M8 H duality viz. Hubble law, and gravitational Planck constant viz. Allais effect and warping

In this article two developments in TGD are discussed. These developments emerged in a "wrong context".

The first discovery was the realization that M⁸-H duality in zero energy ontology implies a fractal generalization of Hubble's law. It emerged in a work related to TGD inspired quantum biology, where gravitational Planck constant h_gr= GMm/β₀ (M and m are masses and β₀ is velocity parameter) introduced by Nottale plays a key role. This already also led to a partial understanding of Hubble tension: the value of β in cosmic scales is very near to 1 but its values differ slightly in long and short cosmic scales.

The second discovery emerged while developing a TGD based model for Allais effect, which has no explanation in the context of general relativity or Newtonian gravitation. The work led to the question concerning the interpretation of the velocity parameter β₀ appearing in the formula of the gravitational Planck constant h_gr introduced already by Nottale. The gravitational field bodies of the Earth and structures of cosmological size scale are characterized by β₀=v₀/c∼ 1 and cannot correspond to a velocity of matter for a matter flow. Solar system characterized by β₀∼ 2^-11, which cannot correspond to light-velocity in the general relativistic framework.

The solution of the problem came from a prediction of TGD, which emerged already 47 years ago during the first year of TGD. TGD predicts warped space-time surfaces which are flat like Minkowski space M⁴ (no gravitation) and have vanishing gauge fields. They have Poincare symmetry but have reduced light-velocity due to the warping. Light-like geodesics of M⁴ are replaced by light-like geodesics of M⁴× S¹⊂ H=M⁴× CP₂. Warped space-time surface can explain the Allais effect, in particular the dramatic reduction of the parabolic oscillator frequency in terms of reduced light velocity. The notion of warping generalizes: one can speak of warped Hamilton-Jacobi (H-J) structures for which the hypercomplex structure of M⁴ and complex structure of CP₂ are mixed in the sense that M⁴ H-J structure is replaced with that of a warped space-time surface.

See the article M⁸ H duality viz. Hubble law, and gravitational Planck constant viz. Allais effect and warping or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.