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The Asymmetry of Time and the Cellular World. Is Immortality Possible?

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The Asymmetry of Time and the Cellular World. Is Immortality Possible? Vol.2, No.1, 49-52 (2011) Journal of Biophysical Chemistry doi:10.4236/jbpc.2011.21007 The asymmetry of time and the cellular world. Is immortality possible? Roberto O. Aquilano1,2 1Instituto de Física Rosario (CONICET-UNR), Rosario, Argentina; [email protected] 2Facultad de Ciencias Exactas, Ingeniería y Agrimensura (UNR), Rosario, Argentina Received 21 August 2010; revised 15 October 2010; accepted 10 November 2010. ABSTRACT time, a time asymmetry to distinguish past from future, which corresponds with our own perception of time. I analyze the flow of time in this article, both in This is clear at the macroscopic level, however, on a gross and in microscopic processes, with a well microscopic scale, since the amount of energy involved defined arrow of time, but as the amount of en- in the process is so small, it is more difficult to assert ergy involved in the microscopic processes is that entropy is increasing, and that therefore time is so small, it is more difficult to argue that the moving forward (toward the future), rather than back- entropy increases, and therefore the direction of ward (toward the past). time becomes confusing and undefined at the molecular level. Therefore, is cell immortality In the macroscopic world, how can we explain the possible? obvious time-asymmetry of the universe if the funda- mental laws of physic are time-symmetric? Physicists Keywords: Entropy; Time; Cell usually answer this question first observing that, if the initial state of the universe would be an equilibrium state, the universe will remain for ever in such state, making 1. INTRODUCTION impossible to find any time-asymmetry. The concept of time is intuitive and easily distin- The set of irreversible processes that began in an un- guishable past from present or future. It was not as easy stable non-equilibrium state constitute a branch system for thinkers. In ancient and found the first human think- [1,2]. That is to say, every one of these processes began ing about time. Plato, for example, said that time is the in a non-equilibrium state, which state was produced by moving image of eternity. Later, Newton described it as a previous process of the set. an absolute, true and mathematical, which runs smoothly. Once I have understood the origin of the initial un- In the twenties of last century, Einstein came to regard as stable state of each irreversible process within the uni- a mere illusion. These ideas reflect the immense com- verse it is not difficult to obtain a growing entropy, in plexity of the time, an issue that has been the subject of any subsystem within the universe. Alternatively, taking reflection for many philosophers and research for many into account the enormous amount of information con- scientists. Scientists are precisely those who now seek to tained in the subsystem we can neglect some part of it address the fact that science does not provide a clear [3,4]. I can use more refined mathematical tools [5,6]. definition of what is time. With any one of these tools I can solve this problem. The only fundamental scientific theory that makes a It remains only one problem: why the universe began preferred direction for time is of the second law of ther- in an unstable low-entropy state? If I exclude a miracu- modynamics, which asserts that the entropy of the Uni- lous act of creation we have only three scientific answer: verse increases as time flows forward. This explanation a) The unstable initial state of the universe is a law of provides an orientation, an arrow of time. Our perception nature. of this would, therefore, a direct consequence of the th- b) This state was produced by a fluctuation. ermodynamic time arrow. c) The expansion of the universe (coupled to the nu- The entropy of any thermodynamically isolated sys- clear reactions in it) produces a decreasing of the (mat- tem tends to increase with time and this has to this law a ter-radiation) entropy gap. definite orientation. That the entropy of the universe to The third solution was sketched by Paul Davies in ref- increase over time is that there is a direction, an arrow of erence [2], only as a qualitative explanation. The expan- Copyright © 2011 SciRes. Openly accessible at http://www.scirp.org/journal/JBPC/ 50 R.O. Aquilano / Journal of Biophysical Chemistry 2 (2011) 49-52 sion of the universe is like an external agency (namely: conditions at any time t yields: external to the matter-radiation system of the universe) tr() t tr () t 1,... tr 0 (2) that