A landscape of time asymmetry

This is a conceptual overview on a polemical subject: the problem of time asymmetry. It is proved that time asymmetry can be considered as a global generalized symmetry breaking, produced by a choice of a physically admissible state space, in a global Gel'fand triplet. The well-known physics of irreversible process can be studied using this mathematical structure and all the arrows of time can be explained and coordinated. But the deeper problems of time definition and time arrow in quantum gravity remain outside of this landscape.     

Asymmetry through time dependency

Given a single network of interactions, asymmetry arises when the links aredirected. For example, if protein A upregulates protein B and protein Bupregulates protein C, then (in the absence of any further relationships between them) Amay affect C but not vice versa. This type of imbalance is reflected in the associatedadjacency matrix, which will lack symmetry. A different type of imbalance can arise wheninteractions appear and disappear over time. If A meets B today and B meets C tomorrow,then (in the absence of any further relationships between them) A may pass a message ordisease to C, but not vice versa. Hence, even when each interaction is a two-way exchange,the effect of time ordering can introduce asymmetry. This observation is very closelyrelated to the fact that matrix multiplication is not commutative. In this work, wedescribe a method that has been designed to reveal asymmetry in static networks and showhow it may be combined with a measure that summarizes the potential information flowbetween nodes in the temporal case. This results in a new method that quantifies theasymmetry arising through time ordering. We show by example that the new tool can be usedto visualize and quantify the amount of asymmetry caused by the arrow of time.     

Born’s Principle, Action-Reaction Problem, and Arrow of Time

We try to obtain Born's principle as a result of a subquantum heat death, using classical -theorem and the definition of a proper quantum -theorem, within the framwork of Bohm's theory. We shall show the possibility of solving the problem of action-reaction asymmetry present in Bohm's theory and the arrow of time problem in our procedure.     

The Universal Arrow of Time

Statistical physics cannot explain why a thermodynamic arrow of time exists, unless one postulates very special and unnatural initial conditions. Yet, we argue that statistical physics can explain why the thermodynamic arrow of time is universal, i.e., why the arrow points in the same direction everywhere. Namely, if two subsystems have opposite arrow-directions at a particular time, the interaction between them makes the configuration statistically unstable and causes a decay towards a system with a universal direction of the arrow of time. We present general qualitative arguments for that claim and support them by a detailed analysis of a toy model based on the baker’s map.     

Ferroelectricity in an ising chain magnet

We report discovery of collinear-magnetism-driven ferroelectricity in the Ising chain magnet Ca3Co2-xMn(x)O6 (x approximately 0.96). Neutron diffraction shows that Co2+ and Mn4+ ions alternating along the chains exhibit an up-up-down-down ( upward arrow upward arrow downward arrow downward arrow) magnetic order. The ferroelectricity results from the inversion symmetry breaking in the upward arrow upward arrow downward arrow downward arrow spin chain with an alternating charge order. Unlike in spiral magnetoelectrics where antisymmetric exchange coupling is active, the symmetry breaking in Ca3(Co,Mn)2O6 occurs through exchange striction associated with symmetric superexchange.     

The Global Arrow of Time as a Geometrical Property of the Universe

Traditional discussions about the arrow of time in general involve the concept of entropy. In the cosmological context, the direction past-to-future is usually related to the direction of the gradient of the entropy function of the universe. But the definition of the entropy of the universe is a very controversial matter. Moreover, thermodynamics is a phenomenological theory. Geometrical properties of space-time provide a more fundamental and less controversial way of defining an arrow of time for the universe as a whole. We will call the arrow defined only on the basis of the geometrical properties of space-time, independently of any entropic considerations, the global arrow of time. In this paper we will argue that: (i) if certain conditions are satisfied, it is possible to define a global arrow of time for the universe as a whole, and (ii) the standard models of contemporary cosmology satisfy these conditions.     

核子中奇异夸克分布不对称性与轻味夸克碎裂效应

核子中奇异－反奇异夸克分布的不对称性是核子结构研究中的重要非微扰效应, 然而至今未被实验所直接检验.为了探讨测量这种奇异分布不对称性的有效方法,考察了轻味夸克碎裂效应对测量奇异分布不对称性的影响.建议通过直接测量高能中微子和反中微子的带电流深度非弹散射中的带电和中性D介子的微分截面来测量奇异分布的不对称性.这种方法能够使奇异分布不对称性与轻味夸克碎裂的效应相分离.     

