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Is there a difference between a postulate and a principle in physics?

Both seem unproved statements taken as true. If thats correct, why the different names?

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Related: physics.stackexchange.com/q/44706/2451 and links therein. –  Qmechanic Aug 27 '13 at 7:03

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up vote 6 down vote accepted

A postulate is an (usually fundamental) assumption a writer makes in order to discuss a subject in a coherent fashion. Examples of postulates are the Born rule in quantum mechanics (which defines how the wave function is to be interpreted), or in classical mechanics the existence of a Lagrangian (which defines the starting point of theoretical mechanics).

A principle is a more or less universally observed (usually fundamental) fact. Examples of principles are the second law of thermodynamics (universal dissipation), the principle of relativity (independence of the reference frame), or Heisenberg's uncertainty relation.

A hypothesis is a theoretical assumption made to develop a (usually alternative) theory. Examples are Planck's and Einstein's hypothesis of quantized light, or the existence of supersymmetry.

One can turn a principle or hypothesis into a postulate, but not a postulate into a principle.

Edit2: Note that it is possible that a principle is derived from a set of postulates. This reflects the fact that there is is some freedom in setting up the foundations. For example, the second law of thermodynamics can be derived from statistical mechnaics, and the principle of relativity can be derived from the postulate of Lorentz invariance.

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Huh, is not the experimental verification of first only theoretical assumptions some kind of an example of turning a postulate into an (observed) principle? I mean things like the observation of first only theoretically predicted antimatter for example. –  Dilaton Sep 5 '12 at 9:11
    
@Dilaton: Not every general observable fact is referred to as a principle. I never saw the existence of antimatter formulated as principle. It is always deduced from theory. –  Arnold Neumaier Sep 5 '12 at 9:53
    
Ah ok, thanks for the clarification. Seems I confused principles and theoretical predictions ... What is generally the difference between a principle and theoretical assumptions, such as say for example an additional symmetry that nature could have ? –  Dilaton Sep 5 '12 at 10:36
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@Dilaton: I expanded my answer to address this. –  Arnold Neumaier Sep 5 '12 at 11:42
    
Thanks Arnold. Is it ok to call a deduced idea by 'principle'? Like Heisenberg uncertainty relation. –  galmeida Sep 6 '12 at 1:52

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