Reference Frames
//Tampan//, Paminggir people. Lampung region of Sumatra, Kota Agung district, circa 1900, 48 x 51 cm. Photograph by D Dunlop. From the library of Darwin Sjamsudin, Jakarta.
Tampan, Paminggir people. Lampung region of Sumatra, Kota Agung district, circa 1900, 48 x 51 cm. Photograph by D Dunlop. From the library of Darwin Sjamsudin, Jakarta.

Let some well-known particle F be characterized by a chain of events noted as

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

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

$\left\{ \sf{P}_{ \it{k}}, \sf{F}_{ \it{k}} \right\}$

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

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

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

$\Psi ^{\sf{P}} = \left( \vphantom{\large{\sum^{2}}} \left\{ \sf{P}_{1}, \sf{F}_{1} \right\}, \ \left\{ \sf{P}_{2}, \sf{F}_{2} \right\} \ldots \left\{ \sf{P}_{ \it{k}}, \sf{F}_{ \it{k}} \right\} \ldots \right)$

Aside from being used to describe change, a frame of reference 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 to specify a non-rotating frame of reference. Let F contain equal numbers of up and down seeds $N^{ \mathsf{U}} \! = N^{ \mathsf{D}}$ so that the spin is zero

$\begin{align} \sigma ^{ \sf{F}} \equiv \frac{ \, \left| \, N^{\mathsf{U}} - N^{\mathsf{D}} \, \right| \, }{8} =0 \end{align}$

Then by definition F is a non-rotating particle. This approach does not appeal to some 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 buckets1, 2 and many experimentally untestable assertions concerning Mach's principleXlink.png.
Right.png Next step: temporal orientation.


Summary
Noun Definition
Reference Frame A particle, usually large, that is used
to make comparative descriptions.
6-2
Adjective Definition
Relative Descriptions $\sf{\text{Descriptions made in comparison with a reference frame.}}$ 6-3
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