Mathematical model of the Space
10. "Paradoxes" of a relativity of systems of
coordinates
Two
P-0 will move with speeds below C if at the moment of time t=0 at their
interaction the distance centre to centre is more 1 (see than the explanatory in
the chapter 2). P-0, moving with speed is lower C, has characteristics of
neutrino. It is obvious, that the weight of neutrino is vector size as speed of
distribution of a wave in moving system of coordinates жv depends on a
direction
m v = 4/
Сv
Tv (94)
At experiments
interaction of neutrino with trial weight occurs on a beam of movement.
Therefore the observably weight neutrino corresponds to size of weight of
frontal area.
Speed of a wave in a
direction of movement СX =
C-v, then
mvX = 4 /
(C - v)Tv = 4 (1 -
v2/C2) 0,5/ (C-v)T0 = 4((C +v) /
(C-v)) 0,5/ CT0
mvX =
m0((C +v) / (C-v)) 0,5
(95)
Here
m0 and T0 - characteristics motionless P-0.
Speed of a wave in a
direction, perpendicular to a direction of movement, СY = (C2 -
v2) 0,5, then
mvY = 4 /
Tv(C2 - v2)
0,5= 4(1 - v2/C2) 0,5/
T0(C2 - v2) 0,5= 4 / CT0
= m0
(96)
The observably weight
of a photon is characterized by that energy which transfers a photon at
collision with a particle. Interaction of photons with particles in a direction,
perpendicular to a direction of its movement, is impossible, since the photon
has speed limit of movement that excludes an opportunity of rapproachement with it. Therefore any influence is carried
out by frontal area, and its character is defined by a corner of a meeting with
a particle. The delayed photon after collision turns in a neutrino, which
interaction with particles gives zero for the period of pulsations energy of
transfer of influence and consequently it is not found out at experiments. For
this reason the photon, having energy, has zero observably weight.
Moving with speed C
P-0 has the maximal kinetic energy which is proportional to acceleration which
is tested with weight P-0 at change of speed of movement from zero up to C in
time T0/4
Eкmax =
m0C2 = 4C2 / CT0 =
At movement P-0 with
speed of a wave the period of its pulsations Tc = ∞. Internal potential energy of
field P-0 thus has maximal size EP = m0C2, and
kinetic energy of internal movement is equal to zero E0 = 0. If speed
P-0 becomes equal to zero kinetic energy of external movement is equal to zero
Eк = 0, and
kinetic energy of internal movement will have the maximal
size
E0 =
m0C2
(98)
P-0, moving with speed
v, has energy of internal movement in a direction of
movement
E0vX = 4(C - v) / Tv
= 4(C - v) (1 - v2/C2) 0,5/ T0 = (
= (4C2 / CT0 - 4C2v /
C2T0) (1 - v2/C2) 0,5= (m0C2 -
m0C2 v/C) (1 - v2/C2)
0,5=
= m0C2 (1 - v/C)
(99)
In a direction,
perpendicular to a direction of movement, P-0 has energy of internal
movement
E0vY = 4(C2 - v2) 0,5/ Tv
= 4(C2 - v2) 0,5(1 -
v2/C2) 0,5 / T0 = 4(C2 -
v2) / CT0 =
= 4C2 / CT0 – 4v2 / CT0 =
m0C2 - m0v2 = m0C2
(1 - v2/C2) =
= E0(1 -
v2/C2)
(100)
The owner of
characteristics of weight of a particle, are spherical spiral waves of
gravitational weight of Vacuum, which cause a degree of influence of this
particle on other structures of substance. Speed of displacement of
gravitational weight on a site of interaction with unit in the motionless
particle having frequency of units and ω, changes under the
law
vg0 = C sinωt
Distance of
displacement of gravitational weight in directions X, Y and Z in time a quarter
of the period of a wave of unit
R0X(YZ) =
0∫To/4C
sinωtdt = - C/ω ·
cosωt│0To/4 = -
C/ω = CT0 / 2π
(101)
If the particle goes
with speed v speed of displacement of gravitational weight in a direction of an
axis X in system of coordinates of a particle will be
vgХ = C sinωt -
vХ
At
vgХ
= 0, sinωt = v/C and t = 1/ω · arcsin
v/C.
