This paper is a commentary on the foundational significance of the Clifton-Bub-Halvorson theorem characterizing quantum theory in terms of three information-theoretic constraints. I argue that: (1) a quantum theory is best understood as a theory about the possibilities and impossibilities of information transfer, as opposed to a theory about the mechanics of nonclassical waves or particles, (2) given the information-theoretic constraints, any mechanical theory of quantum phenomena that includes an account of the measuring instruments that reveal these phenomena must be empirically equivalent to a quantum theory, and (3) assuming the information-theoretic constraints are in fact satisfied in our world, no mechanical theory of quantum phenomena that includes an account of measurement interactions can be acceptable, and the appropriate aim of physics at the fundamental level then becomes the representation and manipulation of information.

One-dimensional particle states are constructed according to orthogonality conditions, without requiring boundary conditions. Free particle states are constructed using Dirac’s delta function orthogonality conditions. The states (doublets) depend on two quantum numbers: energy and parity (”+ ” or ”-”). With the aid of projection operators the particles are confined to a constrained region, in a way similar to the action of an infinite well potential. From the resulting overcomplete basis only the mutually orthogonal states are selected. Four solutions are found, corresponding to different non-commuting Hamiltonians. Their energy eigenstates are labeled with the main quantum number n and parity ”+ ” or ”-”. The energy eigenvalues are functions of n only. The four cases correspond to different boundary conditions: (I) the wave function vanishes on the boundary (energy levels: 1 +,2 −,3 +,4 −,...), (II) the derivative of the wavefunction vanishes on the boundary (energy levels 0 +,1 −,2 +,3 −,...), (III) periodic boundary conditions (energy levels: 0 +,2 +,2 −,4 +,4 − 6 +,6 −,...), (IV) periodic boundary conditions (energy levels: 1 +,1 −,3 +,3 −,5 +,5 −,...). Among the four cases, only solution (III) forms a complete basis in the sense that any function in the constrained region, can be expanded with it. By extending the boundaries of the constrained region to infinity, only solution (III) converges uniformly to the free particle states. Orthogonality seems to be a more basic requirement than boundary conditions. By using projection operators, confinement of the particle to a definite region can be achieved in a conceptually simple and unambiguous way, and physical operators can be written so that they act only in the confined region. Permanent address. 1 Key words: confinement, orthogonality, boundary conditions, Dirac’s formalism, projection operators.

One of the most important quantum algorithms is Grover's search algorithm [G96]. Quantum searching can be used to speed up the search for solutions to NP-complete problems e.g. 3SAT. Even so, the best known quantum algorithms for 3SAT are considered inefficient.

this paper is based is that a theory be developed according to its fundamental underlying symmetry: for the electromagnetic field this is the symmetry of special relativity [1--5], a sub symmetry of general relativity. We accept the Poincar group as the group of special relativity, with ten generators and two invariants [6]. The electromagnetic field is considered to be a physical entity which is described by symmetry guided relations between group generators according to the following prescription [1--5]. Rotation generators are those of magnetic field components; boost generators are those of electric field components; translation generators are those of four potential components. It is shown in Sec. 2 that the Lie algebra of the Poincar group leads to relations between generator eigenvalues which, using the above prescription, are consistent with the Maxwell equations and recently inferred [1--5] cyclic relations between field components. Section 3 develops a helicity equation [7] from the underlying symmetry of the Poincar group as given in Sec. 2. This equation has been inferred independently by Dvoeglazov [8] and by Afanasev and Stepanofsky [9], following the introduction of relativistic field helicity by Ranada [10], and the earlier realization that helicity is a topological invariant [11]. The transition from the static symmetry characteristics of the Poincar group to an equation of motion (the helicity equation) is accomplished through the transition from momentum to coordinate representation P is replaced by i , where P is the translation generator. This is synonymous with the well known quantum hypothesis, which is a successful calculating prescription in field theory and wave mechanics. This transition changes the fundamental group identity [12], P ...

We develop a nonlinear quantum theory of Newtonian gravity consistent with an objective interpretation of the wavefunction. Inspired by the ideas of Schrödinger, and Bell, we seek a dimensional reduction procedure to map complex wavefunctions in configuration space onto a family of observable fields in space–time. Consideration of quasi–classical conservation laws selects the reduced one–body quantities as the basis for an explicit quasi–classical coarse–graining. These we interpret as describing the objective reality of the laboratory. Thereafter, we examine what may stand in the role of the usual Copenhagen observer to localize this quantity against macroscopic dispersion. Only a tiny change is needed, via a generically attractive self–potential. A nonlinear treatment of gravitational self–energy is thus advanced. This term sets a scale for all wavepackets. The Newtonian cosmology is thus closed, without need of an external observer. Finally, the concept of quantization is re–interpreted as a nonlinear eigenvalue problem. To illustrate, we exhibit an elementary family of gravitationally self–bound solitary waves. Contrasting this theory with its canonically quantized analogue, we find that the given interpretation is empirically distinguishable, in principle. This result encourages deeper study of nonlinear field theories as a testable alternative to canonically quantized gravity. Expanded version of a talk presented at the Inaugural Australian General Relativity Workshop,