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Showing posts from April, 2019

How to construct scattering amplitudes?

Lubos Motl ) told about two new hep-th papers, by Pate, Raclariu, and Strominger (see this) and by Nandan, Schreiber, Volovich, Zlotnikov (see this) related to a new approach to scattering amplitudes based on the replacement of the quantum numbers associated with Poincare group labelling particles appearing in the scattering amplitudes with quantum numbers associated with the representations of Lorentz group.

Why I got interested was that in zero energy ontology (ZEO) the key object is causal diamond (CD) defined as intersection of future and past directed M4 light-cones with points replaced with CP2. Space-time surfaces are inside CD and have ends at its light-like boundaries. The Lorentz symmetries associated with the boundaries of CD could be more natural than Poincare symmetry, which would emerge in the integration over the positions of CDs of external particles arriving to the opposite light-like boundaries of the big CD defining the scattering region where pref…

About list of unsolved problems in physics

Thanks to Savyasanchi Ghose for posting to FB a long list about unsolved problems of physics . I descided to write about TGD based answers to the questions. I have done some re-organization to the questions since they contain so many sub-questions. Also some re-ordering.

A. Questions related to time, entropy, causality, and T violation

A1. Arrow of time (e.g. entropy's arrow of time): Why does time have a direction?

Understanding of the arrow of time requires a new ontology. I have talked a lot about zero energy ontology (ZEO) which also solves the basic problem of quantum measurement theory and allows free will without conflict with the deterministic laws of physics such as field equations: in TGD dynamics of space-time surfaces and modified Dirac equation.

ZEO allows to distinguish between geometric time and experienced time and to understand their correlation. One could speak about quantum arrow inducing thermodynamical arrow of time and arrow of psychological time. Ther…

Fluctuations of Newton's constant in sub-millimeter scales as evidence for TGD

Sabine Hossenfelder had a posting about rather interesting article related to possible new gravitational physics appearing in sub-millimeter length scales. Washington group has reported evidence for the variation of the effective value of Newton's constant in sub-millimeter scales. The proposed interpretation in terms of spatially oscillating variation of the effective value of G discussed in the article "Hints of Modified Gravity in Cosmos and in the Lab?" does not look convincing. The reader is encouraged to look for the figure 19 of this article about the observed anomalous torque claimed to have interpretation in terms of spatial oscillations of the gravitational potential. The fit is however far from convincing and several wavelength minimizing the deviation of the fit are possible. A more convincing intepretation is in terms of fluctuations of Newton's constant not predicted by standard modifications of General Relativity. These fluctuations have been…

Scattering amplitudes and orbits of cognitive representations under subgroup of symplectic group respecting the extension of rationals

Number theorist Minhyong Kim has speculated about very interesting general connection between number theory and physics (see this). The reading of a popular article about Kim's work revealed that number theoretic vision about physics provided by TGD has led to a very similar ideas and suggests a concrete realization of Kim's ideas (see this). The identification of points of algebraic surface with coordinates, which are rational or in extension of rationals, gives rise to what one can call identification problem. In TGD framework the imbedding space coordinates for points of space-time surface belonging to the extension of rationals defining the adelic physics in question are common to reals and all extensions of p-adics induced by the extension. These points define what I call cognitive representation, whose construction means solving of the identification problem.

Cognitive representation defines discretized coordinates for a point of "world of classica…

Secret Link Uncovered Between Pure Math and Physics

I learned about a possible existence of a very interesting link between pure mathematics and physics (see this). The article told about ideas of number theorist Minhyong Kim working at the University of Oxford. As I read the popular article, I realized it is somethin g very familiar to me but from totally different view point.

Number theoretician encounters the problem of finding rational points of an algebraic curve defined as real or complex variant in which case the curve is 2-D surface and 1-D in complex sense. The curve is defined as root of polynomials polynomials or several of them. The polynomial have typically rational coefficients but also coefficients in extension of rationals are possible.

