[FOM] 206:On foundations of special relativistic kinematics 1

[Laura Elena Morales Gro.]

I, modestly, disagree with Professor's Friedman appreciation
of the theory of Special Relativity. On the other hand, I could not 
possible write any posting with the quality and extension he accustoms, 
however, I'll simply say that his understanding of the physical facts he 
mentions with respect to the theory is incorrect. Abounding:

 On Wed, 21 Jan 2004, Harvey Friedman wrote:

> Foundational clarification of even elementary quantum mechanics has of
> course been the main topic for philosophers and others, as it appears to be
> an entirely nonsensical theory 

I could not agree more.

> with one particularly interesting attribute -
> in its considerable realm, it predicts reality spectacularly well. 

Well, not always. 

> probably hopeless until we get a far better grip on the foundations 
> of less mysterious physics;

Yes, and in this point I would suggest, classical, Newtonian mechanics.
Not Special Relativity. And probably, in doing so, it'd be wise to inquiry 
about the sense it makes to try to axiomatize physics, as requested in 
Hilbert (no. 8?) problem.

> 2) in fact, we don't even have a good enough idea as to what foundations of
> physical science should or could look like, in the first place.

Yes indeed.

> So, where to begin? Let's try physics. We want to start by slowly crawling.

And I would add: Classical Physics.

> Special relativistic kinematics has some advantages for a slow crawl.

???????

> Special relativistic kinematics is the initial segment of special relativity
> involving only space, time, and light transmission (only as it directly
> impacts space, time). 

Light not only impacts space, time, it is a part of them. The thery of 
relativity (I refuse to consider only kinematics, I do not know 
what Prof. Friedman means) was created to explain, precisely, the 
behaviour of light. Speaking of light means, among other things, to speak 
of time, motion, velocity, mass, energy and distance. It proposes to 
consider the old ideas, about time and space in a new, paradoxical frame.  
Concepts which were, till then, considered axiomatic and undefined 
(undefinable?) through history.

> 2) on the other hand, there is a substantial literature on it, even to this
> day, mostly written by physicists in the name of physics education.

And I wonder how much of that literature is correct. Let me just mention
that, for instance, the great Gamow, in a popular book, could not handle
the behaviour of light correctly when imagining a world in which light
did not have its speed but another, a close one to our terrestrial 
velocities.

> It may sound like 1) and 2) is the kiss of death for foundational work in
> special relativistic kinematics - and of course this is absolutely true in
> academia. 

I would say that it is precisely the great misunderstanding and 
ignorance we have of the behaviour and nature of light that prevents 
us to  follow a task as the one Prof HF is proposing.

> matter what the quality, in foundations of special relativistic kinematics!!

You better do not.

> The physics, and the related mathematics, are now regarded as utterly 
> trivial (not in 1905).

Well, not the physics. 

> despite the triviality of relativistic kinematics, 

I'd not use the word triviality.

> with the way it is taught in University courses. 

Mainly because it is not understood. It is paradoxical theory. The best
minds in physics still wonder about 'light'. A physicist needs about
5 years in contact with the ideas of relativity to feel at home. And not 
because they are complex or obscure, only because they are terribly
strange. 

> What is the stated dissatisfaction? My reading of it stems from the
> antifoundational act of prematurely introducing the Minkowski inner product
> (or even the Minkowski norm) on R x R^3, or even on R x R, and/or the
> antifoundational act of prematurely introducing the Lorentz group of
> transformations or the Poincare group of transformations from R x R^3 into R
> x R^3, or even from R x R into R x R.

The Lorentz group introduces itself in the theory, and not prematurely,
it shows off at the dead level of the topology of the relativity space. 
The 'fine' topology proposed by Zeeman had the remarkable property that 
its homeomorphism group was essentially just the Lorentz group. The, 
perhaps, most important group in all of physics is seen to emerge at the 
very primitive level of topology, i. e., from just an appropriate 
definition of 'nearby' events. 

On the one hand, the physics was there and on the other, the maths were 
there as well, the 'coup' to join them was Einstein's. It came not from 
Lorentz, not from Poincare. That escaped them. The physics needed them
to describe itself mathematically, nothing was 'prematurely' introduced. 

> So most of these papers have titles like "Derivation of the Lorentz
> transformations". 

The automorphisms of space-time that keep invariant (a physical 
requirement of the theory) the (well known) cuadratic (Minkowskian) 
form, obeyed the laws of a symmetry group already introduced by Lorentz. 
Once you understand what those automorphisms are, you need to derive
the Lorentz transformations. You cannot do without them, to begin with.
And this is, no doubt, educational:

> continuing till the present. As I said earlier, the recent ones mostly 
> give the reason for publication as "educational".

> still is to give observational foundations for everything in physical
> science. 

What a loable task!

> Generally, in observational foundations, one has only observers and
> observations. Ideally, there are no theoretical notions such as event,

In physics, you have observers because you have events (observations)
to be recorded.

> space, time, bodies, forces, motion, energy, etcetera. One builds such
> notions by logically piecing together patterns in observations.

Not in physics. 

> Generally speaking, a world history is a well defined mathematical entity
> which declares a (generally finite) number of distinct observers, and the
> entire history of all observations made by those observers.

If you knew how difficult is to define 'an observer' in physics...
An observer has no sense without an event. And the world history will
be defined through *world lines*.

Perhaps, I stop here. And, perhaps, for the moment. The worlds of Maths, 
Physics and Philosophy are 'worlds apart'.

Best wishes,
LE
Instituto de Matemáticas
Universidad Nacional Autónoma de México
México, City.