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Cosmology, 2014, Vol. 18. 212-222 Cosmology.com, 2014 The Law Of Forbids Travel

Marko Popovic Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT 84602, USA Abstract Four -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 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: , 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 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 .

The main idea is that an organism can travel back trough time and therefore reach thermodynamic states of surroundings that belong to or . 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 (i.e. lipofuscin), errors and damage. The process of time is shown at figure 1.

t0 S0’ m0’ n0’ V0’ t1 S1’ m1’ n1’ V1’ Figure 1: The 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 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. Organisms irreversibly accumulate bio-macromolecules and perform growth. Organisms cannot turn back the entropy and mass irreversibly accumulated during life span.

2.2. Case 2: Organism does not change it state during transition of state of the surroundings

In this case the organism does not change its parameters, so they remain S1, m1, n1 and V1 while the parameters of the surroundings change from S1’, m1’, n1’ and V1’ to S0’, m0’, n0’ and V0’. This is not possible because it requires that organism returns entropy, mass and amount of substance imported from the surroundings. The organism cannot return imported substance remaining in the same state.

3. Analysis

Let’s consider open thermodynamic system I surrounded by surroundings U shown on figure 2.

Figure 2: Schematic presentation of System I Surroundings U an open thermodynamic system far -Reversible reactions from equilibrium that exchanges substance and energy with its -Irreversible reactions surroundings. The arrows represent

exchange of substance and energy.

System I is an open thermodynamic system that exchanges substance and energy with its surroundings. The contents of the system are NI particles with mass mI, volume VI at temperature TI and pressure PI. The surroundings are consisted of NU particles, where NU >> NI, with mass mU, volume VU, at temperature TU and pressure PU. The process that we will describe is isothermal and isobaric so TI=TU and PI=PU. Inside system I there are chemical reactions of synthesis and self-assembly processes that lead to accumulation of substance and growth. Therefore, as a consequence of consumption of substance inside the system I a concentration gradient appears. The concentration gradient is a generalized force that drives a flow of substance into the cell. This is described according to Prigogine by

J i   Lij X j j (5) where Ji is the flow of substance i into the system, Lij phenomenological coefficient that relates flow i to generalized force j, and Xj is generalized force. The flow appears from the surroundings where the concentration is higher towards the system where it is lower. Then the system imports a certain amount of substance n, with mass m, and volume V. This substance remains accumulated inside system I which leads to a change in its volume, and therefore growth.

Substance imported into the system I leaves the surroundings U. Therefore there is a simultaneous change of state of both the system and its surroundings. According to the third law of thermodynamics/Nernst-Planck theorem each substance possesses certain entropy (its specific entropy).

The flow of substance therefore leads to a flow of entropy. The flow of entropy is, according to Prigogine

(Prigogine, 1947), given as:

de S   J S dV dt  (6) where JS is given as

 J  i j S  T i i (7) where μi is the chemical potential of substance i and ji is the diffusion flow of substance i. According to

Balmer, the change of entropy of an open system is given as

Q dS  m s  m s  S  T   P dt in out (8)

  where Q is heat transfer, m is mass flow, s is specific entropy, S P is the system’s entropy production rate, S is the total system entropy and t is time (Balmer, 2011). Notice that the change of amount of substance is of the same magnitude, but of the opposite sign for the system and the surroundings, so

dnI = - dnU

However, dSI ≠ -dSU because a part of imported entropy is returned to the surroundings in the form of heat, and entropy of the substances that leave the system according to Popovic (Popovic, 2014)

4 9 7 10 dwexp dHdisp,5 d5, dS  dSin,  dSin,  2  rSidni,  rS jdn j,  rSidni,   rS jdn j, (9) T    T  i1 j8 i1 j8

where dni,α is the change of extent of reaction i in the α cell, dnj,α is the change of extent of reaction j in the α cell, dni,β is the change of extent of reaction i in the β cell, and dnj,β is the change of extent of reaction j in the β cell.

We can generalize this equation to any living system, containing M subsystems (cells) and N (metabolic) reactions in them:

M  dw Ni  dS  dS  exp,i   S dn   in,i T  r i, j i, j  i1  j1  (10) where dS is the entropy change of an open system, M is the number of cells that make the thermodynamic system (if any). If the system isn’t divided into subunits then M=1. dSin,i is the change of entropy caused by the input of substance into the cell i, dwexp,i is the work done by the cell i on its surroundings during growth, T is the temperature, Ni is the number of chemical reactions occurring in cell i, ΔrSi,j is the molar reaction entropy of reaction j occurring in cell i, and dni,j is the change of extent of reaction j occurring in cell i.

If the flow of substance is an because of incorporation and accumulation of substance as a consequence of organism’s growth, the irreversibility applies to both the system and the surroundings. The change of entropy is also an irreversible process. These two irreversible processes are related. They also relate the irreversibility of changes in the system and in the surroundings. Consequently there is an irreversible change of state of both the system and its surroundings. It is impossible to change the state of the surroundings without changing the state of the system. The state of the system can’t change because of the irreversibility of metabolic processes caused by growth, accumulated metabolic errors, degradation processes…

Time travel also faces other challenges. According to Lobo (Lobo, 2008) “The notion of is fundamental in the construction of physical theories, therefore time travel and its associated paradoxes have to be treated with great caution„. The consistency Time travel paradoxes include the grandfather paradox (Lobo, 2008). The paradoxes associated with casual loops are related to self-existing information or objects, trapped in space-time (Lobo, 2008). Twin paradox as a specific case of time travel caused by effects of special relativity was analyzed by Popovic (Popovic, 2012). As shown above, time travel leads to problems with causality and with the second law of thermodynamics according to Bonvin (Bonvin,

2007).

