Characteristics and consequences of the closed curve of type time
Normally causality implies that each event in space-time must be produced by a cause, taking rest as a frame of reference. This is a basic principle in determinism, where according to general relativity, It is established that from the knowledge of the universe on a space-type Cauchy surface, it is possible to determine any subsequent state of space-time.
Instead, in a closed curve of type time, The law of causality does not hold because an event can be simultaneous with its cause., so that the event would become its own cause.
Based solely on knowledge of the past, It would be impossible to determine if something exists in the closed curve of type time that can interfere with other objects in space-time. So one closed curve of type time results in a so-called Cauchy horizon, and in a region of space-time where it cannot be predicted from a past event.
The existence of the closed curve of type time would impose restrictions on the matter-energy field states of physics. Many scientists have used the approach that, if we propagated the configuration of a field along a family of closed time-type world lines, we should obtain a state identical to the original, so that the existence of the closed curve of type time.
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