Is physics taught using phrases that are too easily misinterpreted, and can this be improved?

Question

To explain, let me pick a particular statement: "the electrostatic force is mediated by the exchange of photons".

When a physicist (or a lecturer) says this, they mean one thing: the process described in detail by QED. When a student (or an amateur) hears this, they think of two electrons, and they imagine photons flying between them. You can imagine what follows: questions like "how do they know where to fly", or "what is the frequency of these photons", or "where does the energy to create those photons come from" etc.

When I was growing up, I had no access to anyone who really understood physics. All I had were books filled to the brim with phrases like the above. It is nearly impossible not to misunderstand something when such loose statements are used, as popular literature tends to omit the extremely important "but"s.

For example, in the statement above, the "but"s omitted are "but we don't actually mean photons, in fact we don't mean any particle at all; what we mean is a mathematical tool we use to calculate how the interaction works, which is reminiscent of actual photons in so many ways that we can often treat the calculations as if they involved actual photons".

What is the most effective way to educate students about such phenomena, where our language we use to describe them risks obscuring the reality, and/or misleading the students? Is there evidence in the pedagogic literature on this?

Answer 1

Yes, this is a real issue and yes, we are obligated as a community to address it because we ourselves are the source of so many of the misconceptions and errors we so often complain about. The higher the level, the greater the accountability should be, but frequently isn't.

There are nearly innumerable examples of faulty language all throughout the physics literature and physics textbook at all levels. I will list some here. Before doing so, I also want to point out that science, ALL science, is based on progressively sophisticated models. Each new level of sophistication brings deeper understanding, and the process never ends. It's okay to use simplistic models and accompanying simplistic language as long as we warn the listener that in simplifying things, we're introducing errors that will be addressed in the more sophisticated models. We frequently neglect this warning.

"Vectors are quantities that have magnitude and direction."

It is not the case that every quantity that has a magnitude and direction is a vector (e.g. finite rotations). There are also different kinds of vectors, and unfortunately this is rarely mentioned in introductory courses.

"Vector components are scalars."

Well, not always. Components can be vectors as well. In fact, what we call scalar components are really pseudoscalars because of their behavior under coordinate inversion.

"Energy is the capacity to do work."

This is a model of meaningless circularity if ever there were one.

"The potential energy of the ball..."

A single entity cannot have potential energy assigned to it. Potential energy is a property of a system.

"Energy or momentum flows..."

Neither is a concrete physical substance so they can't flow. What we really should say is that we treat them mathematically as though they flow.

"Charging a capacitor..."

Charge is a fundamental property of matter, and yet we routinely use it as both a noun and a verb, which is a huge potential source of confusion. When we use it as a verb, we really mean and should say "accumulating" because that's the physical process we're trying to describe. "Charging a capacitor" simply means "accumulating charge on the capacitor". Actually, upon deeper thought, it amounts to a "redistribution of charge creating the appearance of accumulation of charge on the capacitor." Sometimes more words enhance the meaning.

"Electricity is..."

I can think of the following words used by students to complete this thought: charge, current, potential difference, electric force, power. Electricity is really a meaningless word used as a substitute for lack of understanding of the concepts behind all those other words. If you mean power, then use the word power. If you mean current, then use the word current.

"Newton's third law says two objects exert equal and opposite forces on each other."

This directly contradicts the definition of force as a vector because two vectors cannot be equal if they have different directions. The term "equal and opposite" is inherently self-contradictory.

"Dot products and cross products are two ways of multiplying vectors."

These are very different from students' conceptions of multiplication. Dot products require both multiplication and addition (and sometimes subtraction). Cross products also require more than trivial multiplication. We shouldn't use the simplistic "multiplying" UNLESS we warn students that we're redefining what "multiplying" means.

"Moving clocks run slow. Moving rods contract."

These are very misleading. Time dilation and length contraction are nothing more than consequences of measurement from different frames.

"Time..."

• This problem took too much time. (time as a quantifiable concept)
• Distance is the product of speed and time. (time as a duration)
• What time is it? (time as a clock reading)
• Six times three is eighteen. (times as repeated addition)
• Please time the oscillations of this pendulum. (time as a verb)
• That was a very timely remark. (time as an adverb)
• Here is a time-dependent function. (time as an adjective)

These are a few from introductory and intermediate physics. Perhaps we should create a community wiki of more examples from advanced physics.

Answer 2

I've been thinking of this exact topic from a pedagogic standpoint for years. I taught high school physics where I had classes that ranged from 9th grade Conceptual Physics, to APB (non-calculus) physics, to APC (calculus-based) physics, to a 12th grade second physics class for students who wanted more physics but didn't want the rigor of the AP classes. I'm about to begin teaching a college-level Physical Science class where I'm faced with the same problem:

How do I teach the students "physics" (quotation marks in bold) without (a) saying something misleading, and (b) so they get a clear understanding that won't hinder them in future classes.

I believe the answer to that question relies most importantly on the level the students are at (teach to their level so they understand), and also with the explicit caveat that the teacher must tell the students that there are subtleties that will become apparent in future classes. Indeed, some of those subtleties are more than that -- saying that

Energy is the capacity to do work

may be circular and meaningless (as JoeH replied), but to a first approximation and definition it works for the time being, and can be improved upon in later classes. When I give that definition to my students, I always caveat it by saying, "Guess what? This definition isn't perfect, and in future classes you'll learn a more refined definition that involves other concepts that aren't within the scope of this class." (I say that a lot in introductory classes!) To the students that want more information immediately, I point them in the direction of other resources, or move the conversation to office hours.

The hardest part about proceeding with this method is to make sure that you don't lead the students into an incorrect conceptual understanding that is hard to break in future classes. Joe's example of "the potential energy of the ball" being incorrect without the idea of a system is a good one -- there are many times when simplifying too much leads to a fundamental misunderstanding, and as teachers we have to avoid that as much as possible. Learning what does and doesn't lead to misunderstanding takes time, but being able to formulate precise assessments (whether test-based, or clicker-based, or on homework, etc.) goes a long way towards determining whether or not a student has a proper understanding that doesn't involve misconceptions. If those misconceptions arise during the assessment, it is the teacher's duty to go back and clarify, or re-teach if necessary.

JoeH listed a number of physics concepts that take a concentrated effort to teach properly, but I think all disciplines have those problems:

Chemistry: electrons do not orbit in "shells," despite what millions of students learn every year in elementary school.

Computer Science: in some cases, bubblesort does beat quicksort.

Mathematics: the internal angles of a triangle do not always add up to 180º. Five times five does not always equal twenty-five.

English: passive voice is not always wrong.

History: a historian does not always have to be unbiased

(apologies for examples that aren't perfectly clear -- I'd be happy to amend my answer with better examples!)

Answer 3

A very good question. I usually deal with this like: "Vectors usually have magnitude and direction. Their components are usually scalars. There are more difficult cases, do you really want to deal with them now? [People sigh or say "noooo"] So, here is an example... Now we can continue.".

Of course, strict definitions give some comfort, but may also result in misunderstanding. It's good to confess that every detail is very difficult and even You, The Teacher, can not answer everything.

By default, you must know very well what you talk about. Then you can give some simple example, then a difficult one and ask them if they want to analyse it now. They usually say "nooo" and you proceed.

There are usually enthusiasts and passive people in a single classroom. It's a good practise to let enthusiasts give one or two questions above the course during the break, so that everyone gets what he's interested in. An interaction with your audience gives better feeling of what they actually need explained.