Epicurus, 341~270 BCE. Drawn from a damaged Roman copy of a Greek original now in the Palazzo Massimo alle Terme, Rome. |

"… time by itself does not exist; but from things themselves there results a sense of what has already taken place, what is now going on and what is to ensue. It must not be claimed that anyone can sense time by itself apart from the movement of things or their restful immobility …"^{1}

The WikiMechanics approach to understanding time follows this Epicurean recipe. First we carefully consider "things themselves" by defining particles. Then we characterize "the movement of things" using the momentum $p$ and "their restful immobility" from the rest mass $m$. These numbers are combined to give the period as

$\begin{align} \hat{\tau} = \frac{ h }{ \sqrt{ c^{2}p^{2} + m^{2}c^{4} \vphantom{\sum^{2}} \ } } \end{align}$

Please notice that this quantity has been entirely defined through a systematic description of sensation. Let particle P be characterized by some repetitive chain of events

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

where each orbit $\sf{\Omega}$ is described by its period $\hat{\tau}$. Definition: The **time of occurrence** or time coordinate of event $\sf{\Omega}_{\it{k}}$ is

$\begin{align} t_{k} \equiv t_{0} + \delta _{t} ^{\, \sf{ P}} \delta _{t} ^{\, \sf{Earth}} \sum_{i=1}^{k} \hat{\tau}_{i} \end{align}$

where $t_{0}$ is arbitrary, $\delta _{ t}^{\, \sf{P}}$ notes P's temporal orientation and $\delta _{ t}^{\, \sf{Earth}}$ is the temporal orientation of the Earth. Let $\Psi$ be historically ordered, then $\delta _{t} ^{\, \sf{ P}} = \delta _{t} ^{\, \sf{Earth}} = \pm 1$ and

$\begin{align} t_{k} = t_{0} + \sum_{i=1}^{k} \hat{\tau}_{i} \end{align}$

So the time of occurrence is given by a sum of periods. Sensory interpretation: The period can be understood as some part of a solar day and so ideas about time are based mostly on the sensation of seeing the Sun. For more detailed discussion see the articles in the menu below that are marked with this icon

Related WikiMechanics articles.