I have a harmless question which involves using the Lorentz transformations. Suppose that I am an observer in reference frame S, which is stipulated to be an inertial reference frame, and i am located at the origin of the frame (0,0,0).(adsbygoogle = window.adsbygoogle || []).push({});

A laser also located at (0,0,0) suddenly fires a photon along the x axis of frame S, in the direction of increasing x coordinates.

Let t denote the time coordinate of inertial reference frame S.

At the moment the photon is emitted, let t=0.

Now, after some amount of time [tex] \Delta t [/tex] has elapsed, the photon will have travelled some distance L, as measured by the X-axisruler.

Now, let reference frame S` be attached to the photon, so that the photon is always at rest in reference frame S`. Furthermore, let the positive x` axis of frame S` coincide with the positive x axis of frame S, let the positive y` axis of frame S` coincide with the positive y axis of frame S, and let the positive z` axis of frame S` coincide with the positive z axis of frame S.

My question is simple.

If, after time amount of time [tex] \Delta t [/tex] has elapsed according to some clock which is permanently at rest in S, the photon has coordinates (L,0,0) in frame S, what is my x` coordinate in frame S`?

For the sake of definiteness, suppose that exactly one second has ticked according to a clock at rest in frame S. Therefore, the location of the photon in frame S is given by (299792458 meters, 0,0).

Let (M,0,0)` denote the location of the origin of inertial reference frame S, in reference frame S`, at the instant that the clock at rest in frame S strikes one. Solve for M.

Thank You

Guru

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# Harmless Lorentz transformation question

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