=========== G previous:: > > Michalchik told us quite rightly that before making > > wisecracks about the cutting edge of physics, it > would > > be advisable to understand one or two of its > fundamental > > equations. > > However, before learning them one should test his > capacity > > to undertake this tough, long and complex task. ============= M: > Well, a basic principal in epistemology is that truth is > truth no > matter its source, but I am game to take your test, though > I do not > consider myself and expert in this subject. I just know > enough to know > that people who think they can tackle it using their common > sense, non > mathematical intuition and a high school education are > deluding > themselves. ============ G: You are really game. Most people get offended. I'll answer here the axial vector question, perhaps too tough even for an educated physicist. The rest I'll comment off list, not to spoil the fun of others, who may wish to try their hand.
AXIAL VECTOR: Let me recall Maxwell's equations in vector form as: curl(E)=-pB/pt (B=mu*H) curl(H)=pD/pt (D=eps*E) div(D)=ro div(B)=0 where: E: polar vector of electric field H: axial vector of magnetic field eps: dielectric constant of vacuum mu: magnetic permeability of vacuum ro: charge density D: vector electric induction B: vector magnetic induction Vector equations with axial vectors, curls, divs etc. may be useful as freshmen tutorials, but are not sufficient for Relativity research. Actually, they are wrong, starting with H, which is not a vector, but an anti-symmetric tensor of rank 2. It happens to have in 3D SPACE 3 independent components, which makes it similar to a vector and allows to consider it in elementary handbooks as "axial vector", or "pseudo-vector". The vector form of Maxwell's equations has to undergo the tensorial unification before becoming usable for several Relativity procedures. An example - my derivation of E=MC**2 provisionally in http://findgeorges.com/ROOT/RELATIVISTIC_DIALECTIC/D_OUTLINE_OF_EINSTEINS_RELATIVITY/DB_SPECIAL_RELATIVITY/dbe_emc2.html Components of the axial vector A are: A((i/)(j/)(k/))= (pA(z/)/py-pA(y/)/pz)i + (pA(x/)/pz-pA(z/)/px)j + (pA(y/)/px-pA(x/)/py)k where i, j, and k are the unit vectors respectively for the x-, y-, z-axes. H describes a counter-clockwise rotation of magnetic angular momentum. We seem to live in a counter- clockwise structured universe. How would a clockwise look? NOTATIONS AND CONVENTIONS. Unless they are elementary displacements dx,dy..., vectors are usually noted with upper case letters (A,B...) and their components with lower case letters designating indexes (i,j,k...) written as upper or lower, following vector's name: A .i .j B In ASCII context we shall write them with help of brackets and slash, as follows: A(i/), B(/j) Upper indexes designate contravariant components and lower indexes covariant ones (definitions below). Thus A(i/) designates the i-th covariant component of vector A and B(/j) the j-th contravariant component of vector B. We shall write derivative of y with respect to x as: d(y)/d(x) and partial derivative of u with respect to v as: p(u)/p(v) Cheers Georges. --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Epistemology" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/epistemology?hl=en -~----------~----~----~----~------~----~------~--~---
