Re: [Phys-l] Re. Simultaneity

[John Denker <jsd@av8n.com>]

On 05/21/2009 07:46 AM, LaMontagne, Bob wrote:
> Aren't both methods correct? ... Neither is right or wrong - it's a
> matter of what you are trying to accomplish.

Well, yes .... but that shouldn't be given too much weight.  
It's true that sometimes you want a carrot and sometimes you 
want a parrot, but they are not equivalent, and not even 
closely related.

> One produces contravariant componets,
> the other produces covariant. 

Nope.

Here's a simple disproof:  The whole idea of covariant versus
contravariant depends on having a metric, i.e. some way to calculate
dot products, lengths, and angles.  In contrast, though, choosing to 
follow the parrot-contours or to follow the carrot-contours is well
defined even in situations (such as thermodynamics) where you don't 
have a metric.

Other disproofs are readily available.

==========

Constructive suggestion:  You can easily make a large majority of such 
projection-related questions go away.  No answer is required;  the question
just never comes up.  As explained in my previous note:  Axes are evil.  
Get rid of the axes.  Instead follow contours of constant X, constant Y, 
constant T, et cetera.