Question

Solve please 2.1 and 2.3.

2.13 Conclusion The theoretical discovery of the Lorentz transformation was an important s the learning process leading to Special Relativity, but its deep meaning was understood before Einstein. In our presentation we have made it clear that the Lorentz transformation can be derived from the two postulates of Special Relativity, which are physically more transparent than what, at first sight, appears "only" as a mathematical transformation. From the physical point of view it is more satisfactory to construct not transparent, mathematical symmetry. However, the Lorentz group constitutes the symmetry group of Special Relativity and suggests a unified view of space and time, the theory beginning from two very clear ideas rather than from a telling, but less a new way of looking at nature which we present in the next chapter. Problems 2.1. Write the mathematical expression of a Lorentz boost with the {et',x', y'.z'j inertial frame sliding along the z- (or z-) axis, and with the x'- and the y - axes parallel to the x-axis and the y-axis, respectively. 2.2. Find eigenvalues and eigenspaces of the matrix describing the Lorentz trans- 2.3. In an inertial frame S, two laser pulses are emitted by points on the x-axis 10km formation and interpret them physically. apart and separated by 3 μ. They reach an inertial observer O' traveling in standard configuration with velocity v away from S. O pulses simultaneously. Find v. Show that the rapidity φ satisfies the relations receives the two las 2.4 e-φ = γ (1-8) , γ = cosh φ, βγ= sinh φ, so that the Lorentz transformation can be written as

Answer 1

c고 2. 2 LM toxl