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The Second Law of Thermodynamics Forbids Time Travel Cosmology, 2014, Vol. 18. 212-222 Cosmology.com, 2014 The Second Law Of Thermodynamics Forbids Time Travel Marko Popovic Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT 84602, USA Abstract Four space-time coordinates define one thermodynamic parameter - Volume. Cell/ organism growth is one of the most fundamental properties of living creatures. The growth is characterized by irreversible change of the volume of the cell/organism. This irreversible change of volume (growth of the cell/organism) makes the system irreversibly change its thermodynamic state. Irreversible change of the systems thermodynamic state makes impossible return to the previous state characterized by state parameters. The impossibility to return the system to the previous state leads to conclusion that even to artificially turn back the arrow of time (as a parameter), it is not possible to turn back the state of the organism and its surroundings. Irreversible change of thermodynamic state of the organism is also consequence of the accumulation of entropy during life. So even if we find the way to turn back the time arrow it is impossible to turn back the state of the thermodynamic system (including organism) because of irreversibility of thermodynamic/ physiologic processes in it. Keywords: Time travel, Entropy, Living Organism, Surroundings, Irreversibility Cosmology, 2014, Vol. 18. 212-222 Cosmology.com, 2014 1. Introduction The idea of time travel has fascinated humanity since ancient times and can be found in texts as old as Mahabharata and Talmud. Later it continued to be developed in literature (i.e. Dickens' “A Christmas Carol”, or Twain's “A Connecticut Yankee in King Arthur's Court”…). In recent times the idea has continued to be used in literature and cinematography. Various ways of time travel were and still are a subject of books (The Time Machine by H. G. Wells…) and movies (i.e. Star Trek - 1980’s… Edge of Tomorrow - 2014). However this dreaming idea is also an interesting subject for the conventional science. The main idea is that an organism can travel back trough time and therefore reach thermodynamic states of surroundings that belong to past or future. Is such a process really possible? Time is defined as one of the coordinates of the space/time continuum, according to Einstein (1905). The other (space) coordinates are X, Y and Z. Actually these four coordinates define an important physical property and state parameter of the thermodynamic system - volume (V). V= X Y Z (1) The change of the volume is given as dV= f (dX,dY,dZ,dt) (2) where t is time and f is a function. Volume is one of the state parameters of thermodynamic systems. The other state parameters are pressure, amount of substance, temperature, entropy… Thermodynamic systems change their state by changing their state parameters. The change of state may be reversible or irreversible. There are three types of thermodynamic systems: 1) Isolated system is outlined by both rigid and isothermal border. It exchanges neither substance nor energy in any form with its surroundings. 2) Closed system border allows exchange of energy, but not substance with its surroundings. 3) Open system exchanges both, substance and energy with its surroundings. Living organisms are open thermodynamic systems according to Theory of open systems in biology (Von Bertalanffy, 1950). The description of a cell/organism exactly fits the description of a thermodynamic system. Both are defined by their content and borders. The borders of the cell/organism are semipermeable, so they exchange both substance and energy with their surroundings. Therefore organisms are open thermodynamic systems. This means that organisms import substance and energy from their surroundings, change the form of these substances in the synthesis reactions and self assembly processes, and accumulate them. The organisms change their volume, mass and entropy, and therefore change their thermodynamic state. Thus organisms grow. Organisms are open thermodynamic systems far from equilibrium, because only in this way they can perform self-assembly processes and avoid equilibrium in which all life professes would cease. In order to describe behavior of such systems it is necessary to use Prigogine’s nonequilibrium thermodynamic approach (Prigogine, 1946, 1947). The main characteristics of the living structures are: 1) Living things are composed of cells. 2) Living things have different levels of organization. 3) Living things use energy. 4) Living things respond to their environment. 5) Living things reproduce. 