Relativistic mechanics - mechanics that studies the motion of bodies at velocities close to the speed of light.
On the basis of special relativity theory to analyze the concept of simultaneity of two events that are taking place in different inertial reference systems.This is the law of Lorentz.Given a fixed system of cooling and system H1O1U1, which moves relative to the system of cooling at a velocity V. We introduce the notation:
HOU = K = K1 H1O1U1.
We assume that the two systems have special installation with solar cells, which are located at the points of AC and A1C1.The distance between them is the same.Exactly in the middle between A and C, A1 and C1 are, respectively, B and B1 in the band of the placement of lamps.Such bulbs are lit simultaneously at the moment when the B and B1 are opposite one another.
Suppose that at the initial time frame K and K1 are combined, but their instruments are offset from each other.During the movement of K1 relative to K with velocity V at some point B and B1 equal.At this time, light bulbs, which are located at these points, light up.The observer, located in the K1 detects simultaneous occurrence of light A1 and C1.Similarly, an observer in the K system captures simultaneous appearance of light in A and C. In this case, if an observer in the K system will record the propagation of light in the K1, he noticed that the light that came out of the B1, does not come at the same time to the A1 and C1.This is due to the fact that the system K1 is moving with velocity V relative to the system K.
This experience confirms that an observer on the clock in the K1 event in the A1 and C1 occur simultaneously and bounds observer in K such events willnot both.That is, the time interval depends on the state of the reference system.
Thus, the results of the analysis show that equality is accepted in classical mechanics, is considered void, namely: t = t1.
Given the knowledge of the basics of special relativity, and as a result of the analysis and of the set of experiments suggested Lorenz equations (Lorentz transformations), which improve classical Galilean transformations.
Let the system K is a segment AB, which coordinates all A (x1, y1, z1), B (x2, y2, z2).From the Lorentz transformation it is well known that the coordinates y1 and y2 and z1 and z2 are changed with respect to the Galilean transformation.The coordinates x1 and x2, in turn, vary with respect to the Lorenz equations.
Then the length of the segment AB in the K1 is directly proportional to the change in the segment A1B1 K. Thus, there is the relativistic length contraction of the segment due to the increased speed.
From the Lorentz transformations do the following conclusion: at a speed that is close to the speed of light, there is a so-called time dilation (twin paradox).Let
in K time between two events is defined as: t = t2-t1, and in the K1 time between two events is defined as follows: t = t22-t11.The time coordinate system, with respect to which it is considered fixed, the system is called the proper time.When the proper time in the K more than the proper time in the K1, it can be said that the rate is not zero.
In the moving system K there is a delay time, which is measured in the stationary system.
From mechanics we know that if the bodies move with respect to a coordinate system with the speed V1, and such a system is moving relative to the fixed coordinate system with a speed V2, the speed of bodies relative to the fixed coordinate system is defined as follows: V = V1 + V2.
This formula is not suitable for determining the velocity of the body in relativistic mechanics.For such mechanics, which uses Lorentz transformation formula holds:
V = (V1 + V2) / (1 + V1V2 / cc).
