Re: [Phys-l] What comes first, the equation or the explanation?

[John Denker <jsd@av8n.com>]

On 12/22/2011 10:02 AM, Paul Nord wrote:
> > Picking up on something Brian Jones said at the summer AAPT meeting,
> > I'll say that experience comes first.  He described how students,
> > allowed to play with florescent sheets and various colored LED's gain
> > understanding from that experience.  When asked specific question
> > about light and energy later they have a sense that blue light has
> > more "something" than red light.

On 12/22/2011 11:52 AM, I wrote:

> I say that (a) sometimes experience comes first, and (b) sometimes 
> it doesn't.  Anecdotes of type "a" don't disprove "b".

I don't want to overemphasize (b), but since others have given
examples of (a) I would like to balance that with examples of (b).

Some good examples of (b) are very familiar to us.  For starters,
consider /energy/.  That is really quite an abstract quantity.  
We are so familiar with it that we have a gut feeling for how it 
works ... but it is a lot easier to say what energy /does/ than 
to say what it "is".  The flow of energy is "mostly" like the flow 
of an indestructible fluid, but if you stop to think about it, it's 
much more abstract than that.  Basically energy is defined by an 
equation, and everything else is either a plausibility argument 
leading to that equation, or a corollary derived from that equation.

Ditto for /electric charge/.  Some things are so fundamental that
they cannot be defined -- or explained -- in terms of anything
more fundamental.

==========

To paraphrase a famous saying from 2500 years ago:
  "The word that can be spoken is not the true Word.  
   The way that can be traveled is not the true Way."
                                   老子 i.e. Lǎozǐ

To that I would add, the quantum mechanics that can be visualized
is not the true quantum mechanics.

As another way of expressing the same idea, there is a saying
about "interpretations" of quantum mechanics:  That which
interprets least interprets best.

This leads directly to the Everett "many-worlds" interpretation,
which I do not endorse, even though it gets the right answer.  I
mockingly call it the many-worlds *non-interpretation* of quantum
mechanics.  I don't like it because it is unnecessarily complex.
It is equivalent to saying invisible angels are conspiring to move 
things around in such a way that the results conform to the equations 
of quantum mechanics.  I prefer to say simply that the equations 
are right.  The equations are necessary and sufficient, whereas 
the supernatural conspiracies are not necessary.

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

Similarly:  Maxwell tried for many many years to come up with an
intuitive explanation of electromagnetism.  He tried and failed.
You can /almost/ explain it in terms of field lines, but not 
quite.  It was only when he gave up on the concrete models and
wrote down the abstract equations that he came up with something
that really worked.

You could say that the concrete models helped him, but you could 
also say that they hindered him.

To his great credit, he recognized that his intuitive models were
not quite right.  (All too often, people are overly impressed by
their own partial successes.)  Knowing when to be dissatisfied is
a tricky judgment call.  As the famous philosopher Rodgers pointed
out, you've got to know when to hold 'em, and know when to fold 'em.

  Nowadays, more than a century after Maxwell, we can make the
  field line model work pretty well in four dimensions.  This
  was not an option for Maxwell, and it is a clear example of
  an "explanation" that came long, long after the equation.

So, this gets back to what I've been saying all along:  The
equations and the intuitions complement each other.  They 
reinforce each other, iteratively.  Itsy-bitsy-spider.  
Chickens and eggs.

If you emphasize one at the expense of the other, you are
severely handicapping yourself.