Hypothesis of Spatial Isotropy
//Tatibin,// Paminggir people. Lampung region of Sumatra, Kota Agung district, 19th century, 91 x 39 cm. From the library of Darwin Sjamsudin, Jakarta. Photograph by D Dunlop.
Tatibin, Paminggir people. Lampung region of Sumatra, Kota Agung district, 19th century, 91 x 39 cm. From the library of Darwin Sjamsudin, Jakarta. Photograph by D Dunlop.

The hypothesis of spatial isotropy is a presumption that almost all of the particles in a description have both phase symmetry, and charge symmetry along the magnetic and electric axes. This condition is easily satisfied for protons, electrons and hydrogen atoms. The hypothesis is useful because it implies that even if the phase $\delta _{\theta} \ ,$ the magnetic polarity $\delta _{\hat{m}}$ or the electric polarity $\delta _{\hat{e}}$ get mixed-up and change sign, the overall description of a particle remains unaffected. And if almost all particles share these symmetries, then we can greatly simplify analysis by usually ignoring $\delta _{\theta}$ $\, \delta _{\hat{m}}$ and $\delta _{\hat{e}} \ .$ These quantities determine the spatial orientation. Disregarding them implies that any one direction is just about the same as another. That is why the assumption is called a hypothesis of spatial isotropy.

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Sensory interpretation: The phase can be explained as a representation of black and white perceptions, the magnetic polarity depends on red and green sensations, and the electric polarity is defined from blue and yellow perceptions. So exercising this hypothesis, and setting aside further consideration of these explanations, is a way of objectifying a description. We can stop paying attention to if an event looks black, or white, or red, or yellow, or any other color. Moreover interpreting the phase as some time-of-day becomes irrelevant. The assumption is an important way for descriptions to transcend these sensory details. It replaces the second hypothesis in part.

How Does It Work?

Implementing the hypothesis requires a few theoretical twists. The following articles discuss more detail. But here is a quick look at the plan for systematically ignoring chromatic visual sensations. First, we change the descriptive framework from quark space to a Euclidean space that has a Cartesian coordinate system. Then by definition the electric and magnetic axes will automatically rotate around the polar axis of any particle as it moves. In the Cartesian view, particles are spinning. Second; we step-back and refocus the description on particles that are larger than quarks, e.g. at least a couple of atoms. Then lengths can be well-defined. And sub-atomic variations in leptonic quarks can be averaged, and cancelled-out, over complete atomic cycles. Leptonic quarks represent chromatic sensations, so colors get blurred-out of the atomic description. Chromatic terms are shifted to photons, for example Balmer-alpha is identified as red. Then a quantitative analysis of frequency supersedes the categorical description of color. The directions of the $x$ and $y$-axes cease to be specified by colors. The axes are still relevant, but their directions are established by other criteria. Likewise, the signs of the electric and magnetic polarities are reset too.

Right.png Next step: a one dimensional space.

Related WikiMechanics articles.

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