Mathematical Physics

1203 Submissions

[6] viXra:1203.0089 [pdf] submitted on 2012-03-24 11:31:41

"Physical Intuition" : What Is Wrong with It ?

Authors: Elemer E Rosinger
Comments: 13 Pages.

It appears not to be known that subjecting the axioms to certain conditions, such as for instance to be physically meaningful, may interfere with the logical essence of axiomatic systems, and do so in unforeseen ways, ways that should be carefully considered and accounted for. Consequently, the use of "physical intuition" in building up axiomatic systems for various theories of Physics may lead to situations which have so far not been carefully considered.
Category: Mathematical Physics

[5] viXra:1203.0087 [pdf] submitted on 2012-03-22 09:37:31

A Discinnect : Limitations of the Axiomatic Method in Physics

Authors: Elemer E Rosinger
Comments: 16 Pages.

This paper presents the phenomenon of disconnect in the axiomatic approach to theories of Physics, a phenomenon which appears due to the insistence on axioms which have a physical meaning. This insistence introduces a restriction which is foreign to the abstract nature of axiomatic systems as such. Consequently, it turns out to introduce as well the mentioned disconnect. The axiomatic approach in Physics has a longer tradition. It is there already in Newton's Principia. Recently for instance, a number of axiomatic approaches have been proposed in the literature related to Quantum Mechanics. Special Relativity, [2], had from its beginning in 1905 been built upon two axioms, namely, the Galilean Relativity and the Constancy of the Speed of Light in inertial reference frames. Hardly noticed in wider circles, the independence of these two axioms had quite early been subjected to scrutiny, [5,3], and that issue has on occasion been addressed ever since, see [8,4,24] and the literature cited there. Recently, [24], related to these two axioms in Special Relativity, the following phenomenon of wider importance in Physics was noted. As the example of axiomatization of Special Relativity shows it, it is possible to face a disconnect between a system of physically meaningful axioms, and on the other hand, one or another of the mathematical models used in the study of the axiomatized physical theory. The consequence is that, seemingly unknown so far, one faces in Physics the possibility that the axiomatic method has deeper, less obvious, and in fact not considered, or simply overlooked limitations. As there is no reason to believe that the system of the usual two axioms of Special Relativity is the only one subjected to such a disconnect, the various foundational ventures in modern Physics, related for instance to gravitation, quanta, or their bringing together in an overarching theory, may benefit from the study of the possible sources and reasons for such a disconnect. An attempt of such study is presented in this paper.
Category: Mathematical Physics

[4] viXra:1203.0059 [pdf] submitted on 2012-03-16 03:56:23

Quantum Adeles

Authors: Matti Pitkänen
Comments: 41 Pages.

A generalization of number concept is proposed. One can replace integer n with n-dimensional Hilbert space and sum + and product × with direct sum ⊕ and tensor product ⊗ and introduce their co-operations, the definition of which is highly non-trivial.

This procedure yields also Hilbert space variants of rationals, algebraic numbers, p-adic number fields, and even complex, quaternionic and octonionic algebraics. Also adeles can be replaced with their Hilbert space counterparts. Even more, one can replace the points of Hilbert spaces with Hilbert spaces and repeat this process, which is very similar to the construction of infinite primes having interpretation in terms of repeated second quantization. This process could be the counterpart for construction of nth order logics and one might speak of Hilbert or quantum mathematics. The construction would also generalize the notion of algebraic holography and provide self-referential cognitive representation of mathematics.

This vision emerged from the connections with generalized Feynman diagrams, braids, and with the hierarchy of Planck constants realized in terms of coverings of the imbedding space. Hilbert space generalization of number concept seems to be extremely well suited for the purposes of TGD. For instance, generalized Feynman diagrams could be identifiable as arithmetic Feynman diagrams describing sequences of arithmetic operations and their co-operations. One could interpret ×q and +q and their co-algebra operations as 3-vertices for number theoretical Feynman diagrams describing algebraic identities X=Y having natural interpretation in zero energy ontology. The two vertices have direct counterparts as two kinds of basic topological vertices in quantum TGD (stringy vertices and vertices of Feynman diagrams). The definition of co-operations would characterize quantum dynamics. Physical states would correspond to the Hilbert space states assignable to numbers. One prediction is that all loops can be eliminated from generalized Feynman diagrams and diagrams are in projective sense invariant under permutations of incoming (outgoing legs).
Category: Mathematical Physics

[3] viXra:1203.0058 [pdf] submitted on 2012-03-16 03:58:04

About Absolute Galois Group

Authors: Matti Pitkänen
Comments: 18 Pages.

Absolute Galois Group defined as Galois group of algebraic numbers regarded as extension of rationals is very difficult concept to define. The goal of classical Langlands program is to understand the Galois group of algebraic numbers as algebraic extension of rationals - Absolute Galois Group (AGG) - through its representations. Invertible adeles -ideles - define Gl1 which can be shown to be isomorphic with the Galois group of maximal Abelian extension of rationals (MAGG) and the Langlands conjecture is that the representations for algebraic groups with matrix elements replaced with adeles provide information about AGG and algebraic geometry.

I have asked already earlier whether AGG could act is symmetries of quantum TGD. The basis idea was that AGG could be identified as a permutation group for a braid having infinite number of strands. The notion of quantum adele leads to the interpretation of the analog of Galois group for quantum adeles in terms of permutation groups assignable to finite l braids. One can also assign to infinite primes braid structures and Galois groups have lift to braid groups.

Objects known as dessins d'enfant provide a geometric representation for AGG in terms of action on algebraic Riemann surfaces allowing interpretation also as algebraic surfaces in finite fields. This representation would make sense for algebraic partonic 2-surfaces, and could be important in the intersection of real and p-adic worlds assigned with living matter in TGD inspired quantum biology, and would allow to regard the quantum states of living matter as representations of AGG. Adeles would make these representations very concrete by bringing in cognition represented in terms of p-adics and there is also a generalization to Hilbert adeles.
Category: Mathematical Physics

[2] viXra:1203.0007 [pdf] submitted on 2012-03-03 03:23:21

The Universe Has 5 Dimensions

Authors: Jake Vlastos
Comments: 16 Pages.

our universe has 5 dimensions adn this project is the proof for this theory
Category: Mathematical Physics

[1] viXra:1203.0005 [pdf] submitted on 2012-03-02 04:06:06

Evidence for a Closed-Curved and Cyclic Double Torus Universe

Authors: Dan Visser
Comments: 7 Pages.

The evidence comes from an alternative calculation of deviations in the dipole fine-structure constant (α). The alternative calculation reveals α deviations spatially and timely connected to a curved dark flow that fits a closed-curved and cyclic Double Torus Universe. This opens-up a new perception the Big Bang is spinning inside another cosmological model. In reality this means the deviation in the dipole α represents the recalculation of the electromagnetic force. Hence, in terms of a cosmological completeness, with also the other forces involved, one could say reality is recalculated by new features of the Double Torus Universe. The features are described earlier in papers posted in the Vixra-archive. Specifically this paper gives the derivations and calculations to show the evidence α deviations are spatially and timely connected in the Double Torus Universe.
Category: Mathematical Physics