In paragraph 5.4 I assumed that Einstein still had to incorporate his bizarre discovery in his theory of gravity inconspicuously. Soon, however, it turned out that Einstein considered the deflection of light near heavy celestial bodies as convincing evidence of the correctness of his field equations for gravity. In fact, with his equations, Einstein pretends to have proven that classical and modern gravity are based on the same principle, which means that the panic scenario I described earlier, in which gravity is based on the existence of a gravitational potential, is incorrect. In the same section, however, I noted that Einstein, in formulating his field equations, made a decision he could not justify scientifically twice, which has been attributed to his unparalleled intuition.

The first one was the starting point for his equation that interstellar space must contain no energy (of any kind) (De Vlieger §14). That condition is logical in itself because the underlying gravitational spacetime (the metric field) of the Einstein tensor (to the left of the equal sign) for calculating modern gravity not may be curved. However, remember that in interstellair space, apart from the mass of a body, there is only one energy that is related to the curvature of spacetime, and that is the flux of the gravitational field (see NB.40). The field, therefore, of the local, classical gravity as we humans know it, but of course Einstein could not tell that.

The second decision, therefore, implied that the Tμν tensor in Einstein's equation included not only the mass of the celestial body to be examined at the μ, ν site, but also the flux of its local gravitational field of the later world. (This is possible simply because the divergence of this gravitational field is proportional to the mass of the relevant celestial body: Expressed in terms of Energy, the flux of gravitational field is therefore always a fixed percentage of the mass of the celestial body.) By claiming that Tμν thus comply with the conservation laws of energy and impulse (De Vlieger §15) Einstein also disguised here that this is about the classical gravitation.

In my view, Einstein demonstrated with this concealment again, that his "unparalleled intuition" is based on his bizarre discovery. By consistently boasting on that intuition, this discovery can, however, be 'forgotten', because education makes, paradigmatically, certain decisions 'self-evident' over the years and you see that happening a hundred years later. However, for the Sphere Observer's theory, the recognition of Einstein's bizarre discovery is very important. To him, the tensor T_μν is therefore the mass of a celestial body at the μ, ν location with a percentage of energy added because of the flux of the associated classical gravity field.

If the above does not convince the reader sufficiently, the difference with the classic gravity, as we humans perceive it, can probably be proven as well. I suppose, for that matter, that Newton's gravity formula in the very direct environment of celestial bodies - for a body like the Earth I'm thinking of distances of at least 1500 km - is far more reliable than the einstein equation. And for two reasons. Firstly, the gravitational potential is an energetic phenomenon of the later world, while the curvature of spacetime is a phenomenon of the earlier world. Secondly, because the curvature of spacetime in the vicinity of celestial bodies is so strong, that the metrics involved in making the laws of physics 'covariant' may no longer be reliable. I hope that further research, in which atmospheric influences are excluded, causes Einstein's bizarre discovery to be recognized, revealing the fact that the earlier world has a shell structure, as described in §5.3.1 and as assumed in the distant past by the Sphere Observer due to his sensitivity hypothesis.

Incidentally, it was also discussed at the end of the previous section that the cosmological constant Λ has been included in the einstein equation since the 90s of the last century because the role of the cosmological constant Λ has been marginally adjusted to the new research results, which rely on the accelerated expansion of the universe (see the repetition of the einstein equation below). And that too is grist to the mill of the Sphere Observer. 

Despite the exact value of Λ is unknown - it belongs to the earlier world (after all, to the left of the equal sign) - the term Λgμν has since always been unequal to zero, if Tμν is zero. This causes a residual energy (tension) in the vacuum of the later world (read: intergalactic space). This way, the cosmological constant Λ indirectly stands for the intrinsic energy density of the vacuum, mathematically indicated by ρ_vac. The ρ_vac, then,  corresponds to the amount of dark energy in intergalactic space, which is causal for the accelerated expansion of the universe.

Note 42 The presence of virtual particles also indicates that energy is still present in the vacuum. Quantum mechanics seems to confirm a non-zero value of Λ.

In the most accepted model of the universe, the Λ-CDM model, Λ is not only associated with dark energy in the intergalac space but with cold dark matter (CDM) as well. The latter is very special because CDM in intergalactic space is the same as hypothetic dark matter in the galaxies. In my opinion, it means that the underlying spacetime of Minkowski will be curved and, therefore, you should consider Λg_μν as a curvature tensor. just like the Einstein tensor, So now not for the interstellar spacetime but for the intergalactic.

Since Λg_μν must have a permanent place in the einstein equation, this means that this equation now also applies to the intergalactic space and so actually to the entire universe. Due to the western dichotomy of the universe, however, that is out of the question. In the einstein equation, therefore, it becomes an either-or-situation:

• either the tensor T_μν is larger than zero (T_μν>0). In that case it concerns matter at location μ, ν, in the form of, for example, a star plus its local gravity. In that case, the einstein tensor shows a clear curvature in the earlier world (the metric field) at location (μ, ν), from which the amount of gravity can be calculated, the star generates in the later world (see big arrow in the illustration below). With T_μν > 0 the intergalactic space is by definition excluded because it contains no matter. The cosmological constant (Λ) is equal to zero in this case, because the intergalactic space is excluded. (Selecting a value of 0 for Λ causes the whole term Λg_μν to be dropped from the equation, revolving to the original version of 1915.)
• or the tensor (T_μν) equals zero (T_μν=0), because there is no matter, which is the case for intergalactic space, the vacuum. In the earlier world of intergalactic space, spacelike Minkowski spacetime, the einstein tensor is zero and the term Λg_μν now expresses its degree of curvature from which it can be determined how much gravity the universe's expansion generates in the intergalactic space (see small arrow in the image below). Due to the lack of material, this must be in terms of CDM.

It should be clear that T_μν is playing a double role in the einstein equation nowadays. To clarify the dual role of the T_μν tensor, I have adjusted the current name. On the one hand, T_μν can be called 'matter tensor' and on the other hand 'vacuum tensor',  I hope to vizualize this dichotomy clearly by the next image.

                                        

The term Λg_μν can now, like the einstein tensor, be seen as a 'curvature tensor'. From the degree of curvature it can subsequently be determined how much gravity the accelerated expansion or dark energy generates in the later world. However, because gravity can not be demonstrated in the absence of matter, this actually means that it has to be assumed that dark matter exists in intergalactic space, which is called 'cold dark matter' (CDM). In this way the einstein equation, in my opinion, meets the aforementioned Λ-CDM model of the universe, in which Λ is associated with both dark energy and CDM. The question "How can the accelerated expansion of the universe generate gravity in intergalactic space?" In the addendum, I hope to be able to provide a satisfactory answer.

With this section I hope to have clarified that Western physics had to split the earlier world into a spacelike Minkowski spacetime (3 + 1) and a timelike gravitational spacetime (2 + 2). This also created a dichotomy in the later world. It is important for the reader to understand this, so he can appreciate the very important role of the earlier world in Western physics since Einstein.

Moreover, the modern version of the einstein equation makes it clear that the earlier world in Western physics is consistent with the theory of the Sphere Observer who assumed that spacetime is always curved. The question that remains is then: "How do you evidence that the curvature of the Western earlier world must be attributed to a shell structure of spacetime?

 Continue to: 5.5. Abandonment of the ether theory as evidence of spacetime shells