The distance of
displacement in a direction of an axis X during interaction with unit in system
of coordinates of a particle will be
Rv±X =
t∫To/4C
sinωtdt - t∫To/4vtdt
= - C/ω · cosωt│1/ω · arcsin v/C
To/4 -
vt│1/ω · arcsin v/C
To/4
= - C/ω(cosωT0/4 – cos(ω/ω arcsin v/C)) –
v(T0/4 ±1/ω · arcsin v/C) =
= CT0 / 2π · (1 - v2/C2)
0,5- vT0 / 2π · (π/2 ± arcsin v/C) =
= CT0
/ 2π · ((1 - v2/C2)
0,5- v / C · (π/2 ± arcsin v/C))
(102)
Comparing (101) and
(102), it is possible to draw a conclusion, that time during which the
gravitational weight tests acceleration, will be
Tv±X = T0 ((1 -
v2/C2)
0,5- v / C · (π/2 ± arcsin v/C))
(103)
Speed of weight in a
direction, perpendicular to a direction of movement of a particle, does not
depend on speed of a particle
vg0 = vgY = vgZ = C sinωt
Therefore
TvY = TvZ = T0 (104)
Speed of distribution
of spiral waves in system of coordinates of a moving
particle
С’v+X = C – v
С’v-X = C + v
С’vY = С’vZ = (C2 - v2)
0,5
(105)
Length of a wave in
moving system of coordinates
λ’v+X = (C – v) Tv+X
λ’v-X = (C + v) Tv-X
λ’vY =
λ’vZ = (C2 - v2)
0,5T0
(106)
If the particle in
weight m2 goes after a particle in weight m1 on an axis X with speed
v characteristics of their interaction will be defined by working length of a
wave be relative each other
λ’vX1-2 = (C v-X – v)
Tv-X1 = С
Tv-X1
λ’vX2-1 = (C v+X + v) Tv+X2 = СTv+X2
(107)
Working lengths of
waves of the particles moving in parallel, on axes Y and Z will
be
λ’vY1-2 =
λ’vY2-1 =(C2 vY +
v2) 0,5T vY =
CT0
λ’vZ =
λ’vY = CT0
(108)
Thus, the moving
particle radiates electromagnetic waves, which length depends on a direction of
movement
λ’v±X = CTv±X = CT0((1 -
v2/C2)
0,5± v / C · (π/2
- arcsin v/C))
λ’vZ = λ’vY = CT0
(109)
The geometrical sizes
of volume of the space filled with a particle and own fields closed on it, it is
characterized by size R0. For any instant of time of distance between
particles are characterized by number K spiral waves through, which
communication between particles is carried out. This number will not change if
to assume free movement of all system of particles. But the length of waves will
change according to (109).
Average value of
length of a wave in volume of space on a direction of axes
λ’vX =
λ’vXav = (λ’v+X + λ’v-X) / 2 = CT0(1 -
v2/C2)
0,5
λ’vZ = λ’vY = CT0
(110)
Thus,
the linear sizes of bodies in a direction of movement will
be
L’ v = L 0 (1 - v2/C2)
0,5
(111)
This
change can not be revealed in moving system of coordinates, if for this purpose
to use the tools which are taking place in the same system of coordinates as
their sizes will undergo similar changes.
