Abstract. A new event is defined as an intervention in the time reversible dynamical trajectories of particles in a system. New events are then assumed to be quantum fluctuations in the spatial and momentum coordinates, and mental action is assumed to work by ordering such fluctuations. It is shown that when the cumulative values of such fluctuations in a mean free path of a molecule are magnified by molecular interaction at the end of that path, the momentum of a molecule can be changed from its original direction to any other direction. In this way mental action can produce effects through the ordering of thermal motions. Examples are given which show that the ordering of 104-105 molecules is sufficient to (a) produce detectible PK results and (b) open sufficient ion channels in the brain to initiate a physical action. The relationship of the above model to the arrow of time is discussed.
Abstract. A new event is defined as an intervention in the time reversible dynamical trajectories of particles in a system. New events are then assumed to be quantum fluctuations in the spatial and momentum coordinates, and mental action is assumed to work by ordering such fluctuations. It is shown that when the cumulative values of such fluctuations in a mean free path of a molecule are magnified by molecular interaction at the end of that path, the momentum of a molecule can be changed from its original direction to any other direction. In this way mental action can produce effects through the ordering of thermal motions. Examples are given which show that the ordering of 104-105 molecules is sufficient to (a) produce detectible PK results and (b) open sufficient ion channels in the brain to initiate a physical action. The relationship of the above model to the arrow of time is discussed.
Abstract. It is shown that if mental influence can change a position or momentum coordinate within the limits of the uncertainty principle, such change, when magnified by a single interaction, is sufficient to order the direction of traveling molecules. Mental influence could initiate an action potential in the brain through this process by using the impact of ordered molecules to open the gates of sodium channels in neuronal membranes. It is shown that about 80 ordered molecules, traveling at thermal velocity in the intercellular medium in the brain, can break an ionic or covalent bond, and that the number needed to initiate an action potential is relatively small. If mental influence can act within the brain, it is reasonable to suppose it can act to some extent outside of it. If mental influence could not only order the direction of individual molecules, but coordinate this effect to produce a longitudinal pressure wave which is reasonably coherent across a macroscopic surface, only 104 molecules need be simultaneously affected to produce a detectible sound wave. Such an effect is not ordinarily observed, which suggests that if mental influence acts by ordering the direction of molecules, it acts at the level of individual molecules, but does not coordinate their motion.
The relationship between 'information' and 'time' is explored in order to look for a 'solution' to the 'Problem of Time'. 'Time' is found to be the result of the conversion of energy into 'information'. The 'time' number or label we assign to 'events' can be manufactured by processing information 'flowing' from a Feynman Clock (FC), via a 'signal', to a Feynman Detector (FD) in causal networks. Macroscopic arrows of time are built from the irreversible Quantum Arrow of Time (QAT) associated with unstable or excited states of quantum systems. The QAT is shown to be connected to the thermodynamic arrow of time. Collective Excitations, and causal networks provide a means for understanding 'time' in complex systems. The ordered set of the 'time' numbers labeling 'events' can be used to construct the 'direction' and 'dimension' associated with the usual conception of a 'time' axis or 'time' coordinate in quantum, classical and realtivistic mechanics.
This manuscript aims to illustrate a quantum-classical dissipative theory (suited to be converted to effective algorithms for numerical simulations) within the long-term project of studying molecular processes in the brain. Other approaches, briefly sketched in the text, have advocated the need to deal with both quantum and classical dynamic variables when studying the brain. At variance with these other frameworks, the manuscript’s formalism allows us to explicitly treat the classical dynamical variables. The theory must be dissipative not because of formal requirements but because brain processes appear to be dissipative at the molecular, physiological, and high functional levels. We discuss theoretically that using Brownian dynamics or the Nosè-Hoover-Chain thermostat to perform computer simulations provides an effective way to introduce an arrow of time for open quantum systems in a classical environment. In the future, We plan to study classical models of neurons and astrocytes, as well as their networks, coupled to quantum dynamical variables describing, e.g., nuclear and electron spins, HOMO and LUMO orbitals of phenyl and indole rings, ion channels, and tunneling protons.
