This question sounds ridiculous, and maybe it is.  So if you’re not in the mood for philosophy right now, you can skip this post.

Nonetheless, I think it makes sense to talk about our general attitude toward the concepts of force and energy.  “Which is more real?” may not be a very well-defined question, but I think it is a very natural one that cuts to the heart of how we think about forces and energies.  Furthermore, it is one to which my  answer has changed over the years.  The change was a difficult one: force and energy are such profoundly important concepts in physics that to change your view of them is to change your view of all topics that are built upon them (basically, everything).  But for me it has been extremely important.  Shifting my position from “force is more real” to “energy is more real” was essential for understanding and enjoying advanced topics in physics.

To my mind, there are two ways basic ways of thinking about force and energy.  I’ll call them “viewpoint #1: force is more real” and “viewpoint #2: energy is more real”.   Both are perfectly conceptually self-consistent, and they lead to the same equations and the same predictions of the natural world.  In this post I’ll try to explain both positions, and why I (and, I’ll venture to say, most people who make a living doing physics) shifted from one camp to another.

Let me first clarify the problem a little bit, and why there is any need to think of either force or energy as “more real” than the other.  Force and energy are not really independent ideas.  There is a well-defined relationship between them ($\vec{F} = -\vec{\nabla}U$, where $\vec{F}$ is the force on an object and U is its potential energy).  So if you know the forces that exist in a given situation, you can define all the energies.  Likewise, knowing the energies allows you to define all the forces.  The question is, which one does Nature really respect, and which is just a convenient definition that we use?  If you’re feeling religious, you can pose the question as “did God decree the forces while man just defined the energies for his convenience, or did God decree the energies and let man define the forces?”.  Let’s look at the two positions:

$\hspace{10mm}$

Viewpoint #1: Force is more real

This is the viewpoint that most of us are taught in high school, not as dogma but as a consequence of the order and context in which the material is presented.  Not surprisingly, this is also the one that historically developed first.  Its fundamental tenet is this: forces exist.  You are not allowed to ask “why do forces exist?”; they just do.  God decreed them, or your physics teacher decreed them.  And since there are four fundamental forces (gravity, electromagnetism, the strong nuclear force, and the weak nuclear force) we must assume that God laid down four separate force laws which were thereafter always obeyed.  You can tell when a force is being applied because it causes the object it is acting on to accelerate (Newton’s Second Law).  Over the years, men studied the forces and derived, experimentally, the equations they obeyed.

The studiers of the universe then used the forces they discovered to make a convenient definition: energy.  Energy was defined as the stored ability to apply a force for a given distance.  An object with kinetic energy, for example, can be directed into a spring and used to apply a compressing force.  An object with gravitational energy can be dropped, and allowed to fall onto that same spring.  By integrating the the force (multiplying its strength by the distance over which it is applied), energy could be given a numerical value.

Eventually, someone made a shocking discovery: energy was conserved.  In other words, the total amount of this arbitrary thing they called energy was always the same.  It could appear in one form or another (the falling object’s “gravitational energy” turned into “kinetic energy” and then “spring energy”) or be dispersed among multiple objects, but the total amount of it that existed in the universe was always the same.

Another interesting coincidence about the forces was that they only came in pairs.  That is, whenever some object A applied a force on B, object B always pushed or pulled back on A with equal and opposite force.  We call this Newton’s Third Law. It states, for example, that if there exists a downward force pulling me to the Earth, there must exist an equally strong upward force pulling the Earth to me.  Strange but true.

The “force is fundamental” viewpoint requires each of these last two facts to be viewed as amazing coincidences, or as additional decrees from the Creator.  From a philosophical standpoint, they seem a little hard to swallow… a little too coincidental.  Is there an explanation with fewer “coincidences”?

$\hspace{10mm}$

Viewpoint #2: energy is more real

If you believe that energy is more “real” than force, then you stop talking about “forces acting on objects” and instead talk about “interactions between objects.”  Your starting assumptions for describing the universe must be the “interaction energies”.  And, just like with the force point of view, you need to make four of them: gravitational interaction energies, electromagnetic interaction energies, and strong/weak nuclear interaction energies.  The interaction energies are the fundamental quantities of the universe, and there is no answer to “where do these energies come from?”.  Nor, by the way, can you really answer the question “where is the energy located?”.  Somehow, there is a certain amount of energy in the universe, and it shifts from one form to another and from one place to another, like ripples moving across the surface of a pond and disturbing lillypads as they go.

If you were to start from this sort of poetic (or wishy-washy, depending on your tastes) view of the universe, then you would soon make a big discovery: whenever the potential energy of the universe can be lowered by moving an object in a particular direction, a “force” will arise pushing the object in that direction.  A ball resting on the slope of a hill can lower the gravitational energy of the universe by falling, so a “force” arises that pushes it down the hill.  A positive charge can lower the electric energy of the universe by moving away from another positive charge, so a force arises to push the two apart.  This is how the “energy is more real” people interpret the force-energy relation $\vec{F} = -\vec{\nabla}U$.  Forces are secondary, a result of the strange desire that the universe has to lower its interaction energy.  Somehow the universe is continuously trying to decrease its interaction energy, and pushing on its constituent parts in order to do so.

