Physics can be though of as the "Art" of constructing models which approximate the Real World. Physicist do not unearth some Absolute Truth about Nature, but rather build mathematical structures which reflects a close facsimile of Nature. This facsimile is like a geological map of some territory. A map has a lot of useful information about the territory, but the map is not the territory.
| * | Models of Science are useful maps which approximate Nature. |
| * | The Laws of Physics are mathematical Models that reflect the underlying order found in Nature. |
| * | Models in Science are not equivalent to, identical with, or a one-to-one match with the aspects of Nature they describe. |
| * | There is always some limited range over which a Model is a useful predictor of Nature. |
| * | The fundamental criteria for the acceptance or rejection of a Model is determined by how close the Model predicts the outcome of measurements and observations. |
| * | Models of Science are not unique. There may be two or more Models which describe the same observations equally well. |
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Preference between competing Models is judged by: a. Size of the error. The smaller the size of the error between actual measurements and predictions, the more accurate the Model. A good Model will be able to predict the uncertainty within its predictions. b. Range of Application. The larger the range over which a Model faithfully reflects Nature, the more universal the Model. If the range is big enough we might even call the Model a Law of Physics. c. Simplicity. A subjective and practical property that makes a Model easier to both understand and manipulate. In Keats words, "Truth is beauty, and beauty is truth." |
Example 1: Mechanics, Relativity, and Quantum Mechanics
Newton's Laws of Motion faithfully reflect the motion of a body as long as the speed of the body is small compared to the speed of light. When the speed of the body approaches the speed of light, Einstein's Theory of Relativity predicts results closer to the actual values measured than Newton's Laws of Motion predict. The Theory of Relativity is itself only a better approximation; it has a bigger but still limited range over which it can be applied.
Both Relativity Theory and Newton's Laws give inaccurate predictions when trying to explain the behavior of matter on the atomic scale. In this range, a model call Quantum Mechanics has proven to make more accurate predictions. None of the well-established Models represent the Absolute Truth about Nature, but they are very close likenesses of the Nature under certain conditions.
Example 2: Flat Earth - Round Earth
A carpenter building a house uses the model that the Earth is flat expect for local irregularities, which are usually flattened out before building. A carpenter makes no practical errors in the accuracy of his measurements in assuming that the Earth is flat. For an airline pilot, the model that the Earth is perfectly spherical, like a ball, is useful for navigating over long distances. The path that uses the least fuel, the shortest path, is the arc of a great circle on a sphere, and not a straight line on a map.
A more complicated model of the shape of the Earth's surface is that of a triaxial ellipsoid of rotation, since the Earth is slightly flatter (about 17 km) at the poles. At one time astronomers did use this model in order to compare measurements of celestial objects made at different observatories scattered across the Earth's surface.
To within the limit of accuracy of a carpenter's tape measure, the Flat Earth Model gives as good predictions as that of the spherical trigonometry of a Round Ball Model or the Triaxial Ellipsoid trigonometry. The Triaxial Ellipsoid Model is more accurate that the Spherical Ball Model which is more accurate than the Flat Earth Model. None of these models, constructed by scientists, represent the "TRUE" shape of the Earth. Which Model you use depends upon the amount of accuracy needed in your measurement.