6) Living things grow. 7) Living things adapt to their environment. It was reported that organisms increase their entropy during their life span (Hayflick, 1977-2007, Silva, 2008, Hansen, 2008, Gems, & Doonan, 2009, Popovic 2014). This means that they increase their entropy and therefore change their thermodynamic state during transition between two selected time coordinates. Growth also causes the increase of the volume, mass and amount of substance of the organisms. Both increase of entropy and volume (and therefore mass and amount of substance) are irreversible. Furthermore, organisms change their states by changing the state of their surroundings because they import a substance from it. So by irreversibly changing their states, they irreversibly change the state of their surroundings (Atkins, 1995). In that case, an organism changes its state while it changes its time coordinate from t0 to t1 by changing its entropy from S0 to S1, mass from m0 to m1, amount of substance from n0 to n1, and volume from V0 to V1. Actually between two selected time coordinates (t0 and t1) organism imports and accumulates substances. Increase in volume and mass in childhood seems obvious. In childhood entropy increases because accumulation of substances. In senescence entropy increases because accumulation of damages and metabolic errors. Silva reported an increase of entropy during lifespan of average individuals to be 11.404 kJ/K per kg of body mass (Silva &Annamalai 2008). Hayflick marked an increase of entropy as the cause of aging (Hayflick, 1977-2007). Hansen concluded that the entropy of an open thermodynamic system doesn’t have to decrease (Hansen, 2008). Gems & Doonan reported that the entropy of the C. elegans pharynx tissues increases as the animal ages (and organizes itself) (Gems & Doonan, 2009). Popovic suggested that organisms increase their entropy during life because of growth (in youth) and accumulation of errors and damages (in senescence) (Popovic, 2014). To put it another way, the organisms grow, therefore they increase the number of particles (N) by exchange with the surroundings and accumulation of substances. Mass is a function of N. Entropy is also a function of N. m = N (Mr/Na)=f(N) (3) S= k ln W=k ln (CV)N=f(N) (4) m is mass, Mr is relative atomic mass, Na is Avogadro’s number, S is entropy, k is Boltzmann constant, C is proportionality constant, V is volume and N is number of particles. In closed systems N is constant, while in open systems it is a variable. So increase of N in open systems causes the change in m (because of growth and accumulation of substances), V (because of growth) and S (because of growth, accumulation of substances and accumulation of errors and damage). Thus the thermodynamic state of the system changes. Simultaneously the surroundings change its state by changing entropy from S0’ to S1’, mass from m0’ to m1’, amount of substance from n0’ to n1’, and volume from V0’ to V1’ according to the conservation law. The change of state of the system causes a change of state of the surroundings. Both changes of states are irreversible, because irreversibility of accumulation of inert molecules (i.e. lipofuscin), errors and damage. The process of time evolution is shown at figure 1. t0 S0’ m0’ n0’ V0’ t1 S1’ m1’ n1’ V1’ Figure 1: The time evolution of an open thermodynamic system – organism. It I grew up, so I changed my can be clearly seen from the image that parameters to S1 the organism irreversibly changes its S0 m0 n0 V0 m1 n1 V1 volume while decreasing the volume of its surroundings. By changing its volume it also changes its mass, as well as amount of substance and entropy. Time travel means that organisms could travel opposite or in the direction of time arrow from the present time coordinate (i.e. t1) to the selected coordinate in past (t0) or in future (t2). This means that surroundings changes its state that is characterized by selected time coordinate in past or in future. The state of the surroundings is characterized by state parameters such as entropy, volume, mass and others. In that case there is one open question left. Does the organism remain in its local state t1, or does it also change its state simultaneously with the surroundings during time travel? Let’s suppose that the man from the figure 1 is subject of time travel. It is an open question does he change his state during transition of the surroundings from state 2 to state 1? 2. Phenomenological consideration Let’s analyze possible thermodynamic ways for time travel. 2.1. Case 1: Organism changes it state during transition of state of the surroundings In that case organism appears younger because it changes its state simultaneously with the surroundings. It means that it must turn back the entropy and mass accumulated during life span (between t0 and t1). It is not possible because of irreversible processes occurring in the organism, processes of growth and accumulation of entropy. According to Prigogine (Prigogine, 1947) entropy change of the organism is given dS = deS + diS deS denoting the change of entropy by import, diS the production of entropy due to irreversible processes in the system, like chemical reactions, diffusion, and heat transport. Chemical reaction and self assembly processes organize imported substance in the form of structural elements or enzymes that organisms require for physiological function.
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