Monday, May 06, 2024

Equivalence Principle in TGD

Understanding Equivalence Principle has been one of the basic challenges of TGD.
  1. If one accepts Einstein's equations as a realization of Equivalence Principle, Equivalence Principle could be seen as a remnant of Poincare invariance of TGD at the quantum field theory limit of TGD. Einstein's equations at QFT limit would express what is left from exact Poincare invariance at the microscopic level. Recall that the microscopic level space-times are 4-D surfaces in H=M4×CP2 realizing holography in terms of generalized holomorphy (see this) implying minimal surface property failing at singularities, which in turn give rise to particle vertices (see this and this).
  2. At the quantum level the situation is not so easy. Here the principle should be global and state the identity of gravitational and inertial masses.
    1. Inertial mass is associated with the conserved four momentum labeling the modes of second quantized free spinor fields of H, whose oscillator operators can be used to build all elementary particles, both photons and fermions.
    2. What about gravitational mass? In zero energy ontology one considers causal diamonds CD=cd×CP2 subset H, where cd is the causal diamond of M4. Now it is natural to perform the quantization of spinors inside a CD. Lorentz group with respect to either tip of CD and instead of unitary representations of Poincare group one has unitary irreps of this Lorentz group. Momentum eigenstates are replaced with unitary irreps of SO(1,3) at the Lorentz invariant hyperbolic 3-space H3 and Minkowski time is replaced with light-cone proper time, cosmic time. Mass spectrum is however the same. Hence Equivalence Principle.
The unitary representations of the Lorentz group are something completely new and have direct physical applications.
  1. The unitary irreps of Lorentz group and H3 allow symmetry breaking to subgroups just as the representations of translation groups do in condensed matter physics. One obtains an infinite hierarchy of tessellations of H3 as counterparts of condensed matter lattices. There are however only a finite number of regular tessellations.
  2. The recent findings of gravitational hum could be understnd in terms of diffraction in a lattice formed by stars (see this).
  3. There is a completely unique tessellation allowing tetrahedrons,octahedrons, and icosahedrons as basic components and one can understand genetic code in terms of this tessellation. This suggests that genetic code is universal and biosystems provide only one particular realization of it (see this) .
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.

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