[FOM] On foundations of special relativistic kinematics 1

Laura Elena Morales Gro. lemg at math.unam.mx
Fri Jan 23 14:51:40 EST 2004

On Thu, 22 Jan 2004, José Félix Costa wrote:
> The principle of relativity of Galileo states ''something'' that we know
> about relative constant motion of systems with respect to other systems: we
> observe the same behaviour of a fly on earth or inside a moving ship,
> objects fall in the same way, etc. It concearns the laws of mechanics.

Laws which are valid, as well as all the laws of physics, in an inertial
reference frame.

> Does the water boil at the same temperature in a train moving at 100 miles
> per hour? Why should it happen?

Yes, the boiling temperature of the water depends only on the height
of the place, that is, the atmospheric pressure. And as long as the 
train keeps its speed, it will boil till acceleration (either in 
the positive or negative sense) changes. Then, the water vessel (and 
even the oven!) will drop. It happens because, when in constant motion, 
the train (as well as an airplane) are inertial reference frames: all laws
of physics hold, as in the 'stationary' earth. Galileo, the really first
person to formulate a principle of relativity (in the Dialogues), used a 
(rather slow) ship to explain this phenomenon. 

> Eintein's formulation of special relativity covers all the physical laws: in
> order to have Maxwell's equations valid we should accept the constancy of
> the velocity of light. But what is exactly a physical law?

Actually, Maxwell's equations found there was an electromagnetic 
radiation moving with the speed of light, so they concluded, light is an 
electromagnetic wave. A physical law is a referent that describes (even, 
predicts) physical phenomena and is formulated through observation, in 
general. Maxwell's eqs, f. i., gave more then was put in then. They were 
called 'the intelligent equations' An extraordinary exception to most of 
physical laws (that surpassed and completed Maxwell's) was Einstein's 
relativity theory which predicted (among other physical facts) stellar 
aberration, before having ever being observed.

> I have in my hands Tolman's Book, and I think that foundational work 
> on this respect is moving to upper abstract levels where we miss 
> referents.
Yes, nature as a whole, is not yet understood. Classical mechanics, as a 
limit of the theory of relativity, and as a finished theory, is one of the 
best referents. But it is not easy, it's indeed against common sense 
somehow. Its simple, but not always well understood laws, are the result 
of deep abstraction. Notions like, for instance, the one of movement are 
primitive notions; first, natural ideas in the intellect for a mathematician, 
while for a physicist, is such an intricate one. I honestly wish some 
foundational work could be done in this direction but I'm not so optimistic 
because it's mainly mathematicians which undertake this kind of work, and 
they find the laws of physics and the way physics is done, untenable.

> ''nevertheless, the *presentation* of the physical science thereby becomes
> incomparably more transparent - after the simplification and synthesis
> process takes hold.''
A nice and veritable thought.


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