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A Prelude to the Study of Physics
Author:
Robert J. Sciamanda, Edinboro University of Pennsylvania
trebor@winbeam.com
This paper was first published in QUANTUM Vol 7 No 2, pg 45, Nov/Dec
1996
I. THEORIES AND MODELS
No physicist or engineer ever solves a real problem. Instead she creates a model of the
real problem and solves this model problem. This model must satisfy two requirements: it must
be simple enough to be solvable, and it must be realistic enough to be useful; ie., it must be both
conceptually understandable and empirically fruitful.
The theories and "laws" of physics are also models. Whether in the solving of a
particular engineering problem or in the search for the wide ranging laws of physics, the art of
scientific analysis consists in the creation of useful models of reality. The model is the interface
between reality and the human mind. As such, the model must be expressed in human terms; it
is cast in terms of concepts which we create from the data of our experience. Our models speak
as much about us, our experience and our modes of thought as they do about the external reality
being modeled.
I prefer to speak of models where others might speak of theories because the word
"model" emphasizes the criterion of usefulness. We tend to think of a theory as a candidate for
some absolute, objective truth; a model is used to convey useful information without the pretense
of being unique, complete or ultimate. As an example of the conception, gestation, birth and
growth of a model in physics let us consider the history of the "ideal gas law" (PV=RT), which you
undoubtedly have studied in your chemistry classes.
II. THE HISTORY OF A MODEL
Despite the voluminous abstractions of ancient philosophers, no useful understanding of
gas behavior emerged throughout ancient history and the middle ages. The possibility of a useful
model awaited the creation of the thermometer and the manometer. Each of these devices uses
a thread of mercury imbedded in glass in order to generate a number (the length of the mercury
thread) which varies in value as the device is subjected to varying conditions. Boyle, Charles and
Gay Lussac investigated the behavior of these devices when connected to a gas under controlled
conditions.
To collapse a very long story, their experimentation resulted in the creation of the
empirical relation PV = RT, the variables P and T representing the readings of the manometer
and thermometer respectively; R is a constant for a fixed quantity of gas. If we then
define P, V and T to be measurements of properties of the gas, PV = RT becomes
a useful model of the gas behavior, even though P and T, at this point, have no deeper meaning
other than the numbers generated by the specified devices.
That there should exist any (let alone such a simple) relation among the numbers
generated by these (or any other) devices is not at all to be expected; such serendipity can only
be gratefully contemplated when it appears. It is an instance of the profound meaning in one of
Einstein's most famous quotations: "The most incomprehensible thing about the world is that it is
comprehensible."
The creation of the model PV = RT was a giant leap forward; and note that the crucial
beginning step consisted in the free creation of a set of concepts in terms of which meaningful
questions might be put to nature so that nature might respond in a meaningful way. These
concepts are not lying in nature awaiting discovery by some passive act of looking; they must be
actively created. This is how the properties of matter come to be. This is how we define into
existence those measurable properties of reality which we find to be useful. They are human
constructs in terms of which we might ask meaningful questions, read nature's answers and
organize our understanding into useful and testable models.
Each of these concepts is quantitative in nature: the number generated by a measuring
device. Our empirical gas law is simply a relation (and very useful) among the numbers (P,V,T)
generated by our measuring devices; it is an empirical model. The numbers generated by
measuring devices have no deeper meaning except within the context of a conceptual
model of the system being measured and its effect upon the measuring devices.
Boyle did his experimentation in the 1600's, while the pilgrims were colonizing America.
It was not until the mid 1800's, while Americans were fighting over slavery, that Joule brought
together the theories (models) of Newtonian mechanics and atomism (then hotly contested) to
create a conceptual model of the ideal gas as a system of randomly moving point
particles. In this model P is quite naturally associated with the Newtonian force concept and
accounts for the behavior of the mercury manometer. However there is no a priori
mechanical association for the empirical quantity T, the "temperature" of the gas as generated by
the thermometer.
