Richard J. Cook

What are Quantum Jumps

This paper answers the title question by giving an operational definition of quantum jumps based on measurement theory. This definition forms the basis of a theory of quantum jumps which leads to a number of testable predictions. Experiments are proposed to test the theory. The suggested experiments also test the quantum Zeno paradox, i.e., they test the proposition that frequent observation of a quantum system inhibits quantum jumps in that system.

V Quantum Jumps

Publisher Summary This chapter describes the quantum jumps. The concept of quantum jumps began with the theory of atomic structure. According to this theory, an atom at rest can exist in any of a discrete set of energy levels, and the fundamental radiative processes proceed by abrupt jumps among these levels. The observation of quantum jumps requires a spectroscopic sample consisting of a single atom or a very few atoms. Only ions have been trapped as single isolated particles. Telegraphic fluorescence is the only effect that permits the observation of quantum jumps. The quantum formalism attributes electron shelving to the lack of fluorescence, whereas the intuitive picture of the process attributed the lack of fluorescence to electron shelving. The observation of photon anti-bunching in single-atom resonance fluorescence and other experiments provide evidence for the discrete nature of quantum transitions in individual quantum systems.

Fizeau’s experiment and the Aharonov–Bohm effect

The electromagnetic wave equations in a moving medium may be approximated by a form similar to that of the Schrodinger equation for a particle in an electromagnetic field, with the velocity v of the medium and the vorticity ∇×v playing the roles of the vector potential and magnetic field, re‐ spectively. A purely classical optical analogue of the Aharonov–Bohm effect follows by consider‐ ation of the interference pattern produced by two beams, each of which propagates in a region with zero vorticity, but such that the flux of the vorticity through the closed loop defined by the optical paths does not vanish. Fizeau’s experiment (1851) on the velocity of light in moving media may be regarded as an example of such a situation.

Interpretation of the cosmological metric

The cosmological Robertson–Walker metric of general relativity is often said to have the consequences that (1) the recessional velocity v of a galaxy at proper distance l obeys the Hubble law v=Hl, and therefore galaxies at sufficiently great distance l are receding faster than the speed of light c; (2) faster than light recession does not violate special relativity theory because the latter is not applicable to the cosmological problem, and because “space itself is receding” faster than c at great distance, and it is velocity relative to local space that is limited by c, not the velocity of distant objects relative to nearby ones; (3) we can see galaxies receding faster than the speed of light; and (4) the cosmological redshift is not a Doppler shift, but is due to a stretching of photon wavelength during propagation in an expanding universe. We present a particular Robertson–Walker metric (an empty universe metric) for which a coordinate transformation shows that none of these interpretation necessarily...

Quantum theory of spontaneous emission and excitation near a phase-conjugating mirror

We present a quantum-electrodynamic theory of spontaneous emission in the presence of a phase-conjugating mirror (PCM) and show that the radiative relaxation rate is increased owing to the amplification of quantum noise by the PCM. For any finite value of the PCM reflectivity an atom in any initial state will relax to a steady state with a finite probability of being excited. In particular, there is a finite probability of spontaneous excitation of a ground-state atom placed near the PCM. The fluorescence spectrum of an atom near a PCM is generally described by two Lorentzian functions.

Radiation reaction revisited

The Abraham‐Lorentz equation of motion for a charged particle admits ‘‘runaway’’ solutions which violate the law of inertia. The integrodifferential form of the Abraham–Lorentz equation eliminates the runaway solutions, but in so doing introduces ‘‘preacceleration’’ which violates the principle of causality. Here it is shown that there exists a form of the equation of motion for a nonrelativistic charged particle which is in accord with both the law of inertia and the principle of causality.

Physical time and physical space in general relativity

This paper comments on the physical meaning of the line element in general relativity. We emphasize that, generally speaking, physical spatial and temporal coordinates (those with direct metrical significance) exist only in the immediate neighborhood of a given observer, and that the physical coordinates in different reference frames are related by Lorentz transformations (as in special relativity) even though those frames are accelerating or exist in strong gravitational fields.

Integral solution for diffraction problems involving conducting surfaces with complex geometries. I. Theory

For an arbitrary conducting surface Z(x, y) we obtained an analytical expression for the local refractive index ν as a function of Z, ∂Z/∂x, ∂Z/∂y, and the Drude conductivity σ by using the complex ray-tracing method. The Fresnel coefficients of reflectance and transmittance are then employed, and the value of ν is obtained to determine the scattered and refracted fields. The proposed method has advantages over the methods of solution by the Debye potential, the Laplace transform, and the vector-wave equation in the computation of the scattering and absorption parameters of a wide range of complex surface and wave-front geometries. The surface integrals obtained in the present study include the surface function in an explicit and concise form.