The article was declined
by the journals “Physics Letters
A” and “Physics Letters B” (Netherlands).
PLANCK’S PARTICLES 
AND 
– POSSIBLE CONNECTION WITH OTHER PARTICLES
V. T. Vertushkoff
Dniepropetrovsk 49128, Ukraine
Date
of place: 14 October 1999 year.
d-, s-, b- quarks
as well as electron are formed by Planck’s massles particles 
and 
.
M0 is the mass of rest of a system consisting of two immovable point
masses m1
and m2. The difference [M0-(m1+m2)]c2=Dmc2 at Dm<0 corresponds to the negative energy of
attraction in gravitation interaction [1]. In the case of
attraction M0=m1+m2+Dm, Dm<0. During the interaction
the immovable same named point charges q1
and q2 with masses m1 and m2 the value Dmc2 is a positive energy of repulsion. Then M0=m1+m2+Dm, Dm>0. It follows to expect that at electric
repulsion mass M0
will be more than the sum of masses m1+m2 at value Dm.
where the planck’s
length lg is the radius of curvature R of closed
space, containing planck’s mass mp[1]. Let’s transform the
formula of intensity g of gravitational field. The field was
created by statical closed world containing the resting mass M [1].
where R is a radius of curvature of closed world; e=–Mc2 is a vacuum energy in volume V of the closed world [1]. If we multiply the left and the right parts of the equality
by M, we shall receive
F is a force, which acting to mass m (energy
E = mc2) at the
point, being at the distance r from the field source. Another formula
Magnetic massless particle Pl represents itself closed space,
containing the charged mass mp. The charge Pl is
equal to qp»1,87´10-18
C [l]. Nonmagnetic
particle 
will
be got as a result of multiplying in early
mentioned ratios [l] lg and tg by 2p:mpc(lg2p)=Eg(tg2p)=h, where lg2p=l is
the wave length, tg 2p=T is the period of oscillation. Let's take without arguments,
that during the transformation from Pl
to 
the speed of mass mp rotating round its own axis w=keg is 35
times diminished. Accordingly the same number of times the charge qp will be diminished. 
has such characteristics:
It is supposed, that quarks d, s,
b arise at the interaction between themselves of negatively charged particles Pl– and 
.
This interaction condition two effects. 1) Particles are attracted owing to the
interaction of gravitation fields which surround
them [1]. 2) Repulsion
is owing to interaction these particles charges 
and 
.
Attraction provides the creation and the existence of quarks. Repulsion is the
creation of mass defect Dm>0 composing quark’s mass. Electrical
repulsion Pl– and 
is
proceeding with defect of mass Dm¹0. For calculations let’s use Coulomb's law and known data such
masses d-, s-, b-quarks. We shall find those distances l between
Pl– and 
in quarks, where
the value Dm>0 of electric repulsion will
correspond to quarks masses.
Ed=Dmc2=mdc2»7,5 MeV. It follows the
distance ld
between Pl– and 
in
d-quark is equal to
ke=1/4pe0 , (e0 – the electrical constant).
After the analogy we shall
receive: ls»3,74´10-17m (Es=msc2»150 MeV),
lb»1,29´10-18 m (Eb=mbc2»4350 MeV). We shall point out that ld, ls, lb,
are the inner dimensions of d-, s-, b-quarks in the space
of positive curvature CG>0. This space
was created by the gravitation field Pl–– particle.
The of electric repulsion Pl– and
is equal F=Ed/ld» 1,60´ 10 3N. Gravitational
interaction of these massless particles is proceeding with defect of mass Dm=0. So the calculation of force F
of mutual attraction Pl– and 
will be done according to the formula (1).
.
With the same force Pl– attracts 
and 
attracts Pl–.
Consequently F=2F¢»-1,13´105N.
"Centre
of masses" of
electric repulsion Pl– and
divides the section ld in relation to the direct proportion
of the particle charges in d-quark. In other words the "centre masses" is at the distance ld/35 from 
-particle
(
). Let's assume that the
position coordinates of "centre of masses"
and mass md=Dm coincide. Then
the mass of d-quark md and its charge qd become localizable at the immovable
region of space with radius r~ld/35.
Let's consider the structure of electron. We can suppose
it is created by three d-quarks. All
six incoming to e– particles (3Pl– and 3
) are rounded up by gravitation fields with the same energy Eg=mpc2
[1]. Suppose the value of energy E of
particles electric repulsion will be also the same. That is in all six pairs of
interacting particles (picture 1) one the same positive mass defect Dm=me/6
arises. Then the electric repulsion energy for each
pair of particles is equal E=Dmc2. Hence the
distance l1
between Pl– and 
in
quarks constructing the electron is equal.
.
In electron the distance l2 between two 
-particles
is equal
.
In electron the values of forces Fe of electric repulsion and Fg of gravitation attraction of particles are shown at figure 1. The powers are calculated according to Coulomb's law and formula (1). Note while d-quarks is entering into e– structure its characteristics are changing.
Magnetic moment pm and angle moment L of d-quark are created by the rotation of the outer electric and gravitation fields of Pl– - particle round the circular orbit. Let¢s assume that Pl– - particles are moving in e– along the orbits of the radius r=l1. Then the value of orbit magnetic moment pm of Pl– particle in a resting electron is equal to
pm=0,5qpcl1=0,5Eet»2mB.
Ee=qpc2 is the energy of Pl– - particle’s electric field
[1], t=l1/c=T is a
period of Pl–-particle’s rotation.
(As a result of space curvature CG >o the length of circumference rotation l of Pl–-particle’s
is equal to its radius l1, that is l/l1=1;
At t=l1/c, Eet =qpc2l1/c=qpcl1
). Orbital angle moment L
of Pl–-
particle in electron is equal L=Egt»4,07´1021ħ. The characteristics one of d-quarks in
the structure of resting electron in magnetic field
are shown at figure 2. (At the figure constructing the results of work [1] were used). The mass of electron me and its charge e
are concentrated at the static region of space of radius r~10-15 m. As a result electron can take part in
interactions which are accompanied by the effect of attraction (Dm<0). In these interactions an electron shows the charge 
and mass me=6Dm. The charge of Pl– –
particles qp»1,87´ 10-18 C doesn’t show itself in similar interactions
because of the space disconnection with electron mass me.
Fig.1 The characteristics of connections between
the particles in an electron.
L»4,07x1021ħ
Pm»4,89x10-22mB
Fig.2 The characteristics of one of d-quarks in the structure of
motionless electron in magnetic field.
References
1. V.T. Vertushkoff, Planck’s units.
E-mail: vertushkov@ua.fm
V. Vertushkoff
Kommunarovskaya str. 16,
Flat 332.
City Dniepropetrovsk,
UKRAINE, 49128