Herein lies a wonderfully simple instance of the incredibly awesome power of an
empirically based analytical science: the fruitful interaction of experimental and theoretical
physics. Newton's laws drove Joule's conceptual model to a very illuminating result: the
numerical value of the product PV for Joule's gas is proportional to the total kinetic energy of the
randomly moving gas particles. Thus Joule's conceptual model bestows upon the empirical
temperature T, in PV = RT, a deeper meaning as a humanly invented property of the gas; it
becomes a measure of the energy of random motion of the gas particles.
III. A MODEL OF MODELS
Thus it is that the mathematical model PV = RT has foundations as both an
empirical model and a conceptual model. I present it as a paradigm to illustrate
the properties of the model in physics:
1) It is a human construct, the offspring of both our experience and our imagination.
2) It is quantitative and speaks of freely defined, measurable properties of matter.
3) It has both an empirical and a conceptual usefulness: it presents a testable
numerical equality involving the numbers generated by specified measuring devices, and it offers
a conceptual framework for associating a deeper meaning with these numbers.
4) The empirical usefulness of a model is a matter of experimental verification, and once verified
this usefulness will remain; future models of a wider scope will include it as a special case.
5) The conceptual usefulness of a model can be a cultural matter, a matter of institutional and
personal taste (more of this later).
IV. CONCEPTUAL
LIMITATIONS
Our conceptual models are of course produced from the data of our experience. Every
now and then I close my eyes and carefully feel an object such as a piece of fruit, a table or my
own face, and try to imagine what it might be like to have never had the sense of sight. What
sort of conceptual models might I fashion as I explore reality using only the sense of touch? (Try
to form the concept of the shape of an object without invoking a visual image.) How could
I appreciate the language of a sighted person? There is no way that a sighted person could
convey to me his conscious experience of light vs. darkness, let alone red vs. green. Our
conceptual models could communicate only through shaky analogies and metaphors, but our
empirical models could unambiguously communicate regarding the numbers generated by
measuring devices.
Conceptual models are observer dependent and observer limited. As the physicist
probes into the behavior of reality she strives to create meaningful conceptual models of that
reality, using as raw materials the concepts fashioned from human experience. As she probes
deeper she finds that she has to become ever more creative and imaginative, generating
abstractions and cross fertilizations of her ideas in order to conceptually model the behavior of
reality in human terms.
There is no reason to expect that this process can be extended indefinitely. It seems
reasonable to anticipate that beyond a certain level of analysis the behavior of reality cannot be
conceptually modeled in literal human terms, even though we may continue to be clever enough
to create numerical equalities involving the readings of our instruments. After all, our instruments
operate on the same superficial level as our senses.
We are already on the doorstep of this conceptual barrier. The mathematical models of
quantum theory defied even the imagination of Albert Einstein; he was never able to conceive a
satisfactory conceptual model of the reality behind these equations. As regards creative
"weirdness", modern art and music are poor seconds to modern physics, even though the arts
operate completely free of any constraints, whereas physics operates under the severe constraint
of empirical usefulness!
V. STANDARDS, TASTE AND
BEAUTY
Suppose that you are shipwrecked on a desert island and, with nothing better to do,
decide to create the science of physics from scratch. You decide that your first task will be to
choose (or design) standards for your measurements of space and time intervals. How should
you choose a standard measuring rod and a standard clock? This is a "catch 22" question: one
would like to have these standards available a priori, so that one can perform experiments
(both physical and gedanken) to ask questions of nature, read her answers and be guided toward
a theory about the behavior of matter. Yet one's choices of a standard clock and measuring rod
already presuppose considerable understanding about the behavior of matter! For example, the
choice of a standard clock already presupposes a theory which will be committed to the
conclusion that this particular mechanism ticks at a constant rate. Logical consistency will force
the theory to this conclusion. Choices among theories and choices among standards are
inextricably intertwined.
