Open Access
Open access

Society

Springer Nature
Springer Nature
ISSN: 01472011, 19364725, 23386932, 25974874, 27155994, 20870493

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SCImago
Q3
WOS
Q2
Impact factor
1.4
SJR
0.245
CiteScore
1.3
Categories
Social Sciences (miscellaneous)
Sociology and Political Science
Areas
Social Sciences
Years of issue
1968, 1971-1999, 2002-2025
journal names
Society
Publications
6 569
Citations
15 074
h-index
45
Top-3 citing journals
SSRN Electronic Journal
SSRN Electronic Journal (290 citations)
Society
Society (155 citations)
The American Sociologist
The American Sociologist (78 citations)
Top-3 organizations
Top-3 countries
USA (3181 publications)
United Kingdom (248 publications)
Canada (108 publications)

Most cited in 5 years

Found 
from chars
Publications found: 699
Quantum Field Theory
Wetterich C.
Springer Nature
Fundamental Theories of Physics 2025 citations by CoLab: 0  |  Abstract
Quantum field theory emerges in a very natural and straightforward way from our general probabilistic setting. We have already seen that very simple unique jump chains or probabilistic cellular automata, like the transport automata, describe twodimensional quantum field theories for free massless fermions. Actually, it is the quantum field theory which arises directly at the most basic level. Single-particle quantum mechanics is obtained as a special case or approximation, rather than being the starting point, as in the historical development of quantum field theory. The generic situation for interesting probabilistic systems describes states with many particles, with a continuum limit admitting an infinite number.
Fundamental Probabilities
Wetterich C.
Springer Nature
Fundamental Theories of Physics 2025 citations by CoLab: 0  |  Abstract
The advent of quantum mechanics has opened a probabilistic view on fundamental physics. It has come, however, with new concepts and rules like wave functions, non-commuting operators, and the rules for associating these quantities with observations. The unusual probabilistic features have opened many debates on their interpretation, as well as on suggestions for extensions of quantum mechanics.
Qubit Automaton
Wetterich C.
Springer Nature
Fundamental Theories of Physics 2025 citations by CoLab: 0  |  Abstract
In the present section, we concentrate on quantum mechanics for a single qubit. A simple local chain with three classical Ising spins already realizes many characteristic features of quantum mechanics, such as non-commuting operators for observables, the quantum rule for computing expectation values, discrete measurement values corresponding to the spectrum of operators, the uncertainty principle, unitary evolution, and complex structure.
Quantum Mechanics
Wetterich C.
Springer Nature
Fundamental Theories of Physics 2025 citations by CoLab: 0  |  Abstract
In this chapter, we discuss probabilistic automata that realize all features of quantum mechanics.We start with quantum mechanics for a two-state system or a single qubit. The quantum spin in an arbitrary direction is associated with a corresponding classical Ising spin. For the quantum subsystem, the deterministic evolution for the automaton results in the unitary evolution according to the von Neumann equation for the quantum density matrix. Suitable updating rules can realize an arbitrary Hamiltonian for a single qubit. Quantum mechanics for a single qubit is the extension of the quantum clock system to rotations in three-dimensional space or on the two-dimensional sphere.
Discussion and Conclusions
Wetterich C.
Springer Nature
Fundamental Theories of Physics 2025 citations by CoLab: 0  |  Abstract
This book proposes a probabilistic formulation of the fundamental laws of nature. On a fundamental level, the description of the universe is entirely based on the concepts of classical statistics: observables that take definite values in the states of the system, probabilities for these states, and expectation values of observables computed from these probabilities. The overall probability distribution covers everything in the world, including all times, all locations, and all possible events.
Fermions
Wetterich C.
Springer Nature
Fundamental Theories of Physics 2025 citations by CoLab: 0  |  Abstract
In this section we present a first simple classical statistical model that is equivalent to a quantum field theory. It is a generalized Ising model which describes free massless fermions in one time and one space dimension. Even though this two-dimensional model remains extremely simple, all aspects of the formalism of quantum mechanics are already visible. This concerns both the Schr¨odinger or von Neumann equation for a unitary evolution and the appearance of non-commuting operators for observables like position or momentum.
