Times arrow

L, S. Schulman, Time Arrows and Quantum Measurement, University Press, Cambridge, 1997,... 

The time arrow is irreversible. The dehydrogenation reaction under superheated liquid-film conditions is initiated again with the facile adsorption of substrate from the solution to the catalyst surface. 

Figure 6 Swelling of hybrid hydrogels in response to temperature. The hydrogels were prepared from HPMA-DAMA copolymers, Ni(II), and KS590 coiled coil. The gels were equilibrated in PBS (pH 7.4) at 25°C prior to an increase in temperature. Rate of heating l°C/min plus 2 min equilibration time. Arrows indicate elevated temperatures of 25°C, 35°C, and 45°C, respectively. Modihed from Reference [35].

Fig. 3. Schematic diagram of the spot photobleaching method of FRAP. (A) Darkened circles represent fluorescently labeled molecules evenly distributed over a two-dimensional surface (assumed to be an infinite plane). (B) White and light gray circles represent the initial postbleach distribution of photobleached molecules within a 1-pm diameter spot. (C) Redistribution of photobleached and unbleached molecules as a consequence of random diffusion over time. (D) Curve representing the fluorescence intensity within the l-pm diameter spot monitored over time arrows a, b, and c indicate the time-points that correspond to their respective panels. The rate of recovery from point b to point c is used to determine the diffusion constant. The magnitude of the recovery is determined by comparing the fluorescence intensity at point c with the initial intensity at point a, and is used to determine the mobile fraction.

FIGURE 1.3 Concentration profile from a mechanism employing three intermediates, /j, /j, I, plus the initial (dark) state /q. /[(O) = 1 is assumed. The cyclic reaction is started (initiated) by a laser flash. Molecules relax through the intermediate states back to the initial state. The concentration profile of intermediate /j shows all three relaxation times (arrows). 

Let us postulate that we live in a 3D hypersurface that slides along the u axis with speed v°u = ca, where the u axis coincides with the arrow of time. The 4-velocity is then a (row or column) vector 1 a = ( ca,vx,vy,vz). The plus (resp. minus) sign corresponds to the speed of preons that enter (resp. leave) our 3D world, parallel (resp. antiparallel) to the time arrow. It will be seen below that this constant ca is the one that enters Einstein s mass-energy equation, and corresponds to the speed of our 3D world along the time axis (interpretation 2 in Fig. 1). The speed of electromagnetic radiation in free space is a different constant c. The value of the latter may be either identical or numerically close to c , depending of whether one adopts a relativistic or an emission theory for photons, respectively (see Section V). 

In the 19th century the variational principles of mechanics that allow one to determine the extreme equilibrium (passing through the continuous sequence of equilibrium states) trajectories, as was noted in the introduction, were extended to the description of nonconservative systems (Polak, 1960), i.e., the systems in which irreversibility of the processes occurs. However, the analysis of interrelations between the notions of "equilibrium" and "reversibility," "equilibrium processes" and "reversible processes" started only during the period when the classical equilibrium thermodynamics was created by Clausius, Helmholtz, Maxwell, Boltzmann, and Gibbs. Boltzmann (1878) and Gibbs (1876, 1878, 1902) started to use the terms of equilibria to describe the processes that satisfy the entropy increase principle and follow the "time arrow."... 

Figure 2.10 Cylindrically symmetric hydrodynamical model of accretion flow with rotation during the early collapse phase, showing the inflow of matter in the meridional plane and the build-up of a flat rotating disk structure after about 1.05 free-fall times. Arrows indicate matter flow direction and velocity, gray lines indicate cuts of isodensity surfaces with meridional plane. Dark crosses outline locations of supersonic to subsonic transition of inflow velocity this corresponds to the position of the accretion shock. Matter falling along the polar axis and within the equatorial plane arrive within 1600 yr almost simultaneously, which results in an almost instantaneous formation of an extended initial accretion disk [new model calculation following the methods in Tscharnuter (1987), figure kindly contributed by W. M. Tscharnuter],...

Entropy in an isolated system increases dS/dt> 0 until it reaches equilibrium dS/dt = 0, and displays a direction of change leading to the thermodynamic arrow of time. The phenomenological approach favoring the retarded potential over the solution to the Maxwell field equation is called the time arrow of radiation. These two arrows of time lead to the Einstein-Ritz controversy Einstein believed that irreversibility is based on probability considerations, while Ritz believed that an initial condition and thus causality is the basis of irreversibility. Causality and probability may be two aspects of the same principle since the arrow of time has a global nature. 

Figure 10 The different processes amenable to NMR spectroscopy are indicated above the time arrow, below are the typical time windows for different molecular motions and events.

Figure 5. Concentration of Ala as a function of pH for solutions B-H at various aging times arrows indicate increasing aging time...

Figure 5.2.4 Evolution of the diffusion field during chronoamperometry at an electrode with active and inactive areas on its surface. In this case the electrode is a regular array such that the active areas are of equal size and spacing, but the same principles apply for irregular arrays, (a) Short electrolysis times, (b) intermediate times, (c) long times. Arrows indicate flux lines to the electrode.

Fig. 2 TLC of the amylaseSOO product from the potato starch. The amylase3(X) was reacted on the 0.2% potato starch solution (pH 7.0) at 40°C. Each lane shows product of each reaction time. Arrow indicates the only one product of maitotetraose. Lane S shows the standard of oligosaccharaides. G1, glucose G2, maltose G3, maltotriose G4, maitotetraose G5, maltopentaose G7, maltoheptaose.

Figure 4 Experimental steady state iodide concentrations as a function of reciprocal residence time. Arrows indicate transitions from one steady state to another (Reprinted from Ref. 14 with permission of the American Institute of Physics.)...

Since that incomprehensible beginning, when the time-arrow of entropy marked the directionality of this outset, entropy seems... 

Eddington underscores his high regard for the second law of thermodynamics in his view that The law that entropy always increases—the second law of thermodynamics—holds, I think, the supreme position among the laws of Nature. As an increase in entropy measures the increase in disorder, that is, the increase in randomness, Eddington developed the concept of times arrow, with the following thought ... 

Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future if the random element decreases the arrow points toward the past. That is the only distinction known to physics. I shall use the phrase times arrow to express this one-way property of time which has no analogue in space. It is a singularly interesting property from a philosophical standpoint. 

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