Bohm theory is a formulation of Quantum Mechanics that characterises the state of a quantum system according to both the wave function, as in the conventional formulation, and the coordinates (positions) of all the particles that evolve in time drawing quantum continuous trajectories. Furthermore, a statistical ensemble of all the possible trajectories, raising from the impossibility to know the initial position of all the particles, establishes the exact correspondence with the traditional Quantum Mechanics. From a computational point of view, Bohm theory has found many applications in Chemical Physics especially to develop new methodologies for solving the Schrödinger equation and to address semi-classical approximations of Quantum Mechanics. From a theoretical point of view, the most appealing feature of Bohm theory is its capability to supply a conceptual map between the quantum formalism and our representation of what a chemical system is. Chemical systems are composed of molecules, but the same idea of molecule requires a specific arrangement in the space of particles, i.e., the nuclei of the atoms. The statistical description of conventional Quantum Mechanics on the basis of wave function alone is insufficient to establish a clear correspondence with such a picture of molecules. Indeed, chemists employ usually Classical Mechanics in order to overcome this drawback of the standard quantum theory. On the other hand, if the particles position is included in the quantum formalism, as Bohm theory does, the map can be defined in a self-consistent way. In other words, Bohm theory appears to be the suitable quantum framework to represent molecules and their motion. The chemical representation of molecular systems finds a natural correspondence with a single Bohm trajectory, since it is always implicitly assumed that molecular components have specific spatial position independently of our knowledge about it. Consequently, we develop a quantum method whose fundamental assumption is that a single Bohm trajectory, i.e., a quantum molecular trajectory, describes the molecular systems and the molecular motion correctly. First of all, we examine the correspondence between a single Bohm trajectory and the conventional Quantum Mechanics, without using the ensemble of trajectories. We verify that such a correspondence exists through numerical simulations and we prove formally that the statistical properties of a single Bohm trajectory explain the probabilistic description of Quantum Mechanics. Once the consistency of this original approach has been established, we investigate the predicted properties. For instance, we take into account the constants of motion (such as the energy) corresponding to the time evolution of the coordinates and the behaviour of simple chemical systems, e.g., the vibrational motion of single molecules interacting with a resonant field. In this way, unexpected features of the molecular motion are found. Secondly, we tackle the challenge of describing many components systems (like the chemical systems in ordinary conditions). As a matter of fact, the computation of the Bohm trajectory and of the wave function is extremely demanding. However, the statistical properties of the Bohm trajectory allow the derivation of stochastic theories for examining the dynamics of open quantum systems, i.e., few molecules (or few degrees of freedom) interacting with their environment (the other molecules). One of the developed stochastic methods correlates the dynamics of the reduced density matrix, for the degrees of freedom of interest, to the evolution of the corresponding Bohm coordinates. In other words, the Bohm equation, determining the set of all the particles velocities according to the full wave function, is replaced with a stochastic one that approximates the velocity of a subset of coordinates according to the reduced density matrix. In such a way, the quantum fluctuations induced by the environment are taken into account. The advantage of this method concerns its capability of describing quantum systems, including open quantum systems, in terms of a quantum trajectory. This could allow the understanding of the molecular motion during a spectroscopical experiment. The possibility of investigating reactive systems, such as conformational changes, is particularly interesting. As a matter of fact, chemical reactions can be completely characterised only through the particles motion and we define the suit- able quantum methodology providing a self-consistent description of the molecular motion.
Deriving an arrow of time from time-reversal symmetric microscopic dynamics is a fundamental open problem in many areas of physics, ranging from cosmology, to particle physics, to thermodynamics and statistical mechanics. Here we focus on the derivation of the arrow of time in open quantum systems and study precisely how time-reversal symmetry is broken. This derivation involves the Markov approximation applied to a system interacting with an infinite heat bath. We find that the Markov approximation does not imply a violation of time-reversal symmetry. Our results show instead that the time-reversal symmetry is maintained in the derived equations of motion. This imposes a time-symmetric formulation of quantum Brownian motion, Lindblad and Pauli master equations, which hence describe thermalisation that may occur into two opposing time directions. As a consequence, we argue that these dynamics are better described by a time-symmetric definition of Markovianity. Our results may reflect on the formulations of the arrow of time in thermodynamics, cosmology, and quantum mechanics.
It is brought forward that viable theories of the physical world that have no variable at all that can play the role of time, do not exist; some notion of time is one of the very first ingredients a candidate theory should possess. Almost by definition, time has an arrow. In contrast, time reversibility, or even the possibility to run the equations of motion backwards in time, is not at all a primary requirement. This means that the direction of the arrow of time may well be uniquely defined in the theory, even locally. It is explained that a rigorous definition of time, as well as a formulation of the causality and locality concepts, can only be given when one has a model for the physical phenomena described. The only viable causality condition is one that is symmetric under time reversal. We explain these statements in terms of the author’s favoured deterministic cellular automaton interpretation of quantum mechanics, also to be referred to as 'vector space analysis', and expand on these ideas. It is also summarised how our more rigorous causality condition affects Bell’s theorems. What distinguishes quantum systems from classical ones is our fundamental inability to control the microscopic details of the initial state when phenomena are studied in the light of some theoretical model.