To
all,
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.
Any
thoughts/criticisms?
Tim
(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.)