Two events [math]E_1[/math] and [math]E_2[/math] are simultaneous when their time variables [math]\phi_1[/math] and [math]\phi_2[/math] are equal. However, this equality implies that the time interval defined as the absolute difference of [math]\phi_1[/math] and [math]\phi_2[/math] is identically zero. On the other hand, this equality does not say anything about their directions. If their directions are equal then they must be pointing along the same orientation regardless of the embedding space dimensions. These suggest that simultaneity exists when comparing events at different dimensional levels not for events at the same dimensional level. Using the analogy of concentric spheres, each sphere signifies one dimensional level and there exist points on these spheres that share a common radial line from the center. Furthermore, all events found on this particular radial line are then said to be simultaneous, that is to say they share the same radial direction from the center and hence all their time axes are aligned.


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