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Griffiths, Introduction to electrodynamics, in problem 12, shows that if a man starts running at moment $t=0$ from position $x>0$, under the influence of a constant force, will never be reached by a light ray that passes at the origin at time $t>0$.

Shown in the picture is the man as the hyperbolic line, photons as dashed lined -

enter image description here The picture is of course pretty clear and it is obvious the man and the ray will never cross paths because they are separated by the trajectory of another.

But on the other hand, the man of course sees the light and the light will always travel faster the him, so how come the light will never reach him?

Qmechanic
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proton
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1 Answers1

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Isn't this diagram wrong? I mean, following the reasoning, you can draw a straight line inside the cone in such way that the inclination is greater than the bisector line. Tracing a vertical line over this diagram, it will intersect our line and the line bisector line in such way that the x point of intersection is greater in our line than in the bisector line, which means we have constructed the line representing a particle moving with speed greater than c.

In another words, shouldn't the hyperbole be symmetric/invariant under reflection wrt the ct axis, and not wrt the x axis, as is show here?

Now, i know this is an older question, but this solution and the book is famous enough to more people come eventually come here to ask that as time passes, so i think it is ok to ask this here.

LSS
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