PROBLEMS OF PHYSICS EDUCATION

Among concerned physicists it is common knowledge that education in physics has almost no effect at all levels of learning. From many thorough studies of this fact, let us select one that is typical and examine it in some detail.¹ We are concerned, not so much with the technicalities of the studies, as with the typical answers given to a sampling of questions in physics.

- To the question, "In a thunderstorm, why is there lightning and thunder?" most people were of the opinion that it is due to friction between clouds.

- The origin of wind most frequently was traced back to the rotation of the earth or the motion of oceanic water.

- The fact that it is cold in December in our region was believed to stem from a greater distance of the earth from the sun.

- The magnetic force attracting nails made of iron was thought to be due to special conditions during the production process of the magnet.

The list could be prolonged indefinitely. It is not unfair to state, that even after more than 300 years of Galilean physics, the general view of people today remains closer to Aristotelian physics, though the latter is no longer being taught in school. The appreciable effort of universities to train physics teachers and their efforts, in turn, to transmit their knowledge to the general public seems to be in vain. Much thought has been given to this fact and a vast literature on teaching has been accumulated, but the results do not live up to expectations. It seems time then to ask on a more fundamental level why this is so and what can be done to change the situation at its root, rather than simply to make a surface or cosmetic effort.

The goal of this chapter is to show that the cause of this astounding phenomenon is an erroneous epistemological concept. The attitude of physics education must be changed in its foundation, namely, in its concept of "truth" and "reality", in order to be able to transport the meaning and the content of physical laws into our general picture of the world and therefore to integrate physics into culture--a goal yet to be achieved.

A BASIC MISUNDERSTANDING

REGARDING LAWS OF NATURE

It is claimed often since the 17th century that physics is a method for discovering the true laws of nature and thus to provide a correct description of our world, or at least its material aspects. Let us, for the moment, accept that point of view and examine its consequences in just two typical examples. According to Aristotelian physics, heavy objects fall to earth faster than do light objects and the force required to move an object is proportional to the velocity of that object. But since Galileo and Newton we "know" that all bodies fall to earth equally fast and that the force necessary to move an object is proportional to its acceleration.

If a pupil points to the observation that from any tree fruit fall faster than leaves and that you get more tired from riding a bicycle faster over a distance than from the acceleration at the start, we explain that this is due to the resistance of the air and the friction within the bicycle (and the tires). These "secondary effects" blur the picture and prevent us from directly observing the true and basic laws of nature. If we added these effects of friction and resistance, we could more or less also describe the more complicated phenomena occurring in our real world--such is the usual argument.

Suppose the pupil insists and wants to know whether the physical laws apply to our real work or only to some fictitious invention. We are probably tempted to point to the great achievements of technology such as airplanes or moon rockets to "prove" that, of course, physical laws have definite consequence within our real world.

The problem becomes even more urgent when we move on to modern physics where the notion of the "model" arises, for example the model of the atom. Unless their pupils are not interested anyway and simply accept what they are told, most teachers are faced with a dichotomy. The interested pupil sooner or later will want to know whether a model describes reality or not. No answer at all can be given, for if it is "yes", then why is it called "model" and why do we have to neglect so may aspects of "reality", and if it is "no", then how is it that we can build a reactor (or even a bomb) on the basis of a model that is not connected to reality?

A teacher unable to grasp the origin of this dichotomy will create the impression that physics is a queer subject, for either it deals with fictitious models and does not pay attention to the real world, or it holds the childish belief that its very simplified models in fact picture the complexity of our world. As neither attitude is that of mature science, the very effort to teach physics may support the dangerous opinion that the influence of science and technology in our society is due not to its intrinsic importance but rather to a sheer power play of lobbies and some industrial interests.

In this way, physics education sometimes achieves the opposite of its goals, even when no obvious mistakes or failures can be uncovered in its day-to-day operation.

Finally, when it comes to questions of physics such as those above, the average pupil will turn to "obvious" answers which come to mind without ever remembering that something pertinent to these questions has been taught in his or her physics courses.

Let us return to the above questions. Obviously, the answers are taken not from "physical models" or even from laws of nature, but rather from analogies with previous experience. Probably, most people have seen sparks originating from collisions between hard objects or from friction of brakes on railway carriages and by analogy claim the same phenomenon for lightning. Similarly, most people have experienced intense heat from hot objects as long as they were close, but when they withdrew the temperature fell notably: hence, the analogy for the low temperature in December.

