Uncertainty Relations and Onion Skin Layering

By Chris Hawkings

From article at http://www.spaceandmotion.com/chris-hawkings-wave-theory.htm

Figure 1

Impression of a typical particle in cross section, showing shells
of high electromagnetic energy density surrounding a central core.

The radial fall-off of the wave's energy density ensures that the particle has no well defined boundary, as shown in figure 1. This poses the difficulty of establishing when a particle is completely detected. Clearly, a particle's detection cannot occur unless its source/sink is absorbed; we take this as the definition of particle detection.

From figure 4, the source/sink is confined to the region of the central core. Thus, particle absorption (source/sink absorption) is assured only with the complete arrival of the central core. For this to occur, the time, , during which the detector is switched on must equal or exceed the time, , it takes for the central core to arrive at the detector (i.e. ). The longitudinal width of the central core is given by and is related to and the group speed, , by . Using these three expressions and , we obtain

      (23)

Figure 4
Detector must be on for a time, Dt, greater than the time, T_g, of total reception of the central core at the detector (i.e. Dt³T_g). The distance of flight, Dz, of the central core must exceed the width, l_g, during reception of the central core at the detector (i.e. Dz³l_g).

The distance, , over which the particle travels while the detector is on must also equal or exceed the core width, , if absorption is to be assured (i.e. ). Thus,

      (24)

Pinpointing the source/sink might be regarded as certain to within the half-width of the central core, in which case the right-hand-side of (23) and (24) becomes . In either case, both the formalism and interpretation here are similar to those of the uncertainty relations.

In accordance with this principle, at rest is zero and is undefined, as expected. There is, however, one significant difference. At rest, is , placing an upper limit on equal to the Compton wavelength, . In other words, the source/sink at rest cannot be located within a region, in absolute terms, smaller than this value. This is because smaller sizes would not include the entire central core. Heisenberg's principle, of course, places no such limit, upper or lower, on . This may allow the Compton wavelength to serve as the standard way of expressing the size of all particles at rest. For the proton, this value is 1.321 fm.

Results of p-p scattering at 90^o found by Akerlof (1966) [12] reveal, for the proton, a central core of radius 0.33 fm and two outer shells at 0.50 fm and 0.92 fm from the centre. The spherical shells predicted by equation (5) are found by maximising . These maxima/minima occur (due to the factor) at , where is an integer. Using the Compton wavelength, 1.321 fm, and enumerating for 1, 2 and 3 yields 0.329 fm, 0.659 fm and 0.898 fm. Although a number of interpretations for the scattering results are possible, the correlation between measured values and those predicted by equation (5) are surprisingly consistent, especially considering that the amplitude function played no role in the calculations. Radial fall-off might explain non-detection of further layers beyond . Electron scattering experiments suggest a picture of the electron that is more akin to a 'fuzzy' point particle and which does not appear to possess the onion skin layering typical of the proton. This is not inconsistent with a particle of very small 'rest mass' (long Compton wavelength), whose energy density distribution is similar to that of figure 1. In this instance, the broad central core and shells of low energy density could readily account for the poor definition, point-like appearance and non-detection of onion skin layering.

(Note from Geoff Haselhurst - The figures in this final article from Chris Hawkings are images, as this is how I formatted his full article. See http://www.spaceandmotion.com/chris-hawkings-wave-theory.htm)Quantum-Physics