In virtue of its features, Bohm's quantum potential introduces interesting and relevant perspectives towards a satisfactory geometrodynamic description of quantum processes. This book makes a comprehensive state-of-the-art review of some of the most significant elements and results about the geometrodynamic picture determined by the quantum potential in various contexts. Above all, the book explores the perspectives about the fundamental arena subtended by the quantum potential, the link between the geometry associated to the quantum potential and a fundamental quantum vacuum. After an analysis of the geometry subtended by the quantum potential in the different fields of quantum physics (the non-relativistic domain, the relativistic domain, the relativistic quantum field theory, the quantum gravity domain and the canonical quantum cosmology), in the second part of the book, a recent interpretation of Bohm's quantum potential in terms of a more fundamental entity called quantum entropy, the approach of the symmetryzed quantum potential and the link between quantum potential and quantum vacuum are analysed, also in the light of the results obtained by the author.

This invaluable book provides a broad and comprehensive introduction to the fascinating and beautiful subject of timeless approaches in physics, focusing the attention in particular on significant models developed recently by the author. It presents relevant and novel perspectives in 21st century theoretical physics as regards the arena of physical processes and its geometry (both in special relativity, quantum mechanics, the quantum gravity domain and about the quantum vacuum). The timeless approach may be used as a source of reference by researchers in theoretical physics and at the same time it is also suitable for graduate students in physics who wish to have an extend view of some of the classic and fundamental models in the subject.

Recently the interest in Bohm realist interpretation of quantum mechanics has grown. The important advantage of this approach lies in the possibility to introduce non-locality ab initio, and not as an "unexpected host". In this book the authors give a detailed analysis of quantum potential, the non-locality term and its role in quantum cosmology and information. The different approaches to the quantum potential are analysed, starting from the original attempt to introduce a realism of particles trajectories (influenced by de Broglie's pilot wave) to the recent dynamic interpretation provided by Goldstein, Durr, Tumulka and Zanghi, and the geometrodynamic picture, with suggestion about quantum gravity. Finally we focus on the algebraic reading of Hiley and Birkbeck school, that analyse the meaning of the non-local structure of the world, bringing important consequences for the space, time and information concepts.

The development of theoretical physics can be seen as a continuous improvement of the models of space and time. In particular, the beginning of the 21st century brought a new vision into quantum physics: quantum particles move in space only, time measured with clocks is merely a numerical order of particles' motion. This so called "a-temporal" view of physics offers a radically new understanding of the micro and macro universe. On the basis of the notion of time as numerical order of material change, in this book the authors introduce suggestive unitary and holistic perspectives in the interpretation and explanation of several physical phenomena of contemporary physics. It is shown that the concept of time as a mathematical quantity measuring the numerical order of material changes resolves Zeno problems on motion, hypothetical travel into past, twin paradox of special relativity and allow new perspectives to be opened in the interpretation and explanation of Einstein-Podolski-Rosen experiment and of non-local correlations between subatomic particles. Moreover, a timeless description of the gravitational interaction and the idea of a timeless three-dimensional quantum vacuum as a fundamental bridge between gravity and quantum behaviour of matter are developed. Finally, in the second part of the book, after analysing the fundamental features of some relevant unitary theories of contemporary physics (such as superstring theory and loop quantum gravity) and making some considerations about being versus becoming and atomism versus monism in modelling physical reality at a fundamental level, it is shown that the replacement of the concept of time with the numerical order of material change provides a new suggestive interpretation of the fundamental unitary field theories opening the doors to a real "timeless theory of everything". The use of a simple and fluid language makes the book accessible to a wide reading public.