How do we know that c is constant regardless of the motion of the observer

[imatfaal]

Which is an example of why the use is different in math vs physics. In math there are things that are true but cannot be proven. In physics, you construct a model of some behavior. A good model will fail if it doesn't describe nature, which is the requirement of falsifiability and the desirable feature of precision. That can be a test of an axiom that is included. It doesn't have to test the axiom, because a model can fail in more than one way. F=ma is tested in that the relationship is linear, and you can construct experiments to show this. The constancy of the speed of light is tested in that there are ramifications of it, such as time dilation, and you would not get those results if c were frame-dependent.

 

In maths there are also things that are demonstrably not true - but using them as an axiom/postulate (that is accepted without proof) can be,or at least has been, highly beneficial. Amongst other things I am thinking, of course, of Euclid's Elements and the parallel postulate. One can make valid and important arguments whilst working with the the parallel postulate - yet non-Euclidean geometry shows that the postulate is not universally correct.

 

Do you not use such things in physics as well? I really would not know - but are there situations where you have to say to yourself "I know this is an incorrect model, but for some reason, in my particular circumstance, it produces predictions that tally with experiment"

[ajb]

Do you not use such things in physics as well? I really would not know - but are there situations where you have to say to yourself "I know this is an incorrect model, but for some reason, in my particular circumstance, it produces predictions that tally with experiment"

 

You often hear of "toy models", which are not expected to model nature particularly well, but exhibit similar phenomenology or mathematical behaviour as (or what one might expect of) "more realistic theories". They can be a place to develop technology and intuition to be applied to more realistic theories.

Edited January 19, 2011 by ajb

[swansont]

Do you not use such things in physics as well? I really would not know - but are there situations where you have to say to yourself "I know this is an incorrect model, but for some reason, in my particular circumstance, it produces predictions that tally with experiment"

 

Incorrect insofar as they are not universally true. Many, many things are modeled as harmonic oscillators. There are other examples of good approximations; they are usually implemented as the first term or two of a Taylor (or other) series expansion, i.e. you set up your model such that x << 1 and get a solution that is good as long as x is small.