: what’s a closed timelike curve ?
In: Physics
In relativity, there are three different “classes” of curves. You have spacelike, timelike, and null. Spacelike curves describe particles which travel faster than light (we don’t have these in nature), null curves describe particles which travel at the speed of light (physical massless particles), and timelike curves describe particles which travel slower than light (physical massive particles). So, a closed timelike curve is one where a physical, massive particle is allowed to loop back on itself by simply traveling through spacetime. This is a big problem since the particle says that it is always travelling forward in time, but it is still possible for it to close the curve and meet its past self. This absolutely wrecks the ability to establish if one thing happened before or after another, which is a HUGE problem if allowed to exist.
It’s a path through spacetime which crosses back upon itself. These aren’t typically possible, but with a wormhole or other special topology it can be possible to conceptually construct a closed 4D curve which a photon could follow and cross back upon itself.
Constructing on in real life could enable certain time machine constructs, which we don’t see in reality.
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