Key 9

  1. Two frames of reference, S and S´, have synchronised their clocks as their origin pass each other. In frame S, one event happens 600 000 km from the origin three seconda ago. In the other frame, it happened four seconds ago. How far from the origin of S´ did it happen?

We have that

\displaystyle {{s}^{2}}={{\left( {ct} \right)}^{2}}-{{x}^{2}}

or

\displaystyle {{s}^{2}}={{\left( {c\cdot (-3)} \right)}^{2}}-{{600000000}^{2}}={{\left( {c\cdot (-4)} \right)}^{2}}-{{x}^{2}}

This gives us

\displaystyle {{x}^{2}}={{\left( {c\cdot 4} \right)}^{2}}-{{\left( {c\cdot 3} \right)}^{2}}+{{600000000}^{2}}

or

\displaystyle x=9.95\cdot {{10}^{8}}\text{ m}=995000\text{ km}

  1. What does a negative s2 mean?

That the point is oudside the lightcone, i.e. that the point cannot have been seen, or that light from the observer cannot reach it.

Last modified: Sep 23, 2025 @ 18:54