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January 12th, 2008, 05:21 PM   #1
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Equations in physics

I am in physics class, and I have feeling that almost every equations used in the field of physics are "approximations", not "exact". Is this true?
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January 12th, 2008, 05:48 PM   #2
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Yes and no... Most physics equations use a constant which is approximated based on observable data, but the rest of the calculation is exact.

On the other hand, physics is the study of the mechanics of the universe around us. Math is only a model which is used (quite effectively) to describe the universe; however given our imperfect ability to observe and comprehend the universe, we can only hope to approximate it.

On that note, there are two primary philosophies on mathematical truth. One is that mathematical Truth is discovered; that is, mathematical theories, logic, proofs, etc., etc. are inherent within the universe, and we as mathematicians are discovering the laws by which the universe works. If this is the case, the discrepancies between physics and math (i.e. approximation) are a result of our inability to properly observe the universe.

The other is that mathematical rules are constructed; that is, mathematical truths have no relation to the universe, and any tie they have to the universe are indicative of math's use as a tool, and the human ability to apply analogies in creative and useful ways. Discrepancies are expected, because the universe is not inherently mathematical.

With the growth of the belief in the subjective nature of truth (primarily in the last 100 years), the second theory has gained a lot of ground recently. It would be interesting to see where mathematicians tend to sit on this...
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January 15th, 2008, 09:26 PM   #3
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but

No problem in physics can ever be solved exactly. We always have to neglect the effect of various factors which are unimportant for the particular phenomenon we have in mind. It then becomes important to be able to estimate the magnitude of the quantities we have neglected. Moreover, before calculating a result numerically it is often necessary to investigate the phenomenon qualitatively, that is, to estimate the order of magnitude of the quantities we are interested in and to find out as much as possible about the general behavior of the solution.

For the last dozen years theoretical physics has undergone strong changes. Under the influence of the theory, new fields of mathematics started being used and developed by theorists. Computational theoretical physics acquired a particular importance. Nevertheless, despite mathematization of physics, qualitative methods became even more important than before elements of the theory. They are sort of mathematical analog of the image-bearing mentality of sculptors and poets, feeding the intuition.

I believe that now more than before, a beginning theoretician should master qualitative methods of reasoning.


[color=red]Although physics is considered an exact science, any practicing physicist knows that everything in physics is approximate.[/color]
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