The Period
//Horlogerie//, Plate IX.5. 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.5. 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 P be a particle with a frequency of $ν$. Definition: the period of P is the number

$\begin{align} \hat{\tau} \equiv \frac {1 }{ \, \nu \, } \end{align}$

According to Planck's postulate the period is related to the mechanical energy $E$ as

$\begin{align} \hat{\tau} = \frac {h }{ \, E \, } \end{align}$

where $h$ is Planck's constant. Then in terms of the momentum $p$ and the rest mass $m$

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

Consider measuring this period based on laboratory observations of the energy. By the usual rules for assessing the propagation of experimental errorsXlink.png in a calculation, the uncertainty in the period is in the same proportion as the uncertainty in the energy measurement so that

$\begin{align} \frac{\delta \hat{\tau} }{ \hat{\tau} } = \frac{\delta E }{ E } \end{align}$

But the hypothesis of temporal homogeneity implies that

$\begin{align} \frac{ \delta E }{ E } \ge k_{S} \end{align}$

where $k_{S}$ is about seven percent. So the uncertainty in the period is bounded by

$\begin{align} \delta \hat{\tau} \ge \hat{\tau} k_{S} \end{align}$

sun.png
Sensory interpretation: The period is the reciprocal of the frequency which is proportional to the number of quark bundles observed per solar day. So the period can be interpreted as some fraction of a day.
Right.png Next step: time.
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