Fundamental Probabilism
Wetterich C.
Springer Nature
Fundamental Theories of Physics 2025 citations by CoLab: 0  |  Abstract
The starting point of the present work is the assumption that the fundamental description of our world is probabilistic [25,52–54]. The basic objects for this description are probability distributions and observables. Deterministic physics arises as an approximation for particular cases. Our description of probabilities remains within the standard setting of classical statistics. No separate laws for quantum mechanics will be introduced. They follow from the classical statistical setting for particular classes of subsystems.
Probabilistic and Deterministic Evolution
Wetterich C.
Springer Nature
Fundamental Theories of Physics 2025 citations by CoLab: 0  |  Abstract
Different types of evolution are distinguished by the way the probabilistic information propagates. This is reflected by the question of how boundary properties influence behavior in the bulk.
Entanglement in Classical and Quantum Statistics
Wetterich C.
Springer Nature
Fundamental Theories of Physics 2025 citations by CoLab: 0  |  Abstract
Entanglement describes situations where two parts of a system are connected and cannot be separated. The properties in one part depend on the properties of the other part. The quantitative description of such situations is given by correlation functions. There is no conceptual difference between entanglement in classical statistics and entanglement in quantum mechanics [185]. In this chapter, we will explicitly construct probabilistic automata that realize the maximally entangled state of a twoqubit quantum system.
Embedding Quantum Mechanics in Classical Statistics
Wetterich C.
Springer Nature
Fundamental Theories of Physics 2025 citations by CoLab: 1  |  Abstract
It has often been asserted that an embedding of quantum mechanics in classical statistics is not possible. The present work demonstrates by explicit examples that this claim is not justified.
Continuous Classical Variables
Wetterich C.
Springer Nature
Fundamental Theories of Physics 2025 citations by CoLab: 0  |  Abstract
The use of continuous classical variables brings us closer to the quantum particle, for which we have argued that it involves an infinite number of degrees of freedom. If we allow for an arbitrary orthogonal evolution of the classical wave function, we can find a bit-quantum map which maps this to the evolution of a quantum particle in a potential according to the usual Schrödinger equation.
Subsystems
Wetterich C.
Springer Nature
Fundamental Theories of Physics 2025 citations by CoLab: 0  |  Abstract
Subsystems are a central ingredient for a probabilistic description of the world. For most practical purposes, one does not want to deal with the overall probability distribution for all events in the universe from the past to the future. One rather concentrates on subsystems.
Probabilistic Time
Wetterich C.
Springer Nature
Fundamental Theories of Physics 2025 citations by CoLab: 0  |  Abstract
Time is a fundamental concept in physics. It is the first structure among observables that we will discuss. Rather than being postulated as an “a priori concept” with physics formulated in a pregiven time and space, probabilistic time is a powerful concept to order and organize observables. There is no time outside the correlations for the observables of the statistical system.
Correlated Computing
Wetterich C.
Springer Nature
Fundamental Theories of Physics 2025 citations by CoLab: 0  |  Abstract
As already emphasized, the crucial feature of quantum computing is the large number of correlations between the associated classical bits. These correlations result from the quantum constraint of positivity of the density matrix for the quantum subsystem.
Introduction
Wetterich C.
Springer Nature
Fundamental Theories of Physics 2025 citations by CoLab: 0  |  Abstract
Since the discovery of quantum mechanics, probabilities have play a central role in fundamental physics. The mathematical formalism of quantum mechanics makes statements about expectation values of observables. The expectation value describes the mean value of an observable for an ensemble of many identical measurements. It is a genuinely probabilistic concept since every possible measurement value of the observable is weighted by the probability of finding it. The quantum laws for the computation of these probabilities are often felt to be mysterious.

