the reciprocal of
ALPHA aka the FINE STRUCTURE CONSTANT
is conjectured to be a variable.
RATIO of SOLID VOLUME to OCCUPIED SPACE VOLUME

defined as the total volume of the spheres within a cluster**
either divided by
the corresponding convex hull volume*
using the sphere centers of the cluster as their point set
or the volume of a containing sphere of least radius

All decimal values in table are to be multiplied by 10-3



radial sweep sqrt value
sphere count

convex hull

volume*
occupied space ratio
times IQ
Physics volume**
occupied space ratio
  
10 201 81
1.294506198
0.910840
 143
0.738451746
50 2,123 1,332
0.834534685
0.799038
 1,503
0.739474053
100 5,979 3,829
0.817537691
0.787482
4,220
0.741804517
500 66,427 45,491
0.764575965
0.755089
46,902
0.741563814
1,000 187,561 130,076
0.754994849
0.748272
132,561
0.740844248
5,000 2,094,189 1,473,491
0.744161328
0.742555
1,481,183
0.740296574
10,000 5,924,709 4,171,165
0.743717919
0.741982
4,189,104
0.740533084
25,000 23,416,947 16,525,763
0.741937635
0.741198
16,558,144
0.740486669
50,000 66,232,665 46,777,615
0.741366197
0.740916
46,832,098
0.740503706
75,000 121,672,483 85,963,900
0.741096706
0.740778
86,036,919
0.740467746
100,000 187,327,915 132,375,520
0.740957746
0.740720
132,462,170
0.740473047
200,000 529,841,021 374,500,404
0.740784541
0.740635
374,658,191
0.740472561
300,000 973,388,007 688,071,580
0.740714751
0.740599
688,290,186
0.740479494
400,000 1,498,629,259 1,059,407,899
0.740678303
0.740579
1,059,691,402
0.740480147
500,000 2,094,392,461 1,480,649,180
0.740635488
0.740560
1,480,963,201
0.740478445
600,000 2,753,155,563 1,946,401,555
0.740622550
0.740550
1,946,776,198
0.740480022
700,000 3,469,367,171 2,452,812,754
0.740601336
0.740541
2,453,217,955
0.740479010
800,000 4,238,749,385 2,996,798,896
0.740591566
0.740533
2,997,257,095
0.740478350
900,000 5,057,848,861 3,575,959,749
0.740579776
0.740529
3,576,454,756
0.740477275
1,000,000 5,923,847,851 4,188,290,493
0.740569829
0.740528
4,188,790,205
0.740480981
2,000,000 16,755,147,489 11,847,692,278
0.740479623
0.740507
11,847,687,835
0.740479901
10,000,000 187,328,343,745 132,459,862,200
0.740487645
0.740472835
 132,461,186,812
0.740480240
100,000,000 5,923,843,773,659 4,188,748,348,300
0.740487871
0.740480466
 4,188,790,236,202
0.740480467

approximated values

IQ = Isoperimetric quotient of a sphere =
36 pi times the volume 2 / area 3

area values have not been included in this documentation

 

Another possible manner would be to use the maximum radius of a sphere center, however, like the other methods, it all dependes upon how one mathematically determines the extent of the container.

* It should be noted that ccp close packed sphere clusters approach 0.7404804897 as do BOTH series above; one from each direction.

This is the same ratio as the volume of a sphere inscribed into a rhombic dodecahedron.

pi / √18
 

Since current Physics would imagine my cluster as solid,

then the the second set is perhaps more appropriate to compare against.

I propose that this ratio; of solid to occupied space,

is one in the same as the fine structure constant.


  The conjucture being that this the fine structure is not a constant

but rather manifests itself as this unique ratio for each cluster.


The contents of this web site are © Copyright Steve Waterman or a third party contributor where indicated. You may print or save an electronic copy of parts of this web site for your own personal use. Permission must be sought for any other use.