We use strong sub-additivity of entanglement entropy, Lorentz invariance, and the Markov property of the vacuum state of a conformal field theory to give a new proof of the irreversibility of the renormalization group in d = 4 space-time dimensions – the a-theorem. This extends the proofs of the c and F theorems in dimensions d = 2 and d = 3 based on vacuum entanglement entropy, and gives a uni...

Recently a wave equation for unified field theory has been derived [1-3] from a lemma of Cartan-Riemann differential geometry [4, 5] and used to give the first self consistent unified description of the gauge invariant gravitational and electromagnetic fields. The former is the Riemann form and the latter is the torsion form. One form is the Hodge dual of the other. The theory has been shown [1...

In his search for a unified field theory that could undercut quantum mechanics, Einstein considered five dimensional classical Kaluza-Klein theory. He studied this theory most intensively during the years 1938-1943. One of his primary objectives was finding a non-singular particle solution. In the full theory this search got frustrated and in the x-independent theory Einstein, together with Pau...

This article explains the idea of unified field theories in particle physics. It starts with a historical review of two successful theories which unified two apparently distinct forces: Maxwell’s theory of electromagnetism and Glashow–Salam–Weinberg theory of electroweak forces. Then it describes known four forces in Nature: gravitational, electromagnetic, weak and strong forces, and what their...

Two previous articles (Bentwich, 2012: a & b) have postulated the existence of a new (hypothet‐ ical) Computational Unified Field Theory (CUFT) which appears to be capable of bridging the gap between Quantum Mechanics and Relativity Theory within a conceptually higher-or‐ dered ('D2') Universal Computational Principle (' י'), thereby representing a potential candi‐ date for a 'Theory of Everyth...

We study a mechanism of symmetry transition upon compactification of 5-dimensional field theory on S/Z2. The transition happens unless all components in a multiplet of a symmetry group have a common Z2 parity on S /Z2. This mechanism is applied to a breakdown of SU(5) gauge symmetry in grand unified theory and phenomenological implications are discussed. ∗e-mail: [email protected]

We address the question “How do people learn new concepts?” from the perspective of Unified Cognitive Science. By Unified Cognitive Science, we simply mean the practice of taking seriously all relevant findings from the diverse sciences of the mind, here focusing on the question of concept learning. The particular perspective on concept learning we advocate here grows out of the Neural Theory o...

The author presents a historical sketch of the projective relativity theory before and (with new qualitative arguments) after World War II. Then he treats the development of his Projective Unified Field Theory since 1957 up till now with applications to a closed cosmological model, with the result of a vanishing big bang and satisfying numerical cosmological parameters in good agreement with th...

I try to argue that the only way out of the black hole information paradox is through a unified quantum field theory of gravity and other interactions. Superstring theory is especially interesting, since in a special limit, the classical picture of ’t Hooft emerges.

We study the effects of the interaction terms between the inflaton fields on the inflationary dynamics in multi-field models. With power law type potential and interactions, the total number of e-folds may get considerably reduced and can lead to unacceptably short period of inflation. Also we point out that this can place a bound on the characteristic scale of the underlying theory such as str...