| Author: | Roman Andie | ISBN: | 9783592132229 |
| Publisher: | Lighthouse Books for Translation and Publishing | Publication: | September 20, 2017 |
| Imprint: | Language: | English |
| Author: | Roman Andie |
| ISBN: | 9783592132229 |
| Publisher: | Lighthouse Books for Translation and Publishing |
| Publication: | September 20, 2017 |
| Imprint: | |
| Language: | English |
1- Quite recently, the number theoretic interpretation of coupling constant evolution (see or in terms of a hierarchy of algebraic extensions of rational numbers inducing those of p-adic number fields encouraged to think that 1/αK has spectrum labelled by primes and values of heff. Two coupling constant evolutions suggest themselves: they could be assigned to length scales and angles which are in p-adic sectors necessarily discretized and describable using only algebraic extensions involve roots of unity replacing angles with discrete phases.
2 Few years ago, the relationship of TGD and GRT was finally understood (see ) . GRT space-time is obtained as an approximation as the sheets of the many-sheeted space-time of TGD are replaced with single region of space-time. The gravitational and gauge potential of sheets add together so that linear superposition corresponds to set theoretic union geometrically. forced to consider the possibility that gauge coupling evolution takes place only at the level of the QFT approximation and αK has only single value. is nice. But if true, one does not have much to say about the evolution of gauge coupling strengths.
3- The analogy of Riemann zeta function with the partition function of complex square root of thermodynamics suggests that the zeros of zeta have interpretation as inverses of complex temperatures s=1/β. Also 1/αK is analogous to temperature. led to a radical idea to be discussed in detail in the sequel.
4- Could the spectrum of 1/αK reduce to that for the zeros of Riemann zeta or - more plausibly - to the spectrum of poles of fermionic zeta ζF(ks)= ζ(ks)/ζ(2ks) giving for k=1/2 poles as zeros of zeta and as point s=2? ζF is motivated by the fact that fermions are the only fundamental particles in TGD and by the fact that poles of the partition function are naturally associated with quantum criticality whereas the vanishing of ζ and varying sign allow no natural physical interpretation.
Quite recently, the number theoretic interpretation of coupling constant evolution (see or in terms of a hierarchy of algebraic extensions of rational numbers inducing those of p-adic number fields encouraged to think that 1/αK has spectrum labelled by primes and values of heff. Two coupling constant evolutions suggest themselves: they could be assigned to length scales and angles which are in p-adic sectors necessarily discretized and describable using only algebraic extensions involve roots of unity replacing angles with discrete phases.
5 Few years ago, the relationship of TGD and GRT was finally understood (see ) . GRT space-time is obtained as an approximation as the sheets of the many-sheeted space-time of TGD are replaced with single region of space-time. The gravitational and gauge potential of sheets add together so that linear superposition corresponds to set theoretic union geometrically. forced to consider the possibility that gauge coupling evolution takes place only at the level of the QFT approximation and αK has only single value. is nice. But if true, one does not have much to say about the evolution of gauge coupling strengths.
6. The analogy of Riemann zeta function with the partition function of complex square root of thermodynamics suggests that the zeros of zeta have interpretation as inverses of complex temperatures s=1/β. Also 1/αK is analogous to temperature. led to a radical idea to be discussed in detail in the sequel.
1- Quite recently, the number theoretic interpretation of coupling constant evolution (see or in terms of a hierarchy of algebraic extensions of rational numbers inducing those of p-adic number fields encouraged to think that 1/αK has spectrum labelled by primes and values of heff. Two coupling constant evolutions suggest themselves: they could be assigned to length scales and angles which are in p-adic sectors necessarily discretized and describable using only algebraic extensions involve roots of unity replacing angles with discrete phases.
2 Few years ago, the relationship of TGD and GRT was finally understood (see ) . GRT space-time is obtained as an approximation as the sheets of the many-sheeted space-time of TGD are replaced with single region of space-time. The gravitational and gauge potential of sheets add together so that linear superposition corresponds to set theoretic union geometrically. forced to consider the possibility that gauge coupling evolution takes place only at the level of the QFT approximation and αK has only single value. is nice. But if true, one does not have much to say about the evolution of gauge coupling strengths.
3- The analogy of Riemann zeta function with the partition function of complex square root of thermodynamics suggests that the zeros of zeta have interpretation as inverses of complex temperatures s=1/β. Also 1/αK is analogous to temperature. led to a radical idea to be discussed in detail in the sequel.
4- Could the spectrum of 1/αK reduce to that for the zeros of Riemann zeta or - more plausibly - to the spectrum of poles of fermionic zeta ζF(ks)= ζ(ks)/ζ(2ks) giving for k=1/2 poles as zeros of zeta and as point s=2? ζF is motivated by the fact that fermions are the only fundamental particles in TGD and by the fact that poles of the partition function are naturally associated with quantum criticality whereas the vanishing of ζ and varying sign allow no natural physical interpretation.
Quite recently, the number theoretic interpretation of coupling constant evolution (see or in terms of a hierarchy of algebraic extensions of rational numbers inducing those of p-adic number fields encouraged to think that 1/αK has spectrum labelled by primes and values of heff. Two coupling constant evolutions suggest themselves: they could be assigned to length scales and angles which are in p-adic sectors necessarily discretized and describable using only algebraic extensions involve roots of unity replacing angles with discrete phases.
5 Few years ago, the relationship of TGD and GRT was finally understood (see ) . GRT space-time is obtained as an approximation as the sheets of the many-sheeted space-time of TGD are replaced with single region of space-time. The gravitational and gauge potential of sheets add together so that linear superposition corresponds to set theoretic union geometrically. forced to consider the possibility that gauge coupling evolution takes place only at the level of the QFT approximation and αK has only single value. is nice. But if true, one does not have much to say about the evolution of gauge coupling strengths.
6. The analogy of Riemann zeta function with the partition function of complex square root of thermodynamics suggests that the zeros of zeta have interpretation as inverses of complex temperatures s=1/β. Also 1/αK is analogous to temperature. led to a radical idea to be discussed in detail in the sequel.
