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Introduction to the Scientific Method
Introduction to the Scientific Method I. The
scientific method has four steps
II. Testing hypotheses
III. Common Mistakes in Applying the Scientific
Method
IV. Hypotheses, Models, Theories and Laws
V. Are there circumstances in which the Scientific
Method is not applicable?
VI. Conclusion
VII. References
Introduction to the Scientific Method
The scientific method is the process by which
scientists, collectively and over time, endeavor to
construct an accurate (that is, reliable, consistent
and non-arbitrary) representation of the world.
Recognizing that personal and cultural beliefs
influence both our perceptions and our
interpretations of natural phenomena, we aim through
the use of standard procedures and criteria to
minimize those influences when developing a theory.
As a famous scientist once said, "Smart people (like
smart lawyers) can come up with very good
explanations for mistaken points of view." In
summary, the scientific method attempts to minimize
the influence of bias or prejudice in the
experimenter when testing an hypothesis or a theory.
I. The scientific method has four steps
1. Observation and description of a phenomenon or
group of phenomena.
2. Formulation of an hypothesis to explain the
phenomena. In physics, the hypothesis often takes
the form of a causal mechanism or a mathematical
relation.
3. Use of the hypothesis to predict the existence of
other phenomena, or to predict quantitatively the
results of new observations.
4. Performance of experimental tests of the
predictions by several independent experimenters and
properly performed experiments.
If the experiments bear out the hypothesis it may
come to be regarded as a theory or law of nature
(more on the concepts of hypothesis, model, theory
and law below). If the experiments do not bear out
the hypothesis, it must be rejected or modified.
What is key in the description of the scientific
method just given is the predictive power (the
ability to get more out of the theory than you put
in; see Barrow, 1991) of the hypothesis or theory,
as tested by experiment. It is often said in science
that theories can never be proved, only disproved.
There is always the possibility that a new
observation or a new experiment will conflict with a
long-standing theory.
II. Testing hypotheses
As just stated, experimental tests may lead either
to the confirmation of the hypothesis, or to the
ruling out of the hypothesis. The scientific method
requires that an hypothesis be ruled out or modified
if its predictions are clearly and repeatedly
incompatible with experimental tests. Further, no
matter how elegant a theory is, its predictions must
agree with experimental results if we are to believe
that it is a valid description of nature. In
physics, as in every experimental science,
"experiment is supreme" and experimental
verification of hypothetical predictions is
absolutely necessary. Experiments may test the
theory directly (for example, the observation of a
new particle) or may test for consequences derived
from the theory using mathematics and logic (the
rate of a radioactive decay process requiring the
existence of the new particle). Note that the
necessity of experiment also implies that a theory
must be testable. Theories which cannot be tested,
because, for instance, they have no observable
ramifications (such as, a particle whose
characteristics make it unobservable), do not
qualify as scientific theories.
If the predictions of a long-standing theory are
found to be in disagreement with new experimental
results, the theory may be discarded as a
description of reality, but it may continue to be
applicable within a limited range of measurable
parameters. For example, the laws of classical
mechanics (Newton's Laws) are valid only when the
velocities of interest are much smaller than the
speed of light (that is, in algebraic form, when v/c
<< 1). Since this is the domain of a large portion
of human experience, the laws of classical mechanics
are widely, usefully and correctly applied in a
large range of technological and scientific
problems. Yet in nature we observe a domain in which
v/c is not small. The motions of objects in this
domain, as well as motion in the "classical" domain,
are accurately described through the equations of
Einstein's theory of relativity. We believe, due to
experimental tests, that relativistic theory
provides a more general, and therefore more
accurate, description of the principles governing
our universe, than the earlier "classical" theory.
Further, we find that the relativistic equations
reduce to the classical equations in the limit v/c
<< 1. Similarly, classical physics is valid only at
distances much larger than atomic scales (x >> 10-8
m). A description which is valid at all length
scales is given by the equations of quantum
mechanics.
