- 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 circ*mstances in which the Scientific Method is not applicable?
- VI. Conclusion
- VII. References
Introduction to the Scientific Method
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, thehypothesis often takes the form of a causal mechanism or a mathematicalrelation.
3. Use of the hypothesis to predict the existence of other phenomena, or topredict quantitatively the results of new observations.
4. Performance of experimental tests of the predictions by several independentexperimenters and properly performed experiments.
If the experiments bear out the hypothesis it may come to be regarded as atheory or law of nature (more on the concepts of hypothesis, model, theory andlaw below). If the experiments do not bear out the hypothesis, it must berejected or modified. What is key in the description of the scientific methodjust given is the predictive power (the ability to get more out of the theorythan you put in; see Barrow, 1991) of the hypothesis or theory, as tested byexperiment. It is often said in science that theories can never be proved, onlydisproved. There is always the possibility that a new observation or a newexperiment will conflict with a long-standing theory.
II. Testing hypotheses
As just stated, experimental tests may lead either to the confirmationof the hypothesis, or to the ruling out of the hypothesis. The scientificmethod requires that an hypothesis be ruled out or modified if its predictionsare clearly and repeatedly incompatible with experimental tests. Further, nomatter how elegant a theory is, its predictions must agree with experimentalresults if we are to believe that it is a valid description of nature. Inphysics, as in every experimental science, "experiment is supreme" andexperimental verification of hypothetical predictions is absolutely necessary.Experiments may test the theory directly (for example, the observation of a newparticle) or may test for consequences derived from the theory usingmathematics and logic (the rate of a radioactive decay process requiring theexistence of the new particle). Note that the necessity of experiment alsoimplies that a theory must be testable. Theories which cannot be tested,because, for instance, they have no observable ramifications (such as, aparticle whose characteristics make it unobservable), do not qualify asscientific theories.
If the predictions of a long-standing theory are found to be in disagreementwith new experimental results, the theory may be discarded as a description ofreality, but it may continue to be applicable within a limited range ofmeasurable parameters. For example, the laws of classical mechanics (Newton'sLaws) are valid only when the velocities of interest are much smaller than thespeed of light (that is, in algebraic form, when v/c << 1). Since this isthe domain of a large portion of human experience, the laws of classicalmechanics are widely, usefully and correctly applied in a large range oftechnological and scientific problems. Yet in nature we observe a domain inwhich v/c is not small. The motions of objects in this domain, as well asmotion in the "classical" domain, are accurately described through theequations of Einstein's theory of relativity. We believe, due to experimentaltests, that relativistic theory provides a more general, and therefore moreaccurate, description of the principles governing our universe, than theearlier "classical" theory. Further, we find that the relativistic equationsreduce 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 scalesis given by the equations of quantum mechanics.
We are all familiar with theories which had to be discarded in the face ofexperimental evidence. In the field of astronomy, the earth-centereddescription of the planetary orbits was overthrown by the Copernican system, inwhich the sun was placed at the center of a series of concentric, circularplanetary orbits. Later, this theory was modified, as measurements of theplanets motions were found to be compatible with elliptical, not circular,orbits, and still later planetary motion was found to be derivable fromNewton's laws.
Error in experiments have several sources. First, there is error intrinsic toinstruments of measurement. Because this type of error has equal probability ofproducing a measurement higher or lower numerically than the "true" value, itis called random error. Second, there is non-random or systematic error, due tofactors which bias the result in one direction. No measurement, and thereforeno experiment, can be perfectly precise. At the same time, in science we havestandard ways of estimating and in some cases reducing errors. Thus it isimportant to determine the accuracy of a particular measurement and, whenstating quantitative results, to quote the measurement error. A measurementwithout a quoted error is meaningless. The comparison between experiment andtheory is made within the context of experimental errors. Scientists ask, howmany standard deviations are the results from the theoretical prediction? Haveall sources of systematic and random errors been properly estimated? This isdiscussed in more detail in the appendix on Error Analysis and inStatistics Lab 1.
III. Common Mistakes in Applying the Scientific Method
As stated earlier, the scientific method attempts to minimize theinfluence 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 forone outcome or another, and it is important that this preference not bias theresults or their interpretation. The most fundamental error is to mistake thehypothesis for an explanation of a phenomenon, without performing experimentaltests. Sometimes "common sense" and "logic" tempt us into believing that notest is needed. There are numerous examples of this, dating from the Greekphilosophers to the present day.
Another common mistake is to ignore or rule out data which do not support thehypothesis. Ideally, the experimenter is open to the possibility that thehypothesis is correct or incorrect. Sometimes, however, a scientist may have astrong belief that the hypothesis is true (or false), or feels internal orexternal pressure to get a specific result. In that case, there may be apsychological tendency to find "something wrong", such as systematic effects,with data which do not support the scientist's expectations, while data whichdo agree with those expectations may not be checked as carefully. The lesson isthat all data must be handled in the same way.
