Classical mechanics is based on the everyday understanding of space and time that everyone can observe. According to it, space and time form the stage of world events, where space is three-dimensional, homogeneous, and isotropic in all directions. Time is one-dimensional and progresses uniformly.
This intuitive idea was challenged by Einstein's theories of relativity and the empirical observations associated with them. According to this theory, the distances in space and time measured by folding rules or clocks depend on the observer's state of motion and the masses in his surroundings. To describe these results mathematically, Hermann Minkowski introduced four-dimensional space-time, which consists of the three spatial coordinates x, y, z and a time-dependent fourth coordinate c*t. Like the three spatial coordinates, the fourth coordinate c*t has the unit of length, but is fixedly associated with time t and has the opposite sign in the metric system. The coordinate systems of two observers S and S', moving against each other with the velocity v, are transformed into each other by the so-called Lorentz transformations.
One consequence of Einstein's special theory of relativity has caused much confusion, namely the fact that two events that appear simultaneous to one observer can be non-simultaneous to other observers. This renders obsolete the intuitive idea of a unified present in which we find ourselves as well as our surroundings. According to Einstein, the "now" has no place in physics. However, laypeople find it very disconcerting that current theories of physics cannot describe what characterizes the now as the present. In order to remedy this deficiency, we proposed in the section "The Present and the Passing of Time" that the phenomenon we perceive as the passage of time is actually a constant change in a physical quantity called effect S. Between the present G1 and the present G2, the effect value of all material objects changes by a certain factor S2/S1, with the temporal distance measured on a clock between G1 and G2 depending on the path taken between G1 and G2. This trick preserves the intuitive idea of a uniform present without contradicting the results of the empirically well-confirmed theory of relativity, and it also justifies the principle of the smallest effect, from which all physical laws of motion can be derived.
However, one thing remained a mystery: what is behind the abstract measure of „effect"?
To unravel this mystery, it may help to take a look at the unit of this physical quantity. The effect is measured in J*s. This unit is obtained by forming the product of energy and time or the product of distance and momentum. At the same time, J*s is also the unit of angular momentum.
Aha! Is the change in the effect that transforms one present into another present perhaps a change in angular momentum? Only one angular momentum could be considered for this - the angular momentum of the universe as a whole! What appears to us as a flow of time would then have its deeper cause in the constant change in the overall rotation of the universe. Whether this is an increase or a decrease in angular momentum is prima facie impossible to say - as long as the sign of the change remains the same, there is no reversal of time.
Is this change in the rotation of the universe continuous or erratic?
Let us make a bold hypothesis: At every moment, the angular momentum of the universe changes by a quantized amount, namely h/4pi. This is exactly the spin of a universal particle. At every moment, therefore, one universal particle is added to the universe (or removed from it, depending on whether the total angular momentum of the universe is increasing or decreasing). However, since our universe is apparently expanding, an increase in the number of particles seems more plausible. Thus, an irreversible event is taking place every moment as a new particle is added and interacts with the existing particles.
If these considerations about the nature of time are correct, then the Minkowskian description of space-time with three spatial coordinates and a fourth coordinate firmly associated with time cannot be the last word in wisdom. This assumption is also suggested by another extremely peculiar finding: fermions - and thus the currently presumed basic universal particle - have the peculiar property that they are identical to themselves only after a rotation of 720°. After a rotation of 360°, the wave function of the particle has the opposite sign - only after a further rotation of 360° is the initial state reached again. This peculiarity occurs not only when the observer is fixed and the particle is rotated around its own axis, but also when the particle is fixed and the observer moves in a circle around the particle. Therefore, this bizarre property cannot be due to the fermions, but must be related to the topological properties of the universe, which we are also subject to when we rotate around another object as an observer.
One possible explanation for this strange behavior of fermions is that the universe has a four-dimensional spatial topology. Mathematicians know that on a four-dimensional sphere, it takes 720° of rotation to get back to the starting point. After 360°, you arrive at the same point, but you are standing upside down. The fact that we don't notice this in everyday life, but have the impression that we have returned to the starting point after a 360° rotation, could be related to the fact that the world of macroscopic bodies is held together by forces whose exchange particles are bosons. Both photons and the exchange bosons of the strong and weak interactions have a rotational symmetry of 360°.
Our reconstruction of relativistic mechanics also shows that the four dimensions of the universe are essentially identical. What appears to us as three-dimensional space depends on a quantity we call the "energy vector". The three spatial coordinates are each perpendicular to this four-dimensional energy vector. When our state of motion changes, the position of our energy vector in the universe changes, and therefore a different section through the four dimensions of the universe appears to us as three-dimensional space.
So while space is measured relative to the observer, there is an excellent time axis in our reconstruction of relativistic mechanics. How far an object progresses on the time axis between two presents depends on the projection of its start and end points onto this time axis. But what could characterize this time axis in the universe? In our opinion, there is only one possible axis - the rotational axis of the universe.
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