We are all familiar with theories which had to be
discarded in the face of experimental evidence. In
the field of astronomy, the earth-centered
description of the planetary orbits was overthrown
by the Copernican system, in which the sun was
placed at the center of a series of concentric,
circular planetary orbits. Later, this theory was
modified, as measurements of the planets motions
were found to be compatible with elliptical, not
circular, orbits, and still later planetary motion
was found to be derivable from Newton's laws.
Error in experiments have several sources. First,
there is error intrinsic to instruments of
measurement. Because this type of error has equal
probability of producing a measurement higher or
lower numerically than the "true" value, it is
called random error. Second, there is non-random or
systematic error, due to factors which bias the
result in one direction. No measurement, and
therefore no experiment, can be perfectly precise.
At the same time, in science we have standard ways
of estimating and in some cases reducing errors.
Thus it is important to determine the accuracy of a
particular measurement and, when stating
quantitative results, to quote the measurement
error. A measurement without a quoted error is
meaningless. The comparison between experiment and
theory is made within the context of experimental
errors. Scientists ask, how many standard deviations
are the results from the theoretical prediction?
Have all sources of systematic and random errors
been properly estimated? This is discussed in more
detail in the appendix on Error Analysis and in
Statistics Lab 1.
III. Common Mistakes in Applying the Scientific
Method
As stated earlier, the scientific method attempts to
minimize the influence of the scientist's bias on
the outcome of an experiment. That is, when testing
an hypothesis or a theory, the scientist may have a
preference for one outcome or another, and it is
important that this preference not bias the results
or their interpretation. The most fundamental error
is to mistake the hypothesis for an explanation of a
phenomenon, without performing experimental tests.
Sometimes "common sense" and "logic" tempt us into
believing that no test is needed. There are numerous
examples of this, dating from the Greek philosophers
to the present day.
Another common mistake is to ignore or rule out data
which do not support the hypothesis. Ideally, the
experimenter is open to the possibility that the
hypothesis is correct or incorrect. Sometimes,
however, a scientist may have a strong belief that
the hypothesis is true (or false), or feels internal
or external pressure to get a specific result. In
that case, there may be a psychological tendency to
find "something wrong", such as systematic effects,
with data which do not support the scientist's
expectations, while data which do agree with those
expectations may not be checked as carefully. The
lesson is that all data must be handled in the same
way.
Another common mistake arises from the failure to
estimate quantitatively systematic errors (and all
errors). There are many examples of discoveries
which were missed by experimenters whose data
contained a new phenomenon, but who explained it
away as a systematic background. Conversely, there
are many examples of alleged "new discoveries" which
later proved to be due to systematic errors not
accounted for by the "discoverers."
In a field where there is active experimentation and
open communication among members of the scientific
community, the biases of individuals or groups may
cancel out, because experimental tests are repeated
by different scientists who may have different
biases. In addition, different types of experimental
setups have different sources of systematic errors.
Over a period spanning a variety of experimental
tests (usually at least several years), a consensus
develops in the community as to which experimental
results have stood the test of time.
IV. Hypotheses, Models, Theories and Laws
In physics and other science disciplines, the words
"hypothesis," "model," "theory" and "law" have
different connotations in relation to the stage of
acceptance or knowledge about a group of phenomena.
An hypothesis is a limited statement regarding cause
and effect in specific situations; it also refers to
our state of knowledge before experimental work has
been performed and perhaps even before new phenomena
have been predicted. To take an example from daily
life, suppose you discover that your car will not
start. You may say, "My car does not start because
the battery is low." This is your first hypothesis.
You may then check whether the lights were left on,
or if the engine makes a particular sound when you
turn the ignition key. You might actually check the
voltage across the terminals of the battery. If you
discover that the battery is not low, you might
attempt another hypothesis ("The starter is broken";
"This is really not my car.")
