Re: The momentum - a cotangent vector?

ram@zedat.fu-berlin.de (Stefan Ram) wrote or quoted:

Explaining objects by their transformation behavior is
classic physicist stuff. A mathematician, on the other hand,
defines what an object /is/ first, and then the transformation
behavior follows from that definition.

  These notions can be somewhat personified by the persons
  of /Albert Einstein/ and /Hermann Minkowski/.

  Einstein's focus was on the algebraic properties of his theory of
  relativity, specifically the equations that express its laws and
  their behavior under transformations, known as /covariance/. The
  fulfillment of the principle of relativity is demonstrated through
  often tedious algebraic manipulations. The equations of the
  theory are transformed using Lorentz transformations, showing
  that the resulting equations maintain their form.

  In contrast, Minkowski emphasized the geometric properties of the
  theory, focusing on the geometric units that remain unchanged behind
  the transformations, which is referred to as /invariance/. Minkowski
  ensures the fulfillment of the principle of relativity through
  entirely different means. The only structures allowed in constructing
  a theory are the invariants of spacetime. This restriction guarantees
  compatibility with the principle of relativity and allows for the
  verification of its fulfillment through inspection.

  BTW: The word "tensor" for Ricci and Levi-Civita's "contravariant
  and covariant systems" was introduced by Einstein and Grossmann.

  I pulled this info (about Einstein, Minkowski, and Grossmann) from
  "General covariance and the foundations of general relativity:
  eight decades of dispute" (1993-03) by John D. Norton.

  I also read somewhere - can't remember where right now - that
  Einstein didn't actually name his theory "theory of relativity".
  That title, like "Big Bang" or "black hole", was thrown out there
  by a journalist or a critic. (Maybe Einstein picked it up later on.)
  So, it's kind of ironic that some folks today blame Einstein for
  giving his "theory of relativity" a name that doesn't really fit.