The Arrow of Time in the Equations of Motion

It is argued that time's arrow is present in all equations of motion. But it is absent in the point particle approximations commonly made. In particular, the Lorentz-Abraham-Dirac equation is time-reversal invariant only because it approximates the charged particle by a point. But since classical electrodynamics is valid only for finite size particles, the equations of motion for particles of finite size must be considered. Those equations are indeed found to lack time-reversal invariance, thus ensuring an arrow of time. Similarly, more careful considerations of the equations of motion for gravitational interactions also show an arrow of time. The existence of arrows of time in quantum dynamics is also emphasized.     

(Global and local) fluctuations of phase space contraction in deterministic stationary nonequilibrium

We studied numerically the validity of the fluctuation relation introduced in Evans et al. [Phys. Rev. Lett. 71, 2401-2404 (1993)] and proved under suitable conditions by Gallavotti and Cohen [J. Stat. Phys. 80, 931-970 (1995)] for a two-dimensional system of particles maintained in a steady shear flow by Maxwell demon boundary conditions [Chernov and Lebowitz, J. Stat. Phys. 86, 953-990 (1997)]. The theorem was found to hold if one considers the total phase space contraction sigma occurring at collisions with both walls: sigma=sigma( upward arrow )+sigma( downward arrow ). An attempt to extend it to more local quantities sigma( upward arrow ) and sigma( downward arrow ), corresponding to the collisions with the top or bottom wall only, gave negative results. The time decay of the correlations in sigma( upward arrow, downward arrow ) was very slow compared to that of sigma. (c) 1998 American Institute of Physics.     

On the Entropy Production of Time Series with Unidirectional Linearity

There are non-Gaussian time series that admit a causal linear autoregressive moving average (ARMA) model when regressing the future on the past, but not when regressing the past on the future. The reason is that, in the latter case, the regression residuals are not statistically independent of the regressor. In previous work, we have experimentally verified that many empirical time series indeed show such a time inversion asymmetry. For various physical systems, it is known that time-inversion asymmetries are linked to the thermodynamic entropy production in non-equilibrium states. Here we argue that unidirectional linearity is also accompanied by entropy generation. To this end, we study the dynamical evolution of a physical toy system with linear coupling to an infinite environment and show that the linearity of the dynamics is inherited by the forward-time conditional probabilities, but not by the backward-time conditionals. The reason is that the environment permanently provides particles that are in a product state before they interact with the system, but show statistical dependence afterwards. From a coarse-grained perspective, the interaction thus generates entropy. We quantitatively relate the strength of the non-linearity of the backward process to the minimal amount of entropy generation. The paper thus shows that unidirectional linearity is an indirect implication of the thermodynamic arrow of time, given that the joint dynamics of the system and its environment is linear.     

Quantum gravity,the origin of time and time's arrow

The local Lorentz and diffeomorphism symmetries of Einstein's gravitational theory are spontaneously broken by a Higgs mechanism by invoking a phase transition in the early universe, at a critical temperature T_c below which the symmetry is restored. The spontaneous breakdown of the vacuum state generates an external time, and the wave function of the universe satisfies a time-dependent Schrödinger equation, which reduces to the Wheeler-deWitt equation in the classical regime for T<T_c, allowing a semiclassical WKB approximation to the wave function. The conservation of energy is spontaneously violated for T>T_c, and matter is created fractions of seconds after the big bang, generating the matter in the Universe. The time direction of the vacuum expectation value of the scalar Higgs field generates a time asymmetry, which defines the cosmological arrow of time and the direction of increasing entropy as the Lorentz symmetry is restored at low temperatures.     

The Arrow of Time: From Universe Time-Asymmetry to Local Irreversible Processes

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 have also shown that, under definite conditions, this global time-asymmetry can be transferred to local contexts as an energy flow that points to the same temporal direction all over the spacetime. The aim of this paper is to complete the global and non-entropic program by showing that our approach is able to account for irreversible local phenomena, which have been traditionally considered as the physical origin of the arrow of time.     

Does a Computer Have an Arrow of Time?

Schulman (Entropy 7(4):221–233, 2005) has argued that Boltzmann’s intuition, that the psychological arrow of time is necessarily aligned with the thermodynamic arrow, is correct. Schulman gives an explicit physical mechanism for this connection, based on the brain being representable as a computer, together with certain thermodynamic properties of computational processes. Hawking (Physical Origins of Time Asymmetry, Cambridge University Press, Cambridge, 1994) presents similar, if briefer, arguments. The purpose of this paper is to critically examine the support for the link between thermodynamics and an arrow of time for computers. The principal arguments put forward by Schulman and Hawking will be shown to fail. It will be shown that any computational process that can take place in an entropy increasing universe, can equally take place in an entropy decreasing universe. This conclusion does not automatically imply a psychological arrow can run counter to the thermodynamic arrow. Some alternative possible explanations for the alignment of the two arrows will be briefly discussed.     

