Sci-Am: Ladders of Effective Theories

I just read an article in the June 2003 issue of Scientific American entitled "The Dawn of Physics Beyond the Standard Model" by Gordon Kane. I found the summary paragraphs the most interesting. I quote them here:

"To fully grasp the relation of the Standard Model to the rest of physics, and its strengths and limitations, it is useful to think in terms of effective theories. An effective theory is a description of an aspect of nature that has inputs that are, in principle at least, calculable using a deeper theory. For example, in nuclear physics one takes the mass, charge and spin of the proton as inputs. In the Standard Model, one can calculate those quantities, using properties of quarks and gluons as inputs. Nuclear physics is an effective theory of nuclei, whereas the Standard Model is the effective theory of quarks and gluons.

From this point of view, every effective theory is open-ended and equally fundamental - that is, not truly fundamental at all. Will the ladder of effective theories continue? The MSSM [Minimal Supersymmetric Standard Model] solves a numbe of problems the Standard Model does not solve, but it is also an effective theory because it has inputs as well. Its inputs might be calculable in string theory.

Even from the perspective of effective theories, particle physics may have special status. Particle physics might increase our understanding of nature to the point where the theory can be formulated with no inputs. String theory or one of its cousins might allow the calculation of all inputs - not only the electron mass and such quantities but also the existence of spacetime and the rules of quantum theory. But we are still an effective theory or two away from achieving that goal."

There are several things about this that bother me. However, I want to focus on one particular point and address it this way: If we take the above approach to this "ladder" of theories with inputs, what does it imply? I try to answer this below.

We can take a theory with a single input and write it abstractly as "F(a)", where 'F' is the theory, and 'a' is the input. We then say that 'a' is calculated from another "deeper" theory, call it "G", which has its own different input, call it 'b'. So, now we have: F(a), and, a=G(b). We can immediately see that we now need another theory, H, which will calculate b for G. But we also see an infinite regress looming if every successively "deeper" theory has some input(s) of its own.

Therefore, we can see the intuitive desire expressed in the article to reach, at some point in this "ladder of effective theories", some theory which has no inputs, as a way to reach some kind of bottom, some way of avoiding an infinite regress.

If we say, for the sake of argument, that theory H has no inputs, then we have: F(a), a=G(b), and, b=H(). Or, in short: F(G(H())). The interesting thing about this picture is that, in Aristotelian terms, there seems to be, at root, no material cause at all. Usually, in a statement like "P(x)", 'P' is the formal plus efficient cause, and 'x' is the material cause. (see EL p. 165) But in the case proposed, we have no arguments, no inputs, and hence no material cause.

But if there is no material cause, then this seems to be saying that, in some basic sense, there are no actual material (physical) objects in existence! We are left with the algorithms of the theories (F, G, H), but ultimately these algorithms seem to act on nothing. As bizarre as this sounds, it seems to me consistent with the very basis of Newtonian mechanics, which requires "structureless particles" with no attributes (see LI p. 90-91) as the entities which are being acted upon. Taken to its logical conclusion, the notion of "structureless" seems to me to be equivalent with "admits no interaction". Because if such a particle admits interaction, then it has some detectable structure or attributes (since interactions are the basis of all measurements). Therefore, Newtonian physics must have completely undetectable particles at its fundamental level, and likewise, a Newtonian "ladder of effective theories" must ultimately have at bottom a complete lack of reference to material cause.

To me, this is wholly unsatisfactory. I suppose that one could propose to believe that physics theories shall get deeper and deeper, until a bottom theory is reached, at which point we shall be left with algorithm plus undetectable particles (which we must simply have faith to assume to exist, since by definition, we can never measure or even detect them).

My tendency is instead to believe that such proposed ladders of theories are simply a way of delaying or avoiding facing one of the unpleasant logical conclusions of Newtonian presuppositions, and therefore, delaying or avoiding facing one of the unpleasant logical conclusions of attempting to construct these ladderworks of "fundamental" Newtonian theories.

(P.S. - I had to increase the maximum lines per post to post this. It is now set to 1000 lines. I may have to tweak it some more. Please let me know if any of you have any problems posting lengthy, yet appropriate, messages.)