Related papers: How do Laws Produce the Future?
All physical theories should obey the second law of thermodynamics. However, existing proposals to describe the dynamics of hybrid classical-quantum systems either violate the second law or lack a proof of its existence. Here we rectify…
Newton's third law states that any action is countered by a reaction of equal magnitude but opposite direction. The total force in a system not affected by external forces is thus zero. However, according to the principles of relativity, a…
Conservation laws are well-established in the context of Euclidean gradient flow dynamics, notably for linear or ReLU neural network training. Yet, their existence and principles for non-Euclidean geometries and momentum-based dynamics…
There are several formulations of the second law, and they may, in principle, have different domains of validity. Here a simple mathematical theorem is proven which serves as the most general basis for the second law, namely the Thomson…
The present work shows that the second law of thermodynamics gets naturally satisfied during the entire cosmic evolution of the universe starting from inflation to the late dark energy era, without imposing any exotic condition. This makes…
Complex systems theory pays much attention to simple mechanisms producing nontrivial patterns, especially power laws. However, power laws with exponent close to one also result from complex mixtures of mechanisms that, in isolation, would…
Exact law of mortality dynamics in changing populations and environment is derived. The law is universal for all species, from single cell yeast to humans. It includes no characteristics of animal- environment interactions (metabolism etc)…
If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below.…
How the energy conservation law is obeyed by the universe during its evolution is an important but not yet unanimously resolved question. Does the universe have a constant mass during its evolution or has its mass been increasing with its…
A hodological law causes the evolution of the universe to tend to follow particular types of path. I give simple illustrations in toy models and discuss how Kolmogorov complexity characterises the extent to which hodological laws explain,…
Considering the hyperbolic nature of the universe, the Hubble's law and the inverse square laws such as, the Coulomb's law and Newton's gravitational law, should be modified in accordance with the special theory of relativity. Consequently…
The principle which allows to construct new physical theories on the basis of classical mechanics by reduction of the number of its axiom without engaging new postulates is formulated. The arising incompleteness of theory manifests itself…
In the present article we have investigated a very natural question regarding the dynamics of the universe, namely, the possibility of its decelerating phase immediately after the present accelerating phase. To begin with, we have focused…
Fully relativistic and causal equations for the flow of charge in curved spacetime are derived. It is believed that this is the first set of equations to be published that correctly describes the flow of charge, and evolution of the…
Non-relativistic de Broglie-Bohm theory describes particles moving under the guidance of the wave function. In de Broglie's original formulation, the particle dynamics is given by a first-order differential equation. In Bohm's…
We discuss some properties of Lorentz invariant theories which allow for superluminal motion. We show that, if signals are always sent forward in time, closed curves along which signals propagate can be formed. This leads to problems with…
Most people agree that human activities are consistent with physical laws. One may naturally think that sensible economic theories can be derived from physical laws and evolutionary principles. This is indeed the case. In this paper, we…
Newton's laws of motion pose an apparent problem, sometimes referred to as "the independence problem": the first law seems to be a simple consequence of the second law, raising the question of why it was included as a separate law. Numerous…
Darwin's theory of evolution by natural selection does not predict long-term progress or advancement, nor does it provide a useful way to define or understand these concepts. Nevertheless, the history of life is marked by major trends that…
In physical theories, boundary or initial conditions play the role of selecting special situations which can be described by a theory with its general laws. Cosmology has long been suspected to be different in that its fundamental theory…