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Originally Posted by GUILLE Actually, isn't a point in spacetime associated with 8 directions? |
a point can have infinite directions to choose from but only 6 are the shortest. These are the unit vectors along the Cartesian axes (+/-). Instead of a lattice Cartesian system, a spherical surface of unit radius separate the point from the outside points. There are still infinite point on the surface of the sphere but there are a lot more points outside. Einstein defined this closed surface as a hole in spacetime. In order for his field equations to be generally covariance, he made the assumption that the metric radius of the hole must be zero, the same as the spacetime interval of special relativity. Another name for this unit vector is the quantum of length, a concept which is still not fully defined in physics. In special relativity, the unit vector or spacetime interval must be zero in order for the speed to reach a maximum of ~186,000 miles (~300,000 km) per second. In quantum field theory both c (light speed) and h (Planck's constant) are normalized to unity.
time is considered as one of the 6 shortest directions, which leaves 5 shortest directions for space. So that a six components spacetime vector can be represented by (1, -1, -1, -1, -1, -1). Negative sign means motion toward the point. Positive sign means motion away from the point. So, if all 6 directions are directed away from the point the vectors are represented by (1,1,1,1,1,1) and if moving toward the point by (-1,-1,-1,-1,-1,-1), these represent a point in true vacuum and a mass point respectively. If all points in spacetime are (1,1,1,1,1,1)'s then they indicate a global expansion of spacetime. Similarly, if all points are (-1,-1,-1,-1,-1,-1)'s then they represent the big bang singularity.