CCL: On orbitals and "reality"

I have been following the discussion on "Orbitals and Reality"
 with
 considerable interest, but wanted to hold off responding until I had a
 chance to examine the Nature paper. "Elements of physical reality"
 formed a
 major component of the early 20th century debates between Einstein and the
 Copenhagen school, but I had not realized that "reality" still
 constitutes
 an element of scientific discourse today. "Reality" is not something
 that
 has a rigorous scientific definition (apart from the unfortunate confusion
 with the real, imaginary and complex nembers of mathematics); so I prefer
 not to talk about "reality" in a scientific discussion. Experimental
 observations constrain the objects and language of theory; theoretical
 concepts, in turn, frame the questions that experiments are designed to
 answer and interpret the experimental observations. If this loop can be
 closed in
 an internally consistent manner, that imparts a degree of experimental
 confirmation to the objects of theory. If not, it is time to either repeat
 the experiments, tinker with the theoretical concepts or design new ones.
 Someone mentioned unicorns. If unicorns (or dark energy or ...) help
 explain experimental observations, then they will constitute legitimate
 objects for scientific discourse and experimental design. That is all there
 is to it! "Reality" is for philosophers (with apologies to the
 philosophers
 here; we are scientists... why should we worry about reality? :-)
 A little over a hundred years ago, theories of motion were formulated in
 terms of the aether and experiments were designed to detect the motion of
 bodies relative to the aether. Today our theories are formulated in terms
 of spacetime and experiments are designed to detect the curvature of
 spacetime. Does that make spacetime "real" and the aether
 "unreal"? Would
 it have made a difference to our world if we had continued using the term
 "aether" with new topological, rather than material, properties?
 We tend to think of molecular structure as "real" -- after all, we can
 "see" structure maps come out of our X-ray machines. But the X-rays
 are
 only producing diffraction patterns and it is the software (guided by the
 concepts and equations of theory) that produces the structure maps. We
 often
 tend to think of electrons as moving around in charge clouds and nuclei as
 quasi-localized at any point in time, with definite internuclear (bond)
 distances and bond angles. But there is no fundamental reason to think this
 way, apart from convenience (and the thousand-fold mass difference).  The
 nuclei too are delocalized in charge clouds with the protrons
 indistinguishable among themselves and the neutrons likewise. But we donot
 usually question whether bond lengths and bond angles are "real".
 Orbitals have no meaning in VB theory or in the Hohenberg-Kohn variational
 version of DFT (as distinguished from the Kohn-Sham version). These
 theories cannot help design experiments to "observe orbitals" and
 would
 interpret the observations of Villeneuve, et al, very differently. While
 historically, orbitals may have derived from Bohr-Sommerfeld orbits, their
 only significance in the quantum mechanics of many-electron systems derives
 > from a theorem of linear algebra which states that the eigenfunctions of a
 Hermitian operator (e.g. the hydrogen atom Hamiltonian) form a complete set
 for the expansion of any (wave) function. Since no one uses a complete set
 (which is infinite), we could as well use plane waves or Gaussians or
 wavelets for our expansions... and we do! For a computational chemist doing
 CI, orbitals have about as much "reality" as primitive Gaussians have
 for
 an organic chemist doing HF computations.
 Nevertheless I donot understand the reluctance to accept the interpretation
 of Villeneuve, et al's observations in terms of orbitals. It is an accepted
 fact that an electron undergoing ionization does not "flow" out
 continuously and uniformly from throughout the atom or molecule. The hole
 formed by ionization of the electron has a definite quantum of charge, a
 definite quantum of spin and a characteristic shape. Let us say Villeneuve,
 et al have observed the hole formed by the ionization of an electron from
 N2 ... would this be more acceptable? Note that they have observed not just
 the density hole, but by coherent recombination, the relative phase as
 well. So what's the problem with calling this an orbital? Unfortunately,
 Villeneuve, et al donot help their case by showing a diagrammatic
 representation of their reconstructed wavefunction alongside a N2 2p
 sigma_g orbital "from an ab initio calculation" but they omit to
 mention
 the basis set or level of theory employed, making any quantitative
 comparison moot.
 The concept of an orbital has different meanings in different contexts, but
 in its essence an orbital is a solution to a one-electron equation or an
 "effective" one-electron equation of motion. The replacement of the
 interelectronic repulsion term by an effective one-electron potential is at
 the heart of the Hartree-Fock and Kohn-Sham procedures that generate a
 system of one-electron equations. Within these theories, it is legitimate
 to
 formulate some explanations in terms of orbitals (bearing in mind the
 approximations involved and thus the approximate nature of the
 explanations)
 and to design experiments to test these approximations (e.g. Koopmans'
 theorem, Wodward-Hoffman rules).
 Dr. N. Sukumar
 Center for Biotechnology and Interdisciplinary Studies
 Rensselaer Polytechnic Institute