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Re: [Phys-l] Absolute four-momentum of massless particles



On 10/01/2010 02:21 PM, David Bowman wrote:
I don't think putting all the laws of nature into a hodgepodge that
one calls the first postulate is a good idea. To my mind the
postulates are supposed to be meta-laws that the observed laws of are
to obey. This means that we ought not assume Maxwell's equations a
priori before we get the meta-laws down. The way I see it Maxwell's
equations *depend on* the Lorentz invariance of SR; they don't
dictate that invariance *to* SR (contrary to the formulations of SR
that one often sees that takes the constancy of the speed of light as
the 2nd postulate of SR).

I agree that we should question the status of the so-called
postulates, and that one often sees formulations that are very
seriously open to question, not just on philosophical grounds
but also on pedagogical and practical grounds.

Indeed, I would go even further, and emphasize that special
relativity doesn't need postulates at all. There is a tradition
in high-school geometry dating back thousands of years whereby
the whole subject is deduced from a handful of axioms. However,
as Feynman and others have pointed out, it doesn't have to be
that way. You can easily take some of the Euclidean theorems
as the axioms of a new system, and derive the Euclidean axioms
as theorems in the new system.

In the narrow Euclidean view, the whole subject is a tree that
grows upward from one small trunk (the set of axioms). In
contrast, Feynman viewed knowledge as a grand tapestry, with
connections in every direction. This means that every fact
is known in more than one way. This has immediate pedagogical
and practical consequences, because a forgotten fact is like
a small hole in the tapestry. It can be repaired by reweaving
up from the bottom, down from the top, and/or in from the sides.

IMHO we should not fuss over what is a postulate and what is
not, but ask simply what is known and what is not. And for
each thing that is known, we need to ask in what ways it is
connected to other things that are known. Last but not least,
we need to ask _how well known_ each thing is. Some things
are so very well known and so intimately connected to other
things that they are well-nigh unshakable. Other things that
we usually take for granted are only very loosely connected
to the rest of the tapestry, such that they could be changed
without causing much of a ripple. For example, reclassifying
the neutrino from "massless" to "non-massless" did not require
overthrowing the established laws of physics.

==========

As a related point: Students -- especially in the introductory
course -- should be given the best evidence, not necessarily
the most ancient evidence. That is: There is no law that says
pedagogy must recapitulate phylogeny. I know there are some
people (even some people on this list) who say they use the
"historical approach" to organize and motivate the study of
physics, but I do not consider this a good idea. I do not
even believe it is possible without grossly falsifying the
history.

The business of "Einstein's first postulate" and "Einstein's
second postulate" falls into the deplorable pseudo-historical
category. First of all, the idea that the laws of physics
are invariant with respect to uniform motion is not due to
Einstein; it was clearly set forth by Galileo in 1632.

Secondly, it is historically true that in 1905 Einstein made
an epochal contribution by finding a way to reconcile Galileo's
relativity with Maxwell's electromagnetism ... but so what?
The fact is that a modern (post-1908) understanding of special
relativity doesn't revolve around electromagnetism. Instead,
we see special relativity as the geometry and trigonometry
of spacetime. The fact that c is the speed of _light_ i.e.
the speed of electromagnetic waves in accordance with the
Maxwell equations is interesting but not central to special
relativity. In fact _c_ is related to the hyperbolic
trigonometry of the xt plane in the same way that a _radian_
is related to the circular trigonometry of the xy plane.
It is little more than a conversion factor, converting from
the conventional units of length in the x direction to the
conventional units of length in the t direction.

Special relativity is the geometry and trigonometry of spacetime.




Von Stund′an sollen Raum für sich und Zeit für sich
völlig zu Schatten herabsinken
und nur noch eine Art Union der beiden
soll Selbständigkeit bewahren.

Hermann Minkowski (1908)

From now on, space of itself and time of itself
are to sink into mere shadows
and only a kind of union of the two
is to maintain its independence.