dorsal/arxiv
View SchemaRotation Representations and e, $pi$, p Masses
| Authors | Richard Shurtleff |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9907012 |
| URL | https://arxiv.org/abs/quant-ph/9907012 |
Abstract
Mass is proportional to phase gain per unit time; for e, $\pi$, and p the quantum frequencies are 0.124, 32.6, and 227 Zhz, respectively. By explaining how these particles acquire phase at different rates, we explain why these particles have different masses. Any free particle spin 1/2 wave function is a sum of plane waves with spin parallel to velocity. Each plane wave, a pair of 2-component rotation eigenvectors, can be associated with a 2x2 matrix representation of rotations in a Euclidean space without disturbing the plane wave's space-time properties. In a space with more than four dimensions, only rotations in a 4d subspace can be represented. So far all is well known. Now consider that unrepresented rotations do not have eigenvectors, do not make plane waves, and do not contribute phase. The particles e, $\pi,$ and p are assigned rotations in a 4d subspace of 16d, rotations in an 8d subspace of 12d, and rotations in a 12d subspace of 12d, respectively. The electron 4d subspace, assumed to be as likely to align with any one 4d subspace as with any other, produces phase when aligned with the represented 4d subspace in 16d. Similarly, we calculate the likelihood that a 4d subspace of the pion's 8d space aligns with the represented 4d subspace in 12d. The represented 4d subspace is contained in the proton's 12d space, so the proton always acquires phase. By the relationship between mass and phase, the resulting particle phase ratios are the particle mass ratios and these are coincident with the measured mass ratios, within about one percent. 1999 PACS number(s): 03.65.Fd Keywords:Algebraic methods; particle masses; rotation group
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"abstract": "Mass is proportional to phase gain per unit time; for e, $\\pi$, and p the\nquantum frequencies are 0.124, 32.6, and 227 Zhz, respectively. By explaining\nhow these particles acquire phase at different rates, we explain why these\nparticles have different masses. Any free particle spin 1/2 wave function is a\nsum of plane waves with spin parallel to velocity. Each plane wave, a pair of\n2-component rotation eigenvectors, can be associated with a 2x2 matrix\nrepresentation of rotations in a Euclidean space without disturbing the plane\nwave\u0027s space-time properties. In a space with more than four dimensions, only\nrotations in a 4d subspace can be represented. So far all is well known. Now\nconsider that unrepresented rotations do not have eigenvectors, do not make\nplane waves, and do not contribute phase. The particles e, $\\pi,$ and p are\nassigned rotations in a 4d subspace of 16d, rotations in an 8d subspace of 12d,\nand rotations in a 12d subspace of 12d, respectively. The electron 4d subspace,\nassumed to be as likely to align with any one 4d subspace as with any other,\nproduces phase when aligned with the represented 4d subspace in 16d. Similarly,\nwe calculate the likelihood that a 4d subspace of the pion\u0027s 8d space aligns\nwith the represented 4d subspace in 12d. The represented 4d subspace is\ncontained in the proton\u0027s 12d space, so the proton always acquires phase. By\nthe relationship between mass and phase, the resulting particle phase ratios\nare the particle mass ratios and these are coincident with the measured mass\nratios, within about one percent. 1999 PACS number(s): 03.65.Fd\nKeywords:Algebraic methods; particle masses; rotation group",
"arxiv_id": "quant-ph/9907012",
"authors": [
"Richard Shurtleff"
],
"categories": [
"quant-ph",
"hep-ph"
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"title": "Rotation Representations and e, $pi$, p Masses",
"url": "https://arxiv.org/abs/quant-ph/9907012"
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