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Qmechanic ♦
Qmechanic ♦
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Can 2 different events in spacetime be connected by both a time-like and a space-like curve  ?

With flat Minkowski metric I don't think so, because any global orthonormal map $(x,y,z,t)$ of spacetime has its coordinate $t$ strictly increasing for all timelike (continuous) curves.

I'm not so sure with a general curved metric. Are there sufficient conditions on it so that these weird connections cannot happen  ?

Is it because the light cone of an event $E$ (the collection of all light-like geodesics going through $E$) separates spacetime in 3 connected components : past, future and space  ?

Can 2 different events in spacetime be connected by both a time-like and a space-like curve  ?

With flat Minkowski metric I don't think so, because any global orthonormal map $(x,y,z,t)$ of spacetime has its coordinate $t$ strictly increasing for all timelike (continuous) curves.

I'm not so sure with a general curved metric. Are there sufficient conditions on it so that these weird connections cannot happen  ?

Is it because the light cone of an event $E$ (the collection of all light-like geodesics going through $E$) separates spacetime in 3 connected components : past, future and space  ?

Can 2 different events in spacetime be connected by both a time-like and a space-like curve?

With flat Minkowski metric I don't think so, because any global orthonormal map $(x,y,z,t)$ of spacetime has its coordinate $t$ strictly increasing for all timelike (continuous) curves.

I'm not so sure with a general curved metric. Are there sufficient conditions on it so that these weird connections cannot happen?

Is it because the light cone of an event $E$ (the collection of all light-like geodesics going through $E$) separates spacetime in 3 connected components : past, future and space?

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V. Semeria
V. Semeria
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Causality in general relativity

Can 2 different events in spacetime be connected by both a time-like and a space-like curve ?

With flat Minkowski metric I don't think so, because any global orthonormal map $(x,y,z,t)$ of spacetime has its coordinate $t$ strictly increasing for all timelike (continuous) curves.

I'm not so sure with a general curved metric. Are there sufficient conditions on it so that these weird connections cannot happen ?

Is it because the light cone of an event $E$ (the collection of all light-like geodesics going through $E$) separates spacetime in 3 connected components : past, future and space ?