I'm ferociously serious, for many reasons. Physics is about Nature, mathematics is about human thought patterns. Mathematics is the primary language of physics. Just as is the case with ordinary language, the language of physics has referents in Nature -- nouns like space, time, speed, electric charge refer to aspects of Nature -- they have no meaning without Nature.
The idea, for example, of a closed set, as one containing all its limit points is quite a different matter, just like the idea of of an integer or real number -- these all spring from the depths of our minds -- its not crazy to think that some of the basic ideas of math are ultimately empirical in nature. But math, to a substantial degree, is purely an exercise in abstract thinking with no reference to anything but the work of other mathematicians, with no reference to the natural world. Thus mathematicians are looking for internal consistency, upon which more consistency can grow -- although when the consistency is absent, a new math path might open up.
Physicists, on the other hand, are all about trying to figure out what's going in in Nature. Some are intensely pragmatic, others are extraordinarily abstract and abstruse. The plain fact is: Nature is not very orderly, and it's is full of surprises. Stuff changes, so why be overly shackled to some ideas that, in fact, might turn out to be wrong.
I have no problem in teaching QM, going from Planck to Bohr to modern QM, and simply making the Schrodinger EQ. plausible, based on a whole bunch of experiments, ideas of waves and diffraction, and contact transformation and Hamilton's Principle, which puts optics(eikonal) and mechanics into tantalizing proximity. Is there a problem with this way?
If physics can be axiomitized, then why was not QM invented before it was?
OK. Let's do relativity.
!., What is the speed of light? (Don't forget Faraday)
2. What is an observer?
3. What is a reference frame?
4. Where do the definitions you refer to come from?
What are they?
Einstein himself is a master at expressing some of my concerns about the importance of empirical evidence. His great papers of 1905 were all directly based on empirical concerns -- photoelectric, Brownian Motions,...--. In a sense his first SR is directly based on empirical evidence as well -- he cites Maxwell's Eq. Do read Einstein's monograph entitled Relativity. He goes to extraordinary means to explain space and time in terms that 1. we can understand, and 2. which dovetail in a very elegant way with his further discussion -- the train expt., etc.
I'm still far from convinced that you've got all the postulates you require. For example, do you not need to say something about the relationship or roles of humans and Nature? (See David Hume)
lightarrow has got it right.Regards,
Reilly Atkinson
peter0302 said:
I'm not sure if you're being facetious, or if this is some kind of trick question, but:
Postulates:
1) Speed of light is invariant for all observers
2) There is no preferred reference frame
Those, along with definitions of velocity, force, acceleration, momentum, and energy, yield the most familiar parts of special relativity, including E=mc^2, and E=pc (without which, ironically, QM would not be possible to formulate). Most importantly, these formulas are totally derived from postulate, not formulated ad hoc through observation. They were only experimentally verified later.
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