Prespacetime Journal最新文献

On the Maxwell Equations 关于麦克斯韦方程

Prespacetime Journal Pub Date : 2018-11-29 DOI: 10.1017/9781108292566.004

L. Ioan-Piscoran, J. López-Bonilla, R. López-Vázquez

引用次数: 0

Cosmological Models in Lyra Geometry with Linearly Varying Deceleration Parameter 线性变减速参数的天琴座几何宇宙学模型

Prespacetime Journal Pub Date : 2018-04-30 DOI: 10.20944/PREPRINTS201804.0380.V1

Kalyani Desikan

引用次数: 0

On Stirling Numbers of the Second Kind 论第二类斯特林数

Prespacetime Journal Pub Date : 2017-06-19 DOI: 10.3840/08003072

V. Barrera‐Figueroa, R. López-Vázquez, J. López-Bonilla

引用次数: 13

On Exponential Operators 关于指数算子

Prespacetime Journal Pub Date : 2017-01-08 DOI: 10.1016/b978-0-12-395704-7.50016-7

J. Morales, A. Iturri-Hinojosa, J. López-Bonilla

引用次数: 7

Overcoming the Bradyon–Tachyon Barrier 克服慢速子-超速子屏障

Prespacetime Journal Pub Date : 2016-10-04 DOI: 10.20944/PREPRINTS201610.0061.V1

L. Nanni

引用次数: 0

On the Legendre Polynomials 关于勒让德多项式

Prespacetime Journal Pub Date : 2015-08-02 DOI: 10.1142/9789813142831_0014

J. López-Bonilla, R. López-Vázquez, H. Torres-Silva

引用次数: 16

Microscopes and Telescopes for Theoretical Physics: How Rich Locally and Large Globally is the Geometric Straight Line? 理论物理中的显微镜和望远镜:几何直线在局部有多丰富，在全局有多大?

Prespacetime Journal Pub Date : 2011-04-01 DOI: 10.1063/1.3688983

E. Rosinger

{"title":"Microscopes and Telescopes for Theoretical Physics: How Rich Locally and Large Globally is the Geometric Straight Line?","authors":"E. Rosinger","doi":"10.1063/1.3688983","DOIUrl":"https://doi.org/10.1063/1.3688983","url":null,"abstract":"One is reminded in this paper of the often overlooked fact that the geometric straight line , or GSL, of Euclidean geometry is not necessarily identical with its usual Cartesian coordinatisation given by the real numbers in R . Indeed, the GSL is an abstract idea , while the Cartesian, or for that matter, any other specific coordinatisation of it is but one of the possible mathematical models chosen upon certain reasons. And as is known, there are a variety of mathematical models of GSL, among them given by nonstandard analysis, reduced power algebras, the topological long line, or the surreal numbers, among others. As shown in this paper, the GSL can allow coordinatisations which are arbitrarily more rich locally and also more large globally , being given by corresponding linearly ordered sets of no matter how large cardinal. Thus one can obtain in relatively simple ways structures which are richer locally and large globally than in nonstandard analysis, or in various reduced power algebras. Furthermore, vector space structures can be defined in such coordinatisations. Consequently, one can define an extension of the usual Differential Calculus. This fact can have a major importance in physics, since such locally richer and globally larger coordinatisations of the GSL do allow new physical insights, just as the introduction of various microscopes and telescopes have done. Among others, it and general can reassess special relativity with respect to its independence of the mathematical models used for the GSL. Also, it can allow the more appropriate modeling of certain physical phenomena. One of the long vexing issue of so called “infinities in physics\" can obtain a clarifying reconsideration. It indeed all comes down to looking at the GSL with suitably constructed microscopes and telescopes, and apply the resulted new modeling possibilities in theoretical physics. One may as well consider that in string theory, for instance, where several dimensions are supposed to be compact to the extent of not being observable on classical scales, their mathematical modeling may benefit from the presence of infinitesimals in the mathematical models of the GSL presented here. However, beyond all such particular considerations, and not unlikely also above them, is the following one: theories of physics should be not only background independent, but quite likely, should also be independent of the specific mathematical models used when representing geometry, numbers, and in particular, the GSL. One of the consequences of considering the essential difference between the GSL and its various mathematical models is that what appears to be the definitive answer is given to the intriguing question raised by Penrose : “Why is it that physics never uses spaces with a cardinal larger than that of the continuum?\".","PeriodicalId":216707,"journal":{"name":"Prespacetime Journal","volume":"118 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128110000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 16

