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The set of transformation equations for space and time valid in the range 0 ≤ v < c. Suppose an event that occurs at some point P is reported by two observers, one at rest in a frame S and the other in frame S’ that is moving to the right with speed v as in figure below:
The observer in S reports the event with space-time coordinates (x,y,z,t) and the observer in S’ reports the same event using the coordinates (x’,y’,z’,t’). The equations that are valid from v =0 to v = c and enable us to transform the coordinates from S to S’ are the Lorentz transformation equations:
The inverse Lorentz transformation equations are the equations which enable us to transform coordinates from S’ to S:
Measuring the Space-Time Coordinates of an event: The space-time coordinates of an event can be measured by using the Lorentz transformations within the range where the velocity ranges from v = 0 to v = c. When v << c then the Lorentz transformations can be reduced to Galilean transformation equations:
x’ = x – vt
y’ = y
z’ = z
t’ = t
The maximum speed that can be achieved by any object is the speed of light. Thus, the space-time coordinates can either be measured by using the Galilean transformation equations or by using the Lorentz transformation equations.
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Relativity