \mathsf{P}} \equiv \, \delta_{t}^{\, \mathsf{P}}  \!  \cdot \delta_{t}^{\mathsf{\, Earth}}

When P is like the Earth both particles have the same temporal-orientation, so \delta_{t}^{\, \mathsf{ P}} \! = \delta_{t}^{\mathsf{\, Earth}} = \pm 1. If this condition obtains, then

 \epsilon_{t}^{\, \mathsf{P}} = 1

and we say that P’s events are in historical order.

The historical-order is locked into the numerical-order of event-index  k using the following nomenclature. Let  \mathsf{P}_{i} and  \mathsf{P}_{f} be an arbitrary pair of events in   \Psi^{\mathsf{P}} . If  \epsilon_{t}^{\, \mathsf{P}} =1 and  i<f, then we call  \mathsf{P}_{i} the initial event, and  \mathsf{P}_{f} the final event of the pair.

Temporal orientation is a binary description of thermal sensations like those shown in this icon.

Sensory interpretation: When we call a chain-of-events a history we imply it is historically ordered. The ice cubes in a summer drink melt away. Fires burn-out. People are born, and then they die. These event chains are understood as going forward in history. To label initial and final events consistently within this collective grasp of order, consider using a thermal reference provided by the absorption of a tepid particle.

Historical order is exemplified in this engraving of an 18th century clock mechanism.
Encyclopédie, ou Dictionnaire Raisonné des Sciences, des Arts et des Métiers. Edited by Denis Diderot and Jean le Rond d’Alembert, Paris 1768. Photograph by D Dunlop.

Let  \epsilon_{t}^{\, \mathsf{P}} =1 so that P has the same temporal orientation as the Earth. Then the temperature of both P and the Earth are on the same side of tepid. Both are either higher or lower. So they both describe the absorption in the same way; as either a warming process or a cooling process. But not one of each.

The terms initial and final can therefore be used uniformly for describing both P and the Earth. This agreement applies to any thermally-similar particle. And the similarity only needs to be a crude, binary distinction. So, the events happening to most particles are automatically described as going forward in history because almost all of our experience happens in Earth-like conditions.

We refer back to  \epsilon_{t} later to make a formal definition of time. But next we discuss the prehistoric foundation for all timekeeping, the solar clocks.

Solar Clocks

Solar clocks are like this radiant icon.

Any clock that depends on observing the brightness or darkness of visual sensations from the Sun is called a solar clock. The most basic solar clock is just squinting at the Sun. But historically, complex sundials have been widely used for solar clocks as well. By the foregoing definition, all solar clocks are at least partly objectified from black and white sensations.

So any solar clock  \mathbf{\Theta}, may be characterized by its helicity. And if  \mathbf{\Theta} is part of a reference frame, then it can be used to establish the phase  \delta_{\theta} for any other particle. When this phase is used to make relative descriptions of terrestrial events, it can be understood as \delta_{\theta} = +1 if an event occurs during the day, or \delta_{\theta} = -1 if an event occurs at night.

Solar clocks are suggested by this radiant circular bead panel from a hat.
Bead panel, Bahau people. Borneo 20th century, diameter 18 cm. Photograph by D Dunlop.

One cycle for a solar clock may be called a solar day, or twenty-four hours, or a nychthemeron. But usually we just call it a day. Solar clocks are always available to provide this semantic anchor for interpreting the phase because seeing the Sun is assumed to be a reference sensation for EthnoPhysics.

Ideas about time are based on solar sensations because the Sun is such a prominent and lofty feature of human consciousness. But the Sun does not have a celestial monopoly, and other clocks may be defined from moons, planets and stars.

Sometimes it is more appropriate to tell time by these other clocks, for example astronomers make extensive use of variable stars . But telling the time by a non-solar clock might be quite meaningless for use with events here on Earth. So making a unified description of celestial and terrestrial events requires some additional systematic connection between clocks.

Astronomers bridge the logical gap by measuring stellar spectra and comparing their observations with nuclear processes seen here on Earth. This is an example of how physics is extended by recognizing recurrent patterns.

