Related papers: The End of Time?
It is now well established that there is no lower bound for the energy dissipated during a computation. The relevance of the zero-energy limit is unclear, however, because it entails computations that are unreliable or infinitely slow, or…
Derrick's theorem on the nonexistence of stable time-independent scalar field configurations [G. H. Derrick, J. Math. Phys. 5, 1252 (1964)] is generalized to finite systems of arbitrary dimension. It is shown that the "dilation" argument…
Hawking's proposal that the Universe has no temporal boundary and hence no beginning depends on the notion of imaginary time and is usually referred to as the "no-boundary proposal." This paper discusses a simple alternative approach by…
For many years now it has become conventional for theorists to argue that "space-time is doomed", with the difficulties in finding a quantum theory of gravity implying the necessity of basing a fundamental theory on something quite…
The Jacobi-Maupertuis metric provides a reformulation of the classical N-body problem as a geodesic flow on an energy-dependent metric space denoted $M_E$ where $E$ is the energy of the problem. We show that $M_E$ has finite diameter for $E…
We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the full classical…
We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…
It is a remarkable fact that all processes occurring in the observable Universe are irreversible, whereas the equations through which the fundamental laws of physics are formulated are invariant under time reversal. The emergence of…
Temporal Relationalism is that there is no time for the universe as a whole at the primary level. Time emerges rather at a secondary level; one compelling idea for this is Mach's: that time is to be abstracted from change. Temporal…
The nature of the change in perspective that accompanies the proposal of a unified physical theory deriving from the single dimension of time is elaborated. On expressing a temporal interval in a multi-dimensional form, via a direct…
The paper discusses recent proposals by Carroll and Chen, as well as Barbour, Koslowski, and Mercati to explain the (thermodynamic) arrow of time without a Past Hypothesis, i.e., the assumption of a special (low-entropy) initial state of…
The existence of a global time is often taken for granted but should instead be considered as a matter of investigation. By using the tools of global Lorentzian geometry I show that, under physically reasonable conditions, the impossibility…
The absence of unique time evolution in Einstein's spacetime description of gravity leads to the hitherto unresolved `problem of time' in quantum gravity. Shape Dynamics is an objectively equivalent representation of gravity that trades…
In several previous papers we have argued for a global and non-entropic approach to the problem of the arrow of time, according to which the ''arrow'' is only a metaphorical way of expressing the geometrical time-asymmetry of the universe.…
We present an introduction to the orbital stability of relative equilibria of Hamiltonian dynamical systems on (finite and infinite dimensional) Banach spaces. A convenient formulation of the theory of Hamiltonian dynamics with symmetry and…
We examine the properties of open quantum systems with respect to their time evolution in different regimes, Markovian and non-Markovian. We analyze their behaviour with respect to their coherent or decoherent time evolution by means of…
We propose a new wiew on the structure of quantum mechanics and postulate a q-deformed algebra of observables. We find equations of motion for this system, which guarantee a unitary time developement. We solve this equations for simple…
All observational evidence for dark matter and dark energy is so far exclusively gravitational. Hence, the dark sector may be equivalently described by a theory of the spacetime metric whose dynamics is affected by interactions with an…
Thirty years after the introduction of port-Hamiltonian systems, interest in this system class still remains high among systems and control researchers. Very recently, Jacob and Laasri obtained strong results on the solvability and…
In this work we analyze recent proposals by Das and D\"{u}rr (DD) to measure the arrival time distributions of quantum particles within the framework of de Broglie Bohm theory (or Bohmian mechanics). We also analyze the criticisms made by…