Correspondence Principle
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[edit] Definition
The Correspondence Principle as applied to Quantum Mechanics states that any theory of mechanical systems must duplicate the classical theory when very large quantum numbers are used. The principle can be extended to science in general, as:
- A new theory must predict the same results as the established theory, in the limited domain that the established theory has been confirmed.
[edit] Example
According to classical mechanics, if X moves at speed v with respect to Y, and Y moves at speed w with respect to Z, then X moves relative to Z at speed:
- z = v + w
However, Special Relativity suggests that the formula should be:
where c is the speed of light in a vacuum.
Prior to the twentieth century, the addition of speeds had only been observed with objects moving much slower than c, which would make the denominator of the fraction in the Special Relativity equation very close to 1. This would make it indistinguishable from the classical equation, at least as far as 19th-century measurements were concerned.
[edit] Rationale
When an established theory is contradicted by a rival new theory, we are forced to ask why, if the rival theory is correct, was it ever possible to prove the established theory? Equivalently, why should a new contradictory theory be investigated, when the established theory has already been proven? The Correspondence Principle suggests that if a rival theory is correct, then the established theory must then have been a very good approximation.
[edit] Use in Scientific Method
The Correspondence Principle can then be used as a kind of “sniff test” for new theories. If a new theory predicts something totally contradictory to the established theory, (as far as it has been tested), then it can be rejected on its face. For example, the suggestion that the “addition of speed” formula above should be
- z = v + 2w
could be rejected without further experimentation, simply because it disagrees with the classical theory in ways that would have been obvious throughout centuries of observation.
[edit] Use in Practice
The Correspondence Principle can be used to justify retaining older, simpler theories as a “limiting case” when new theories supplant them. For example, an astrophysicist could plan the trajectory of a space probe by using the “disproven” formulas of classical mechanics, since the speeds involved are small enough.
