A Fluid Model of the Proton
EXTRACT: Qualitative parallels are draw between a kinetic fluid configuration in a 5 dimensional space, and 12 properties of the proton.
The model space is a simple (closed, continuous) 5 dimensional space filled with a viscid, incompressible fluid [ether].
Toroidal Energy Wave Structure
We postulate an expanding toroidal kinetic energy wave, which in cross section can be viewed as a vortex pair in a flow (Figure 1). The wave is expanding radially, which locally we associate with x5, with x4 orthogonal to the ring.
The solution to the Navier-Stokes in 5D cylindrical coordinates (Appendix A) is similar to the 3D solution, so we may use the 3D function for the velocity equationb.
Figure 1 shows the width in X5 of the fairly quiescent portion of fluid at the leading edge of the wave. This is the model’s ‘observable space’.
Such a wave could be generated by a ‘structured bang’.
Within the ‘observable space’ portion of this wave, vortex-sinks/sources could form (Figure 2). This would be a field of 4D rotation cylindrically symmetric in X5, with a sink/source at the center. This is the nuclear particle for the model.
The 4 dimensional rotation can be viewed as 2 ‘doubly orthogonal’ planes of 2 dimensional rotation. In this case the planes of rotation are: X4=X1 , X1=X2
and: X2=X3 , X3=X4
The particle’s cross-section radius would be at the discontinuity between the rotational flow and the sink/source flow.
The vortex would have 3 degrees of freedom; that is, could move in three orthogonal directions without change in energy.
Were it were not constrained by boundary conditions, the vortex would propagate with wave velocity c. Figure 3 shows the vortex-sink at an angle (θ) to UWave, It now has velocity in 3 space.
‘Acceleration’ of a vortex means increasing its angle (θ4) to the normal (X5). This would be by means of a torque and resulting precession.
The basis for inertial mass is the vortex apparent mass (ma) which is a function of its total kinetic energy. Obviously, ma is proportional to the vortex length. Figure 4 shows how this results in relativistic mass dilation.
Inertial mass as measured in particle accelerators is different for mass parallel to velocity and mass perpendicular to velocity (mlongitudinal = 3 m0, mtransverse = m0). What is actually being measured is resistance to change in angle, that is, moment of inertia (I). Figure 4 shows how this leads to the measured ‘mass’ dilation.
Electric, Magnetic Field
When stationary, the vortex rotational field is the electric field. Far field, vortices of like rotation repel, and those of opposite rotation attract. Near field, vortices of opposite rotation orbit each other, as in atomic structures.
When the vortex has velocity, it has both a rotational field in ω5, and a rotational field orthogonal to ω5: (ωnot5). ωnot5 is the magnetic field, which similarly attracts and repels rotational fields in its plane.
If the wave front trailed vorticity at the back of the wave it would experience dragb; so too, when it creates vorticity at the front of the wave. The vortex-induced drag deforms the wave. ‘Space’ is slightly warped in x5 by the vortex. This depression is a potential well.
If the vortex is a source, the jet at the front edge of the wave would induce turbulence, reducing the drag on the wave front. This would slightly mitigate the induced drag.
Any wave equation satisfying the Schroedinger equation ‘plugs into’ existing quantum theory. It remains to be shown if the wave equation for the vortex-sink meets this criterion.
The model for quantized energy states of the particle is the energy states of the ‘contained, driven, rotating, axisymmetric’ vortex. Greenspan develops and verifies the resonance eigenvalues of such driven, contained vortices. The eigenvalues he develops for the driven spherical container map closely to the allowable integers for eigenvalues of the excitation states of both the atomic and nuclear spectra.
Particle magnetic dipole
A stationary nuclear particle exhibits a magnetic dipole.
Each rotation of the tensor can be resolved into ω5 and ωnot5. ω5 is the particle’s electric field. The doubly orthogonal ωnot5 components would be the magnetic dipole.
A stationary nuclear particle has angular momentum. Obviously, so does a vortex-sink.
We know light travels long distances at a constant velocity, and that it has angular and linear momentum. It is generated by accelerating a charged particle, and has orthogonal electric and magnetic fields. It is radiated in a dipole pattern along the acceleration vector.
This points to a pair of rotating Hill’s vortices, radiated in opposite directions along the fairly quiescent front and/or back of the energy wave.
The red shift then is a reaction to the change in momentum as the photon follows the curve of ‘observable space’.
Antimatter would be a short-lived vortex-sink.
Disparity Between Electron, Proton Mass
The disparity between electron and proton masses would indicate a ‘preference’ for one rotational direction over its opposite. This could be accounted for by coriolis force, if we postulate the entire energy wave ring is rotating. This is not a very satisfying explanation.
Another option would be to say the vortices of the energy wave were not exactly identical in strength. A cross-section of the wave would describe a great circle in x4, x5. Over time, the expansion of space would appear to slow, and eventually reverse.
Very near field, the vortex-sink pair experiences the attraction of a sink for a cylinder, which may become greater than the repulsion of the ‘electric field’.
This may also bind the electron to the proton to form the neutron.
12 properties of the nuclear particle appear to have correlation to a 5 dimensional kinetic fluid model. Parallels are also found for the ‘big bang’, expanding universe