In (1899?), together with the introduction of his thermal
description of light and the introduction of this novel constant
that seemed to be characteristic of it, Planck made another
observation that at the time seemed something like the
hocus-pocus of numerology compared with his other ``hard
science''. He observed that, just as length, mass and time,
taken together, form a dimensionally complete set for expressing
all dimensional scaling relations, the constants h/, G and c
constitute another such set. But unlike the simple notions of
length, mass and time, which can be recognized as useful
abstracations but have no obvious ``building-block''
interpretation, these dimensionful constants *DO* make such
a description at least imagineable.

This is because, not only are the dimensions of an angular
momentum (also called an action, for reasons that will become
important to us in chapter 5) (those of h/), a speed (of c)
and a
()
(which has been given no special name, but is the dimension of
G), useable abstractions, but the particular constants that were
discovered as properties of nature *have definite numerical
values*. In particular, they can be combined and recast (which
is left as an exercise), as any dimensionally complete set can
be combined to go from one form to another, to give a mass, a
length and a time. But these equivalent formulations are every
bit as essentially properties of nature as are h/, G and c.
Thus with these constants, there is now a fundamental
``building-block scale'' that can be associated with the
dimensions of mass, length and time but which seems to come
entirely from nature.

At the time, Planck had no idea how to even begin construction of a building-block picture of anything that made use of these constants, so the recognition that the numbers existed was not directly useable to solve any problem.

But with hindsight from subsequent history, this turns out to have been a profound observation. In the century since its recognition, physicists have been led, through tortuous and varied solutions to many independent problems, to develop a language for the descriptions of fundamental processes, which incorporates the discoveries of relativity, Planck's work and much more that led to the quantum theory, and Newton's and eventually Einstein's descriptions of gravity (both of which intrinsically require G). The way in which the refinements of this language have taken place, to account for new effects and to include new ranges of scale (smallness of particles and extents in distance and time in the universe), has strongly encouraged casting it as a languge of building blocks, in which the blocks combine at one scale into collections that make the structures we see at the next larger scale. And in this language, which is still far even from seeming complete, Planck's fundamental building-block sizes can almost be made to appear as the starting scale from which everything else we understand is assembled.

Fascinatingly, we still do not know most of the intermediate steps in this picture. The Planck scales for length, mass and time are phenomenally smaller than anything that anyone has been able to measure outright. Yet all of the theoretical framework that people have been led to invent to describe the hierarchy of problems at hand has ``cast itself'' into a form in which such dimensionful starting points are a natural part. Thus it seems that between the explicit construction of the language to describe the things that we already understand, and the presentation of the basic size scales that derive from the constants of proportionality that appear in them, as if we have seen the beginning and one aspect of the end of the theory that will be built in this language, and our task now is to figure out how the two are related.

Thu Aug 31 12:01:42 CDT 1995