Phase

Consider a frame of reference F that is employed to describe some particle P so that the events of F and P are associated in pairs

\left\{ \mathsf{P}_{k}, \, \mathsf{F}_{k} \rule{0pt}{9px} \right\}

Let the frame of reference include a clock noted as  \mathbf{\Theta}^{\mathsf{F}} that is used to represent F so that events of P and  \mathbf{\Theta} are associated in pairs like

\left\{ \mathsf{P}_{k}, \, \mathbf{\Theta}^{\mathsf{F}}_{k} \rule{0pt}{10px} \right\}

Finally let the frame’s clock be characterized by its helicity  \delta_{z} \! \left( \mathbf{\Theta}^{\mathsf{F}} \right). To develop a more objective scientific account of time we make a description of P that is relative to the reference frame F. But, we give  \delta_{z} \! \left( \mathbf{\Theta}^{\mathsf{F}} \right) a new name that is less explicit about the sensory relationship between P and F. Accordingly, the phase of P is defined as

\delta_{\theta}^{\, \mathsf{P}} \; \equiv \; \delta_{z} \! \left( \mathbf{\Theta}^{\mathsf{F}} \right)

If two particles share the same value of  \delta_{\theta} then we say that they are in phase with each other. If not, they are said to be out of phase.

Solar clocks are like this radiant icon.

Sensory interpretation: The helicity can be explained as a representation of achromatic visual sensation. So the phase of P depends on the brightness or darkness of the sensations that are objectified as the reference frame F.

If the Earth is taken as a reference frame, and the brightness of daily events on Earth are used for a simple clock, then the phase indicates whether the background provided by terrestrial events is bright or dark. That is, the phase depends on if events occur in the day or at night.

We exploit this ancient notion of phase when using quark icons. In the images and movies that follow, the phase of a quark is represented by the brightness of the background. For example, here are two southern quarks that are out-of-phase with each other

The phase of a southern quark is indicated by the bright border of this icon.
  \delta_{\theta}^{\, \sf{a}} = +1
The phase of a southern quark is indicated by the dark border of this icon.
  \delta_{\theta}^{\, \sf{a}} = -1

These images emphasize that  \delta_{\theta} is determined by the reference frame, then attributed to an associated particle. The phase is a very relative characteristic.

Phase relationships are suggested by this ritual textile from Indonesia.
Usap, Sasak people. Lombok, circa 1900, 49 x 52 cm. Photograph by D Dunlop.

Phase Symmetry

Consider some particle P that is defined by a chain of repetitive events. And let each repeated cycle \mathsf{\Omega} be parsed into two sets of quarks, noted by  \mathsf{P}_{\mdsmwhtcircle} and  \mathsf{P}_{\mdsmblkcircle}, that are out of phase with each other. This is expressed mathematically as

\mathsf{\Omega} = \left\{ \mathsf{P}_{\mdsmwhtcircle} , \, \mathsf{P}_{\mdsmblkcircle} \rule{0pt}{9px} \right\}

and

\delta_{\theta} \! \left( \mathsf{P}_{\LARGE{\circ}} \right) = - \, \delta_{\theta} \! \left( \mathsf{P}_{\mdsmblkcircle} \right)

The compound quarks \mathsf{P}_{\mdsmwhtcircle} and  \mathsf{P}_{\mdsmblkcircle} are called phase components of P. If these two sets are composed from the same selection of quarks, then a description of the whole cycle \mathsf{\Omega} is unaffected if there is any confusion or mix-up about the sign of the phase. This robust indifference to the phase is useful, so we give particles like this a special name: If

\mathsf{P}_{\mdsmwhtcircle} = \mathsf{P}_{\mdsmblkcircle}

then we say that P has phase symmetry. Alternatively, if \mathsf{P}_{\mdsmwhtcircle} = \overline{\mathsf{P}_{\mdsmblkcircle}} then we say that P has phase anti-symmetry. The most important examples of particles with phase symmetry are protons and electrons. So it is possible to make descriptions of protons and electrons that ignore the phase.

Solar clocks are like this radiant icon.

Sensory interpretation: When the phase indicates whether an event is diurnal or nocturnal, then indifference to phase means that a description does not depend on whether it is day or night. So physicists in different time-zones can easily work together when considering particles like protons and electrons.

Phase symmetry is suggested by this tightly structured Indonesian weaving.
Usap, Sasak people. Lombok, 20th century, 46 x 52 cm. From the collection of Dr. Yong Li Lan, Singapore. Photograph by D Dunlop.

