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

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 Plparticle. 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