Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-l] approximations



On 07/07/2010 01:48 PM, Pete Lohstreter wrote:

As with most "laws" of Physics, they work great for everything they work
for - but they don't work for everything. I would include Ohm, Kirchhoff,
Hooke... probably more...

That's absolutely true as far as it goes ... but it
also misses a couple of important points.

We agree that almost everything (in physics and otherwise)
involves approximations. For example, when I go to buy shoes,
I never seem to get the exact right size. (Maybe elementary
arithmetic is exact, but philosophers argue about even that.)

On the other hand we *must* not let students get the
impression that we fatalistically accept any approximation
that comes along. Some approximations are verrrry much
better than others.
++ The Maxwell equations do not solve all the world's
problems. They describe only half of the electroweak
interaction, and they don't describe gravitation at all.
On the other hand, we understand pretty well what falls
into their domain, and within that domain the equations
apply at the sub-nuclear scale and the cosmic scale and
everywhere in between. In some cases they have been
checked to one part in 10^12.
-- In contrast, Kirchhoff's laws are grossly violated in
all sorts of ordinary situations. There seems to be some
difference of opinion as to whether we should even expect
them to apply to a helicopter.

If you want to understand "ground loops" and other grounding
and shielding issues, and low-noise instrumentation more
generally, your first step, the sine-qua-non, is to stop
relying on Kirchhoff's laws and start using the Maxwell
equations. To say the same thing in other words: if you
think in terms of Kirchhoff-style circuits, then ground
loops will forever remain black magic. The ground loop is
neither understandable nor measurable. In contrast, as soon
as you formulate the problem in terms of electromagnetic
concepts such as flux and flux_dot, it is possible to
understand and even measure what you are dealing with.
For example,
http://www.av8n.com/physics/grounding-shielding.htm#sec-measure-phi-dot

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

More generally: Students need to understand that
approximations are necessary, but not all approximations
are created equal. Deciding which approximation to use
in any given situation requires skill and judgment.