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Clocks and Frames

EthnoPhysics begins with the premise that we can understand time by describing what we see, hear and feel. And, according to Albert Einstein , time is what a clock tells1To 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 articles 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 below. Ultimately clocks are mathematically modeled just like other particles. They are usually noted using the Greek letter  \mathbf{\Theta}, and 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}        \; \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 clocks are terrestrial devices that have been calibrated for time-keeping consistency with their historical forerunners, the solar clocks.

Frames of Reference

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   \vphantom{X^{X^{X}}} \ \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 non-testable assertions concerning Mach’s principle. Next, we discuss how to establish a temporal orientation within F.

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.
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.