From mboxrd@z Thu Jan 1 00:00:00 1970 Message-Id: <3.0.6.32.20020204085524.0099aee0@pop3.clear.net.nz> To: 9fans@cse.psu.edu From: Andrew Simmons In-Reply-To: <3C5A091B.5EE62DB0@null.net> References: <3C57AF73.727F8CE9@null.net> <3C58DFD7.33AFB32B@null.net> <87d6zqsww6.fsf@becket.becket.net> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Subject: [9fans] Cross products - longish & boring, but now officially on topic! Date: Mon, 4 Feb 2002 08:55:24 +1300 Topicbox-Message-UUID: 4acf38a8-eaca-11e9-9e20-41e7f4b1d025 Since this topic is now in the FAQ, I presume that I'm allowed to drone on about it a bit more. Besides, it means I can put off wrestling with CORBA for a few minutes. I'm confused. When I was a lad we were taught that there were two types of vector, polar and axial which differed in their behaviour under reflection of the co-ordinate system. The fact that the cross product of two polar vectors is an axial vector doesn't mean that axial vectors aren't really vectors, any more than the fact that the product of two negative integers is a positive integer means that positive integers aren't really integers. I'm not sure what the problem with Maxwell's equations is. The electric field E is a polar vector, but the magnetic field B is an axial vector. Since the curl of an axial vector is polar, and vice versa, it is perfectly kosher to relate the curl of E to the time derivative of B, both terms being axial vectors, and hence the equation being invariant under reflection. Similarly with the equation involving the curl of B, where both sides are polar. As far as I understand Lee & Yang's analysis of the parity experiments, which is admittedly not very far, they explained the asymmetry in the decay of the Cobalt nucleus by mixing polar (momentum) and axial (angular momentum) vectors in the same equation, and so unlike Maxwell's equations theirs does change under reflection. >I have my own reasons to think that mirror symmetry *has* to >be a fundamental property of physics and that any asymmetry >is environmentally induced. > I'm suspicious of any attempt to say what nature has to look like on a priori grounds, but to pursue this would be majorly off-topic. Unless Mr Kotsopoulos can be persuaded to add a new entry to the FAQ, perhaps with the title "Can there be synthetic a priori propositions?" The above probably indirectly addresses Boyd's musing about the physics/computing crossover. I don't think I could possibly support a wife, a child, and a gin habit doing this sort of stuff. Oh well, back to CORBA. I feel SO much better having to deal with the whole filthy mess since Reiser told us it was influenced by Plan 9.