Re: [Phys-l] Re. Simultaneity

[John Denker <jsd@av8n.com>]

On 05/21/2009 06:11 AM, Michael Edmiston wrote:

> .... Students misinterpret the diagrams because they have been taught an 
> improper way to find the projections of points onto the graph's axes.

I heartily agree with this in spirit.  I won't quote the whole message,
but I encourage everyone to read it:
  https://carnot.physics.buffalo.edu/archives/2009/5_2009/msg00277.html



A couple of follow-ups:

 1) The problem is not confined to spacetime diagrams.  I first encountered
  the problem when I was 11 or 12 years old in the context of a psychrometric
  chart.  The whole story is here:
     http://www.av8n.com/physics/axes.htm

> Perhaps some of you have figured out a better way of saying or explaining 
> what I am trying to explain.  Maybe I shouldn't be using the word 
> "projection." 

 2) The more I think about it, the more it appears that the notion of "axis"
  is the problem.  The notion of "projection" is not the fundamental problem,
  technically speaking and/or pedagogically speaking. By the time  you have
  formulated the problem as projection onto an "axis", you have already 
  fallen into the pit.

  The constructive suggestion is to focus on _contours of constant value_ of
  this-or-that variable.  Such contours are hinted at by the tick marks on each 
  axis, so when you erase the axis-line be sure to keep the tick marks.  Extend
  the ticks (contours) so that they fill the entire diagram, as on the psychrometric
  chart
    http://www.av8n.com/physics/axes.htm#fig-PsychrometricChart-SeaLevel-SI
  and also on my spacetime diagram paper:
    http://www.av8n.com/physics/spacetime005blue-only.pdf
    http://www.av8n.com/physics/spacetime005blue.pdf
    http://www.av8n.com/physics/spacetime005red-only.pdf
    http://www.av8n.com/physics/spacetime005red.pdf
    http://www.av8n.com/physics/spacetime005redblue.pdf

  To repeat:  When dealing with the X variable, you never need the X axis,
  but you always need the contours of constant X.

  Grid-style graph paper has the nice property that it shows the contours of 
  constant X and contours of constant Y ... but it has the drawback that only
  orthogonal contours are shown.  On a spacetime diagram, the contours of one
  frame are not orthogonal to the contours of another frame.  Even within a 
  frame, contours that are orthogonal in real spacetime must be drawn as non-
  orthogonal on the diagram, because of the funny business that occurs when 
  spacetime is projected onto the page.  In thermodynamics, the contours are 
  often not even straight, let alone orthogonal.