Spatial Isotropy

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 it 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 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 may replace the second hypothesis under certain circumstances. Indeed, here is a quick look at a plan for systematically glossing-over visual sensations to obtain the necessary conditions for spatial isotropy.

First, Take a Different Viewpoint

The descriptive framework is changed 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. The four quark coefficients that describe the distribution of rotating quarks $\, n^{\mathsf{u}}$, $n^{\mathsf{\overline{u}}}$, $n^{\mathsf{d}}$, and $n^{\mathsf{\overline{d}}}$, are then used to define four atomic quantum numbers $\, \mathrm{n}$, $\ell$, $s$ and $j$ that describe angular momentum.

Second, Objectify Visual Sensations as Experimental Observations

Vast quantities of complex visual information are described in the scientific literature of experimental physics. There are millions of pages carefully recording how laboratory conditions are controlled, samples prepared, equipment arranged and data presented. Laboratory reports all have some dependence on visible objects like dials, meter-needles, cathode-ray tubes, printer output, computer screens, etc. These visual details are then included in analysis that ultimately produces a measurement of something. Thus the experimental process objectifies visual sensations and reports them as some property of a particle. For an isotropic space, talk of dynamic quarks is replaced by discussing the dynamics of atoms, molecules and Newtonian particles.

Describe Atoms using Lengths

//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.

Next we step-back and refocus the description on particles that are larger than quarks, starting with atoms. Then lengths can be well-defined and used to determine Cartesian coordinates. Also sub-atomic variations in leptonic quark distributions may be averaged, and cancelled-out. Leptonic quarks represent chromatic sensations, so colors are smeared-out of the description of atoms. That is, red and green sensations cancel each other, and likewise for yellow and blue. When considered all together, the quarks in atoms are collectively greyish or colorless. So for isotropic descriptions, colors are not attributed to atoms based on their dynamic quarks. Instead, dynamic characteristics like velocity and acceleration are determined by measuring lengths. Then chromatic terms may be freely redefined to convey other meanings. For example in the laboratory, red plastic insulation on a wire often means that it is connected to a positive electrode. But this meaning is obtained by convention, not from the quark content of positive electrodes or red plastic. Instead, the 'color' of an atom is explained by the color of photons coming from the atom.

Describe Photons using Wavelengths

For WikiMechanics, the color of a photon is fundamentally known by the personal experience of seeing it. We also have a more communal and categorical method of describing colors, but the procedure is coarse and still partly subjective. On the other hand, we can objectively measure photon wavelengths using prisms and gratings. And wavelengths are correlated with colors. So to do physics in an isotropic space, quantitative measurements of wavelength supersede the categorical description of a photon's color. For instance, absorbing a Balmer-alpha photon is an archetypal example of seeing a red photon. But this perception is not attributed to the colors of leptonic quarks in the photon. Instead, the color of Balmer-alpha is explained by the common human experience that any photon with a wavelength of about 650 (nm) looks like seeing blood.

Finally, Adopt Some New Conventions

The direction of the $x$ and $y$-axes cease to be specified by using colors. The axes are still relevant, but their directions are now established by conventional landmarks like mountains and obelisks. Likewise, electric and magnetic polarities are no longer defined by color. They are conceptually retained, but their signs are set by new conventions such as alignment with the Earth's magnetic field, or perhaps details about the construction of a battery.

Thus, with a fresh Cartesian point-of-view and some updated conventions, descriptions can methodically gloss-over color. Discussion becomes more objective and scientific. And the hypothesis of spatial isotropy becomes valid. But we are left with a reduced cast of particles. In three-dimensional isotropic space, mechanics is mostly about atoms, photons and their composites. There are also some limited roles for protons and electrons. But seeds, quarks, other nuclear particles and field quanta are not usually given space-time descriptions. Please see the following articles for more detail.

Here is a link to the most recent version of this content, including the full text.

favicon.jpeg Spatial Isotropy
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-ShareAlike 3.0 License