Re: [Phys-L] phase velocity, one kind of charge, and other intangibles

[John Denker <jsd@av8n.com>]

On 05/09/2017 10:22 AM, I wrote:

> you can make graphs of the wavefront
>   positions as a function of time.  This can be used to illustrate
>   the idea that if you are trying to send /information/, that is
>   not determined by the phase velocity.

Here's what I meant by that.  Let's start simple.  Here is a red
pole that casts shadow on the ground.  The pole is 1 foot tall,
and the geometry is such that the shadow is 10 feet long.
  https://www.av8n.com/physics/img48/leveraged-shadow-0.png

Next, we keep the red shadow for reference, and add a couple of
other features:
  https://www.av8n.com/physics/img48/leveraged-shadow.png

The green pole started out the same as the red pole.  However,
about 4 nanoseconds ago the top half of the green pole became
transparent.  (It could be a thin flat vane that rotated 90
degrees, or whatever.)  The speed of light is 1 foot per nanosecond,
and you can see that /information/ about the change in the green
pole has not reached the ground anywhere.

Things get even more interesting when we consider the blue pole.
About 9.75 nanoseconds ago somebody started pounding on the top
of the pole with a pile driver.  On every stroke, the pole gets
pushed down into the ground a distance of 0.12 feet, which takes
0.75 nanoseconds.  Then it is stationary for another 0.75 ns
in preparation for the next stroke, and the process continues.
The peak speed is 0.16 of the speed of light, and the average
speed is half that, i.e. 0.08 of the speed of light.

The parts of the blue curve that slope down to the right come
from intervals when the pole is stationary.  They have the simple
1-in-10 slope that you expect from the geometry of the situation.
As a check, you can see just to the left of the 4 foot mark that
the blue slope matches the green slope.

Since the blue pole is getting shorter from the tip downwards,
we expect the shadow to contract from the tip back toward the
base, i.e. from right to left.  This is what happens on average.
The average speed with which the shadow contracts is enormous.
Because of the leverage, you might guess that the shadow would
move 10 times as fast as the pole itself, but it's weirder than
that, because of propagation delays.

  It must be emphasized that this has little if any connection
  to special relativity;  you would obtain all the same results
  using the speed of sound, e.g. in a sonar experiment.  It's
  just old-school wave propagation.

In fact, if the pole were contracting at 1/10th of the speed
of light, the shadow would move at infinite speed, when you
combine the effects of leverage with the propagation delays.

Since our blue pole is moving faster than 0.1 ft/ns half the
time, and there is 10-to-1 leverage, the shadow moves "faster
than infinity" half the time.  Not just faster than light,
faster than infinity.  That manifests itself as a shadow that
moves the wrong way, i.e. from the base out toward the tip,
i.e. left to right.  You can see this happening near the 9
foot mark, where the shadow has already disappeared, even
though the shadow at 9.75 has not.

Somebody ought to make an animation of this, but that's more
work than I feel like doing at the moment.

=====

Last but not least, such diagrams can be used to explain that
you can't use such schemes to send *information* faster than
the speed of light.  You can set up situations where the
shadow moves right-to-left faster than the speed of light
/once it starts moving/ ... but it doesn't start moving until
a full 10 ns after the pole starts contracting.

So the formula for phase velocity tells you /something/, and
it's correct as far as it goes, but it's not the whole story.
There is a velocity, but also a delay.  The velocity is real
enough, but it doesn't tell you about the delay.  So there is
no problem with relativistic causality.

This is absolutely typical of situations where the phase velocity
seems hard to interpret.  It's not wrong;  it's just not the
whole story.

Indeed, this is typical of science and life in general.  The
fundamental principles are like legos, or like full-sized
building blocks.  A pile of disconnected blocks is not very
interesting.  The point of the exercise is to use your skill
and creativity and sense of purpose to put them together in
interesting and useful ways.

This is what's wrong with certain "Conceptual" physics books.
Students rightly conclude that a pile of disconnected concepts
is boring and useless.  Although there are problems with what's
in the book, that is *not* what I'm talking about here;  I'm
talking about what's /missing/ from the book, i.e. the part
about multi-step reasoning, block upon block, putting things
together in interesting and useful ways.

  Sure, you have to start with a couple of disconnected concepts
  on Day One, but you ought to move away from that as soon as
  possible.  Where you start out is not where you want to end
  up.  The importance of /connections/ has been known in the
  educational psychology literature for quite a while (e.g.
  James, 1898).

Phase velocity by itself is useless or worse, but it makes
sense as part of a larger picture.