from g+posted by wendy kriegerShared publicly QuoteA weird problem. This is advanced physics, which means that ye might have at least a good grounding in matters like 'electricity' and 'gravity'.If you are into a different base, like base 120, then you make all sorts of efforts to root out tens and log tens and so forth out. In part, you come to weights and measures, and apart from converting 10's to 120's, you decide to fix things on the way.Sooner or later, you decide that SI is pretty much a train-wreck in slow motion, which started way back in the 1860's, and despirately needs a fix. For example, it has seven base units: you can generally thin this back to four, since we can replace the ampere, the mole, and the candela with derived units. Of course useful things come out of activities, if ye do it right. One of these is the Rule of Substance, which has quite an extraordinary result when it is thinned out.Those of ye who wrangle older mathematical texts, and those on cosmology, will no doubt be aware of the c.g.s. system, and its use of 4pi in different places to SI. If ye use Heaviside's electric to gravity analogy, the current cosmology is written in 'gaussian' units. [Gauss had no part of this - i don't know why he sholders the blame].The fix for this is to write out a set of equations in six base units, of which two or three are made numeric, to give, eg gaussian, e.s.u,, e.m.u. and SI like equations, but these are not the only game in town.Ye can follow the leads of Fitzgerald, and of Kennelley (1932), and write, for example \epsilon c = \mu c = 1. It's just a case of taking the sorts of equations you see in your undergrad books, and replacing \epsilon and \mu with 1/c. So, eg E = cD. and H = cD. The real magic is the measure of 4pi. Leo Young (1961) used a value S which S=1 in SI and S=4pi in c.g.s.. He also uses U=1 in SI and U=1/c in c.g.s., to include the gaussian and HLU units. By Young, ye have Flux = S.Charge, and so forth. You get then a system of equations SISU, which is SI with S and U tossed in to pull out c.g.s.The thing is six-dimensional, and the over-all symmetry is that there are eight vectors, which form a cube (orthogonal to the LMT dimension, with the centre of the cube running to pressure or energy density. You can write these as eg P, and D=P.S and so forth. But a bit of reanalysis, one can write the mechanical point as E^2.bhk, where E is the electric field, and b,h,k are three axies of the cube. I use \beta, \eta and \kappa here. \beta corresponds to 1/S, and \kappa to 1/U of Young's theory. \beta corresponds to the appearence of 4pi, eg Q/\Phi. \eta is a symmetry element, as H = \eta.E \kappa is an assymetry element, as in I.\kappa . t = Q (ie biot . \kappa . second = franklin).If you use the coordinate system as described above, a truly interesting thing happens. You have \beta dividing the quantities into substance and spaces. mass and charge are substances, while fields and fluxes are are spaces. Spaces: Length, area, volume, time, velocity, acceleration, fields and fluxes of all kinds, permittivity, permeability, \beta = 0Substances: Mass, energy, force, power, pressure, charges, dipoles and polarisations, susceptabilities, conductances and admittances. Capacitances. \beta = 1Anti-substances: Resistances. Inductions \beta = -1.It's then a matter of going through an equation, and ticking off which are substances. A dimensional analysis of the ticks gives an inbalance which is corrected by a ticked 4pi. (or going the other way, a crossed 4pi. So, eg F = Q^2 / R^2 gives F and Q as substances, so you have one tick on the LHS and two on the RHS, the balance is to divide by a ticked 4pi. F = Q^2 / 4pi.R^2.\mu_r = 1 + 4\pi \chi_mHere gives only one tick, on susceptability \chi_m. You divide through by 4pi, to get the rationalised form \mu = 1+\chi_m.SubstanceSo if \beta is a substance, what is it. Leo Young's theory gives \beta = 1/S = 1 / solid-angle, say. (SI treats the three radiant fields of light, gravity and electricity entirely differently).So there is a substance-like quantity that has the dimensions of 1/sr.Where space has a variable curvature, does this mean that substance is a cause of curvature. Lots of mystery questions here, but ye can readily see that the use of different units puts a whole different prospective on things.