$\hspace{10mm}$

So which viewpoint is more correct?  In a sense, it doesn’t matter: both give results that are perfectly consistent with our observations of nature.  The second one seems a little crazier, but in fact it requires fewer assumptions.  It also manages to explain why all forces come in pairs: between two objects there is only one interaction energy, to which both objects will respond.  In my mind, the “energy is more real” viewpoint is much more compatible with advanced physics concepts like thermodynamics (where energy is really the only consideration), quantum mechanics (where our force laws are no longer strictly obeyed, but energy remains absolute) and field theory (where we are given a way of picturing where the energy is really stored). Perhaps most importantly, I find the energy viewpoint much more conducive to wonder.

This all brings me to a mini-rant about physics education.  Why was I taught viewpoint #1 first when viewpoint #2 seems more beautiful and more useful?  Why does every introductory physics class begin with forces and accelerations, and not a discussion of energy?  Maybe the concept of energy is too confusing, too foreign-seeming, or too hard to visualize.  Viewpoint #1 lends itself to straightforward rules and procedures, and simple diagrams with arrows adding together.  But it also makes physics seem more arbitrary and disconnected, like a series of rules that must be learned and accepted without a nice overall picture of how the universe works.  No one was ever inspired to write poetry from an introductory physics class, that’s for sure.

And maybe that’s part of the reason we teach physics the way we do.  It seems more pragmatic this way, and part of the goal of a physics class (apparently) is to teach students to be level-headed, analytical, and detail-oriented.  Certainly my peers and I were selected largely for our pragmaticness and analytical ability.  Maybe forcing students to plow through viewpoint #1 helps them develop the mathematical competencies necessary to do upper-level physics.  But if a particular approach is more compelling, more conducive to further learning, and more beautiful, shouldn’t we teach it?  I think so.

August 9, 2009 1:04 am

GL – you make a good point and I certainly am inclined toward the “energy is more real” way of thinking. But I will say that I didn’t have a hard time starting with forces in high school. Forces didn’t seem disconnected from how the universe works for me because I could experience force very easily: the sensation of pushing a heavy bookcase versus pushing a chair taught me the connection between mass and force; the sensation of a heavy package on my shoulders gave me the sense of “force of gravity”; holding two magnets near each allowed me to feel the magnetic force. So learning to apply rules to something I could “feel” was natural for me. I won’t argue that viewpoint 1 is more beautiful, but it didn’t feel “arbitrary and disconnected” from the universe to me.

MG

2. August 11, 2009 4:36 pm

When I was reading about forces and energy I got into “action principle” and Lagragians. I am also more inclined to believe energy as something that “exists” and Force is an outcome of interactions of a body.

August 11, 2009 4:39 pm

The principle of least action definitely needs its own post. Hopefully some time in the next month or two.

3. August 17, 2009 2:45 am

It’s also worth noting that Newtonian mechanics — which language is rooted in viewpoint #1 — is sufficient for almost all engineering. Remember that just as you view mathematics as “just a tool” with which to express physics, physics itself is seen as “just a tool” which can be used to build things. We start by teaching about forces because almost everything we want someone to be able to build can be built using forces instead of energies.

August 17, 2009 4:50 pm

Yes, that’s what I think. It’s the Engineering Viewpoint versus the Metaphysical Viewpoint. The engineer uses the model that best fit his needs; the fact that mathematical formulas can describe our world at all is coincidental. The metaphysicist physicist wants to find actual underlinings of our universe. The first might be easier to teach but physics cannot advance much in it; physics needs to push beyond conventional models of the universe.

I always hated engineering, the tendency to round out variables, to use what works without a thought to why it works. I was quite surprised to find that I loved physics, that it can be more deep and beautiful that engineering jargon.

4. May 6, 2010 6:59 pm

I know this post is really old, but I think it’s worth commenting on.

In my opinion, the question of which is “more real” is, as my first intuition suggests, a little misguided, since they are (as you yourself point out) derivable from one another. From that perspective, each one must be as real as the other. Of course, certain problems in physics are more amenable to one point of view than to the other. For instance, I think most problems in simple mechanics are easier to think of in terms of forces; conversely, most problems in thermodynamics are easier to think of in terms of energy. (And since we generally learn the former before the latter, I think there’s your answer to why we learn forces before energy.)

But because both views are essentially equivalent, we don’t worry ourselves over whether we’ve missed something because we solved our problem “using forces” or “using energy.” Note that this is a stronger duality than is exhibited by the optics wave-ray duality: In most macroscopic cases, geometric ray theory gives you the same answer as wave theory (a la Huygens), but it will fail you on anything involving diffraction, of course. Ray theory can’t predict the Poisson spot or the Airy disc (much to the consternation of small-telescope aficionados, I’m sure). But force-energy duality is more reliable, I think. So rather than choose one over the other, shouldn’t classes teach both?

The problem, in my estimation, is that energy is just more ethereal-seeming to the average high-school physics student. You can feel a force, viscerally. Energy in many forms just isn’t tangible. You can’t feel gravitational potential energy the same way you can feel the impact of a physical tug. The fact that the two are essentially two ways of viewing the same thing doesn’t really change that. And as I said before, the elementary subjects of high-school physics are probably more amenable to force-thinking than energy-thinking. Certainly some of that is cultural and/or historical. But perhaps force-thinking came before energy-thinking, historically, because it seems more “natural” to us. Once the non-physics students have been weeded out, so to speak, the dual approach might be practical.