U27  The orbit in endless space: the uniform (k = 0) motion
  1    D(k -> 0 along x) / w_p^2: longitudinal xx (expect 1), transverse yy (expect 0)      1.000000 -1.31e-10 
  2    force on one quon from all other quons when every quon shifts by the same vector     0 (relative positions unchanged) 
  3    so the restoring force on the uniform motion comes only from the continuum (U23), as Aspden uses                    
  4    orbital current density of the two frames, sigma x (relative speed c)                         1.855e+26 A/m^2
  5    balanced exactly by the displacement current eps0 dE/dt of the k = 0 mode, so B = 0                     

U28  Normal modes of the endless simple cubic quon lattice (Ewald dynamical matrix, rigid continuum)
  1    eigenvalues w^2/w_p^2 at k = (0.7, 1.3, 0.4) with Ewald eta = 1.5                    -0.000113 0.072386 0.927728 
  1    eigenvalues w^2/w_p^2 at k = (0.7, 1.3, 0.4) with Ewald eta = 1.9                    -0.000113 0.072386 0.927728 
  1    eigenvalues w^2/w_p^2 at k = (0.7, 1.3, 0.4) with Ewald eta = 2.4                    -0.000113 0.072386 0.927728 
  2    sum rule: trace D(k)/w_p^2 at 5 random k (sum rule: exactly 1)                       1.000000 1.000000 1.000000 1.000000 1.000000 
       path    point      w^2/w_p^2 (three branches; negative = unstable)
       G-X   t=0.00   -0.00000  -0.00000  +1.00000
       G-X   t=0.25   -0.00768  -0.00768  +1.01535
       G-X   t=0.50   -0.02615  -0.02615  +1.05229
       G-X   t=0.75   -0.04453  -0.04453  +1.08906
       G-X   t=1.00   -0.05212  -0.05212  +1.10424
       X-M   t=0.00   -0.05212  -0.05212  +1.10424
       X-M   t=0.25   -0.05808  +0.04804  +1.01003
       X-M   t=0.50   -0.07244  +0.27063  +0.80181
       X-M   t=0.75   -0.08677  +0.46978  +0.61698
       X-M   t=1.00   -0.09269  +0.54635  +0.54635
       M-G   t=0.00   -0.09269  +0.54635  +0.54635
       M-G   t=0.25   -0.08060  +0.45365  +0.62695
       M-G   t=0.50   -0.04935  +0.24934  +0.80002
       M-G   t=0.75   -0.01510  +0.06877  +0.94633
       M-G   t=1.00   -0.00000  +0.00000  +1.00000
       G-R   t=0.00   +0.00000  +0.00000  +1.00000
       G-R   t=0.25   +0.05855  +0.05855  +0.88290
       G-R   t=0.50   +0.18949  +0.18949  +0.62102
       G-R   t=0.75   +0.29773  +0.29773  +0.40453
       G-R   t=1.00   +0.33333  +0.33333  +0.33333
       R-X   t=0.00   +0.33333  +0.33333  +0.33333
       R-X   t=0.25   +0.27203  +0.32957  +0.39840
       R-X   t=0.50   +0.13119  +0.25930  +0.60951
       R-X   t=0.75   -0.00024  +0.07281  +0.92743
       R-X   t=1.00   -0.05212  -0.05212  +1.10424
  3    lowest w^2/w_p^2 found (path and 16^3 Brillouin-zone grid)                                     -0.09269 
  4      at k (units of pi/d)                                                               +1.000 +1.000 +0.000 
  5    fraction of grid modes with w^2 < 0 (unstable)                                                    0.184 
  6    at X: branch frequencies hbar w (keV), using hbar w_p = 361.3 keV                    -82.5 -82.5 +379.7 keV (neg = imaginary)
  7    spin frequency of Aspden's photon unit, Omega/4                                                   127.7 keV
  8    body-centred cubic lattice, same method: lowest w^2/w_p^2 and unstable fraction          +0.00297 0.000 

U29  Magnetic (Darwin) coupling between the moving quons of a spinning 3x3x3 photon unit
  1    pair sum over the 351 pairs, [v_i.v_j + (v_i.n)(v_j.n)]/r (units w^2 d)                         97.4412 
  2    added inertia I_D/I = (3b/d) S / 36, unscreened                                                  29.342 %
  3    skin depth of the surrounding lattice c/w_p (units of d)                                         0.8568 
  4    added inertia with the surrounding lattice screening the field (Yukawa, length c/w_p)              9.059 %
  5    change actually needed to close the 0.6 ppm gap (U22)                                          0.000041 %
  6    carried through Aspden's chain (unscreened): odd N and 1/alpha                          3991  177.22292 
  6    carried through Aspden's chain (screened): odd N and 1/alpha                            2391  149.44549 

U30  Speeds do not depend on the picture: 27 quons holding hbar at Omega/4
  1    kinetic energy hbar Omega/8                                                                       63.87 keV
  2    rest energy of 27 quons                                                                          562.66 keV
  3    ratio                                                                                            0.1135 
  4    rms speed sqrt(2 KE / 27 m0), any pattern of circular motion at that frequency                   0.4765 c

U31  The wave picture: spreading the same angular momentum over more quons
  1           27 quons sharing it (same sum of squared radii, same I): rms speed, mass correction 0.47649 c   1.14e+05 ppm 
  1         1000 quons sharing it (same sum of squared radii, same I): rms speed, mass correction 0.07830 c   3.07e+03 ppm 
  1       100000 quons sharing it (same sum of squared radii, same I): rms speed, mass correction 0.00783 c   30.7 ppm 
  1     10000000 quons sharing it (same sum of squared radii, same I): rms speed, mass correction 0.00078 c   0.307 ppm 
  2    quons needed for the mass correction (v^2/2c^2) to fall below 0.41 ppm                         7.47e+06 
  3      side of that cube of quons, in lattice spacings and in metres                           195  1.25e-10 m
  4    Bohr radius, for scale                                                                         5.29e-11 m
