Re: [Phys-L] mass, energy, and spacetime

[John Denker <jsd@av8n.com>]

On 03/16/2013 05:58 AM, Brian Blais wrote:

> I was just reading John Denker's lovely spacetime intro, 
  http://www.av8n.com/physics/spacetime-welcome.htm,

:-)

> I have never seen in 8th grade or earlier any plot of x vs t which
> looked like Figure 4
> (http://www.av8n.com/physics/spacetime-welcome.htm#fig-ruler-cart-t-const-x-red-transp).
> It is this non-orthogonal axis plotting which is the tough part for
> students, not the fact that we are plotting x vs t.

Ah, yes.

The fact that the problem is described in terms of "non-orthogonal
axes" -- AXES -- is part of the problem!  People have been trained to 
think in terms of axes.  However ... it would be much safer to think 
in terms of contours, such as the contours of constant X.

In the simplest case, the contours of constant X run perpendicular
to the X-axis, so we see these are very different concepts indeed.
What's more, the X-contours are not even guaranteed to be perpendicular
the X-axis, so there is not even an equivalence(*) between the two.

I just now rewrote the paragraph in question at
  http://www.av8n.com/physics/spacetime-welcome.htm#fig-ruler-cart-t-const-x-blue-transp
Among other things, I narrowed the focus of the "8th grade" remark.
I also spelled out the point about axes:

  So far, the diagrams in this section haven’t told us much we 
  didn’t already know. The idea of plotting x versus t as we have
  done in figure 5 is completely standard. It’s something you should 
  have seen in 8th grade (if not before), and seen many times since 
  then. The only thing that is even slightly special is that rather 
  than showing the x-axis we have shown the contours of constant x.
  Similarly, rather than showing the t-axis we have shown the contours 
  of constant t. This is a useful tactic. It doesn’t make much difference 
  in figure 5, but it makes figure 4 considerably easier to interpret.
  For a fuller explanation of why contours are better than axes, see 
     http://www.av8n.com/physics/axes.htm

(*) Note that "equivalence" is a very strong word;  see also next message.