A few weeks ago, during a PHYS-L discussion of Newton's laws, I referred
readers to an insightful article by David Hestenes, downloadable in pdf
from his web site. Joel Rauber laster posted that he couldn't find it. I
finally found time today to browse Hestenes' web site. I copied and pasted
an excerpt below so that you can see if you like the article.
Hestenes' 21-page paper is entitled "Foundations of Mechanics". It was
originally chapter 9 in the first edition of his massive text, "New
Foundations for Classical Mechanics" (which I love to read!) You can
download this article at
modelingnts.la.asu.edu/pdf/Foundations.pdf .
Alternatively, go to his web site, then click on "modeling", then click on
"Foundations of Mechanics".
Cheers,
Jane
[Article design: Hestenes begins by discussing scientific realism, models,
theories, and laws. On page 9 he introduces the zeroth law of physics:
"Every real object has a continuous history in space and time." My excerpt
begins on page 11.]
EXCERPT:
3. Generic Laws and Principles of Particle Mechanics
The spatiotemporal properties of real objects are described by the
Zeroth Law. To produce a complete physical theory, the Zeroth Law must be
supplemented by a set of dynamical laws which describe the nature and
effect of interactions between objects. In Particle Mechanics the
interaction property is represented by force functions. A set of generic
laws implicitly define the concepts of mass and force and assign them a
physical interpretation. To produce a specific model of interacting
particles, the generic laws must be supplemented by specific force laws
which specify definite force functions.
Our formulation of the general theory consists of four generic
laws, one hypothesis and three generic principles. Let us present them all
at once, and then comment on each one separately. Of course, our
formulation presumes the Zeroth Law, so the notions of particle, time,
position, velocity and acceleration are all well-defined. In addition, the
formulation is presumed to hold only for a certain kind of reference system
called an inertial system, which is implicitly defined by the First Law.
Now we are ready.
First Law (Law of Inertia):
In an inertial system, every free particle has a constant velocity. A
particle is said to be free if the total force on it vanishes.
Second Law (Law of Causality)
The total force exerted on a particle by other objects at any specified
time can be represented by a vector f such that
f = ma ;
where a is the particle's acceleration and m is a positive scalar constant
called the mass of the particle.
Third Law (Law of Reciprocity):
To the force exerted by any object on a particle there corresponds an equal and
opposite force exerted by the particle on that object.
Fourth Law (Superposition Law):
The total force f due to several objects acting simultaneously on a
particle is equal
to the vector sum of the forces fk due to each object acting independently,
that is [oops - I don't know how to reproduce the equation here. JJ]
To relate formulations of the laws in different inertial systems, we adopt the
Hypothesis of Absolute Simultaneity:
Local events which are simultaneous in one inertial system are simultaneous
in every inertial system.
A local event is defined as a change in the position or velocity of a particle.
Specific force laws need not be regarded as part of the general
theory. However, they are restricted in form by generic principles. The
principles function as laws when force functions are unknown. In
particular, they sharpen the general concept of force defined by the
generic laws. However, when we have specific force laws that satisfy the
principles, the principles are superfluous. For this reason we do not call
them laws. In Section 3-1 we introduced The Principle of Analyticity. Two
other principles are important:
The Principle of Local Interaction:
The force on a particle at any time is a unique function of particle
position and position time derivatives; it is independent of the particle's
past or future history.
The Principle of Relativity:
The laws of mechanics have the same functional form in all inertial systems.
[Hestenes then comments on each of these laws and principles, followed by a
discussion of procedural knowledge of science, i.e., scientific method and
its relation to modeling development and deployment. JJ]
Jane Jackson, Co-Director, Modeling Instruction Program
Box 871504, Dept.of Physics & Astronomy,ASU,Tempe,AZ 85287
480-965-8438/fax:965-7331. http://modeling.la.asu.edu