In order to demonstrate that gravity is generated in intergalactic space as well, on the basis of emergence, Verlinde started from the quantum mechanical point of view, that in the earlier world the qubits are to be regarded as the smallest information units of spacetime. The world, as we humans experience it, would in such a case be based on the emergence of local information from the qubits. In contrast, gravity would be based on the emergence of their non-local or their entangled information (§6.3).

In order to determine the magnitude of gravity in the later world, the entangled information has to be examined. For this purpose, Verlinde relies on the quantitative description of the 'glue hypothesis' of Van Raamsdonk, mentioned in section 6.3. This description demonstrates how division of a region of spacetime (read: a piece of earlier world) into two areas, such as 1 and 2 in the picture below, the amount of entangled information between these areas, the so-called entanglement entropy 'S', is equal to:

S = A / (4)

Entanglement, information and surface. (Quantum Universe)

The entropy of entanglement 'S' in this formula, is the indicator of the amount of information two spacetime areas, such as 1 and 2 in the image, share. A is the size of the imaginary tangent plane of spacetime 1 and spacetime 2. S will become larger as the tangent planes of the spacetime regions increase. (The factor 4 only determines the exact relation between quantities S and A.)

Note 53 Newton’s constant, G, determines how strong gravity is, while Planck's constant, ħ,  indicates the scale at which quantum effects play a role.

 

A tangent plane, as depicted in the image above, has to be spherical. If you want to represent more of these planes, you get a 'matryoshka' of spheres, making these spacetime areas look very similar to the curved spacetime shells of the Sphere Observer, which overlap like the skirts of an onion. It will therefore probably not surprise the reader that Verlinde's research indicates that the entangled information of qubits only applies to areas where gravity prevails (with reference to Ted Jacobson 1995). The above formula for S therefore, only applies to the earlier world of the galaxies and not to the earlier world of intergalactic space.

 

Nevertheless, according to Verlinde, it is quite possible that the earlier world of intergalactic space as well contributes to gravity, because there the information of the qubits will also be entangled. But now, he states, this is not possible on the basis of an entanglement entropy S associated with the surfaces of spacetime areas (see the upper arrow in the diagram below), but on the basis of an entanglement entropy S, that is associated with the volumes of spacetime areas (see the bottom arrow in the diagram below).

                    Entropy of entanglement S according to Verlinde

This has been very cleverly devised by Verlinde. For on the one hand this entails that he meets the Western physics' direction of intergalactic space being based on flat, non-curved Minkowski spacetime, while on the other hand he realizes that his proof only requires a very small amount of gravity being generated. (A little bit of gravity in interstellar space is always better than not finding dark matter in the galaxies.) So he can save both the goat and the cabbage. This way he can have the wolves sated and the sheep intact.

The contribution to gravity by volume as calculated by Verlinde is very small indeed. Much smaller than what one would expect based on the estimated shortage of gravity in the universe. Nevertheless, according to Verlinde, it is already sufficient for concluding that it explains why the Einstein equation is not correct on the scale of galaxies. Verlinde is therefore optimistic about his research. A larger contribution would have been a lot more convincing. however, especially for the (many) colleagues who cannot appreciate his research.

 

It should be clear that with his solution, Verlinde has in fact met the paradigm of Western physics , which does not allow the existence of an abstract earlier world. By not taking this paradigm into account, Verlinde would have been able to use the same formula for S as the one of the galaxies, probably resulting in a much better result. But even a convincing result does not outweigh the state of incommensurability that would have arisen in such a case. Nobody would benefit from that!

In order to prevent the latter and, nevertheless provide convincing evidence, there is, in my view, a better solution, which I would like to present to Verlinde.

                                                                                          

Continue to: 6.6. Letter to Erik Verlinde

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