Re: [Phys-l] three central misconceptions about relativity

[John Denker <jsd@av8n.com>]

On 10/14/2011 04:21 AM, Moses Fayngold wrote in part:

> The space-time geometry is beautiful, 

Yes.

> but it is precisely the length
> contraction and time dilation effects that make this geometry.

No.

The contraction / dilation approach is *incompatible* with the
geometric approach ... as we can see quite easily:

 *) Suppose we have a ruler.  Just one ruler.  It has some
  definite length.

 *) Suppose we have two coordinate systems, red and blue, which are
  rotated with respect to one another.

 *) Using the red coordinate system, find the coordinates of each
  endpoint of the ruler, and use this to compute the length.  Ditto
  for the blue coordinate system.

 *) The two length-computations should come out the same!  This
  should be obvious in physical terms, based on the fact that there 
  is only one ruler;  choosing a new coordinate system cannot
  possibly affect the ruler.

  If the two length-computations come out different, there is
  something desperately wrong with your coordinate systems, or
  with your notion of rotation, or with your definition of length.

  The x-components will differ from frame to frame, and the y-components
  will differ from frame to frame, but the length is invariant.

  There is nothing tricky going on here.  This is just high-school
  math, namely analytic geometry.

 *) What's true for a rotation in the xy plane is true for a rotation
  in the tx plane ... which corresponds to a velocity.  If the red
  frame is moving relative to the blue frame, this cannot possibly
  affect the length of the ruler.

  If the two length-computations come out different, there is something
  desperately wrong with your coordinate systems, or with your notion of
  relative motion, or your definition of length.

  The t-components will differ from frame to frame, and the x-components
  will differ from frame to frame, but the length is invariant.

=================

Naive students do *not* have misconceptions about this.  The only
people who have a problem are those who have been taught the
wrong ideas.

If it takes you a while to overcome these misconceptions, that's
OK.  It took Einstein some time to figure out what Minkowski had
done.  He did eventually figure it out ... and relied on it for
all future work, including general relativity.

Again:  Just because Einstein used contracted rulers and dilated
clocks in 1905 doesn't mean it is a good idea.  In fact it is a
terrible idea.  It is *incompatible* with a modern (post-1908)
understanding of the subject.