For instance, Fermat's theorem is about whether xn+yn=1, n=1,2,3,... has rational solutions for n≥1. For n=1, and n= 2 it has and these solutions can be found. It is now known that for n>2 no solutions do exist. Quite generally, it is known that the number is finite…

About the physical interpretation of ramified primes in TGD framework

Adelic physics corresponds to a hierarchy of extensions of rationals inducing extensions of p-adic number fields and the proposal is that ramified primes of extension correspond to preferred p-adic primes.




Adelic physics suggests that prime p and quite generally, all preferred p-adic primes, could correspond to ramified primes for the extension of rationals defining the adele. Ramified prime divides discriminant D(P) of the irreducible polynomial P (monic polynomial with rational coefficients) defining the extension (see this).

Discriminant D(P) of polynomial whose, roots give rise to extension of rationals, is essentially the resultant Res(P,P') for P and its derivative P' defined as the determinant of so called Sylvester polynomial (see this). D(P) is proportional to the product of differences ri-rj, i≠ j the roots of p and vanishes if there are two identical roots.

Remark: For second order polynomials P(x)=x2+bx+c one has D= b2-4c.



Ramified primes divide D. Since the …

Shnoll effect decade later

As I wrote the first version of this chapter about Shnoll effect for about decade ago I did not yet have the recent vision about adelic physicsas a unification of real physics and various p-adics and real number based physics to describe the correlates of both sensory experience and cognition.

The recent view is that the hierarchy of extensions of rational numbers induces a hierarchy of extensions of p-adic number fields in turn defining adele. This hierarchy gives rise to dark matter hierarchy labelled by a hierarchy of Planck constants and also evolutionary hierarchy. The hierarchy of Planck constants heff=n× h0 is and essential element of quantum TGD and adelic physics suggests the identification of n as the dimension of extension of rationals. n could be seen as a kind of IQ for the system.

What is also new is the proposal that preferred p-adic primes labelling physical systems could correspond to so called ramified primes, call them p, of extension of rationals for…

Number theoretical view about unitarity conditions for twistor lift

Twistorialization leads to the proposal that cuts in the scattering amplitudes are replaced with sums over poles, and that also many-particle states have discrete momentum and mass squared spectrum having interpretation in terms of bound states. Gravitation would be the natural physical reason for the discreteness of the mass spectrum and in string models it indeed emerges as "stringy" mass spectrum. The situation is very similar to that in dual resonance models, which were predecessors of super string theories.

Number theoretical discretization based on the hierarchy of extensions of rationals defining extensions of p-adic number fields gives rise to cognitive representatations as discrete sets of space-time surface and discretization of 4-momenta and S-matrix with discrete momentum labels. In number theoretic discretization cuts reduce automatically to sequences of poles. Whether this discretization is an approximation reflecting finite cognitive resolution or whe…

Icosa-tetrahedral and icosa-dodecahedral bioharmonies as candidates for genetic code

Both the icosa-tetrahedral (see this) and icosa-dodecahedral harmony to be discussed below can be considered as candidates for bio-harmony as also the harmony involving fusion of 2 icosahedral harmonies and toric harmony (see this). The basic reason is that the third harmony corresponds to doublets. One cannot exclude the possibility of several equivalent representations of the code.

Icosa-tetrahedral harmony

Icosahedral harmonies can be characterized by a subgroup of icosahedral isometries A5 having 60 elements. If reflections are included the isometry group, oneas A5× Z2 with 120 elements. The group of symmetries is Z6,Z4, or Z2. There are two choices for Z2 and the interpretation has been that Z2 correspond to either reflection or rotation by π. A5 however allows also Z2× Z2 as subgroup. Amino-acids (AAs) correspond to orbits of the symmetry group and DNA codons coding for the AA correspond to triangles (3-chords) at the orbit. In purely icosahedral model on o…