Re: [9fans] Cross products - longish & boring, but now officially on topic!

Re: [9fans] Cross products - longish & boring, but now officially on topic!

[forsyth]

	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.

it's really rather awful, isn't it.  it ought to have been called COBRA.
in the same way, SOAP isn't cleansing.  so many misleading acronyms!

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Douglas A. Gwyn]

paurea@gsyc.escet.urjc.es wrote:
> I don't think so. [The "cross product"] is the dual of the
> sesquilineal projection of the tensorial product. ...

As usually defined the c.p. is supposed to result in the same
type as its arguments, but e.g. the c.p. of two vectors is
*not* a vector (it's a so-called pseudo- or axial vector,
which can indeed be thought of as a *component* of the tensor
product).  So while it might be a "product" it is not as nice
as the kinds of products that map from space x space into space.
The "non-conservation of parity" work that was awarded a Nobel
prize seems to actually have been confusion on this very score.

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Douglas A. Gwyn]

Non-conservation of parity is usually discussed under "CPT",
which should be in the index of many textbooks, predating the Web.
My assessment of the analytical error dates back to around 1967 but
has not been published.  In fact I got out of physics as a profession
mainly because my attempts to publish (other) theoretical work met
with repeated opposition from reviewers who did not want to
recognize that they had been chasing chimeras.  I didn't want to
be frustrated my whole career, so I moved into computing instead.

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Thomas Bushnell, BSG]

DAGwyn@null.net (Douglas A. Gwyn) writes:

> Non-conservation of parity is usually discussed under "CPT",
> which should be in the index of many textbooks, predating the Web.
> My assessment of the analytical error dates back to around 1967 but
> has not been published.

So the usual rule (as I was taught it) is that parity alone is not
conserved, but the product of parity, time, and charge is conserved.
(Perhaps I've got that slightly wrong.)  Is this not actually correct?
Gardner says roughly what I said.

So are there references that back up what you are saying, that this is
not in fact the case?

Re: [OT] Re: [9fans] Getting started in Plan9 - help

[Douglas A. Gwyn]

"Thomas Bushnell, BSG" wrote:
> So are there references that back up what you are saying, ...

What I am saying is that if parity was *not* conserved, the
theoretical analysis behind the famous experiments (on weak
decay) did not demonstrate it, due to not accounting for the
non-vectorial nature of the c.p. in the form of Maxwell's laws
used in the analysis.

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.

[9fans] Cross products - longish & boring, but now officially on topic!

[Andrew Simmons]

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.