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14PHYSICS AND MATHEMATICS
FORCE OF INERTIA AS SORT OF INTERACTION
Parfentev N.
AllRussian Institute of Kinematografy, Moscow, RF
Parfenteva N.
AllRussian Institute of Civil Engeneering, Moscow, RF
ABSTRACT
Interaction of temporary positions of the moving body is now an experimental fact. The patterns of this interaction are easily determined by the assumption that time is the imaginary coordinate. As a result, the force of inertia can be presented along with other forces as a form of interaction of time positions. The result confirms the universality of Newton's third law. General expressions for the force of inertia for the case of equal accelerated movement and movement in circumference, leading to classical formulas in non-relations interval of velocities. The offered model allows to recognize as superfluous experiments to determine the equality of gravitational and inertial masses, since in both cases we are talking about the same mass participating in different types of interaction.
Keywords: Force of inertia, interaction of time states, Wheeler experiment.
Formula of inertia Introducing
The interaction of temporary positions of the body is currently an experimental fact [5..16]. At the heart of such experiments is Wheeler's thought experiment [1], which tried to solve the problem of elementary particle dualism. The author's previous publication on this topic contained an error leading to unrealistic formulas for the force of inertia.
Previous steps by the author [2,3] attempts to interpret experiments that reveal the influence of the past and future positions of the body on its condition at any given time. However, on the basis of the formulas proposed in it, it is impossible to create a model that gives a classical expression for the force of inertia at any speed values, while the formula for Einstein's mass, as the work [4] suggests, easily leads to this expression. This removes the question of the interaction of temporary positions. In this paper, an attempt is made to develop the idea of interaction of temporal states, leading to the emergence of the power of inertia. Analysis of temporary interaction Einstein's Special Theory of Relativity is based on the transformation of Lorenz's coordinates, operating by the sum of increment of spatial coordinates from which the square of the work of increments of time is deducted at the speed of light. By imagining time as an imaginary component of a complex number, you can limit yourself to summing up all members in the interval formula. In this case, the speed should be expressed in the form of -jv, and acceleration -a. Thus, time, speed and m pulse are imaginary values, and acceleration, the forces of interaction (e.g., the strength of the elasticity of the R.Hooke) and energy are real values.
The generalization of coordinates raises the question of possible interaction in time. Like any interaction, it must be symmetrical and expressed as a work of indicators that characterize each of the temporal positions of the body. It is logical to assume that the immobile body does not experience any interaction of neighboring positions, and the interaction itself is proportional to the change in the spatial coordinate of the
body. The simplest form that meets these requirements will be the T indicator:
T =
mc2Ax
VAx2 + (jcAt)2
(1)
m-mass of a particle, c - the speed of light, (At and (Ax - small time intervals and coordinates, counted from this position. Indeed, since we are talking about one body, the product of T indicators gives the main characteristic of the body - its mass m, and the Ax in the numerator will provide zero temporary interaction of the stationary body, as well as an increase in interaction with the increase in speed. This is not the first time that physics has used a similar approach - in quantum physics the wave function is a complex number, but the square of its module gives a density of probability of finding a quantum particle in a given area of space at a given point in time. It is also interesting that the indicator contains body energy, calculated according to Einstein's formula. This suggests that the phenomenon of inertia is associated with the transformation of this energy over time.
By dividing into jcAt , we get
T =
N
-jmc v
M)2
(2)
Force of interaction of two time position body may be calculated as
T1T2
F =■
jcAt12
(3)
Let us consider the case of rectilinear uniformly accelerated motion. A body moving with speed v and T0 will be affected by the difference in forces from the temporary positions T + and T-, which are interacted in time with the position T0. In the first two states, the body has a velocity (v + Av) and (v - Av), respectively. Obviously, the forces corresponding to the temporal interaction are repulsive forces, otherwise, when moving around a circle, the sum of the forces would be differently directed towards the center.
F
1 m
_ T±To jcAt
T- Tp jcAt
—m At
M)2
\
1—(^)2
)
At speed Av « v
Vv
F =
1 m
At
1-(-)2
KCJ
1 — (S±Él)2
V C J
1 — (^)2 C
(4)
=) (5)
Assuming that for small relative values of Av,
F =
1 m
"(-)2 C
(6)
Formula (6) is a particular case of general formula (5) for relatively small speed increments. It is quite remarkable that when the body leaves the state of complete rest, this law is violated, since at zero velocity in the initial position, the interaction force is zero.
When moving in a circle between adjacent temporal positions, separated from each other by a temporal distance jAt, a force arises equal to the product of indicators divided by this interval
"= (7)
F =
1 m
The centrifugal force in this case arises due to the deviation of each of the forces from the vertical at an
angle equal to ^
As rezult Fm =
«J1—(C)2
(8)
It should be noted that with a temporary effect, the force of attraction, which is usual for the interacting masses, changes to the force of repulsion.
Conclusions
The offered model allows:
l.interpret the results of experiments carried out according to Wheeler's scheme,
2. use a harmonious form for the Lorentz interval,
3. apply a unified definition for force as a measure of interaction - Newton's second law in the accepted representation means equality of forces of spatial and temporal interaction,
Concept for force as a measure of interaction -Newton's second law in the accepted representation means equality of forces of spatial and temporal interaction,
4. to confirm the universality of Newton's third
law.
5. to obtain general expressions for the force of inertia, leading at low speeds to the classical expressions for accelerated motion and motion in a circle.
6. to recognize as superfluous experiments to determine the equality of gravitational and inertial masses, since in both cases we are talking about the
same mass participating in different types of intetrac-tion.
References
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V
v—Av
Av
AV
(
Av
m
At
1
2
Ati1-(-)
2
—mv
