Lightlike Interval

Light travels from spacetime point x x to spacetime point y y in Minkowski space. What is the value of the invariant interval between x x and y ? y?

1 -1 0 0 c c Not enough information

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1 solution

Matt DeCross
May 10, 2016

The value of the interval between any two points light travels between is always zero. This is because the speed of light is c c in all inertial frames, so:

c 2 = ( d x d t ) 2 , c^2 = \left(\frac{dx}{dt}\right)^2,

in all frames. This rearranges to:

0 = c 2 d t 2 + d x 2 , 0 = -c^2 dt^2 + dx^2,

which is to say that the invariant interval is always zero for any "lightlike interval."

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