The error is not the argumentation by analogy, which plays a very important role in physics! To give but one example, let me quote from a paper delivered on the occasion of the 50 year jubilee of Yukawa's Meson Theory. Herbert Fröhlich writes, "It was in this year that Yukawa conceived the novel idea that a field must exist that carries this interaction, in analogy to the electromagnetic field."²

But argumentation in physics is never mere analogy and even this is not the main difference. The basic misunderstanding stems from the fact that pupils draw analogies from observation and/or experience, i.e. from occurrences in their own lives or what seems to be the "real world" (notice that Yukawa took his analogy from another physical theory, namely electrodynamics). In so doing, and perhaps without realizing it, the pupils identify the physical description of a phenomenon with their "reality". Since they remember (at least subconsciously or emotionally) that this identification does not work, they simply forget the content of what they learned in physics courses and draw direct analogies between two phenomena, both of which they believe to be subject to physical description.

LIFE-WORLD AND MICRO-WORLD

The theory of constructive realism does not use the terms "real world" or "true description" at all. It does not deny the existence of reality, but insists that there is no direct access to it. Hence talk about "nature", "reality", "the world" or the like always refer to a construction. These constructions are not completely arbitrary, however, for they can contradict reality, in which case they have to be "improved" to eliminate the contradiction.

What usually is referred to as the "real world", i.e. the world we experience in our daily life, is termed the "life-world".³ It too is a construction, but it is a very complex phenomenon since it results from the elimination of two contradictions to reality, which show up as false predictions or accidents, even catastrophes.⁴ A typical example is the calendar, which in the 16th century no longer agreed with the natural seasons. The contradiction was eliminated by the introduction of the new calendar in 1582 by Pope Gregory XIII in most of Catholic countries. Since they were in contradiction with reality, even the Protestant parts of Europe followed suit in 1699. But this took more than a century!

This brings us to the second kind of contradiction occurring in the life-world, that is, between different constructions! This kind shows up as conflicts, powerplays, even wars of extinction. The fact, that it took so long for the Protestant countries to follow the new calendar proclaimed by the Pope, shows clearly that the distinction between the two categories of contradiction is not very obvious in the life-world, which is precisely the reason why physics cannot aim at a re-construction of the life-world. As Werner Heisenberg once put it: physics deals with those statements about the world, with which everybody must necessarily agree! If unanimous agreement cannot be achieved eventually, it is simply not physics.⁵ (Quantum Mechanics may be an exception.)

The great achievement of the "New Science" born in the 17th century was the renunciation of a description of the life-world. The laws of a falling body are valid in a vacuum, not in the life-world. Whereas the notion of a "model" often is used in modern physics, constructive realism uses the term "micro-world"; there is an important difference. The "model" for freely falling bodies is described by a "point mass" under the influence of gravitational force. (Of course, it presupposes such other "models" as the axioms of Newton). In other words, this model assumes a "universe" in which there is absolutely nothing but gravitational force and one single "point mass". Likewise, the model of the hydrogen atom assumes a "universe" in which there is absolutely nothing but a single electron under the influence of a Coulomb force. Not even photons are allowed in this "universe", or we could not solve exactly the basic time-independent Schrödinger equation.

One can proceed to complicate the model, and in this way achieve greater accuracy of prediction, but losing thereby the power to solve exactly (i.e. one has to use perturbation expansions). If the Coulomb force is replaced by a proton of finite mass the model still can be solved exactly. But as soon as we add radiation, spin or relativistic corrections, approximate solutions are the best we can achieve. Thus, physics as taught at universities distinguishes between theoretical and experimental physics. Theoretical physics teaches the multitude of models, together with the ingenious methods of solving the basic equations in order to derive predictions; experimental physics is supposed to describe the methods and tools for actually doing experiments.

A micro-world, however, is neither of these nor both together, but a very subtle construction which contains:

1) the theoretical model,

2) the experimental conditions for support or refutation of the model, and

3) the connection between the micro-world and the life-world, for actual experiments are always carried out in the life-world, but tell us about the micro-world.

What we learn about the micro-world can be used in turn to restructure the life-world, which is the reason that technological achievements are appealed to as a "proof" for reality as mentioned in section 2. A micro-world is completely devoid of any aspects which could lead to contradictions of the second category present in life-world. Though their remnants may be felt in the sometimes fervent and ridiculous fights about units, normalization, metric or symbols used by different schools of authors, these fights are superficial for there is always a complete one-to-one correspondence between different formal approaches. Thus, on the occasion of the 60th birthday of Max Planck, Albert Einstein said:

Mankind searches to shape a simplified and distinct picture of the world in an adequate way and in so doing to overcome the world of experience by replacing it with that picture. . . . He transfers the center of his emotional life into that picture and its formation to search for rest and steadiness which he cannot find in the all too narrow circle of whirling and personal experience.