The dilemma exposed in the above paragraph is not debilitating; we need only replace
the word "theory" (a candidate for an absolute, objective truth) with the word "model" (a useful
way of describing reality in human terms). In this view, the choice of a clock simply defines into
existence a measurable parameter "t" which will be used as a linear time base for the description
of the evolution of phenomena. We will be comparing the course of all other phenomena to the
succession of ticks of this clock.
Clearly the choice of standards is a matter of free definition. The criterion is not one of
truth; it is simply one of usefulness: which choices lead to the most "desirable" empirical and
conceptual models of reality? Put another way: how "weird" does the conceptual model have to
get in order to be empirically useful? The words "desirable" and "weird" must be defined by you
and/or current scientific culture; they are a matter of taste. Historically, and logically, this is an
iterative process, as we see more and more details of where the model is leading.
Let me tease you with a famous example (which hopefully you will study in detail later):
Einstein, in his 1905 relativity theory, was the first to capitalize upon this freedom of choice (of
rods and clocks) in a radical way. His definitions of "desirable" and "weird" were not mainstream.
To him the desirable model must preserve the invariance (sameness) of physical law (in
particular Maxwell's equations of electrodynamics) for all non-accelerated observers. But
conventional wisdom said that the velocities appearing in Maxwell's equations must be measured
from an absolute frame of reference (the "aether" frame). This was "desirable" to many; they
found it satisfying that the laws of physics should be simple only to an observer at absolute rest.
In fact, any deviation of your experimental results from the laws of physics would then furnish you
with sufficient data to measure your own absolute velocity. They had been disappointed that
Newton's model of mechanics did not allow us to measure our absolute velocity by
mechanical experiments (Newton himself must have been disappointed). They were
overjoyed that now Maxwell's model of electrodynamics (which includes light) would allow us to
measure our absolute velocity using optical experiments.
Einstein conceived a completely different conceptual model for Maxwell's
electrodynamics. He sought a model in which these equations could be used with equal validity
by all non-accelerated observers, each using the numerical values of all quantities (eg.,
velocities) as measured from her frame. He dared to redefine the measurement of space and
time intervals to make this so. It is to be expected that such a redefinition would force new and
worse weirdities into the model; we surely should expect that we will have to design new clocks
and measuring rods, with exotic "relativistic" properties. The remarkable result has been that the
new weirdities were only cultural, that ordinary clocks and meter sticks behave relativisticaly, and
that a vast scope of phenomena have become more simply describable, even phenomena far
removed from Maxwell's equations. Widespread acceptance did not come quickly or easily, but
today relativity is not only accepted as empirically and conceptually useful; it has become
beautiful!
The search for beauty in our conceptual models has always been a driving force and
sometimes, as with Einstein's relativity, it seems to have been the sole motivation. Today many,
like Einstein, are disappointed in their search for intuitive beauty in the quantum aspects of
modern physics. Unlike relativity, the beauty of quantum theory still eludes visceral human
appreciation. Perhaps with time we can acquire a taste, but it must begin with an adjustment of
our expectations, toward models rather than "theories". Physics does not offer any quieting and
ultimate answers.
VI. YOUR PERSONAL PHYSICS
Physics has not been idle; there is much for you to learn. To learn means to make your
own; it is an active process which only begins with listening and reading. You must
return often to listening and reading, but meaningful learning comes only from contemplation.
Each person must construct his own models and his own philosophy of what physics is; these
will grow and develop; construction is never complete. What I have said here is subject to
criticism by scientists, philosophers, students and even myself, as my appreciation of physics
continues to develop. These words should be taken as providing only a beginning for discussion
and contemplation. I have tried to express my current philosophy to you; over the years you will
build your own unique and personal version. Even more than the appreciation of a symphony or
painting, the understanding of physics is a unique and personal encounter of a consciousness
with reality.
-Bob Sciamanda, Edinboro Univ of PA trebor@winbeam.com
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