The mathematical expression for the electromagnetic current of a quantum particle describes an extended charge in the sense that it is non-vanishing over the volume of the wave packet or the Schroedinger wave for the particle. In the hydrodynamic model this charge current and associated density are interpreted as a physical reality. Coupling such a current to a classical electromagnetic field in the soft photon limit then results in a theory for radiation. It is shown that this predicts that bremsstrahlung is sometimes greatly suppressed when the force acting on the particle is due to a classical potential field and when the volume over which the force is active is small compared to the volume of the particle's wave packet. Solving the same problem using conventional quantum radiation theory gives a different result. Therefore it is possible to test this effect experimentally and either confirm or rule out a hydrodynamic model for Schroedinger wave mechanics. An experiment is proposed to make such a test. It involves an electron microscope with a Wien filter for producing monochromatic beam electrons and an accurate energy measurement of the particle after passing through a local force field.
The mathematical expression for the electromagnetic current of a quantum particle describes an extended charge in the sense that it is non-vanishing over the volume of the wave packet or the Schroedinger wave for the particle. In the hydrodynamic model this charge current and associated density are interpreted as a physical reality. Coupling such a current to a classical electromagnetic field in the soft photon limit then results in a theory for radiation. It is shown that this predicts that bremsstrahlung is sometimes greatly suppressed when the force acting on the particle is due to a classical potential field and when the volume over which the force is active is small compared to the volume of the particle's wave packet. Solving the same problem using conventional quantum radiation theory gives a different result. Therefore it is possible to test this effect experimentally and either confirm or rule out a hydrodynamic model for Schroedinger wave mechanics. An experiment is proposed to make such a test. It involves an electron microscope with a Wien filter for producing monochromatic beam electrons and an accurate energy measurement of the particle after passing through a local force field.
It is shown that the hydrodynamic interpretation of a charged quantum particle leads to a different theoretical prediction for low energy bremsstrahlung than does quantum electrodynamics (QED). In the calculations, the electromagnetic fields are treated classically in the hydrodynamic case, but are quantized in QED. Calculations show the hydrodynamic model to have a different and more sensitive dependence on the size and shape of the radiating particle's wave packet then does QED. In particular it is shown that bremsstrahlung is sometimes greatly reduced when the force acting on the particle is localized to a volume small compared to the particle's wave packet. QED exhibits no such reduction. Therefore it is possible to test this effect experimentally. An experiment is proposed. It involves an electron microscope with a Wien filter for producing monochromatic beam electrons and an accurate energy measurement of the particle after passing through a local force field.
Low energy bremsstrahlung formulae are derived for a particle beam of charged bosons forming a Bose-Einsten condensate. The expression for energy radiated consists of two terms in this case. One of them, the larger one in the limit of large numbers of Bosons in the state, is proportional to the number of bosons squared and has the same form as one obtains in a hydrodynamic model of quantum wave mechanics. This term is sensitive to the size and shape of the wave packet especially when the force field causing acceleration is localized in extent. The second term, identical to the single particle scattering formula, is less sensitive to the wave packet size and shape and is proportional to the number of bosons in the condensate. The conclusion is that for a Bose-Einstein condensate the radiated bremsstrahlung is a sensitive function of the wave packet shape which is quite different than for a beam of incoherent particles which do not show very much dependence on the wave packet. Only lowest order radiation is calculated. It is also found that to lowest order there does not exist any situation in which the radiation loss from a coherent state of bosons vanishes completely, so that there is no analog of superconductivity in a particle beam of this type at least within the net of assumptions made in this paper. The amount of radiation can be greatly suppressed however, as it is a sensitive function of the form of the wave function.
We investigate, both experimentally and theoretically, the interpretation of the free-electron wave function using spontaneous emission. We use a transversely wide single-electron wave function to describe the spatial extent of transverse coherence of an electron beam in a standard transmission electron microscope. When the electron beam passes next to a metallic grating, spontaneous Smith-Purcell radiation is emitted. We then examine the effect of the electron wave function transversal size on the emitted radiation. Two interpretations widely used in the literature are considered: (1) radiation by a continuous current density attributed to the quantum probability current, equivalent to the spreading of the electron charge continuously over space; and (2) interpreting the square modulus of the wave function as a probability distribution of finding a point particle at a certain location, wherein the electron charge is always localized in space. We discuss how these two interpretations give contradictory predictions for the radiation pattern in our experiment, comparing the emission from narrow and wide wave functions with respect to the emitted radiation's wavelength. Matching our experiment with a new quantum-electrodynamics derivation, we conclude that the measurements can be explained by the probability distribution approach wherein the electron interacts with the grating as a classical point charge. Our findings clarify the transition between the classical and quantum regimes and shed light on the mechanisms that take part in general light-matter interactions.
The quantum theory of radiation, formulated in wave-mechanical language but in terms of running waves, is shown to lead under suitable conditions to the classical theory of emission by a particle as a first approximation. Non-relativistic mechanics is used, and the limitations of the method are brought out in terms of classical theory. The characteristic quantum phenomenon of the Compton effect requires that the Compton recoil shall exceed the spread in momentum of the particle, and so that the wave-packet shall greatly exceed in diameter the wave-length of the incident radiation; this condition is realizable on any scale of magnitude. For quasi-classical motion just the reverse is required; furthermore, if the motion is to last for a number of waveperiods, the wave-length must greatly exceed mch (m=massoftheparticle). The classical packet-motion arises from combinations between quantum-states of the particle-field system; this fact suggests that the photon is not a fundamental constituent of the field but only one possible aspect of its action. The infinite "zero-energy" associated apparently even with the lowest energy-state of the field implies no electromagnetic field intensities at any point. Whereas for problems on energy or momentum it is customary to represent an incident wave-train by a single typical quantum state, to obtain motional phenomena of classical type a more complete expression such as that given in the paper must be used. The physically empty field likewise corresponds to a mixture of quantum states but without correlation among their amplitudes.
Classical electromagnetic radiation from quantum currents and densities are calculated. For the free Schrodinger equation with no external force it's found that the classical radiation is zero to all orders of the multipole expansion. This is true of mixed or pure states for the charged particle. It is a non-trivial and surprising result. A similar result is found for the Klein-Gordon currents when the wave function consists of only positive energy solutions. For the Dirac equation it is found that radiation is suppressed at lower frequencies but is not zero at all frequencies. Implications of these results for the interpretation of quantum mechanics are discussed.
In recent articles by this author, [ S. Karp , Statistical properties of ensembles of classical wave packets, J. Opt. Soc. Am.65, 421 ( 1975); S. Karp , Test for the nonexistence of photons, J. Opt. Soc. Am.66, 1421 ( 1976)], a radiation model was proposed that could lead to the identification of certain classical properties of the field, based upon photoelectric counting experiments. Mandel [ L. Mandel , Photoelectric counting measurements as a test for the existence of photons, J. Opt. Soc. Am.67, 1101 ( 1977)] responded by asserting that “It follows that for any field for which a classical wave description exists, in the sense that the phase-space density ϕ({ν}), and therefore P(u), are non-negative it is impossible to distinguish between photons and light waves in photoelectric counting experiments.” This statement is based upon the derivation of similar photoelectron counting equations using quantum and classical techniques. It is the mathematically loose associations and subsequent rigid physical interpretation implied in relating the two equations that is under contention. It seems to us that the model-computation-effect approach to physics is still solvent. In particular, if we can model an effect as small as the radiation from an individual electron and produce a predictable effect, then the physics underlying the model must be seriously considered.