Another common mistake arises from the failure to estimatequantitatively systematic errors (and all errors). There are manyexamples of discoveries which were missed by experimenters whose data containeda new phenomenon, but who explained it away as a systematic background.Conversely, there are many examples of alleged "new discoveries" which laterproved to be due to systematic errors not accounted for by the "discoverers."
In a field where there is active experimentation and open communicationamong members of the scientific community, the biases of individuals or groupsmay cancel out, because experimental tests are repeated by different scientistswho may have different biases. In addition, different types of experimentalsetups have different sources of systematic errors. Over a period spanning avariety of experimental tests (usually at least several years), a consensusdevelops in the community as to which experimental results have stood the testof 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 thestage of acceptance or knowledge about a group of phenomena.
An hypothesis is a limited statement regarding cause and effect inspecific situations; it also refers to our state of knowledge beforeexperimental work has been performed and perhaps even before new phenomena havebeen predicted. To take an example from daily life, suppose you discover thatyour car will not start. You may say, "My car does not start because thebattery is low." This is your first hypothesis. You may then check whether thelights were left on, or if the engine makes a particular sound when you turnthe ignition key. You might actually check the voltage across the terminals ofthe battery. If you discover that the battery is not low, you might attemptanother hypothesis ("The starter is broken"; "This is really not my car.")
The word model is reserved for situations when it is known that thehypothesis has at least limited validity. A often-cited example of this is theBohr model of the atom, in which, in an analogy to the solar system, theelectrons are described has moving in circular orbits around the nucleus. Thisis not an accurate depiction of what an atom "looks like," but the modelsucceeds in mathematically representing the energies (but not the correctangular 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'sprinciple, or Hook's model), which states that the force exerted by a massattached to a spring is proportional to the amount the spring is stretched. Weknow that this principle is only valid for small amounts of stretching. The"law" fails when the spring is stretched beyond its elastic limit (it canbreak). This principle, however, leads to the prediction of simple harmonicmotion, and, as a model of the behavior of a spring, has been versatilein an extremely broad range of applications.
A scientific theory or law represents an hypothesis, or a group ofrelated hypotheses, which has been confirmed through repeated experimentaltests. Theories in physics are often formulated in terms of a few concepts andequations, which are identified with "laws of nature," suggesting theiruniversal applicability. Accepted scientific theories and laws become part ofour understanding of the universe and the basis for exploring lesswell-understood areas of knowledge. Theories are not easily discarded; newdiscoveries are first assumed to fit into the existing theoretical framework.It is only when, after repeated experimental tests, the new phenomenon cannotbe accommodated that scientists seriously question the theory and attempt tomodify it. The validity that we attach to scientific theories as representingrealities of the physical world is to be contrasted with the facileinvalidation implied by the expression, "It's only a theory." For example, itis unlikely that a person will step off a tall building on the assumption thatthey will not fall, because "Gravity is only a theory."
Changes in scientific thought and theories occur, of course, sometimesrevolutionizing our view of the world (Kuhn, 1962). Again, the key force forchange is the scientific method, and its emphasis on experiment.
V. Are there circ*mstances in which the Scientific Method is not applicable?
While the scientific method is necessary in developing scientificknowledge, it is also useful in everyday problem-solving. What do you do whenyour telephone doesn't work? Is the problem in the hand set, the cabling insideyour house, the hookup outside, or in the workings of the phone company? Theprocess you might go through to solve this problem could involve scientificthinking, and the results might contradict your initial expectations.
Like any good scientist, you may question the range of situations (outside ofscience) in which the scientific method may be applied. From what has beenstated above, we determine that the scientific method works best in situationswhere one can isolate the phenomenon of interest, by eliminating or accountingfor extraneous factors, and where one can repeatedly test the system understudy after making limited, controlled changes in it.
There are, of course, circ*mstances when one cannot isolate the phenomena orwhen one cannot repeat the measurement over and over again. In such cases theresults may depend in part on the history of a situation. This often occurs insocial interactions between people. For example, when a lawyer makes argumentsin front of a jury in court, she or he cannot try other approaches by repeatingthe trial over and over again in front of the same jury. In a new trial, thejury composition will be different. Even the same jury hearing a new set ofarguments cannot be expected to forget what they heard before.
VI. Conclusion
The scientific method is intricately associated with science, theprocess of human inquiry that pervades the modern era on many levels. While themethod appears simple and logical in description, there is perhaps no morecomplex question than that of knowing how we come to know things. In thisintroduction, we have emphasized that the scientific method distinguishesscience from other forms of explanation because of its requirement ofsystematic experimentation. We have also tried to point out some of thecriteria and practices developed by scientists to reduce the influence ofindividual or social bias on scientific findings. Further investigations of thescientific method and other aspects of scientific practice may be found in thereferences 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).
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