produces a decreasing of its entropy gap, with re- *1 The last equations show that is not a state but spect to de maximal possible entropy, S (and there- 1 max only the coefficients of a correction around the equilib- fore an unstable state), not only at t = 0 but in a long * period of the universe evolution. We shall call this dif- rium state ()t . It is explicitly proved in paper [10], that has a vanishing trace. ference the entropy gap ΔS, so the actual entropy will be 1 I am now able to compute the entropy gap S with SSact max S. * In the microscopic world Feng and Crooks created a respect to the equilibrium state ()t at any time t. It will be the conditional entropy of the state ()t with method to accurately measure the time asymmetry of the * microscopic. In fact have found that, on a microscopic respect to the equilibrium state ()t [3]: 1 scale and for some intervals, entropy can actually de- Str[ log(* )] (3) crease. And that while the general entropy increase on Using now Eq.1, and considering only times average, each time the experiment does not, that is, time tt 1 is not always a clear direction. My work aims at under- NR I can expand the logarithm to obtain: standing the relation between time asymmetry and en- t 12 Setr()*1 (4) tropy, which would also be crucial for the development where I have used Eq.2. I can now introduce the equilib- of future molecular and cellular studies. rium state i for T . Then: 2. THE ENTROPY 13 t T 2 SZTetre()1 (5) We know that the universe isotropic and homogeneous where e t is a diagonal matrix with this function as expansion is a reversible process with constant entropy diagonal. But as is peaked around we arrive to [7]. The matter and the radiation of the universe are in a 1 1 a final formula for the entropy gap: thermic equilibrium state * ()t at any time t. As the radiation is the only important component, from the 1 3 t T * SCTee (6) thermodynamical point of view, we can chose ()t as a black-body radiation state. where C is a positive constant. Let us consider an isotropic and homogeneous model of universe with radius a. From the conservation of the 3. EVOLUTION OF THE ENTROPY GAP ∆S energy-momentum tensor and radiation state equation, -1 I have computed of S for times larger than decoup- we know that , we can verify that S const. 2/3 1 T a ling time and therefore, as at and Ta , The irreversible nature of the universe evolution is where t is the age of the universe and T the present not produced by the universe expansion, even if ρ 0 0 temperature. Then: * ()t has a slow time variation. Therefore, the main 2 t process that has an irreversible nature after decoupling 1 ()0 3 t 2 Tt0 time is the burning of unstable H in the stars (that pro- SCete1 (7) duces He and, after a chain of nuclear reactions, Fe). where C is a positive constant. The curve St() it has This nuclear reaction process has certain mean life-time 1 1 a maximum at tt and a minimum at tt . Let us t and phenomenologically we can say the state cr1 cr2 NR compute these critical times. The time derivative of the of the universe, at time t, is: entropy reads: ()tte () t 0[( t )1 ] (1) *1 1 2 t 3 where 1 is certain phenomenological coefficient St 2 1 1 0 S (8) constant in time, since all the time variation of nuclear 3 tT t 00 reactions is embodied in the exponential law e t . I can foresee, also on phenomenological grounds, that 1 This equation shows two antagonic effects. The uni- must peak strongly around 1 the characteristic en- verse expansion effect is embodied in the second and ergy of the nuclear process. third terms in the square brackets an external agency to All these reasonable phenomenological facts can also the matter-radiation system such that, if we neglect the be explained theoretically: Eq.1 can be computed with second term, it tries to increase the entropy gap and, the theory of paper [9] or with rigged Hilbert space the- therefore, to take the system away from equilibrium (as ory [5]. In reference [10] it is explicitly proved that 1 we will see the second term is practically negligible). On peaks strongly at the energy 1 . The normalization the other hand, the nuclear reactions embodied in the Copyright © 2011 SciRes. Openly accessible at http://www.scirp.org/journal/JBPC/ R.O. Aquilano / Journal of Biophysical Chemistry 2 (2011) 49-52 5151 y-term, try to convey the matter-radiation system to- However, on a microscopic scale, since the amount of wards equilibrium. These effects become equal at the energy involved in the processes is very small, it is very critical times tcr such that: difficult to say that entropy is increasing, and therefore 1 time to move forward rather than backward.
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