Are Spacelike Movements Physically Possible in Our Universe?

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so all movements in spacetime are timelike except light which is lightlike. are any spacelike? i understand this essentially means going backward in "time" but if it's impossible, which it is generally is believed to be, it seems to me like there is no physical significance to being outside the lightcone.
 
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Events can be outside the lightcone, and two events which are spacelike do not have any "temporal order," i.e., event A happens before event B in one frame, and the other way in another frame. But once you start moving, say, at the origin of some lightcone, you are bound to move within it, since you will have go at or greater than the speed of light to cross the light cone.
 
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