- ...
inadequate.
^{1} - Note that Quantum Mechanics does
*not*"prove Newtonian Mechanics wrong;" it merely reveals its shortcomings and the limits of its straightforward applicability. All paradigms have such shortcomings and limits, even Quantum Mechanics! Bridges did not fall down when Quantum Mechanics was "discovered," nor did engines or electromagnetic devices cease to function; we simply learned that Newtonian Mechanics and electromagnetic theory were*approximations*to a more fundamentally accurate picture furnished by Quantum Mechanics and Relativity, and where the approximation was no longer adequate to give a qualitatively correct description of the actual behaviour of matter.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ... truth
^{2} - I should say "truth" or
otherwise indicate that I don't mean there
*is*some sort of ultimate Truth that we can discover and then relax.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ... Earth.
^{3} - It is of course easy for us to see the error
of such thinking, because we are privy to Newton's paradigms;
this should not delude us into scorning the efforts of the "giants"
on whose shoulders Newton stood to "see further than other men."
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...
^{4} - This
can be checked by applying a force to two identical objects stuck together
and seeing if they accelerate exactly half as fast as either one
individually subjected to the same force.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ... itself.
^{5} - This
may seem absurdly self-evident, but in fact there
*are*physical properties that are*not*additive! So we want to explicitly point out this assumption as a point of vulnerability of the model, in case it is found to break down later on. This sort of "full disclosure" is characteristic of any enterprise designed to get at the truth rather than to win an argument.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ... "law."
^{6} - Recent
re-measurements by Dicke
*et al.*challenged Eötvös' ability to measure so accurately; they tentatively reported*deviations*from the expected results, suggesting that there might be an incredibly weak "fifth force" between the Earth and other matter that is different for protons than for neutrons. This was hot news for a while, but the excitement seems to have died down now, presumably due to new measurements that once again agree with Galileo and Eötvös.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ... constant
^{7} - Counterexamples
are not as rare as you might think!
Consider for instance a
*rocket*, which is constantly losing mass as the motor burns fuel. In such cases the original form of the SECOND LAW is essential.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ... force.
^{8} - If we mess up
and draw the force in the opposite direction from its
actual direction of application, we needn't worry,
as the mathematics will automatically deliver up a result
with a - sign as if to say, "This force is in the opposite
direction from the way you drew it, dummy!"
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ... measurements
^{9} - Aha!
another
*Gedankenexperiment*! But this time we can actually imagine performing it in our basement - or in a teaching lab at the University (where in fact it is almost always one of the required experiments in every first year Physics course). Of course, the actual experiment is beset by numerous annoying imperfections that interfere with our cherished idealizations and require tedious and ingenious corrections. Even simple experiments are hard in real life!. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1998-08-04