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 fundamental 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. tt2  3 Feng and Crooks say have a method to accurately  t 2 001 (9) 0  measure time asymmetry at the microscopic level. They tTtcr3 0  cr found that during some intervals the entropy may de- For almost any reasonable numerical values this equa- crease. And, although the overall entropy increases at tion has two positive roots: ttt . each moment of the experiment does not, then the time cr120 cr For the first root we can neglect the y tterm0  and I has no clear direction and time asymmetry is not secured, obtain: but time has a symmetrical (not unlike this past or fu- 3 ture). As time progresses in the macroscopic world, it is T 2 unclear at the level of a single molecule, and if we asso- tt 3 0 (10) cr2 0  ciate this phenomenon to stem cells, as these remain 1 unchanged we could say that would be the only natural (this quantity, with minus sign, gives the third unphysi- case of detention of the arrow of time, which could be cal root). associated with natural perennial or cell immortality. And for the second root I can neglect the

2(tt0 /cr )  term, and I find: 5. ACKNOWLEDGMENTS 3 2  T I wish to thank to Jack Szostak of Howard Hughes Medical Institute tt 1 NR (11) cr2 0  to fruitful discussions. This work was supported by grant of National 3 TT00 University of Rosario (UNR), PID 1ING198. If I chose appropriate numerical values we can see that it probably produces also a growing order, and REFERENCES therefore the creation of structures like clusters, galaxies and stars [12]. [1] Reichenbach, H. (1956) The direction of time. University Also I have a growing of entropy, a decreasing order of California Press. [2] Davies, P.C.W. (1994) Stirring up trouble. In: Halliwell, and a spreading of the structures: stars energy is spread J.J., et al., Ed., Physical Origin of Time Asymmetry, in the universe, which ends in a thermic equilibrium Cambridge University Press, Cambridge. [13]. In fact, when t  the entropy gap vanishes [3] Mackey, M.C. (1992) Time’s arrow: The origin of ther- (see Eq.7) and the universe reaches a thermic equilib- modynamic behavior. Springer Verlag, Berlin. rium final state. [4] Zwanzig, R.W. (1966) Statistical mechanics of irreversi- Since 10414t 1.5 10 years after the big-bang all bility. In: Meijer, P., Ed., Quantum Statistical Mechanics, 0 Gordon and Breach, New York. the stars will exhaust their fuel [13], so the border be- [5] Bohm, A. (1986) Quantum mechanics: Foundations and tween the two periods most likely have this order of applications. Springer Verlag, Berlin. magnitude and must also be smaller than this number. [6] Castagnino, M., Gaioli, F. and Sforza, D. (1993) Sub- This is precisely the result of our calculations. stantial irreversibility in quantum cosmology. Proceed- In the molecular world, we can associate this with the ings of the V International Workshop on Instability and stem cells, seeing that the gap of entropy is close to Nonequilibrium Structures, Santiago de Chile, 1993. [7] Tolman, R.C. (1987) Relativity, thermodynamics, and zero or zero. Feng and Crooks [14] contributed to de- cosmology. Dover Publications, New York. veloping a measure of the time-asymmetry of recent [8] Landau, L.D. and Lifshitz, E.M. (1958) Statistical phys- single molecule RNA unfolding experiments. ics. Pergamon Press, Oxford. With the previous calculations but consistent with the [9] Sudarshan, E.C.G., Chiu, C.B., and Gorini, V. (1978) body temperatures of animals, we see that the equations Decaying states as complex energy eigen vectors in gen- are reduced almost naturally to zero entropy, and spread eralized quantum mechanics. Physical Review D, 18, over time, reaching the level of Feng and Crook, pro- 2914-2929. doi:10.1103/PhysRevD.18.2914 ducing the possibility that this occurs also mentioned [10] Laura, R. and Castagnino, M. (1998) On a minimal irre- that the cells could become immortal. versible quantum mechanics: The mixed states and de diagonal singularity. Physical Review A, 57, 4140-4142. 4. CONCLUSIONS doi:10.1103/PhysRevA.57.4140 [11] Jones, C. and Forman, W. (1992) Clusters and super- We see that nature, at the macroscopic level, has a ten- clusters of galaxies. In: Fabian, A.C., Ed., NATO ASI Se- dency to mess up, which in physics called entropy effect. ries, Kluwer Academic, Dordrecht, 366, 49-60. [12] Reeves, H. (1993) The growth of complexity in an ex-

panding universe. In: Bertola, F. and Curi, U., Ed., The 248, 90-101. Anthropic Principle, Cambridge University Press, Cam- doi:10.1038/scientificamerican0383-90 bridge. [14] Feng, E.H. and Crooks, G.E. (2008) Length of time´s [13] Dicus, D.A., Letaw, J.R., Teplitz, D.C. and Teplitz, V.L. arrow. Physical Review Letters, 101, 090602-1-090602-4. (1983) The future of the universe. Scientific American, doi:10.1103/PhysRevLett.101.090602