P-Adic Statistical Field Theory and Deep Belief Networks

Zúñiga–Galindo, W. A.

doi:10.2139/ssrn.4241508

Cited by 2 publications

(5 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We draw attention to certain parallels between our approach, which leads to the emergence of quantum theory from DHT, and the neural network model of the universe presented in articles [35][36][37][38][39] . In that sense a machine learning, ML, (or neural network) is naturally identified with a probability density function p(x; θ ) depending on a set of parameters.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Quantization of events in the event-universe and the emergence of quantum mechanics

Shor,

Benninger,

Khrennikov

2023

Sci Rep

View full text Add to dashboard Cite

Quantum mechanics (QM) is derived based on a universe composed solely of events, for example, outcomes of observables. Such an event universe is represented by a dendrogram (a finite tree) and in the limit of infinitely many events by the p-adic tree. The trees are endowed with an ultrametric expressing hierarchical relationships between events. All events are coupled through the tree structure. Such a holistic picture of event-processes was formalized within the Dendrographic Hologram Theory (DHT). The present paper is devoted to the emergence of QM from DHT. We used the generalization of the QM-emergence scheme developed by Smolin. Following this scheme, we did not quantize events but rather the differences between them and through analytic derivation arrived at Bohmian mechanics. We remark that, although Bohmian mechanics is not the main stream approach to quantum physics, it describes adequately all quantum experiments. Previously, we were able to embed the basic elements of general relativity (GR) into DHT, and now after Smolin-like quantization of DHT, we can take a step toward quantization of GR. Finally, we remark that DHT is nonlocal in the treelike geometry, but this nonlocality refers to relational nonlocality in the space of events and not Einstein’s spatial nonlocality. By shifting from spatial nonlocality to relational we make Bohmian mechanics less exotic.

show abstract

Section: Discussionmentioning

confidence: 99%

“…Then, giving a probability density p(x; θ ) for x ∈ S ⊂ Q p and θ ∈ R k is equivalent to define an ML on S . Recently, p-adic neural networks have been studied in connection with Euclidean quantum field theory 38,39 .…”

Section: Discussionmentioning

confidence: 99%

Quantization of events in the event-universe and the emergence of quantum mechanics

Shor,

Benninger,

Khrennikov

2023

Sci Rep

View full text Add to dashboard Cite

show abstract

“…In these studies, the laws of physics are shown to emerge as a learning procedures. Thus, action principles might be referred trivially as a particular learning procedure [34][35][36][37][38]. In recent studies [5,6], we have already drawn attention to intriguing parallels between our approach, which yields the emergence of quantum theory from DHT, and the neural network model of the universe as described in articles [34][35][36][37][38].…”

Section: P-adic Treelike Formalization Of Leibniz's Principlementioning

confidence: 99%

“…Thus, action principles might be referred trivially as a particular learning procedure [34][35][36][37][38]. In recent studies [5,6], we have already drawn attention to intriguing parallels between our approach, which yields the emergence of quantum theory from DHT, and the neural network model of the universe as described in articles [34][35][36][37][38]. Notably, we should highlight that p-adic neural networks have been investigated in conjunction with Euclidean quantum field theory, as detailed in references [37,38], thereby establishing a closer connection between our approach and the domain of ML.…”

Section: P-adic Treelike Formalization Of Leibniz's Principlementioning

confidence: 99%

See 1 more Smart Citation

Relational information framework, causality, unification of quantum interpretations and return to realism through non-ergodicity

Shor,

Benninger,

Khrennikov

2024

Preprint

View full text Add to dashboard Cite

In the framework of relational information, we explore analogs of physical theories and their properties. Specifically, we investigate the causal characteristics of relational information, examining how initial knowledge impacts future relational understanding of the universe/system. To achieve this, we establish a parameter space defining relational structures called dendrograms, exhibiting causal properties akin to those of Minkowski metric. Subsequently, we propose a statistical-dynamical model on this Minkowski-like parameter space, unifying Bohmian and Many Worlds interpretations of quantum theory in the framework of relational information. Additionally, we provide an analytical proof of the non-ergodicity of the relational information framework, revealing CHSH inequality violations as an emergent phenomenon. Our focus on relational information underscores its significance across scientific disciplines, where a single measurement or observation lacks meaning without context.

show abstract

P-Adic Statistical Field Theory and Deep Belief Networks

Cited by 2 publications

References 29 publications

Quantization of events in the event-universe and the emergence of quantum mechanics

Quantization of events in the event-universe and the emergence of quantum mechanics

Relational information framework, causality, unification of quantum interpretations and return to realism through non-ergodicity

Contact Info

Product

Resources

About