Thermodynamic Processes

Let particle P be described by a historically ordered chain of events  \Psi. Consider some pair of events  \mathsf{P}_{i} and  \mathsf{P}_{f} from the sequence

\Psi^{\mathsf{P}} = \left( \mathsf{P}_{1}, \, \mathsf{P}_{2}, \, \mathsf{P}_{3} \; \ldots \; \mathsf{P}_{i} \; \ldots \; \mathsf{P}_{f} \; \ldots \, \right)

Since  \Psi is in historical order we call  \mathsf{P}_{i} the initial event and  \mathsf{P}_{f} the final event of the pair. If these events always have the same quark coefficients  n , for each sort of quark  \mathsf{q} , then we say that P is isolated.

But if they are not all the same, then we say that P has undergone an interaction with some other particle generically called  \mathsf{X}. Recall that quarks are conserved. So each kind of interaction implies a specific relationship between quark coefficients. Some possibilities are shown in the following table.

Thermodynamic Processes
InteractionCoefficients ∀ q
isolation  \mathsf{P}_{i}  \to \mathsf{P}_{f}   n^{\mathsf{q}} \left( \mathsf{P}_{i} \right) = n^{\mathsf{q}} \left( \mathsf{P}_{f} \right)
emission \mathsf{P}_{i}  \to \mathsf{P}_{f} + \mathsf{X}    n^{\mathsf{q}} \left( \mathsf{P}_{i} \right) = n^{\mathsf{q}} \left( \mathsf{P}_{f} \right) + n^{\mathsf{q}} \left( \mathsf{X} \right)
absorption  \mathsf{P}_{i} + \mathsf{X}  \to \mathsf{P}_{f}   n^{\mathsf{q}} \left( \mathsf{P}_{i} \right)  + n^{\mathsf{q}} \left( \mathsf{X} \right) = n^{\mathsf{q}} \left( \mathsf{P}_{f} \right)
annihilation  \mathsf{P}_{i} + \mathsf{\overline{P}}_{i}  \to \mathsf{P}_{f}  \Delta n^{\mathsf{q}} \left( \mathsf{P}_{f} \right) = 0
pair production  \mathsf{P}_{i} \to \mathsf{\overline{P}}_{f}  + \mathsf{P}_{f}   \Delta n^{\mathsf{q}} \left( \mathsf{P}_{i} \right) = 0

If the events in  \Psi are described by their temperature   T, then any changes are noted by subtracting initial from final values. We write  \Delta T \, \equiv \, T_{f} - T_{i}.

Thermal Processes
warming    T_{f}    > T _{i}
isothermal    T_{f}   = T _{i}
cooling    T_{f}    < T _{i}

Any thermal changes due to a process can be classified by  \Delta T as indicated in the accompanying table. And so for example we might make a combined description of some process as isothermal absorption, or perhaps cooling by emission etc.

Processes, both thermal and thermodynamic, are represented by this six sensation icon.

Sensory interpretation: The quarks that are explicitly enumerated in the processes discussed above are named after their thermodynamic seeds. These seeds are in-turn defined by Anaxagorean sensations. So all the foregoing interactions are just detailed, systematic descriptions of thermal, visual and somatic sensations. Thermodynamic processes are objectified ways of recounting changes in what we see, hear and feel.

Clock talk is winding-down now. So next we take a good look at some EthnoPhysics faviconSpectacular Photons.

Processes, both thermal and thermodynamic, are suggested by this sacred weaving from Indonesia.
Usap, Sasak people. Lombok, 20th century, 49 x 51 cm. From the collection of Dr. Yong Li Lan, Singapore. Photograph by D Dunlop.
References
1To be more precise, this quotation has been translated by Robert W. Lawson as “… we understand by the time of an event the reading (position of the hands) of that one of these clocks which is in the immediate vicinity (in space) of the event. In this manner a time-value is associated with every event which is essentially capable of observation.” From: Albert Einstein, Relativity the Special and the General Theory, page 24. Published by Methuen & Company, London 1936.
2Isaac Newton, Mathematical Principles of Natural Philosophy, page 10. Translated by Andrew Motte and Florian Cajori. University of California Press, 1946.
3Ernst Mach, The Science of Mechanics, second edition page 231. Translated by Thomas J. McCormack. The Open Court Publishing Company, Chicago 1902.