[Phys-L] Re: Buoyancy question

[jsd at AV8N.COM (John Denker)]

Let me try to shift the emphasis here, and perhaps make
this into a "teachable moment".

Michael Edmiston wrote:
> ....  I think most people believe a 15 g object must literally push
> away 15 g of water in order to float.  Everybody I asked today thought
> of it that way, and they all said that a 15-g object could not float in
> 10 g of water.  How can you displace 15 g of water if there isn't that
> much water present?
>
> The usual dictionary definition of displace is "to move something away
> from its normal position."

   Wow, a dictionary entry is not exaaactly right!  Film at 11!

   Wow, a textbook passage is not exaaactly right!  Let's call a
   meeting of the General Assembly!

Sarcasm aside, now, my recommendation is to treat such
imperfections as the rule rather than the exception.
Almost everything we do is less-than-exactly right.

Lots of non-scientists think that science consists of going
into unexplored territory and discovering entirely-new things.
But really, quite a bit of science, including some very
important and creative science, consists of figuring out
which bits of what we "know" are in need of refinement.

We can use Michael's buoyancy demo as a good example of how
science really works.

1) We have an old theory that doesn't quite work.

2) We can replace it with a new theory:  The new idea of
displacement is that you remove a floating object and see
how much water you need to replace in order to restore things
to the way they were.  Perhaps we should call this the
REplacement theory of buoyancy rather then the DISplacement
theory.

3) We need to check the new theory against the
_correspondence principle_.  You can easily convince yourself
that the new theory makes the same predictions in the old
theory, in all the "legacy" situations, i.e. in all the
situations where the old theory had been checked against
experiment.

We can even quantify how the _correspondence limit_ works:
it has to do with the surface loading, i.e. the mass of
the boat relative to the area of the body of water.  (By
way of example, I can testify that the mass of my catamaran,
relative to the area of the ocean, is firmly in the classical
limit.)

4) As sort of the opposite of the correspondence limit, we
can understand how the old less-than-perfect theory could
come to be conventional.  It's validity rests on unstated
assumptions, such as small surface loading, or equivalently
that the surface level is not much affected by the presence
of the boat.



We can make an interesting connection to the "accelerated
charges" thread, which provides another example of two
inequivalent theories that agree on all the legacy data.
I am referring to the (X dot dot)(X dot dot) theory versus
the (X dot)(X dot dot dot) theory, which necessarily
agree on all easy-to-check cases.  One or the other of
these (or perhaps both) rests on less-than-perfect
assumptions.


You can illustrate the key idea with a Venn diagram.
Draw two big ellipses, largely overlapping, but neither
contained in the other.  The current experimental and
theoretical evidence lies within the intersection.  To
refine our understanding, we need some evidence that
contradicts one of the theories, i.e. evidence that
lies in the region(s) of non-intersection.


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


As a possibly amusing tangent:  The two versions of the
buoyancy rule remind me of second quantization:
  1) measure how much water comes out when you insert
   the object, versus
  2) measure how much water goes in when you remove
   the object.

This is analogous, in some twisted sense, to
  1) (a dagger)(a), versus
  2) (a)(a dagger).

I doubt this analogy is very useful, but there it is.

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

Summary:  Words fail to describe how un-excited I am by
less-than-perfect theories in reference books.  We are
not lawyers here, or religious fanatics.  The physics
is what it is, and if the books fail to reflect the
physics, that's the book's problem, not mine.

I have often suggested we adopt the rule that every
book contain a large number of outright errors, just
to exercise the readers' powers of critical thinking.
I reckon the cost of compliance with this rule will
be small, since most books are already in compliance.

Think of that Venn diagram:  No theory is ever safe, no
matter how well established, because for every theory
there are other theories that are inequivalent in
general, yet agree with it on all the legacy data, i.e.
all the known test-data.  Whenever you apply a standard
theory in a non-standard situation, there is some
possibility that you will falsify the theory, whereupon
we need to figure out which of the other theories survive.