The Direction of Time: From the Global Arrow to the Local Arrow

In this paper we discuss the traditional approaches to the problem of the arrow of time. On the basis of this discussion we adopt a global and nonentropic approach, according to which the arrow of time has a global origin and is an intrinsic, geometrical feature of space-time. Finally, we show how the global arrow is translated into local terms as a local time-asymmetric flux of energy.     

Black Hole Evaporation Entails an Objective Passage of Time

Time's apparent passage has long been debated by philosophers, with no decisive argument for or against its objective existence. In this paper we show that introducing the issue of determinism gives the debate a new, empirical twist. We prove that any theory that states that the basic laws of physics are time-symmetric must be strictly deterministic. It is only determinism that enables time reversal, whether theoretical or experimental, of any entropy-increasing process. A contradiction therefore arises between Hawking's [1] argument that physical law is time-symmetric and his controversial claim [2] that black-hole evaporation introduces a fundamental unpredictability into the physical world. The latter claim forcibly entails an intrinsic time-arrow independent of boundary conditions. A simulation of a simple system under time reversal shows how an intrinsic time arrow re-emerges, destroying the time reversal, when even the slightest failure of determinism occurs. This proof is then extended to the classical behavior of black holes. We conclude with pointing out the affinity between time's arrow and its apparent passage.     

Supernovae and the Arrow of Time

Supernovae are explosions of stars and are a central problem in astrophysics. Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities develop during the star’s explosion and lead to intense interfacial RT/RM mixing of the star materials. We handle the mathematical challenges of the RT/RM problem based on the group theory approach. We directly link the conservation laws governing RT/RM dynamics to the symmetry-based momentum model, derive the model parameters, and find the analytical solutions and characteristics of RT/RM dynamics with variable accelerations in the linear, nonlinear and mixing regimes. The theory outcomes explain the astrophysical observations and yield the design of laboratory experiments. They suggest that supernova evolution is a non-equilibrium process directed by the arrow of time.     

Arrow of Time in Rigged Hilbert Space Quantum Mechanics

Arno Bohm and Ilya Prigogine's Brussels–Austin Group have been working on the quantum mechanical arrow of time and irreversibility in rigged Hilbert space quantum mechanics. A crucial notion in Bohm's approach is the so-called preparation/registration arrow. An analysis of this arrow and its role in Bohm's theory of scattering is given. Similarly, the Brussels–Austin Group uses an excitation/de-excitation arrow for ordering events, which is also analyzed. The relationship between the two approaches is initially discussed focusing on their semi-group operators and time arrows. Finally a possible realist interpretation of the rigged Hilbert space formulation of quantum mechanics is considered.     

Normal state of a polarized fermi gas at unitarity

We study the Fermi gas at unitarity and at T=0 by assuming that, at high polarizations, it is a normal Fermi liquid composed of weakly interacting quasiparticles associated with the minority spin atoms. With a quantum Monte Carlo approach we calculate their effective mass and binding energy, as well as the full equation of state of the normal phase as a function of the concentration x=n downward arrow/n upward arrow of minority atoms. We predict a first order phase transition from normal to superfluid at x(c)=0.44 corresponding, in the presence of harmonic trapping, to a critical polarization P(c)=(N upward arrow - N downward arrow/(N upward arrow + N downward arrow)=77%. We calculate the radii and the density profiles in the trap and predict that the frequency of the spin dipole mode will be increased by a factor of 1.23 due to interactions.     

Can inflation explain the second law of thermodynamics?

The inflationary model of the universe can explain several of the cosmological conundra that are mysteries in the standard hot big bang model. Paul Davies has suggested that inflation can also explain the second law of thermodynamics, which describes the time asymmetry of the universe. Here I note several difficulties with this suggestion, showing how the present inflationary models must assume the arrow of time rather than explaining it. If the second law is formulated as a consequence of the hypothesis that there were no long-range spatial correlations in the initial state of the universe, it is shown how some of the cosmological conundra might be explained even without inflation. But if the ultimate explanation is to include inflation, three, essential elements remain to be demonstrated which I list.     

Causality in quantum mechanics

We show explicitly how the causal arrow of time that follows from quantum mechanics has already been inserted at a deeper level by the choice of normalisation conditions. This prohibits information being sent backwards in time but does not determine a time direction for state propagation.