Reference Frames

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

$\mbox{\fontsize{14}{18}\selectfont $ \Psi ^{\sf{F}} = \left( \sf{F}_{0} , \sf{F}_{1} \ \ldots \ \sf{F}_{\it{k}} \ \ldots \ \right) $}$

We might use this widely known sequence to provide a sort of background-scene or context when reporting on the events of some other particle P. Then if P changes, the variation could 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

$\mbox{\fontsize{14}{18}\selectfont $ \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

$\mbox{\fontsize{14}{18}\selectfont $ \Psi ^{\sf{P}} = \left( \sf{P}_{0} , \sf{P}_{1} \ \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

$\mbox{\fontsize{14}{18}\selectfont $ \Psi ^{\sf{P}} = \left( \vphantom{\large{\sum^{2}}} \left\{ \sf{P}_{0}, \sf{F}_{0} \right\} , \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 and inertia I. For example, a rigid frame has the same inertia for all events. Here are two more important special cases.

Tampan, Paminggir people. Lampung region of Sumatra circa 1900, 55 x 56 cm. Photograph by D Dunlop. From the library of Darwin Sjamsudin, Jakarta.

Inertial Frames

Definition: if the total number N of all types of quarks in F is enormous compared to the number of quarks in any other particle P

$\mbox{\fontsize{14}{18}\selectfont $ \it{N}^{ \sf{F}} \gg \it{N}^{ \sf{P}} $}$

then we say that F provides an inertial frame of reference. This condition implies that F is rigid because presumably no interaction could involve enough quarks to make a significant change to F's quark coefficients. It also implies that the inertia of a typical quark in F is very small

$\mbox{\fontsize{14}{18}\selectfont $ \widetilde{I}^{\, \sf{F}} \equiv \overline{I}^{\, \sf{F}} / N^{ \sf{F}} \approx \left( 0, 0, 0 \right) $}$

because if the total number of quarks is huge there will likely be a mix of quarks and anti-quarks. Then the ∆n terms in the inertia will tend to zero. But the denominator N is supposed to be enormous, so the average is very small. When we say a frame is inertial, we often mean that the inertia of an average quark is so small that it can be neglected.

Non-rotating Frames

Let F contain the same number of up and down seeds so that

$\mbox{\fontsize{14}{18}\selectfont $ \it{N}^{ \sf{U}} = \it{n}^{ \sf{u}} + \it{n}^{ \overline{ \sf{u}}} = \it{n}^{ \sf{d}} + \it{n}^{ \overline{ \sf{d}}} = \it{N}^{ \sf{D}} $}$

In this case the spin is zero

$\mbox{\fontsize{14}{18}\selectfont $ \sigma ^{ \sf{F}} = \left| N^{\mathsf{U}}-N^{\mathsf{D}} \right| /8 =0 $}$

and F is a non-rotating frame of reference.

Sensory interpretation: non-rotating frames are objectified from equal amounts of black and white sensation. This interpretation does not appeal to yet another spatial framework like the distant stars. But it still uses a celestial body, the Sun, as a reference sensation to define rotating quarks. It eschews several hundred years of inconclusive discussion about rotating buckets¹ and experimentally untestable ideas concerning Mach's principle.²

Next step: temporal orientation.

Page tags: frame inertial mach rotating

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Inertial Frames

Non-rotating Frames