Friday, June 30, 2023

TGD view of the gravitational hum as gravitational diffraction

The revolution in cosmology is continuing. The latest breakthrough was announced yesterday (see this). See also the popular article. There is a collection of articles related to the discovery.

The dicovery

Scientists from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) have now officially made the first detections of the gravitational wave background. This gravitational hum was not detected by Earth bound instruments.

The wavelength of the oscillations makes itself visible as correlations between the variations of the spinning  rates  for pulsars having relative  distances measured using a light year as a unit.   The wavelength of the oscillations is measured in light years. In the LIGO experiment  the  periods are measured as fractions of a second.  

Where could this length scale come from? What might make bells ringing is that the star nearest to the Sun is at a distance of 4 light years and the typical distance between stars is 5 light years.

Near to the end of the talk also the wavelength scale of millions of light years is mentioned. This scale corresponds to a typical distance between galaxies, which is few Mpc, pc= 3.26 ly.

Remark: I am grateful to Marko Manninen for noticing a rather stupid mistake: I talked about a period of millions of light years for the detected gravitational radiation. The period is of course a few years as is obvious from the fact that it is not easy to find graduate students able to stay motivated for millions of years.

The unexpectedly large amplitude of the oscillations motivates the hypothesis that pairs of galactic supermassive blackholes or interacting groups of them could generate the gravitational hum. There are candidates for these pairs but no established pair. The group hypothesis seems to work better.

TGD explanation in terms of astrophysical gravitational quantum coherence and diffraction in hyperbolic tesselation

TGD suggests a radically different hypothesis based on TGD view of gravitational quantum coherence an diffraction in a hyperbolic tessellation.

  1. TGD predicts quantum gravitational coherence in astrophysical scales characterized by gravitational Planck constants hgr = GMm/β0 characterizing big mass M and small mass m. β0=v0/c<1 is a velocity parameter. The Equivalence Principle is realized as the independence of the gravitational Compton length Λgr= GM/β0= rs/2β0 on mass m.
    1. For the Sun Λgr is 1/2 of Earth radius. If the TGD proposal, which explains Cambrian explosion in terms of rapid increase of the Earth radius by factor 2, this scale is the radius of Earth before the explosion (see this).
    2. For the Earth Λgr is .45 cm and the size scale of a snowflake, which is a zoomed version of the unit cell of the ice crystal: a fact which still remains a mystery.
    3. For the galactic black hole, Λgr is about 1.2×107 km=1.2× 10-2 light seconds and corresponds to a frequency of about 100 Hz, the upper bound of EEG frequencies by the way (which might put bells ringing!). For β0=1 Λgr happens to correspond to the radius of the lowest Bohr orbit for Sun Λgr in Bohr orbit model for planetary orbit (another bell ringing!) and defines only a lower bound for the quantum coherence scale.
  2. Where could the wavelength of order of distance between neighboring stars emerge? TGD strongly suggests that the tessellations (lattices) associated with hyperbolic 3-space identified light-cone proper time a= constant surface play a key role in all scales, in particular in biology.

    There could exist a fractal hierarchy of hyperbolic tessellations (see this) formed by astrophysical objects of various mass scales. Could the stars with average distance of 5 light years form tessellations of this kind analogous to lattices in a condensed matter system. The wavelength for the diffracted gravitational waves in cubic tessellation would have the upper bound 2d, d the lattice constant, which would be now about 5 light years.

  3. There is empirical evidence for these tessellations. So called cosmic fingers, discovered by Halton Arp (see this or this), correspond to astrophysical objects appearing at single light of sight (first mystery) and having redshift coming as multiples of a basic redshift (second mystery). This could serve as a direct signature of the hyperbolic counterpart for a line of atoms located along a lattice. Redshift is proportional to distance and also to the recession velocity, which would therefore be quantized in the observed manner.
  4. What kind of tessellations could be involved? There is an infinite number of tessellations for H3 but only 4 regular uniform honeycombs. For two of these the unit cell is a dodecahedron, for 1 of them it is an icosahedron and for 1 of them it is a cube. Note that in Euclidian 3-space one has just one regular honeycomb consisting of cubes.

    There are also more general uniform honeycombs involving several cell types. There is a unique "multicellular" honeycomb for which all cells are Platonic solids. This is icosatetrahedral (or more officially, tetrahedral-icosatetrahedral) honeycomb for which the cells are tetrahedrons, octahedrons, and icosahedrons (see this). All faces are triangles and I have proposed a universal realization of genetic code in which genetic codons correspond to the triangular faces of icosahedra an tetrahedra (see this).

The key prediction is gravitational diffraction in this cosmic lattice.
  1. In diffraction in the lattice the diffracted amplitude concentrates in specific directions corresponding to the reciprocal lattice. Something analogous should happen for tessellations in hyperbolic 3-space. Already the concentration to beams would mean an amplification effect (note that the lowest order prediction for the intensity of the radiation does not depend on the value of the effective Planck constant).

    Furthermore, by quantum coherence the scattered amplitude is proportional to N2 rather than N, where N is the number of atoms in the lattice, now stars in the tessellation. Could these two amplification effects explain why the observed effect is so much larger than expected? Professionals could easily find whether this idea fails at the quantitative level.

    TGD view suggests that the dark gravitational radiation propagates along the monopole flux tubes connecting stars.

  2. In the ordinary diffraction from a cubic lattice in Euclidian space E3, the condition of constructive interference for the two rays scattered from to neighboring points of the cubic lattice states, requires that the difference of lengths for the paths travelled is a multiple of the wavelength of the incoming radiation. This gives the Bragg condition: sin(θ)= nλ/2d, where θ is the glance angle defined as the angle of incoming ray with respect to the normal direction of the lattice plane. The condition gives λ <2d/n and implies λ <2d for n=1. Therefore the diffraction occurs only for frequencies ω > nωn, ωn>c/2d.

    In the case of gravitational radiation, this would give for a cubic lattice λ<2d/n, d ≈ 5 light years, which conforms with the scale of few years for the periods. The lower bound for the period T would be about Tmin=10 years. The condition that the scattered beams connect lattice points, gives an additional quantization condition to the glance angle θ. Most naturally it would correspond to a line connecting lattice points.

See the for instance the articles Magnetic Bubbles in TGD Universe: Part I and Magnetic Bubbles in TGD Universe: Part II.

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

No comments: