Robert Karplus, Introductory Physics – A Model Approach
Review of chapter 3, The Interaction Concept
by James Vesenka, University of New England, Biddeford Maine (2005)
and Jeffrey Steinert, Edward Little School, Auburn, Maine (in 2005)
Dr. Vesenka’s review.
Dr. Karplus introduces the chapter with a quote from William Gilbert describing the
misconceptions of learned men about the properties amber and loadstone. The allusion
refers to the importance of the scientific method and makes a very nice introduction to
his chapter on "The Interaction Concept". Out of the starting gate Karplus makes a
statement that the novice might find surprising: "We take the point of view that
influence and interaction are abstractions that we cannot observe directly. What we can
observe are the effects or results of interaction." The novice might disagree, claiming
that they can "see" a bat hitting a ball, hear the sound of the interaction, see the ball
changing direction etc. Karplus makes a compelling argument to the reader that these
observations are indirect evidence for interactions, mere illusions, without plunging the
reader into advanced topics, such as field theory, that ultimately can best model the
interaction. He follows up the discussion on the scientific method by examining
alternative interpretations of the evidence and developing control experiments (a
comparison) to help determine if an interaction has taken place. A historic background
provides context for seeking patterns in nature, based on observations of cause and
effect. As new phenomena are observed the modern scientific approach requires
systematic examination of the components that are suspected to be responsible for the
phenomena. At this point Karplus introduces a key concept – the idea of a "system".
The concept of a system plays a central role in the discussion of interactions and
energy transfer, discussions that receive at best short shrift in most introductory
physics texts. A system is comprised of objects that interact with each other, with each
object being a sub-system of the whole. Conservation of systems demands there be no
addition and subtraction of objects to the defined system, even though these objects
might only be kept separate as mental images. Karplus goes on to describe the state of
the system: The identity of a system refers to the material ingredients, while the state
refers to the form or condition of all the material ingredients. He provides an example
of ingredients for iced tea before (hot water, tea, sugar, ice) and after (cool, sweet)
they are mixed as a model for changes of state in the system. Resistance to change of
state of the system is described as "inertia". As Karplus puts it: "Inertia is the property
of objects of systems to continue as they are in the absence of interaction, and to show a
gradually increasing change with the elapse of time in the presence of interaction." Thus
photoreactive objects will not change their state unless exposed to radiation (e.g. skin
exposed to sun). Similar arguments can be made for thermal and chemical inertia, and
the inertia of motion. The latter can defined through the number of oscillations a 1 kg
Pt-Ir mass oscillates on an inertial balance. Whereas the inertia of motion is easily a
recognizable consequence of the lack of interaction with a moving object, Karplus states
that radiation presents "an element of mystery", because of the apparent "Interactionat-a-distance" between a lit candle, a pair of parabolic mirrors, and a photodetector.
What is responsible for the interaction? As he states:
"The discovery of evidence of interaction is a challenge to identify the
interacting objects and to learn more about the interaction: the conditions
under which it occurs, the kind of objects that participate, the strength and
speed with which the evidence appears, and so on. It can be the beginning of
a scientific investigation."
My particular preference is not to use the commonly used term action at a distance
because of the implication of a lack of connectivity between interacting objects. Karplus
does NOT use this term – rather he very specifically states interaction at a distance.
From a pedagogical stand point I can buy into this. Though subtle, interaction at a
distance means two objects are interacting via a "field", a term that most students of
physics typically lack comfort with. Karplus' term makes for a nice transition until that
comfort level is bridged. As he claims: "Do radiation and fields really exist, or are they
merely 'theoretical objects' in a working model? …the answer to this questions depends
on how familiar you are with radiation and fields." I believe Karplus picture in Fig. 3.8
summarizes the concept nicely. A flag is attached to a slinky stretched horizontally
between two posts. Disturbing the slinky with a ruler anywhere along its length will
eventually disturb the flag, because the slinky transfer energy along its length until the
flag moves. In a thought experiment that Karplus does not mention, but is no less
accurate, covering the slinky from view without blocking the motion of the ruler and
subsequent motion of the flag might appear to be magic, until it is clear of the source of
interaction – the slinky. The slinky is nothing more than the physical field in which energy
can be transmitted. I plan to use this demonstration both in the discussion of fields and
the classical description of energy transfer through waves. Karplus follows with a
systematic introduction to gravitational, magnetic and electric fields because of the
importance they play later in his text.
In summary, this chapter alone clearly indicates Karplus' brilliance in approaching the
presentation of physics from a different viewpoint, that of model construction. The
storyline of the text is the most compelling I have come across after years of
examination of introductory physics texts. In part I (which includes chapter 3) he
provides background information. Part II introduces waves and atoms, part III discusses
different forms of energy, and part IV deals with motion. The last three parts are
presented, with almost no exceptions in other introductory physics texts, in reverse
order. All practitioners of physics will agree that the last three chapters are the most
important themes in physics. So why do we start with Newtonian Mechanics so singlemindedly? As a modeler who prefers the presentation of mechanics first, my only
defense is that it "seems" easier to understand single particles first, followed by multiple
particles (e.g. fluids, matter, sound, etc) second. His text will give me much pause for
thought, and perhaps over time such a story line may appear in my teaching notes.
Sincerely, Jamie Vesenka
Associate Professor of Physics
University of New England
Biddeford, ME
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comments byJeffrey Steinert, Edward Little High School, Auburn, Maine (in 2005)
I think Jamie has succinctly summarized much of what makes this text unique in its
approach to “The Interaction Concept”. In particular, the definition of a system and the role
that interactions within systems and between systems have on them is key to a clear
understanding of Newtonian mechanics. Karplus lays the foundations well. I especially like
the way he emphasizes the idea that inertia is a property of an individual object but that
interactions require two objects, each of which experiences an observable effect as a result of
the interaction. While he leaves the explicit discussion of forces (interactions) and
accelerations (observable effects) for the latter half of this text, as a teacher I couldn’t help but
reflect on how Karplus’ approach could be used with my students to help them understand that
inertia is not a force because it resides solely in the properties of the objects and does not
arise as a result of their interactions with one another. How you get them to replace the
Aristotelian conception that properties of the object determine its motion with the Newtonian
idea that it is the forces arising from interactions with other objects that matters is the subject
of more than a little physics education research.