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RE: IMAGINARY NUMBERS





On Sun, 1 Feb 1998, Tim Sullivan x5830 wrote:

"Real" and
"Imaginary" are just historical terms and don't mean "physical" and
"unphysical". I suppose this is the price we pay for rejecting complex roots of
polynomials by saying "Well they are Imaginary!, that's why."

Tim Sullivan
sullivan@kenyon.edu


Horrors, Tim! Do teachers really say such a thing? They should lose their
license to teach.

When we encounter "unphysical" solutions, we should inquire (with the
students) about why those solutions arose. Often it's because we didn't
input sufficient information about the physical problem into the
mathematics.

Consider the common example of the ball moving with speed v toward a
stationary ball of the same mass. When you apply conservation of energy
and conservation of momentum (two equations), you will of course get two
roots from the quadratic.

(1) One root tells you that the moving ball comes to rest and the one
initially at rest moves off with speed v.

(2) The other root tells you that the moving ball continues to move with
speed v and the one initially at rest continues at rest.

The first solution is the one which agrees with the experiment, and we go
on to the next problem.

But wait. What does the second root mean? It could mean

(a) The balls do not hit each other. We didn't input anything into the
mathematics to say that the velocity of the moving ball was colinear with
the line joining their centers.

(b) The moving ball penetrates through the stationary one without
interacting with it. We didn't input anything into the equtions about the
substantiality of the balls, their elastic constants, their atomic
structure, interatomic forces, etc.

Don't blame the mathematics if we don't supply sufficient information.

-- Donald

......................................................................
Dr. Donald E. Simanek Office: 717-893-2079
Professor of Physics FAX: 717-893-2048
Lock Haven University, Lock Haven, PA. 17745
dsimanek@eagle.lhup.edu http://www.lhup.edu/~dsimanek
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