ONE PATTERN FITS ALL?

A "biggie" in the development of Physics has been "unification of Physics".

A notable advance was made by Newton's "law of gravitation" which, in effect, provided "the same law for earth and for the heavens". Newton explained planets moving in orbit around the sun by the same force (gravity) which made Humpty Dumpty fall down on earth.

Some where along the last millenia, the field of Mechanics became "unified" as a distinct field. A significant advance was made in mechanics when it was realized that "Galilean Relativty" characterized it. This involves the notion of inertia (which Galileo was credited with introducing) and "coordinates" two different "inertial frames".

Galilean relativity links translation along a line of two inertial frames, F, F' -- one moving uniformly, the other a rest relative to "the origin" (hence, inertial or "secure from forces" -- by the Galilean velocity transformations, for a "body" moving with velocity v along the x axis: 

		x' = x - vt, y' = y. z' = z, t' = t
But, in the latter part of the 19th century, it was discovered -- as shown in another file at this Website -- that light and other electromagnetic waves do not conform to the Galilean transformation. The inertial pattern can only be recovered by means of the Lorentz transformation, which Einstein discovered independently and used as the basis of the theory of special relativity. (At velocities significanlty less than that of light the Lorentz transformation reduces to the Galilean transformation.)

So a useful pattern -- the inertial fame -- has been "saved". Is there any pattern in common to the "physics before and after this saving"? For we are dealing with two pattern-problems:

  1. What is the "pattern of reality"?
  2. How do we "match" that pattern?
Elsewhere, I've a file about the "Activithm Strategy":
  1. Impose a pattern upon what you are dealing with.
  2. Search for subpatterns of this imposed pattern.
  3. See if these subpatterns are invariant under some transformation.
  4. Declare your subject to the the set of all subpatterns or properties invariant under the group underlying this transformation.
For example, we actively impose a pattern of coordination-axes upon geometric space, with enlightening.

Similarly, in physics, we impose the pattern of an inertial frame. This results in various subpatterns invariant under the "Galilean Group".