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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?

galmeida
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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.

Arnold Neumaier
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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 05 '12 at 09:11
  • @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 05 '12 at 09:53
  • 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 05 '12 at 10:36
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    @Dilaton: I expanded my answer to address this. – Arnold Neumaier Sep 05 '12 at 11:42
  • Thanks Arnold. Is it ok to call a deduced idea by 'principle'? Like Heisenberg uncertainty relation. – galmeida Sep 06 '12 at 01:52
  • @galmeida: According to my formulation, yes. I made it more explicit in my second edit. – Arnold Neumaier Sep 07 '12 at 06:46
  • By this 'freedom' it seems to me that there is no critter. Even if it is the case that the 'classification' intrinsically allows flexibility (like, 3 statements on some subject, if two are taken as postulates the other could be derived from them as a 'law', so it doesn't matter which pair is a postulate, but at least a pair is a postulate) this condition and all statements should be recognized as such. I expected at least that a 'principle' was a principle - something which comes before the rest. A complete list of what is assumed, what is deduced and what is observed is probably what I want. – galmeida Sep 09 '12 at 00:09
  • @galmeida: Oh yes. The freedom is only in exposition of the matierial, by choosing form the known theory a number of things as postulates and deriving the remaining stuff from it. It doesn't matter for the complete theory, but it may matter for didactical purposes. [ctd] – Arnold Neumaier Sep 09 '12 at 13:15
  • [ctd] If one starts with principles, one usually needs a fair amount of handwaving argument to arrive at the postulates from which one can derive all of physics as practiced. If one starts from the postulates, one is right at the start, and can do everything deductively (and in principle rigorously). Then one shows that the informal principles are indeed satisfied. The point is, one can give up (but therefore also choose) postulates but not principles. – Arnold Neumaier Sep 09 '12 at 13:19
  • I'd add that I think it would be interesting that these facts were more emphasized on physics courses. Maybe professors do not feel comfortable talking about it or have weak arguments to deal with comparisons between concepts. – galmeida Nov 03 '12 at 17:49
  • @galmeida: There is very little incentive for physicists to improve their conceptual clarity, so very few try. And because of the lack of discussion in the literature, thouse who try have a hard job and arrive at their insights only after a long time of trial. – Arnold Neumaier Nov 04 '12 at 16:04