Lorentz Transformations Relativity Lorentz Transformations MARLON FLORES SACEDON

Recall: Galilean Transformation The Galilean Coordinate transformation The Galilean Velocity transformation

The Lorentz Transformation

The Lorentz Coordinate Transformation First question: When an event occurs at point (x, y, z) at time t, as observed in a frame of reference S, what are the coordinates (x’, y’, z’) and time t’ of the event as observed in a second frame S’ moving relative to S with constant speed u in the +x-direction? Galilean Transformation: For Relativistic transformation from S to S’ be identical to that from S’ to S.

The Lorentz Coordinate Transformation First question: When an event occurs at point (x, y, z) at time t, as observed in a frame of reference S, what are the coordinates (x’, y’, z’) and time t’ of the event as observed in a second frame S’ moving relative to S with constant speed u in the +x-direction?

The Lorentz Velocity Transformation The principle of relativity tells us there is no fundamental distinction between the two frames S and S’. Thus the expression for vxx in terms of v’x must have the same form, with vx changed to v’x , and vice versa, and the sign of u reversed.

Time that Stanley heared (t=?) Problem 1: Was it received before it was sent? Winning an interstellar race, Mavis pilots her spaceship across a finish line in space at a speed of 0.600c relative to that line. A “hooray” message is sent from the back of her ship (event 2) at the instant (in her frame of reference) that the front of her ship crosses the line (event 1). She measures the length of her ship to be 300 m. Stanley is at the finish line and is at rest relative to it. When and where does he measure events 1 and 2 to occur? Finish line 300 m Event 1 Event 2 -x +x +y 0.600C Time that Stanley heared (t=?) Distance of sound measured by Stanley. (x=?) Stanley and Mavis measure event 1 to be at x = 0 = x and t = 0 = t Rest frame Mavis measures event 2 at x = -300 m and t = 0.

Problem 2: Relative Velocities (a) A spaceship moving away from the earth at 0.900c fires a robot space probe in the same direction as its motion at 0.700c relative to the spaceship. What is the probe’s velocity relative to the earth? (b) A scoutship is sent to catch up with the spaceship by traveling at 0.950c relative to the earth. What is the velocity of the scoutship relative to the spaceship? b) a)

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