The article of C. D. White entitled "The double copy: gravity from gluons explains in more detail the double copy duality and also shows that it relates in many cases also exact classical solutions of Einsteins equations and YM theories. One starts from L-loop scattering amplitude involving products of kinematical factors n_{i} and color factors c_{i} and replaces color factors with extra kinematical factors ñ_{i}. The outcome is an L-loop amplitude for gravitons.

As if gravitation could be regarded as a gauge theory with polarization and/or momenta identified giving rise to effective color charges. This is like taking gauge potential and giving it additional index to get metric tensor. This naive analogy seems to hold true at the level of scattering amplitudes and also for many classical solutions of field equations. Could one think that gravitons as states correspond to gauge singlets formed from two gluons and having spin 2? Also spin 1 and spin 0 states would be obtained and double copies involve also them.

TGD view about elementary particles indeed predicts that gravitons be regarded in certain sense pairs of gauge bosons. Consider now gravitons and assume for simplicity that spartners of fundamental fermions - identifiable as local multi-fermion states allowed by statistics - are not involved: this does not change the situation much. Graviton's spin 2 requires 2 fermions and 2 anti-fermions: fermion or anti-fermion at each throat. For gauge bosons fermion and anti-fermion at two throats is enough. One could therefore formally see gravitons as pairs of two gauge bosons in accordance with the idea about graviton is a square of gauge boson.

The fermion contents of the monopole flux tube associated with elementary particle determines quantum numbers of the flux tube as particle and characterizes corresponding interaction. The interaction depends also on the charges at the ends of the flux tube. This leads to a possible interpretation for the formation of bound states in terms of flux tubes carrying quantum numbers of particles.

- These long flux tubes can be arbitrarily long for large values of ℏ
_{eff}=n× ℏ_{0}assigned to the flux tube. A plausible guess for for the expression of ℏ in terms of ℏ_{0}is as ℏ= 6× ℏ_{0}. The length of the flux tube scales like ℏ_{eff}. - Nottale proposed that it makes sense to speak about gravitational Planck constant h
_{gr}. In TGD this idea is generalized and interpreted in framework of generalized quantum theory. For flux tubes assignable to gravitational bound states along which gravitons propagate, one would have ℏ_{eff}= ℏ_{gr}= GMm/v_{0}, where v_{0}<c is parameter with dimensions of velocity. One could write interaction strength asGMm = v

_{0}× ℏ_{gr}. - ℏ
_{gr}obtained from this formula must satisfy ℏ_{gr}>hbar. This generalizes to other interactions. For instance, one has one would haveZ

_{1}Z_{2}e^{2}= v_{0}hbar_{em}for electromagnetic flux tubes in the case that ones h

_{em}>hbar. The interpretation of the velocity parameter v_{0}is discussed in at here.One could even turn the situation around and say that the value of ℏ

_{eff}fixes the interaction strength. ℏ_{eff}would depend on fermion content and thus of virtual particle and also on the masses or other charges at the ends of the flux tube. The longer the range of the interaction, the larger the typical value of ℏ_{eff}. - The interpretation could be in terms long length scale quantum fluctuations at quantum criticality. Particles generate U-shaped monopole flux tubes with varying length proportional to ℏ
_{gr}. If these U-shaped flux tubes from two different particles find each other, they reconnect to flux tube pairs connecting particles and give rise to interaction. What comes in mind is tiny curious and social animals studying their environment. - I have indeed proposed this picture in biology: the U-shaped flux tubes would be tentacles with which bio-molecules (in particular) would be scanning their environment. This scanning would be the basic mechanism behind immune system. It would also make possible for bio-molecules to find each in molecular crowd and provide a mechanism of catalysis. Could this picture apply completely generally? Would even elementary particles be scanning their environment with these tentacles?
- Could one interpret the flux tubes as analogs of virtual particles or could they replace virtual particles of quantum field theories? The objection is that flux tubes would have time-like momenta whereas virtual particle analogs would have space-like momenta. The interpretation makes sense only if the associated momenta are between space-like and time-like that is light-like so that flux tube would correspond to mass shell particle. But this is the case in twistor approach to gauge theories also in TGD (see this).
Perhaps the following interpretation is more appropriate. Flux tubes are accompanied by strings and string world sheets can be interpreted as stringy description of gravitation and other interactions.

See the article More about the construction of scattering amplitudes in TGD framework or the chapter The Recent View about Twistorialization in TGD Framework of "Towards M-theory: Part II".

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

## Comments

## Post a comment