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What does postulate mean in physics? What is its role in physical theories?

Is it possible to break physical postulates?

marked as duplicate by Qmechanic Oct 8 '13 at 14:51

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  • Related: physics.stackexchange.com/q/35660/2451 and links therein. – Qmechanic Apr 10 '13 at 16:27
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    Hi @Emilio Pisanty: Philosophy-like tags are not allowed, cf. this meta Phys.SE post. – Qmechanic Apr 10 '13 at 18:27
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    Yes, just as in mathematics it's possible for a postulate to be violated. In math, the parallel postulate is violated in noneuclidean geometry. In physics, Newton explicitly stated as a postulate that time is invariant, and we now know that's not true. A big difference between math and physics is that a mathematician never considers axioms to be objectively verifiable; the only mathematical truths are statements that a certain theorem follows from certain axioms.That 2+2=4 isn't a mathematical truth. 2+2=4 follows from the Peano axioms is. The Peano axioms can be true or false. – Ben Crowell Apr 10 '13 at 20:44
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    @Qmechanic - fair enough, I'll take it down. For the record, I disagree - I think this is a perfectly valid, specific question about physics and the language and concepts physicists use to understand it, which is what "philosophy of science" is about. I would rather this be asked, tagged, and answered here, where physicists will see it, than in a philosophy forum. – Emilio Pisanty Apr 10 '13 at 21:37
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    @Emilio Pisanty: Yeah, your classification is in principle completely relevant and correct. However, it is my understanding, that in practise we try to avoid philosophy-like tags on Phys.SE in order not to attract too many philosophy-type post in the future. – Qmechanic Apr 10 '13 at 21:52

I believe the distinction between postulates and axioms is archaic, and presumably not your direct concern. From there on:

Axioms play a key role not only in mathematics, but also in other sciences, notably in theoretical physics. In particular, the monumental work of Isaac Newton is essentially based on Euclid's axioms, augmented by a postulate on the non-relation of spacetime and the physics taking place in it at any moment.

In 1905, Newton's axioms were replaced by those of Albert Einstein's special relativity, and later on by those of general relativity.

Another paper of Albert Einstein and coworkers (see EPR paradox), almost immediately contradicted by Niels Bohr, concerned the interpretation of quantum mechanics. This was in 1935. According to Bohr, this new theory should be probabilistic, whereas according to Einstein it should be deterministic. Notably, the underlying quantum mechanical theory, i.e. the set of "theorems" derived by it, seemed to be identical. Einstein even assumed that it would be sufficient to add to quantum mechanics "hidden variables" to enforce determinism. However, thirty years later, in 1964, John Bell found a theorem, involving complicated optical correlations (see Bell inequalities), which yielded measurably different results using Einstein's axioms compared to using Bohr's axioms. And it took roughly another twenty years until an experiment of Alain Aspect got results in favour of Bohr's axioms, not Einstein's. (Bohr's axioms are simply: The theory should be probabilistic in the sense of the Copenhagen interpretation.)

As a consequence, it is not necessary to explicitly cite Einstein's axioms, the more so since they concern subtle points on the "reality" and "locality" of experiments.

Regardless, the role of axioms in mathematics and in the above-mentioned sciences is different. In mathematics one neither "proves" nor "disproves" an axiom for a set of theorems; the point is simply that in the conceptual realm identified by the axioms, the theorems logically follow. In contrast, in physics a comparison with experiments always makes sense, since a falsified physical theory needs modification.

Wikipedia

The exact sciences use reasoning. But reasoning not come from empty. Science need a start point. This are hypothesis and axioms/postulates.

  • Hypothesis:

Observing the nature we make hypothesis. An example is the quantum hypothesis by Max Planck, there is discrete "energy elements". see. Hypothesis is the start point of the logical machinery in physics. see

  • Axioms:

We don't worry about axioms are satisfied into real world only that none of the axioms directly or indirectly contradict themselves. Axioms/postulates is the start point of the logical machinery in mathematics.

When we established the hypothesis and postulates/axioms we can start reasoning to find the logical implications. In physics we will test implications with experiments.

  • Postulate in physics:

Furthermore, mathematics an physics often kissing: In physics we say postulate when we are developing a mathematical model, notably in theoretical physics. For example the Einstein postulate: speed of light is constant regardless of one's frame of reference. But postulate in physics often implies satisfied into real world, not the case in mathematics.

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    I don't think there is any widely recognized distinction between an axiom and a postulate. – Ben Crowell Apr 10 '13 at 19:10
  • You are right @BenCrowell. A translation failure. I change the post. – Edoot Apr 11 '13 at 7:06

protected by Qmechanic Jul 10 '13 at 13:29

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