Lorentz Transformation For Frames in Standard Configuration
Consider two observers O and O', each using their own Cartesian coordinate system to measure space and time intervals. O uses (t, x, y, z) and O ' uses (t', x', y', z' ). Assume further that the coordinate systems are oriented so that, in 3 dimensions, the x-axis and the x' -axis are collinear, the y-axis is parallel to the y' -axis, and the z-axis parallel to the z' -axis. The relative velocity between the two observers is v along the common x-axis. Also assume that the origins of both coordinate systems are the same, that is, coincident times and positions.
If all these hold, then the coordinate systems are said to be in standard configuration. A symmetric presentation between the forward Lorentz Transformation and the inverse Lorentz Transformation can be achieved if coordinate systems are in symmetric configuration. The symmetric form highlights that all physical laws should remain unchanged under a Lorentz transformation.
Below the Lorentz transformations are called "boosts" in the stated directions.
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