Reply to comment on “variational formulation for the equilibrium condition of a conducting fluid in an electric field”

In this comment we respond to the several criticisms of the paper by Sujatha et al. raised by Kingham and Bell. In particular, we demonstrate that, contrary to their assertion, Taylor's solution for the electrostatic fields can never satisfy the boundary conditions for the actual experimental configurations involving field emission liquid metal ion sources and other experiments on electrostatically stressed conducting fluids. It is further argued that a careful analysis of Taylor's experimental procedure and observations suggests that although the observed static structures have a macroscopic axial-symmetry they have not the idealized conical shapes of prescribed angle. Furthermore, the formation of the Taylor cone structure is shown to be inconsistent with the principle of energy minimization.It is concluded that none of the criticism raised by Kingham and Bell invalidate any of the analysis or conclusions presented in the paper by Sujatha et al.This work has been supported in part by the Division of Materials Research, National Science Foundation, Grant No. DMR-81008829     

Variational formulation for the equilibrium condition of a conducting fluid in an electric field

In this paper the variational formalism is used to derive a set of equations describing the equilibrium configuration of a conducting fluid in an applied electric field. The validity of the variational equations is confirmed by application to the well-defined problem of concentric spherical electrodes. It is further shown that a cone, including the so-called Taylor cone used to model the equilibrium configuration of liquid metal ion sources, is inconsistent with the general equations. An analysis of the Taylor derivation suggests that reasons for the disagreement are the omission of the pressure difference term in the Laplace formula and use of only an approximate solution to the electrostatic cone problem. Finally a quasi-empirical method is suggested for the self-consistent solution of the variational equations.     

Difficulties with the partial quantization of systems

Proposals of quantizing matter without also quantizing fields are assessed. In one of these the principle of superposition is given up and an estimate of its violation is suggested. Another proposal, which retains the principle of superposition, is shown to be inconsistent with the equations of motion.     

Blue laser dye spectroscopic properties in solgel inorganic-organic hybrid films

A blue solid-state laser material based on 4,4' dibenzyl carbamido stilbene-2,2' disulfonic acid incorporated into solgel zirconia and inorganic-organic hybrid matrices is presented. The absorption maxima of the dye in various matrices are around 339-361 nm, and the broad fluorescence peaks are at 411-413 nm. Optical gain measurements using the variable stripe method show amplified spontaneous emission peaking at 437 nm.     

Generalized gauge independence and the physical limitations on the von Neumann measurement postulate

An analysis is presented of the significance and consequent limitations on the applicability of the von Neumann measurement postulate in quantum mechanics. Directly observable quantities, such as the expectation value of the velocity operator, are distinguished from mathematical constructs, such as the expectation value of the canonical momentum, which are not directly observable. A simple criterion to distinguish between the two types of operators is derived. The non-observability of the electromagnetic four-potentials is shown to imply the non-measurability of the canonical momentum. The concept of a mechanical gauge is introduced and discussed. Classically the Lagrangian is nonunique within a total time derivative. This may be interpreted as the freedom of choosing a mechanical (M) gauge function. In quantum mechanics it is often implicitly assumed that the M-gauge vanishes. However, the requirement that directly observable quantities be independent of the arbitrary mechanical gauge is shown to lead to results analogous to those derived from the requirement of electromagnetic gauge independence of observables. The significance of the above to the observability of transition amplitudes between field-free energy eigenstates in the presence (and absence) of electromagnetic fields is discussed. E- and M-gauge independent transition amplitudes between field-free energy eigenstates in the absence of electromagnetic fields are defined. It is shown that, in general, such measurable amplitudes cannot be defined in the presence of externally applied time-dependent fields. Transition amplitudes in the presence of time-independent fields are discussed. The path dependence of previous derivations of E-gauge independent Hamiltonians and/or transition amplitudes in the presence of electromagnetic fields are related to the inherent M-gauge dependence of these quantities in the presence of such fields.     

Gauge invariance and gauge independence of the S-matrix in nonrelativistic quantum mechanics and relativistic quantum field theories

The gauge independence of transition rates as opposed to the gauge invariance of the equations of motion and gauge dependence of operators and state vectors is critically examined and explicitly demonstrated, both in nonrelativistic quantum mechanics and quantum field theory. Time independent as well as time dependent gauge transformations are explicitly analyzed using several techniques in order to clarify the physical content and significance of gauge independence and the conditions for its applicability.