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.

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 partly replaces the second hypothesis.

How Does It Work?

Implementing spatial isotropy requires a few theoretical twists. The following articles discuss more detail. But here is a quick look at the plan for systematically ignoring 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 revolve around the polar axis of any particle as it moves. In the Cartesian view, particles are rotating. Second; we step-back and refocus the description on particles that are larger than quarks, i.e. atoms and molecules. Then lengths can be well-defined. And sub-atomic variations in leptonic quark distributions can be averaged, and cancelled-out, over complete atomic cycles. Leptonic quarks represent chromatic sensations, so colors get blurred-out of the description of atoms. Chromatic terms are retained for photons, but a quantitative analysis of energy supersedes the categorical description of their color. The direction of the $x$ and $y$-axes cease to be specified by color. The axes are still relevant, but their directions are now established by landmarks like mountains and obelisks. Likewise, electric and magnetic polarities are retained, but their signs are set by other criteria such as the Earth's magnetic field, or details about the construction of a battery.

Right.png Next step: a one dimensional space.

Related WikiMechanics articles.

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