This paper will present the Reciprocal System theory of electrons and currents and compare it with the conventional theory
1. The Electron
According to present theory1 electrons are classified (along with muons and neutrinos) as leptons, meaning that they are not affected by the strong interaction of nuclear forces but suffer the weak interaction that causes beta decay. These subatoms are all considered to be fermions: they obey Fermi-Dirac statistics, have spin s =½, and have spinor-wave functions that satisfy the Dirac equation. The present theory does not yield equations enabling the calculation of electron mass, charge, and magnetic moment. The empirical values are:
| mass: m = 9.109*10-31 kg |
(1)
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| charge: e = -1.601*10-19 coulombs |
(2)
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| magnetic moment: ue = 9.28*10-24 joule/tesla |
(3)
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It is obviously tempting to picture an electon as a spinning sphere of electric charge whose radius is determined by the dimensional relation e2/a = mc2 at which the electrostatic self-energy of the charge distribution is comparable with the relativistic energy of the rest mass. This classical electron radius, a = 2.81785*10-15 m, is an important scale parameter in physics; but the uniqueness of e, the arbitrariness of the quantization rules, and the difficulty of making it properly relativistic, forbid such a purely classical model.
Note that for this radius, and for a spin angular momentum of ½ Ã3h, the angular velocity of the electron must be 2*1025 rad/sec — giving an equatorial speed of about 200c!
b. Reciprocal System
The Reciprocal System is much more specific on the details of electron attributes than conventional theory. My previous papers3 4have described the shape, size, and all motions constituting the electron.
The electron is a spherical particle resulting from the rotation of a single photon. The frequency of the photon is
| n phot = 2R = 6.576115*1015 cycles/sec |
(4)
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(Here R is the Rydberg frequency). The rotational speeds in revolutions per second around the three axes are r/p- 2R/p - 4R/p or in terms of rev/sec
| welec= 1.0466212*1015rev/sec. - 2.0932424*1015 rev./sec -4.1864848*1015 |
(5)
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The electron may be charged or uncharged. If charged, the electron has an added rotational vibratory motion of
| n-elec = R/2p = 5.233106*1014 cycles/sec |
(6)
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The diameter d of the electron is one natural space unit, reduced by the appropriate inter-regional ratio (142.22 here). Thus,
| d = 4.55884*10-8/142.22 = 3.2054 Å |
(7)
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2. Electron Flow
a. conventional theory
According to present theory, conduction in metals takes place by movement of the electrons in the outermost shells of the atoms making up the crystalline structure of the solid. These electrons reach an average drift velocity which is directly proportional to the electric field intensity
| vd = mE |
(8)
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where µ, the mobility, has the units m2/V*s. For a conductor of length l, conductivity ó(siemans per meter), and cross-sectional area A, eq. (8) may be rewritten as
| vd = (m*1/(s*A))*I m/s |
(9)
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EXAMPLE: For a copper conductor 100 mm long and 3 mm in diameter, what is the average drift velocity of the electrons if the current is 10 amps?
For copper,
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s = 5.8*107 S/M - |
Here
| A = ¼ p (3*10-3)2 = 7.0686*10-6 m² |
Thus,
| vd = (.0032*.1/(5.8*107*7.0686*10-6))*10 = 7.805*10-6 m/s |
b. Reciprocal System
In the Reciprocal System, the natural unit of velocity is 2.99793*108 m/s (the speed of light) and the natural unit of current, which is also a velocity, is 1.0535*10-3 amperes. The conversion is thus
| 2.99793*108 m/s/1.05353*10-3 amps = 2.8456048*1011 m/s/amps. |
Hence the “drift” velocity of electrons (here uncharged and massless) in the Reciprocal System is
| vd = 2.846*1011*I m/s |
(10)
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EXAMPLE: For the case of the previous example,
| vd = 2.846*1011*10 = 2.846*1012 m/s |
(11)
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The answer of the Reciprocal System is 3.646*1017 times the answer of conventional theory!
Of course, the number of electrons passing a given point per second must be the same in both theories.
In the conventional theory,
| N = (10 C/s)(1 electron/1.6*10-19C) = 6.25*1019 elec/s |
In the Reciprocal System,
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N = 3.15842*106 esu/s*1 electron/4.80287*10-10esu *10 amps/1.05353*10-3 amps |
The difference in “drift” velocities must therefore be due to vastly different numbers of electrons in the matter of the two theories. More about this in another paper.
- Encyclopedia Britannica, Vol. 6, pp. 665-672.
- Ibid., p. 667.
- R. Satz, “Further Mathematics of the Reciprocal System,” Reciprocity, Vol. X, No. 3.
- R. Satz, “Photoionization and Photomagnetization in the Reciprocal System,”Reciprocity, Vol. XII, No. 1.