causal connectivity

[AntonioLao]

Establishing a connection (worldline) between two events (worldpoints) in space-time creates a time axis. Consequently, the creation also sets the direction for the flow of time. This is not a ‘flow’ in the usual sense of displacements in distances but more of an angular displacement, of the reality of angle measurements. Still, it is mathematically feasible to relate distances and angles by the use of circular functions (sine and cosine and tangent, etc.) of trigonometry. However, principle of similarity asserts that angular measurements are independent of distance measurements. Furthermore, the principle of orthogonality in angular measurements does not have an equivalent analogy with distances even though distances are only definable through the principle, for example, the applicability and validity of the Pythagorean Theorem, implying the existence of right angles, separating the space-time domain into four quadrants by four axes, two for time and two for space.

[Guille]

OK. But what makes you "Know" that one event happened before the other, that one was caused by the other?

Nothing. Your view of the things. But it's all relative. If I see a film backwards, then I would say that the guy was dead and he came back to life, and at the end he was born. Maybe for you, we have seen the film correctly, the guy would be born, then live, and finally killed.

But we cannot determine what is the true arrow of time, simply because time itself has no arrow. Also space doesn't have arrow. It's only the objects in the dimensions that have arrows. I am moving towards my computer in space, is my arrow, and forward is my time arrow, but space isn't moving, and neither is time.

[AntonioLao]

But we cannot determine what is the true arrow of time

Yes, we cannot. But the change of time is not linear, it is angular. It is a change in orientation of an infinitesimal time axis. To conserve this axis, there must be rotational motion. This rotational motion is then related to the quantum mechanical concept of spin. This spin is discrete (two-valueness) to distinguish from the classical mechanics' continuous spin such as the rotation of earth around its axis.

[Guille]

Yes, we cannot. But the change of time is not linear, it is angular. It is a change in orientation of an infinitesimal time axis. To conserve this axis, there must be rotational motion. This rotational motion is then related to the quantum mechanical concept of spin. This spin is discrete (two-valueness) to distinguish from the classical mechanics' continuous spin such as the rotation of earth around its axis.

If this rotational motion has to do with the concept of spin, then it must have to do with the concept of angular momentum?

If so, could it be that angular momentum is not only spatial but also temporal?

[AntonioLao]

could it be that angular momentum is not only spatila but also temporal?

The angular momentum is doubly rotational. It completes the spatial rotation as describe by its angular frequency. Its temporal rotation is bounded by (if the speed of light is equal to unity) 0º to 45º. It is 0º if and only if the space axis is zero. If 45º then matter is in the form of pure energy and time motion stops. At 0º matter becomes pure space. In between 0º and 45º, matter exists as quantum of spacetime in a quantum universe. Please note that temporal rotation never really made a complete rotation unless spacetime is warped and twisted.