As was described above, time travel is a change of thermodynamic state of the surroundings. This change of thermodynamic state, whether it’s an earlier or later state (travel to past or future) isn’t possible without the change of state of the organism (system I). The change of state of the organism isn’t possible because of irreversibility of metabolic reaction described above. From this we can conclude that time travel is impossible.

The consideration above was made with the following assumptions:

1) The universe is by definition everything that surrounds us.

2) There is at list one open system inside the universe. This was done in order to simplify the

analysis.

3) The system is open and far from equilibrium. Therefore it exchanges both substance and

energy with its surroundings.

4) The system exhibits growth.

4. Conclusions

Based on analysis of an open thermodynamic system far from equilibrium and its surroundings, the thermodynamic basis of time travel was considered. A growing organism inside the universe exchanges amount of substance, mass and entropy with its surroundings. These changes are irreversible. The irreversibility of changes implies the impossibility of change of thermodynamic state of both the organism and its surroundings. Time travel is nothing more than an unreachable dream. It is forbidden by the second law of thermodynamics.

References

Atkins, P. (1995). Physical Chemistry 5th edition. Oxford University Press, Oxford, UK. Bertalanffy, L. v. (1950). The theory of open systems in and biology. Science, New series, v. 111 no. 2872, pp. 23-29. Balmer, R. T. (2011). Modern Engineering Thermodynamics. Academic Press, Burlington, Massachusetts, USA.

Bonvin, C., Caprini C., Durrer, R. , (2007), Superluminal motion and closed signal curves. http://arxiv.org/pdf/0706.1538v2.pdf Einstein, A. (1905). On the Electrodynamics of Moving Bodies. Annalen der Physik, v. 17, pp.891-921. Gems, D., Doonan, R. (2009). Antioxidant defense and aging in C. elegans, Is the oxidative damage theory of aging wrong?. Cell Cycle, v. 8, no. 11, pp. 1681. Glansdorff, P., Prigogine, I. (1971). Thermodynamic theory of structure, stability and fluctuations. Wiley – Interscience, New York City, New York, USA. Hayflick, L., Moorhead, P.S. (1961). The serial cultivation of human diploid cell strains. Exp Cell Res., v. 25, no.3, pp. 585-621. Hayflick, L. (1965). The limited in vitro lifetime of human diploid cell strains. Exp. Cell Res., v. 37, no. 3, pp. 614- 636.

Hayflick, L. (1977). The cellular basis for biological aging. Handbook of the Biology of Aging, Van Nostrand Reinhold, New York, pp. 169. Hayflick, L. (1985). Theories of biological aging. Exper. Gerontol., v. 24, pp. 355. Hayflick, L. (1998). How and why we . Experimental Gerontology, v. 33, no 7-8, pp. 639-653. Hayflick, L. (2007). Biological Aging Is No Longer an Unsolved Problem. Annals of the New York Academy of , Biogerontology: Mechanisms and Interventionspages, v. 1100, pp. 1-13. Hayflick, L. (2007). Entropy Explains Aging, Genetic Determinism Explains Longevity, and Undefined Terminology Explains Misunderstanding Both. PLoS Genet, v. 3, no. 12, e220, pp. 2351-2354. Hansen, L. D., Macfarlane, C., McKinnon, N., Smith, B. N., Criddle, R. S. (2004). Use of calorespirometric ratios, heat per CO2 and heat per O2, to quantify metabolic paths and energetics of growing cells. Termochim. Acta, v. 422, pp. 55-61. Hansen, L. D., Criddle, R. S., Battley, E. H. (2008). Equilibrium thermodynamics and metabolic calorimetry of living systems. Proceedings of 20th. ICCT, Warsaw, Poland. Hansen, L. D., Criddle, R. S., Battley, E. H. (2009). Biological calorimetry and the thermodynamics of the origination and evolution of life. Pure Appl. Chem., v. 81, no. 10, pp. 1843. Lobo F. S. N. (2007), Nature of time and causality in Physics. Los Alamos National Laboratory, Preprint Archive, General relativity and Quantum Cosmology, pp.1-14, http://arxiv.org/pdf/0710.0428v2.pdf Prigogine, I. (1947). Etude thermodynamique des phenomenes irreversible. Dunod, Paris, France. Prigogine, I., Wiame, J. M. (1946). Biologic et Thermodynamique des phenomenes irreversible. Experimentia, v. 2, no. 11, pp. 451-453. Popovic, M. (2014). Entropy change of open thermodynamic systems in self-organizing processes. Thermal Science,

Popovic, M. (2012). There are two twin shadows but Einstein is one. Thermal Science, vol.16, no.1, pp 1-6 Silva, C., Annamalai, K. (2008). Entropy generation and human ageing: Lifespan entropy and effect of physical activity level. Entropy, vol. 10, pp. 100.