Particle theory at Chicago in the late sixties and <i>p</i>-Adic strings

Frampton, Paul H.

doi:10.1088/1751-8121/ab8243

Cited by 8 publications

(6 citation statements)

References 22 publications

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“…This hypothesis was formulated in the framework of string theory, and it was supported by consideration of the p-adic analogue of the Veneziano amplitude and discussion on the main properties of the p-adic string theory. Since that paper, p-adic theoretical physics has been intensively developed [ 9 , 10 , 11 , 12 , 13 , 14 , 15 ] consistently with the development of the string theory ([ 9 , 16 , 17 , 18 , 19 ]) and complex disordered systems (The methodology of DH theory is like one used in ultrametric modeling of complex disordered systems: the aim is to find relational order which is not visible in the straightforward representation of data. Parisi and Sourlas [ 20 ] coupled this methodology to p-adic number theory and p-adic theoretical physics (see also Section 9 )) [ 20 ] (p-adic representation of the Parisi matrix for spin glasses).…”

Section: Introductionmentioning

confidence: 99%

“…The mathematical background for this model was developed in the works on p-adic mathematical physics [ 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 ]. However, in contrast to it, in DH theory p-adic points are not points of a kind of space-time (say space-time at the Planck scale) [ 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ], but all possible events which would happen in the universe. This p-adic (ontic) universe is classical.…”

Section: Introductionmentioning

confidence: 99%

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Towards Unification of General Relativity and Quantum Theory: Dendrogram Representation of the Event-Universe

Shor

Benninger

Khrennikov

2022

Entropy

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Following Smolin, we proceed to unification of general relativity and quantum theory by operating solely with events, i.e., without appealing to physical systems and space-time. The universe is modelled as a dendrogram (finite tree) expressing the hierarchic relations between events. This is the observational (epistemic) model; the ontic model is based on p-adic numbers (infinite trees). Hence, we use novel mathematics: not only space-time but even real numbers are not in use. Here, the p-adic space (which is zero-dimensional) serves as the base for the holographic image of the universe. In this way our theory is connected with p-adic physics; in particular, p-adic string theory and complex disordered systems (p-adic representation of the Parisi matrix for spin glasses). Our Dendrogramic-Holographic (DH) theory matches perfectly with the Mach’s principle and Brans–Dicke theory. We found a surprising informational interrelation between the fundamental constants, h, c, G, and their DH analogues, h(D), c(D), G(D). DH theory is part of Wheeler’s project on the information restructuring of physics. It is also a step towards the Unified Field theory. The universal potential V is nonlocal, but this is relational DH nonlocality. V can be coupled to the Bohm quantum potential by moving to the real representation. This coupling enhances the role of the Bohm potential.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Towards Unification of General Relativity and Quantum Theory: Dendrogram Representation of the Event-Universe

Shor

Benninger

Khrennikov

2022

Entropy

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“…By using the complexity measure on dendrograms and its p-adic string representation, we demonstrate the emergence of time arrow from the p-adic zero-dimensional field, where space and time are absent. Keywords: event-universe, dendrograms, hierarchic relational representation, dendrogramic dynamics, shape dynamics, stability of event-universe, arrow of time 1 See [16][17][18][19][20][21][22][23][24][25][26][27][28][29] for applications to strings and quantum theory; see [30][31][32] for applications to disordered systems (spin glasses).…”

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confidence: 99%

Holographic Dendrogramic Theory: Predictability of Relational Dynamics of the Event Universe and the Emergence of Time Arrow

Shor¹,

Benninger²,

Khrennikov³

2022

Preprint

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Recently we started the development of Holographic Dendrogramic Theory (DH-theory). It is based on the novel mathematical representation of the relational event universe (in the spirit of (Smolin, Barbour, Rovelli). Elementary events are represented by branches of dendrograms, finite trees, which are generated from data with clustering algorithms. In this note we study the dynamics of the event-universe generated by the appearance of a new event. Generally, each new event can generate the complete reconstruction of the whole dendrogramic universe. However, we found (via numerical simulation) unexpected stability of this universe. Its events are coupled via the hierarchic relational structure which is relatively stable with respect even random generation of new events. We also observe the regularity patterns in location of new events on dendrograms. In the curse of evolution, the dendrogram’s complexity increases and determine the arrow of time the event universe. We use the complexity measure from particle shape dynamics which was shown to be increase in both direction away from a Janus point and thus determine the arrow of time in symmetrical manner away from a Janus point. The particle shape dynamics theory is a relational theory with close ideological resemblance to DH-theory as both relays on Mach’s principle and Leibniz’s relationalism and his principles. By using the complexity measure on dendrograms and its p-adic string representation, we demonstrate the emergence of time arrow from the p-adic zero-dimensional field, where space and time are absent.

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“…In later years, Peter became interested in p-adic numbers in physics. The Freund-Witten paper [39] on p-adic string amplitudes and related work [40][41][42] created significant excitement in the theoretical physics community, briefly recalled here in the contribution by Frampton [43]. Although interest in p-adics then waned, it has recently experienced a renaissance in the context of the AdS/CFT correspondence, largely due to Steven Gubser, who (together with his students) contributed to this special issue [44].…”

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confidence: 99%

A Passion for Theoretical Physics: a special issue in memory of Peter G. O. Freund

Harvey,

Martinec,

Nepomechie

2020

Preprint

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Particle theory at Chicago in the late sixties and p-Adic strings

Cited by 8 publications

References 22 publications

Towards Unification of General Relativity and Quantum Theory: Dendrogram Representation of the Event-Universe

Towards Unification of General Relativity and Quantum Theory: Dendrogram Representation of the Event-Universe

Holographic Dendrogramic Theory: Predictability of Relational Dynamics of the Event Universe and the Emergence of Time Arrow

A Passion for Theoretical Physics: a special issue in memory of Peter G. O. Freund

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