The weight of a moving
particle is equal
m’v±X = 4 / λ’v±X = 4 / CT0((1 -
v2/C2)
0,5± v / C · (π/2
- arcsin v/C)) =
= m0 / ((1 - v2/C2)
0,5± v / C · (π/2
- arcsin v/C))
m’vY = m’vZ = m0 (112)
The gradient of energy
of a moving particle is equal
E’v±X = 4 / T’v±X =
= E0 / ((1 - v2/C2)
0,5± v / C · (π/2
- arcsin v/C))
E vY = E vZ = E0
(113)
Macro bodies consist of the big number of cooperating
particles. This interaction is carried out by means of the spiral spherical
waves extending as in direct, and in the opposite direction. And, all directions
are equal in rights, as waves of cooperating particles move towards. Therefore
characteristics of the body consisting from N of number of particles of various
weight conditionally it is possible to present as the characteristic of the
body, consisting them N numbers of particles of identical weight mav and average length of a wave in all
directions. Thus lengths of waves concerning a direction of movement of a body
will be
λ’ vXav = λ 0 (1 - v2/C2)
0,5
λ’ vY = λ’ vZ = λ 0
(114)
The physical processes
occuring in bodies, consist on macro level of the big
number of the interactions extending in direct and return directions. Therefore
in moving system of coordinates time of transfer of interaction for the big time
interval also is equal to average time of transfer of
interaction
T’vX = (T’v+X + T’v-X ) /2 = T0(1 -
v2/C2)
0,5
T’vY = T’vZ = T0
(115)
In
absolute (motionless) system of coordinates time of moving system of coordinates
can be expressed
TvX = T’vX / (1 - v2/C2)
0,5
TvY = TvZ = T0
(116)
Full
time of fulfilment of event for the moving
object, including
set of elementary time intervals of transfer of influences on all directions, in
absolute system of coordinates will be
3Tv =
(TvX +
TvY + TvZ ) = ((T’vX / (1 - v2/C2)
0,5+ T’vY + T’vZ)) = ((T’vX / (1 - v2/C2)
0,5+ TvY + TvZ))
But
TvY = TvZ = Tv, therefore from here
follows
Tv = T’vX / (1 - v2/C2)
0,5
(117)
The weight and energy
of the moving object consisting from N of average particles, will
be
M vX = Nmv = Nm0 / (1 -
v2/C2) 0,5
M vY = M vZ = Nm0 = M0
(118)
E vX
= NEmv = NEmo / (1 - v2/C2)
0,5
E vY = E vZ = NEmo
= E0
(119)
Kinetic energy of
moving object is equal to increase of its energy a direction of movement (see
97)
E К = E vX - E0 =
= 4C2 / СT0(1 - v2/C2)
0,5-
4C2 / СT0 = M vC2 -
M0C2
E К = M vC2 -
M0C2
(120)
The level of density
of Vacuum in the field of existence P-0, particles or macro bodies can change
the waves of density caused by dynamics of Space. Thus the quantity of
M+ and the M- participating in pulsations
P-0 will change accordingly. But simultaneously proportionally force of
interaction between these weights will change also. Therefore the period of
pulsations and length of a wave will not change. According to the theory of
elastic fluctuations
T = 2π(m / f) 0,5= 2π(P / f)
0,5
(121)
Where T
– period of pulsings,
m – gravitational weight of
Vacuum,
P – density of Vacuum,
f -
force of interaction М+ and
М- .
Speed of
a wave at changes of density also will not change
C = (f / P) 0,5
(122)
From
here follows, that observably weight P-0 does not change at any changes of a
level of density of Vacuum from positive up to a negative phase of peak surfaces
of gravitational waves.
If the zero level of
density of Vacuum has changed from Р10 up to Р20, that force of interaction of
M+ and M- has changed thus from
fR1 = 1/R P1max up to fR2 = 1/R
P2max . But Р0 =
1/R0 Pmax , where
R0 = CT0 / 4, therefore
Р10
= 4/CT0
· P1max
Р20
= 4/CT0
· P2max
Or
Р10
/
Р20
=
P1max / P2max
(123)
Change of amplitude of
density changes power characteristics P-0. Gravitational energy of absolute
weight P-0 is an energy of density
МВ of
Vacuum. Gravitational energy P-0 for Р10 and for Р20
E g1 =
МВ1C2 и E g2 = МВ2C2
(124)
Potential energy of these two conditions
E g2-1 = E g2 - E
g1 = (МВ2 - МВ1)C2
(125)
Here
МВ1 =
1/R·Р1max
cosωtR
МВ2 = 1/R·Р2max cosωtR
From
here
МВ2
= МВ1P2max /
P1max = МВ1P20 / P10
(126)
Potential gravitational energy
E
gP2-1 = МВ1 (P20 / P10 -
1) C2
(127)
At
moving P-0 from area Р10 in area Р20 work is made W =
E gP2-1.
The increase of
density of Vacuum in the field of existence of a particle conducts to occurrence
of a stream of energy of more dense Vacuum, which is
transferred by positive electric gravitational fields to units of a particle and
is involved in the closed streams of M+ and
M- of its fields. The density of M+ and
M- in these streams grows. Gravitational energy of a
particle is accordingly increased. At decrease of a level of density of Vacuum
in the field of existence of a particle, it gives Vacuum via negative electric
gravitational fields. Gravitational energy of a particle thus is reduced.
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