SPATIAL EXTENSIONS AND MAGNETIC MOMENTUM OF THE
ELECTRON, THE PROTON AND THE MUON
--------------------------------------------By Ove Tedenstig, Sweden 20/8 -1998
Performing calculations on the spatial extensions of
protons and electrons, show that the proton is able
to be inhoused into the limits of an electron.
The electron, as well as the proton, are supposed being torus
particles, having radii, R , and , r , respectively, where
, R , is the radius associated to a main spin axis and
, r , is associated to the spin movements of matter in
the outer parts of the torus ring.
We start with investigating the dimensions of an
electron, based on calculations done in our electromagnetic theory and in our particle theory (see my
book "Matter Unified" ).
The magnetic momentum of the electron is determined by
the area enclosed by the radius, R , and the equivalent
electric current flow produced by its spin around
the main axis.
The velocity around the main axis is equal to the limit
velocity of space, C , calculated to :
1) ===================
C = Kt. c
===================
see 3.15C
2) ===================
where Kt = 5.3557
===================
see 3.54D
and by analogy of a higher spin velocity around, R , compared
with, r , where r = re (the classical electron radius), we get :
2
me. c
----re
2
me. C
= ------R
;
2
2
R = (C/c) .re = Kt .re
3) ===================
2
the electron main
axis radius
R = re. Kt
===================
Hence, the spin time around the electron main axis will be :
2
2. Pi.R
2. Pi. Kt .re
te = --------- = -------------C
Kt.c
4) =================
2.Pi.re
te = --------.Kt
c
=================
2.Pi.re
= -------- .Kt
c
the spin time of
electron round the
main axis, R. re =
classic electron radius
Magnetic momentum is calculated by the product of current and
the area enclosed by this current loop, hence :
5) ===============
u = i. A
===============
common formula for
calculation of magnetic
momentum, u , of a
current loop.
The area enclosed for the electron will be :
6) ===============
2
Ae = Pi. R
===============
Inserting known values of the electron as calculated above, then
gives :
e
2
2
= e/te . Ae = --------- .(Kt.re)
2.Pi.re
-------.Kt
c
e.re.c
3
= --------. Kt
2
ue = i . A
7) ========================
e.re.c
3
ue = -------- .Kt
2
=======================
=
For common use, we calculated the product e.re.c/2 to
1.6021773349E-19 x 2.8179409238E-15 x 2.99792458E8/2 =
6.7675765E-26
Hence :
8) =======================
3
ue = 6.7676E-26 x Kt
=======================
Kt has been calculated to 5.3557 before (formula 2) givning :
9) ======================
ue = 1039,64 E-26
======================
the measured value is
928.49E-26, hence some
10% too large.
The radius, R , then will be :
10) =========================
2
R = Kt .re = 80.8 fermi
=========================
The electron volume is mostly empty, meaning having the same
mass density as for vacuum itself. The matter is concentrated
into a thin shell. We will calculate the thickness of this
shell. From 3.54D we have found, that the effective active
area of the electron, taking part in different electromagnetic
processes, is equal to :
11) ==========================
2
Ae = 4.Pi. re
==========================
the effective
active area
of the electron
taking part in
physical processes
This area is represented by the area of the thin skin of matter
flowing out continuously from the electron surface, represented
by the product :
12) =========================
Ae = 2.Pi.R x d
=========================
d = then shell
thickness
Equalizing 11), 12) gives :
2
4.Pi.re = 2.Pi. R x d
;
2. re
d = --------R
13) =======================
2. re
d = ------- = 0.2 fermi
R
=======================
the shell thickness
of an electron
For the mu-on and the proton, it's also true that they are
torus particles, but their spin velocities are much slower.
Of that reason the radii, R , and , r , are near the same,
giving that the area on which the magnetical momentum shall
be calcualted on :
14) ==================================
2
Aup = Pi. (R+r)
(where r = R )
==================================
The radius, R , is calcualted from 2.17A to :
15) =======================
1/3
R = (M/me) . re
=======================
and the spin velocity from 3.23A
to :
16) =======================
2/3
v = c. (me/M)
=======================
On basis on that, the magnetic momentum for the muon and the
proton can be calcualted from :
e
2
uup = ------- . Pi.(R+R)
2.Pi.R
-----v
e.re.c
1/3
e
2/3
= ----------------. 4.Pi.(M/me)
=
2.Pi.re
------- . (M/me)
c
=
--------. 4. (me/M)
2
17) =================================
1/3
uup = 6.7676E-26 . 4.(me/Mup)
=================================
common formula for
magnetical momentum
of muon, k-on, proton
and similar particles
Hence we see, that for a muon, the magnetical momentum
(the muon mass = 206.77 electron masses ) :
will be
uu = 6.7676E-26 x 4 x 0.16911 = 4.5779E-26
The measured value is 4.49047E-26
For the proton of mass 1836.12 electron masses we get :
up = 6.6767E-26 x 4 x 0.081685 = 2.18E-26
The measured value is 1.441062E-26
Taking the relation ue/uu (formula 7 and formula 17) gives :
3
6.7676E-26
Kt
3
ue/uu = ----------- . ---------1/3 -- = 1.4783 x Kt
6.7676E-26
4.(me/Mu)
=
= 227
That is near the mass relation between the muon and the electron,
206.77, and taking this realtion with start from the measured,
exact values we confirm that:
ue/uu = 928.49E-26/4.49047E-26 = 206.77
Another observed fact is that if ue is devided by the factor
e.re.c/2, as in the formula 7) above, we get :
928.49E_26/6.7676E-26 = 137.196.
That figure is very near the fine structure constant as
apperaring in the quantum physics, inverse, equal to 137.035989..
Perhaps all that is a matter of coincidence, perhaps not because
the equivalence not is perfectly exact.
Observe, hovewer, that generating particle masses in accordance
with my particle theory, also is a function of a constant, Kt,
or Pi, rised to cube , see 8.42A.
The extension of a proton then will be :
18) ==========================================
1/3
Rp = 2* R = 2.re. (Mp/me)
= 69 fermi
(re = 2.817 940 92(38) fermi )
==========================================
The main radius of the electron (10) , was 80.8 fermi, hence
the proton get place into the electron. There is 5.5 fermi
space between the proton surface and the inner electron surface.
Interesting, indeed !