CONTRADICTIONS TO REALITY

A very subtle aspect of science is its negative relation to reality. Reality can never be reached directly, but contradictions of reality may appear in our constructions.

Within logic, we learn that a contradiction is possible only between statements. This is the problem of "basic" or "protocol" statements much discussed in epistemology.⁷ How, then, can we observe contradictions of reality?

Let us begin with the example of the 16th century calendar. In the life-world, contradictions of the second category are eliminated by agreement (whether forced or voluntary). Agreement is reached by consent, i.e. by verbal expression. Thus, if there is agreement that spring has come, though the calendar says otherwise, then a contradiction to reality has been agreed upon! However, because micro-worlds do not allow contradictions of the second category, they have implicitly to contain a mechanism to determine contradictions to reality other than by agreement. Here the keywords are "quantification" and "reproducability", the definitions of a physical experiment.

Let us clarify this by means of an example. In the late 60s, the micro-worlds of electrodynamics and "weak interaction physics" were unified. A new micro-world was created, "electroweak interactions" or the "unified model" of those interactions: the basic equations⁸ (i.e. the so-called "Lagrangian") are often referred to as the "Standard Model" and represent what we could call a "model". But there was a crucial prediction, namely, the existence of new kinds of particles (the charged W-boson and the neutral Z-boson) at exactly prescribed mass values! Measurable quantities given in numbers are the crucial link between the micro-world and life-world, on the one hand, and allow for the discovery of contradictions to reality, on the other hand. Thus, the micro-world of electroweak interactions also suggests particular test experiments, that is to say, certain action in the life-world whose result is again a number which can be compared to the prediction and thus either support or rule out the underlying model.

However, all that is contained in the micro-world is the possibility (or suggestion) to aim at the wanted numbers, whereas the experiment itself has to be done in the life-world. Hence, usually there is disagreement as to the best way actually to carry it out. An experimental physicist is a person who knows what kind of actions have to be taken in the lifeworld so that the result is a number which can be compared to the prediction. These actions are by no means unique! Some are cheap, but more indirect (such as precisely measuring certain atomic spectra), others are more expensive (such as building a big accelerator) but directly yield the wanted numbers.

This is the point at which reproducability enters in a crucial way. It requires not only that repetition of the same experiment yield similar quantitative numbers, but moreover that totally different paths towards the same number (such as the two mentioned above) finally agree numerically. Thus, in the lifeworld very different actions may be undertaken, but the sufficient reason for doing so is founded in the relevant micro-world. Only when there is numerical agreement between the results of these experiments (different chains of actions in the lifeworld) and yet a disagreement on the number predicted by the model can we speak of a contradiction between the micro-world and reality.

It is quite obvious also that this description is a quite abstract generalization, for we know all too well that complicated chains of actions do not always produce the same result, even when we deal with such relatively simple, man made objects as starting an engine or riding a bicycle. Therefore, the question of whether different experiments yield the same result (or even what the result is) is one of agreement among experts and cannot "objectively" be answered.⁹ Because the extraction of a number from a chain of actions is by no means trivial it is not required (and cannot be!) that numbers perfectly agree.

Any number extracted from an experiment is meaningful if so-called "errorbars" are added. "Experimental errors" are of two kinds: statistical and systematic (they are frequently given separately in that order). Statistical errors stem from the fact that even the identical repetition of a chain of actions in the lifeworld never produces identical numbers. (Statistical errorbars indicate the probability of 2/3 that the "intersubjective" number lies within the error limits).

Systematic errors are the unavoidable gap between the lifeworld and the micro-world. The often referred to "chain of actions" is done in the lifeworld, but it is invented from the micro-world. Therefore, a number of limiting procedures has to be carried out in order to extract the resulting number (for example, in a free fall experiment, the density of air can be varied for extrapolation to perfect vacuum. In "measuring" the mass value of the above mentioned particles, the energy of the accelerator has to be set exactly (which is only possible up to another error!) It is very important to know that the published "result" of an experiment is never the actually measured number because many corrections due to this "gap" between lifeworld and micro-world have to be applied.

To illustrate this subtle procedure by our example, let me quote the numbers given in the original literature for the masses of particles W and Z from both theoretical prediction and experimental result.

M_w (theor) = 80 G_eV M_w (exp) = (79,91 ± 0.39) G_eV at Fermilab

(USA)

(80,49 ± 0.37) G_eV at Cernlab

(Europe)

M_z (theor) = 91 G_eV M_z (exp) = (91,175 ± 0.021) G_eV

Theoretical predictions can be refined to agree fully with experimental results.