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Publishing countries

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USA, 3181, 48.42%
United Kingdom, 248, 3.78%
Canada, 108, 1.64%
Germany, 55, 0.84%
Republic of Korea, 55, 0.84%
Ireland, 45, 0.69%
Australia, 41, 0.62%
Israel, 40, 0.61%
France, 29, 0.44%
China, 29, 0.44%
Italy, 28, 0.43%
Czech Republic, 19, 0.29%
Netherlands, 17, 0.26%
Nigeria, 15, 0.23%
Sweden, 13, 0.2%
South Africa, 12, 0.18%
India, 11, 0.17%
Denmark, 9, 0.14%
Japan, 9, 0.14%
Turkey, 8, 0.12%
Austria, 6, 0.09%
Spain, 6, 0.09%
Finland, 6, 0.09%
Switzerland, 6, 0.09%
Georgia, 5, 0.08%
Iran, 5, 0.08%
New Zealand, 5, 0.08%
Norway, 5, 0.08%
USSR, 5, 0.08%
Poland, 4, 0.06%
Serbia, 4, 0.06%
Yugoslavia, 4, 0.06%
Russia, 3, 0.05%
Argentina, 3, 0.05%
Belgium, 3, 0.05%
Bulgaria, 3, 0.05%
Greece, 3, 0.05%
Saudi Arabia, 3, 0.05%
Singapore, 3, 0.05%
Jamaica, 3, 0.05%
Portugal, 2, 0.03%
Brazil, 2, 0.03%
Ghana, 2, 0.03%
Egypt, 2, 0.03%
UAE, 2, 0.03%
Tanzania, 2, 0.03%
Kazakhstan, 1, 0.02%
Estonia, 1, 0.02%
Bangladesh, 1, 0.02%
Benin, 1, 0.02%
Brunei, 1, 0.02%
Hungary, 1, 0.02%
Zimbabwe, 1, 0.02%
Qatar, 1, 0.02%
Cuba, 1, 0.02%
Luxembourg, 1, 0.02%
Malaysia, 1, 0.02%
Mexico, 1, 0.02%
Monaco, 1, 0.02%
Myanmar, 1, 0.02%
San Marino, 1, 0.02%
Slovakia, 1, 0.02%
Thailand, 1, 0.02%
Tunisia, 1, 0.02%
Uganda, 1, 0.02%
Philippines, 1, 0.02%
Chile, 1, 0.02%
Ethiopia, 1, 0.02%
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USA, 207, 33.93%
United Kingdom, 148, 24.26%
Ireland, 43, 7.05%
Germany, 19, 3.11%
Canada, 17, 2.79%
Australia, 16, 2.62%
Nigeria, 14, 2.3%
India, 10, 1.64%
China, 8, 1.31%
Italy, 8, 1.31%
Israel, 6, 0.98%
Netherlands, 6, 0.98%
Finland, 6, 0.98%
Czech Republic, 6, 0.98%
South Africa, 6, 0.98%
France, 5, 0.82%
Austria, 4, 0.66%
Spain, 4, 0.66%
New Zealand, 4, 0.66%
Republic of Korea, 4, 0.66%
Greece, 3, 0.49%
Denmark, 3, 0.49%
Iran, 3, 0.49%
Turkey, 3, 0.49%
Argentina, 2, 0.33%
Belgium, 2, 0.33%
Ghana, 2, 0.33%
Saudi Arabia, 2, 0.33%
Tanzania, 2, 0.33%
Sweden, 2, 0.33%
Japan, 2, 0.33%
Russia, 1, 0.16%
Portugal, 1, 0.16%
Bangladesh, 1, 0.16%
Benin, 1, 0.16%
Bulgaria, 1, 0.16%
Brunei, 1, 0.16%
Zimbabwe, 1, 0.16%
Qatar, 1, 0.16%
Monaco, 1, 0.16%
Myanmar, 1, 0.16%
Norway, 1, 0.16%
UAE, 1, 0.16%
Poland, 1, 0.16%
Slovakia, 1, 0.16%
Uganda, 1, 0.16%
Philippines, 1, 0.16%
Chile, 1, 0.16%
Switzerland, 1, 0.16%
Ethiopia, 1, 0.16%
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