Re: Waves and Energy

[Leigh Palmer <palmer@sfu.ca>]

> I wonder if I can get help on this question from a high school class.
>
> If two electromagnetic waves interfere destructively, what happens to the
> energy associated with the waves. I am guessing that on the large scale,
> in a double slit experiment that additional energy shows up at the points
> of constructive interference that compensates for the loss at the nodes.
> But, what about looking as just the waves that are meeting at a node?
>
> Any help would be appreciated.  David Abineri

As with any physical problem, one must examine the phenomenon as a whole,
not just the smaller portion of it that appears to be most interesting.
For example, if two plane electromagnetic waves are made to interfere
destructively in a Michelson interferometer, it will be found that the
same two waves' reflections from the beam splitter back toward the source
interfere constructively, giving twice the irradiance that would be
expected on energetic grounds alone. Your guess above is correct, of
course, in the case of the double slit.

There is no law that says the energy delivered to a particular point must
have some particular value. Indeed it is dufficult, perhaps impossible, to
determine the location of something called "energy" any more precisely
than within the bounds of a system. Another example may serve to illustrate
(perhaps even illuminate) this fact. Consider a charged vacuum capacitor.
The energy stored is 1/2 Q*V. It is also equal to the integral over the
volume of the capacitor of 1/2 epso*E**2. Where is the energy? does it
reside in charges +Q and -Q, or is it stored in the E-field between the
plates? Our two formulae suggest different answers to this question, and
there is general agreement that neither of them is correct.

Energy is a function of the state of a physical system. As such it may have
a perfectly definite value, but it has no corporeal entity - there is no
such thing as "pure energy", even though unsophisticated science fiction
authors might wish there to be. When entropy was named its name was chosen
because, like the energy, entropy enheres to a physical system and can be
calculated from the parameters which define the state of the system.
Entropy is conceptually on an identical footing with energy, but energy is
often thought to be the easier to understand of the two. That is usually
because energy itself is misconceived.

Leigh