Re: conservation of energy not substance

[John Denker <jsd@MONMOUTH.COM>]

Hi Folks ---

First, a parable:

I have here a flat, disk-shaped piece of cardboard.  On it are marked two
points: A and B.  I have done experiments showing that displacements obey
the following property:  If I place a token on point A and then displace it
  * four inches left
  * three inches up
  * four inches right, and
  * three inches down
the token gets back to point A, even though the outbound route is different
from the inbound route.   This leads me to formulate a law that says that
the displacement vector is conserved.

Now suppose that some wise-guy does the following experiment.  He displaces
the token
  * four inches left
  * three inches up
  ** then he moves himself around the table to view the disk from a new
angle, and displaces the token
  * four inches right (in the new frame), and
  * three inches down (in the new frame)

The token does not return to the starting point, so he claims to have
"disproved" my assertion that the displacement vector is conserved.

The disproof is ridiculous.  My conservation law stands firm.

The law says the displacement vector is conserved in any *particular*
reference frame.  It does not (and need not) specify what happens when you
switch from frame to frame.  [There is a large but not unlimited set of
possible frame-to-frame transformations consistent with conservation in
each frame.  Rotations are not the only mathematical possibility, nor even
the only physical possibility.]

Note that conservation of the displacement vector implies that each of the
vector's components is separately conserved (in any particular reference
frame).  This is quite different from the conservation of the scalar
distance between A and B, which happens to be conserved in a
frame-independent way.

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

So it is with energy.

At 10:31 PM 9/10/99 -0700, Leigh Palmer set forth with remarkable clarity
his  definition of "substance" (his examples of which were all locally
conserved *scalar* quantities) and his alleged disproof of conservation of
energy, on the grounds that energy is not a substance.

Sure enough, energy is not a scalar.  But scalar-ness, i.e. being invariant
to change of reference frame, has nothing to do with the conventional and
useful definition of local conservation of energy and momentum.

The law applies in any *particular* reference frame.  It does not (and need
not) specify what happens when you switch from frame to frame.

Note that in any particular reference frame, the four components of the
energy,momentum vector are separately conserved.  This is very different
from the conservation of the scalar norm thereof, i.e. the rest mass, which
happens to be conserved in a frame-independent way.

At 10:31 PM 9/10/99 -0700, Leigh Palmer wrote:
> All observers would agree on the number of atoms in each car and
> on the charge borne by each car; accelerated observers would do so
> as well. Consider the kinetic energies, however. In two inertial
> frames of reference observers would ascribe a zero value to one or
> the other of K1 and K2. That is about as insubstantial a quantity
> as I can imagine.

It's true!  It's true!  Energy is not a substance.  It's not a scalar.
It's not independent of reference frame.  Never was.  Never will be.  BUT
STILL IT IS CONSERVED.  Always was.  Always will be.  Indeed, it's locally
conservered, which is a stronger statement.

Different observers will disagree as to how the vector breaks down into
components.  But still the vector, and each of its components, is conserved
in any particular reference frame.  That's important.