Theatre, Film and Show techniques
for Science Education
Stefan
Heusler,
University of Münster, Wilhelm-Klemm-Str.
10
D-48149 Münster, Germany
Abstract
In
this article, we motivate our interest in theatre, film and show techniques for
science education and explain our methods with one specific example taken from
the DVD-project “QED – Matter, Light and the Void”
(www.sciencemotion.de).
Introduction
Mathematical
formulas are like pieces of music. They need to be performed to come alive.
Mathematics
is a language which is needed to communicate observations and findings in
physical research. But are mathematical formulas the best medium to reveal the
fascination for the laws of nature to students? The answer to this question is
obvious using the analogy to a piece of music: Are music scores the best medium
to reveal the fascination for music to students?
Obviously,
the answer is no. A fascinating and emotional
experience of music can only be
achieved if music comes alive through performance.
It is this experience which motivates students to learn the technicalities,
that is, performing the music scores.
How
can we motivate students to learn abstract, mathematical models in physics?
I
claim that theatre, film and show techniques are important to create a
fascinating and emotional experience of science. It is this
experience which motivates students to learn the language of mathematics.
The DVD and internet project
”QED – Matter, Light and the Void“
The
interaction of electromagnetic radiation with electrons and positrons is
successfully described by quantum electrodynamics (QED). A fascinating history
of research has led to the success of this theory. J. Schwinger, one of the
fathers of QED, describes the development of the theory as follows:
“Only
when the theory is finally frozen in the textbooks can one speak of the
‘physicist‘s conception‘. At any interesting moment of the development of the
theory, there are discordant viewpoints of individual physicists. “
These
discordant viewpoints stem from our limited understanding of nature. Our
mathematical models are not the reality but only an attempt to describe some
parts of reality. Only if the predictions of a model agree with observations in
nature, does the model survive and develop further.
Mathematical
models reflect concepts and ideas the
scientist has for his view on nature. Even if the mathematical implementation
of the model becomes very complicated, the underlying concepts and ideas can be
simple and beautiful.
How
can we teach pupils at high school the simple and beautiful ideas which stand
behind the mathematical model without teaching the complicated technicalities
of the mathematical model itself?
We
approach the problem how the simple and
beautiful concepts underlying quantum electrodynamics (QED) can be explained
on three levels:
Level
I: A puppet animation movie about QED. In five chapters, the concepts
behind the theory are introduced without mathematical equations. Here, we use
the following methods:
(i)
Two puppet characters discuss the question what light is and debate
different models to explain their experimental observations.
(ii)
Visualization of the models and underlying physical concepts using
modern computer graphics.
(iii)
Performance of experiments,
comparison with the models, and once more: discussion of the results.
Level II: 30 short clips (3-4
minutes each) in which the intuitive concepts introduced in the puppet
animation movie are related to mathematical equations.
Level
III: Further explanations of the models introduced on the DVD are provided
through the internet on the webpage”Cinema and Science“, (www.cisci.net). This material enables teachers
to use parts of the movie in classroom.
The
EU-funded project “Cinema and Science“ (CISCI, www.cisci.net)
combines two media, the internet and the DVD to raise the interest of young
people for science.
In
classroom, short sequences (3-4 minutes) of the movies can be presented to
introduce a topic and to motivate the scientific analysis. From the DVD “QED –
Matter, Light and the Void“, more than a dozen short clips can be used in
classroom to introduce the physical properties of light.
The commutator
The
so-called commutator is of uppermost
importance in physics. In quantum mechanics, the position x and the momentum p
of a particle do not commutate, meaning that “x*p” is not equal to “p*x”.
Rather, the commutator x*p – p*x is proportional to Planck’s constant h.
Likewise, creation and annihilation operators of photons in an electromagnetic
field do not commutate.
In
level I of the QED-project, the commutator does not occur explicitly. However,
the consequence of the non-commutativity of position and momentum is shown in
the staircase model of the atom (Chapter IV). Furthermore, we introduce a
simple model of the absorption and emission of light quanta (Chapter II).
In
level II of the QED-project (Chapter IV b), a simple mathematical model of the
commutator is introduced, which will be discussed below.
In
level III of the QED-project, additional educational material about the
commutator is provided on the webpage www.cisci.net.
How
can we perform the concept of the
commutator? The model which we propose is the following: We
use an empty glass, a bottle of water and two operations: The first operation turns
the glass upside down (described by the operator U) and the second operation
pours water from the bottle (described by the operator W).
The
operators U and W are applied to a glass. It is a simple (and funny!) exercise
to show that the two operations do not commutate. Before any equations are
introduced, pupils can experience the effect of these operations by using a
real glass and a bottle of water. Doing so, the fact that ordering is important
if operators are applied to a state emerges naturally. It is also possible to
assign the role of the operators U and W to two pupils and to show the
non-commutativity as a little on-stage demonstration.
After
this demonstration, pupils feel motivated to learn how this experiment can be
translated into mathematical equations. It is fascinating that there exists a
fundamental relation between mathematical
equations and the experiment. Once
the mathematical model is introduced, we can compare predictions which follow from the equations with experiments which are performed on the
glass with the operators U and W.
We
introduce three possible states of the glass:
1.)
Glass upright, empty
2.)
Glass turned upside down, empty
3.)
Glass upright, filled
Operating
with U and W changes the state of the glass from an initial state to a final
state. We can introduce for U a 3 times 3 matrix which shows all possible
initial states (line of the matrix) and all possible final states (column of
the matrix). The final state which emerges when applying the operator is
defined by the entry “1“ in the matrix, all other entries are “0“. With this
definition, the operations U and W are represented as two different 3 times 3
matrices. Using this mathematical representation, we can compare predictions of
the theory with experiments, and vice versa.
The
experiment tells us that the operations U and W do not commutate. Translated
into mathematical language, this signifies that the matrix product U*W - W*U
does not vanish. Indeed, the calculation shows that this is the case.
In
level III of the QED-project, we introduce a basis transformation and
diagonalize the matrices U and W. It is interesting to discuss the experimental
realization of these mathematical calculations, which is rather unexpected.
More
examples for pupils’ exercises are:
1.) Calculate U2 and W2 using
matrix multiplication. Compare the resulting matrices with the experimental realization of the U2
and W2 operators.
2.) Discuss the inverse of the operations U and W both
experimentally and mathematically.
3.) Find non-commuting operations which are isomorphic
to U and W
Summary
The
DVD and internet project “QED – Matter, Light and the Void“ is briefly
introduced in this article. The project is part of the EU-funded initiative
“Cinema and Science“ (www.cisci.net). Our
aim is to find possibilities to perform
mathematical equations, that is, to a give direct, intuitive and emotional
access to the underlying ideas behind the abstract formalism. The backbone of
the project consists of computer graphics and character animation techniques.
List of references
Schwinger, “A Report on Quantum Electrodynamics”, in J. Mehra (ed.), The
Physicist's Conception of Nature (Dordrecht: Reidel, 1973).