Physics redeemed

Physics is the most basic of the natural sciences

Physics is the most basic of the natural sciences. It is concerned with the properties of matter and energy and the relationship between them.

It is based on mathematics and the traditional branches of the subject are mechanics, optics, electricity and magnetism, acoustics and heat. Modern physics, based on quantum theory, includes atomic, nuclear, particle and solid-state studies.

Because this science is so fundamental to science students at third level, whether or not they intend to take degrees in physics they must have at least an elementary grounding in the principles of physics. Many students find physics difficult and are put off from pursuing the subject beyond the obligatory first-year introduction.

Physics describes the world in mathematical terms and lack of fluency in mathematics is frequently proposed to explain why many students have problems with physics. This is not a good general explanation.

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Obviously, if you can't do the necessary mathematicals, you cannot solve quantitative problems in physics. However, I understand it is not uncommon for a student to perform well in maths courses but nevertheless to experience difficulty in the physics course. It has also been reported that some students who are otherwise good at maths become very clumsy in their mathematical manipulations when trying to solve physics problems.

The study of physics requires the student to flip backwards and forwards at will between concrete observation of the external world and the abstract mathematical representation of that world. This is a skill which some people have naturally, which many can learn, but with which some will always have grave difficulties.

In order to illustrate the last point, consider map-reading as an analogy. A map is an abstract representation of a piece of territory in the concrete world. When using a map you have to be able to flip your mind easily from the abstract delineations on the map to the features on the actual landscape around you.

One of the first concepts taught in physics is acceleration. Acceleration lies at the core of dynamics, the study of motion, and dynamics has been the model for many branches of physics.

Acceleration is used to define mass, and mass and acceleration are used to define force, which leads to a definition of energy. And so it goes on, ascending a ladder of conceptual complexity. Clearly it is important to have a good understanding of acceleration.

An approximate way to measure acceleration is to record the position of a moving object at a specific time, wait for a precise time interval (say, five seconds) and record the position again, wait for a further five seconds and record the position once more.

Now calculate the displacement in metres of the object from the first to the second position and divide by five seconds to give the earlier velocity in metres per second. Calculate the displacement from the second to the third position and divide by five seconds to give the later velocity.

Next calculate the difference between the two velocities and divide by five seconds to find the acceleration in metres per second per second. This procedure gives acceleration averaged over a few seconds. In order to get a more precise measure (instantaneous acceleration) you have to make the time intervals much shorter.

Newton showed that you only get the true acceleration when the time intervals are made infinitesimally short and he invented the mathematical system calculus for manipulating these quantities. It is easy to visualise the approximate method for calculating acceleration, but the imagination struggles with the infinitesimals involved in the exact determination.

No real clock or ruler can measure infinitely small time or distance intervals. Here we have an interface between the real and the abstract world, and reducing acceleration to an instantaneous quantity can severely test the imagination of many students.

Why is it that some students' mathematical skills deteriorate when they attempt to solve quantitative problems in physics? A similar phenomenon is seen with students of English.

In the latter case, it can happen that a student who is good at writing essays on general subjects is reduced to semi-literacy when asked to write a critical appreciation of some aspect of a Shakespearean play. The problem seems to be the same in both cases.

In the first case, the student who can confidently manipulate symbols while they remain in the abstract mathematical world has difficulty in bringing these symbols to bear on physical concepts. In the other case, the student who can, separately, write well and understand Shakespeare has difficulty merging the discipline of writing with appreciation of Shakespeare. Both students have difficulty in moving smoothly between the concrete and the abstract realm.

Because confrontation between the real and the abstract world lies at the heart of physics, direct experience in the form of laboratory experiment or demonstration must be an integral part of every physics course. Courses which rely entirely on "chalk and talk" are not really teaching physics.

My thoughts on this subject have been informed by the writings of Hans Christian Van Baeyer, the American physicist and science writer.

William Reville is a Senior Lecturer in Biochemistry and Director of Microscopy at UCC.