Historical Order
//Horlogerie//, Plate IX-7. 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.
Horlogerie, Plate IX-7. 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.
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Our knowledge of time's arrow comes from the ordinary run of human affairs. So for WikiMechanics, 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 $\Psi ^{\, \sf{ Earth}}$. Consider comparing these terrestrial-events with another chain-of-events associated with particle P

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

Make the comparison using $\, \delta _{ t} \,$ their temporal orientation, to define $\, \epsilon_{ t} \,$ as the direction-of-time for P's events

$\epsilon_{t}^{\, \sf{P}} \equiv \, \delta _{ t}^{\, \sf{ P}} \! \cdot \delta _{ t}^{\sf{\, Earth}}$

When P is like the Earth both particles have the same temporal-orientation; $\delta _{ t}^{\, \sf{ P}} \! = \delta _{ t}^{\sf{\, Earth}} \! = \pm 1 \, \,$. If this condition obtains then

$\epsilon _{t}^{\, \sf{P}} =1$

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 $\sf{P}_{\it{i}}$ and $\sf{P}_{ \it{f}}$ be an arbitrary pair of events in $\Psi^{ \sf{P}}$. If $\epsilon _{t}^{\, \sf{P}} =1$ and $\it{i} < \it{f} \;$, then we call $\sf{P}_{ \it{i}}$ the initial event, and $\sf{P}_{ \it{f}}$ the final event of the pair. Later we also use $\epsilon_{t}$ to make a formal definition of time.

Thermal Processes
warming ${ T_{ \it{f}} \, > T _{\it{i}} }$
cooling ${ T_{ \it{f}} \, < T _{\it{i}} }$
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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. Let $\epsilon_{t}^{\, \sf{P}} = 1$ so that P has the same temporal orientation as the Earth. Then the temperature $T$, 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 be used uniformly for describing both P and the Earth. This agreement applies to any thermally-similar particle. And 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.
Right.png Next step: Describing vibrations.
Summary
Adjective Definition
Direction of Time $\epsilon_{t}^{\, \sf{ P}}\equiv \, \delta _{ t}^{\, \sf{ P}} \! \cdot \delta _{ t}^{\sf{\, Earth}}$ 6-6
Adjective Definition
Historical Order $\epsilon_{t} = 1$ 6-7
Noun Definition
Initial Event The event with the lowest event-index
in a historically ordered pair of events.
6-8
Noun Definition
Final Event The event with the highest event-index
in a historically ordered pair of events.
6-9
Adjective Definition
History $\sf{\text{A chain of events that is in historical order.}}$ 6-10
Verb Definition
Warming Process $T_{ \it{f}} > T _{\it{i}}$ 6-19
Verb Definition
Cooling Process $T_{ \it{f}} < T _{\it{i}}$ 6-21
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