CONSEQUENCES FOR EDUCATION IN PHYSICS

In view of all this it is quite obvious that physics "teaching" cannot be done in the form of a "transfer of knowledge" from teacher to pupil. When it is tried, the result is harmful, as shown in the first section above. For what should this "knowledge" be? If it should be the "laws of nature", we have seen that they do not make any sense whatsoever when they are applied directly in the lifeworld.

Unless the student of physics understands at least in some way the subtle difference between the lifeworld and the micro-world and the ingenious inventions to find out about contradictions of the latter with reality, there is no way even to transfer a remote idea of what it is all about. How can this goal be reached? Certainly not by traditional memorizing and repetition for the sake of a test or examination.

Let me then attempt to paint an idealized picture of teaching physics, being well aware that the lifeworld is not as simple-minded as my invention. Understanding in physics proceeds only via the discovery of one's false notions. Here "false" is meant with respect to a micro-world, not within the lifeworld, as can be inferred from the examples in the first section above. The role of the educator is thus to represent the micro-world which is yet unknown to the pupils. But he or she should not simply explain that world to them, but must find ways to uncover false notions.

Teaching the aerodynamic paraoxon can be used as an example. Traditionally, one would explain Bernoulli's equation in some way and afterwards infer from it that an air current blown between two sheets of paper will narrow the gap instead of widening it, as could be naively expected. Doing the "experiment" (which in this case requires only two sheets of paper usually is taken as "proof" for Bernoulli's equation.

I will suggest the opposite approach, that is, in the very beginning to ask the opinion of pupils (and hope that they are divided into "wideners" and "narrowers"). I would then let them argue, and would support the weaker group, not necessarily the correct answer. When most of the important arguments had been issued, I would do the "experiment" to show which answer is correct, not because the teacher tells them, but because the experiment has decided the issue.

Next I would ask them whether they can recall some effects which may be similar or analogous (roofs blown off houses vertically, not in the wind direction; skis on racks of cars, laundry on a line going above the horizontal when the wind blows, the flying of airplanes, etc.). Some examples may be truly analogous within the micro-world (such as those above); others may only seem so in the lifeworld (such as the answers of the first section above).

Finally, a thorough discussion of these examples should give the pupils a feeling for the difference between the lifeworld and the micro-world. Bernoulli's equation should come in the end as a sort of summary, not as a starting point.

One goal of physics education must be achieved: the affective acceptance that it is completely meaningless to give a number as a result of a measurement without giving at the same time its errors. A possible example to get this across could be a comparison between gauged and ungauged speedometers in cases; another would be the scales for personal weight since they differ enough to show an explicit error. Many of our measuring instruments in the lifeworld have reached a precision which hides the error behind the last given decimal. Most thermometers for measuring body temperature fulfill this condition, but weather thermometers usually do not, in particular since their reading depends very much on the location of the instrument (systematic error).

If physics education could achieve just a little insight into these exciting differences, I would gladly forego the wealth of formulae and statements now often taught in physics. However, a prerequisite for this is a new education of physics teachers at the university level, for I fear that many physics teachers--though knowledgeable in the "material"--have gained little understanding of these basic facts during their own education.

1. R. Brämer, "Über die Wirksamkeit des Physikunterrichts, Naturwiss, im Unterricht", Phys. Chem., 1 (1980), p. 10. K. Daumenlan, "Physicalische Konzepte junger Erwachsener", Dissertation, Nürnberg, 1969.

2. H. Fröhlich, "The Development of the Yukawa Theory of Nuclear Forces", Progress of Theoretical Physics, Supplement, 85 (1985), p. 9.

3. F. Wallner, Acht Vorlesungen über den Konstruktiven Realismus. Wien: Wiener University Verlag (1990).

4. H. Pietschmann: Die Wahrheit liegt nicht in der Mitte (Stuttgart: Ed. Weitbrecht, 1990).

5. W. Heisenberg, Collected Works, Philosophical and Popular Writings, eds. W. Blum, H.P. Rechenberg (München: Piper Verl., 1984).

6. A. Einstein, Mein Weltbild (Amsterdam, 1934).

7. For example K. Popper, Logik der Forschung (4th ed.; Tübingen: J. Mohr Verl., 1971).

8. For a simple description see H. Pietschmann, "Vereinheitlichung von schwachen und elektromagnetischen Wechselwirkunger," Phys. Blätter, 35 (1979), 569; a somewhat more mathematical introduction is found in H. Pietschmann, "Elementary Introduction to Gauge Theories," Acta Physica Austriaca, Suppl., 19 (1978), 5.

9. H. Pietschmann, "The Rules of Scientific Discovery Demonstrated from Examples of the Physics of Elementary Particles," Foundations of Physics, 8 (1978), 905.