The word model is reserved for situations when it is
known that the hypothesis has at least limited
validity. A often-cited example of this is the Bohr
model of the atom, in which, in an analogy to the
solar system, the electrons are described has moving
in circular orbits around the nucleus. This is not
an accurate depiction of what an atom "looks like,"
but the model succeeds in mathematically
representing the energies (but not the correct
angular momenta) of the quantum states of the
electron in the simplest case, the hydrogen atom.
Another example is Hook's Law (which should be
called Hook's principle, or Hook's model), which
states that the force exerted by a mass attached to
a spring is proportional to the amount the spring is
stretched. We know that this principle is only valid
for small amounts of stretching. The "law" fails
when the spring is stretched beyond its elastic
limit (it can break). This principle, however, leads
to the prediction of simple harmonic motion, and, as
a model of the behavior of a spring, has been
versatile in an extremely broad range of
applications.
A scientific theory or law represents an hypothesis,
or a group of related hypotheses, which has been
confirmed through repeated experimental tests.
Theories in physics are often formulated in terms of
a few concepts and equations, which are identified
with "laws of nature," suggesting their universal
applicability. Accepted scientific theories and laws
become part of our understanding of the universe and
the basis for exploring less well-understood areas
of knowledge. Theories are not easily discarded; new
discoveries are first assumed to fit into the
existing theoretical framework. It is only when,
after repeated experimental tests, the new
phenomenon cannot be accommodated that scientists
seriously question the theory and attempt to modify
it. The validity that we attach to scientific
theories as representing realities of the physical
world is to be contrasted with the facile
invalidation implied by the expression, "It's only a
theory." For example, it is unlikely that a person
will step off a tall building on the assumption that
they will not fall, because "Gravity is only a
theory."
Changes in scientific thought and theories occur, of
course, sometimes revolutionizing our view of the
world (Kuhn, 1962). Again, the key force for change
is the scientific method, and its emphasis on
experiment.
V. Are there circumstances in which the Scientific
Method is not applicable?
While the scientific method is necessary in
developing scientific knowledge, it is also useful
in everyday problem-solving. What do you do when
your telephone doesn't work? Is the problem in the
hand set, the cabling inside your house, the hookup
outside, or in the workings of the phone company?
The process you might go through to solve this
problem could involve scientific thinking, and the
results might contradict your initial expectations.
Like any good scientist, you may question the range
of situations (outside of science) in which the
scientific method may be applied. From what has been
stated above, we determine that the scientific
method works best in situations where one can
isolate the phenomenon of interest, by eliminating
or accounting for extraneous factors, and where one
can repeatedly test the system under study after
making limited, controlled changes in it.
There are, of course, circumstances when one cannot
isolate the phenomena or when one cannot repeat the
measurement over and over again. In such cases the
results may depend in part on the history of a
situation. This often occurs in social interactions
between people. For example, when a lawyer makes
arguments in front of a jury in court, she or he
cannot try other approaches by repeating the trial
over and over again in front of the same jury. In a
new trial, the jury composition will be different.
Even the same jury hearing a new set of arguments
cannot be expected to forget what they heard before.
VI. Conclusion
The scientific method is intricately associated with
science, the process of human inquiry that pervades
the modern era on many levels. While the method
appears simple and logical in description, there is
perhaps no more complex question than that of
knowing how we come to know things. In this
introduction, we have emphasized that the scientific
method distinguishes science from other forms of
explanation because of its requirement of systematic
experimentation. We have also tried to point out
some of the criteria and practices developed by
scientists to reduce the influence of individual or
social bias on scientific findings. Further
investigations of the scientific method and other
aspects of scientific practice may be found in the
references listed below.
VII. References
1. Wilson, E. Bright. An Introduction to Scientific
Research (McGraw-Hill, 1952).
2. Kuhn, Thomas. The Structure of Scientific
Revolutions (Univ. of Chicago Press, 1962).
3. Barrow, John. Theories of Everything (Oxford
Univ. Press, 1991).
Reprinted with permission from Frank L. H. Wolfs
Department of Physics and Astronomy University of
Rochester, NY.
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