Lightlike Interval

Classical Mechanics Level 1

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

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c

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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 $c$ in all inertial frames, so:

$c^2 = \left(\frac{dx}{dt}\right)^2,$

in all frames. This rearranges to:

$0 = -c^2 dt^2 + dx^2,$

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

Lightlike Interval

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