Review of Palle Yourgrau's Book: A World without Time: The Forgotten Legacy of Godel and Einstein 《没有时间的世界:哥德尔和爱因斯坦被遗忘的遗产

Prespacetime Journal Pub Date : 2010-05-31 DOI: 10.5860/choice.43-0280

Stephen P. Smith

{"title":"Review of Palle Yourgrau's Book: A World without Time: The Forgotten Legacy of Godel and Einstein","authors":"Stephen P. Smith","doi":"10.5860/choice.43-0280","DOIUrl":"https://doi.org/10.5860/choice.43-0280","url":null,"abstract":"Yourgrau tells us that Godel was a philosophy-loving Platonist, and writes (page 23) on Platonists: \"who like Plato believed in the objective, independent existence of ideal, disembodied forms, of which the natural numbers are a paradigm.\" Here truth discovered objectively becomes conflated with existence, while the person that discovers truth fades in importance. Godel would have been better served by resolving his issues with the \"Dutch anti-Platonist, intuitionist mathematician L.E.J. Brouwer,\" who also visited Vienna as Yourgrau (page 29) indicates. Yourgrau (page 40) tells us that Einstein`s thinking impacted the Vienna Circle, as well as Godel: \"It was precisely the hegemony of positivism, Godel wrote later, that allowed the members of the circle to mistake Einstein for an ally and to underestimate the difficulty of rendering mathematics empirically acceptable by reconstructing it as a system for formal manipulation of signs. Einstein himself would awaken the positivists from their misconceptions about the ultimate relationship between his thoughts and theirs. You can find this book at Amazon: A World Without Time: The Forgotten Legacy of Godel and Einstein .","PeriodicalId":216707,"journal":{"name":"Prespacetime Journal","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121285576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Particle Massivation in TGD Universe TGD宇宙中的粒子质量

Prespacetime Journal Pub Date : 1900-01-01 DOI: 10.2174/9781681081793116010016

M. Pitkänen

{"title":"Particle Massivation in TGD Universe","authors":"M. Pitkänen","doi":"10.2174/9781681081793116010016","DOIUrl":"https://doi.org/10.2174/9781681081793116010016","url":null,"abstract":"This article represents the most recent view about particle massivation in TGD framework. This topic is necessarily quite extended since many several notions and new mathematics is involved. Indeed, the calculation of particle masses involves five chapters of [11]. In the following my goal is to provide an up-to-date summary whereas the chapters are unavoidably a story about evolution of ideas. The identification of the spectrum of light particles reduces to two tasks: the construction of massless states and the identification of the states which remain light in p-adic thermodynamics. The latter task is relatively straightforward. The thorough understanding of the massless spectrum requires however a real understanding of quantum TGD. It would be also highly desirable to understand why p-adic thermodynamics combined with p-adic length scale hypothesis works. A lot of progress has taken place in these respects during last years. Zero energy ontology providing a detailed geometric view about bosons and fermions, the generalization of $S$-matrix to what I call $M$-matrix, the notion of finite measurement resolution characterized in terms of inclusions of von Neumann algebras, the derivation of p-adic coupling constant evolution and p-adic length scale hypothesis from the first principles, the realization that the counterpart of Higgs mechanism involves generalized eigenvalues of the modified Dirac operator: these are represent important steps of progress during last years with a direct relevance for the understanding of particle spectrum and massivation although the predictions of p-adic thermodynamics are not affected. During 2010 a further progress took place. These steps of progress relate closely to zero energy ontology, bosonic emergence, the realization of the importance of twistors in TGD, and to the discovery of the weak form of electric-magnetic duality. Twistor approach and the understanding of the Chern-Simons Dirac operator served as a midwife in the process giving rise to the birth of the idea that all particles at fundamental level are massless and that both ordinary elementary particles and string like objects emerge from them. Even more, one can interpret virtual particles as being composed of these massless on mass shell particles assignable to wormhole throats so that four-momentum conservation poses extremely powerful constraints on loop integrals and makes them manifestly finite. The weak form of electric-magnetic duality led to the realization that elementary particles correspond to bound states of two wormhole throats with opposite K\"ahler magnetic charges with second throat carrying weak isospin compensating that of the fermion state at second wormhole throat. Both fermions and bosons correspond to wormhole contacts: in the case of fermions topological condensation generates the second wormhole throat. This means that altogether four wormhole throats are involved with both fermions, gauge bosons, and gravitons (for gravitons t","PeriodicalId":216707,"journal":{"name":"Prespacetime Journal","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126184470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0