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 "Interaction-at-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 single-mindedly?  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




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.