The asymmetry of time and the cellular world. Is immortality possible?

doi:10.4236/jbpc.2011.21007

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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; aquilano@ifir-conicet.gov.ar

2Facultad de Ciencias Exactas, Ingeniería y Agrimensura (UNR), Rosario, Argentina

Received 21 August 2010; revised 15 October 2010; accepted 10 November 2010.

ABSTRACT

I analyze the flow of time in this article, both in

gross and in microscopic processes, with a well

defined arrow of time, but as the amount of en-

ergy involved in the microscopic processes is

so small, it is more difficult to argue that the

entropy increases, and therefore the direction of

time becomes confusing and undefined at the

molecular level. Therefore, is cell immortality

possible?

Keywords: Entropy; Time; Cell

1. INTRODUCTION

The concept of time is intuitive and easily distin-

guishable past from present or future. It was not as easy

for thinkers. In ancient and found the first human think-

ing about time. Plato, for example, said that time is the

moving image of eternity. Later, Newton described it as

an absolute, true and mathematical, which runs smoothly.

In the twenties of last century, Einstein came to regard as

a mere illusion. These ideas reflect the immense com-

plexity of the time, an issue that has been the subject of

reflection for many philosophers and research for many

scientists. Scientists are precisely those who now seek to

address the fact that science does not provide a clear

definition of what is time.

The only fundamental scientific theory that makes a

preferred direction for time is of the second law of ther-

modynamics, which asserts that the entropy of the Uni-

verse increases as time flows forward. This explanation

provides an orientation, an arrow of time. Our perception

of this would, therefore, a direct consequence of the th-

ermodynamic time arrow.

The entropy of any thermodynamically isolated sys-

tem tends to increase with time and this has to this law a

definite orientation. That the entropy of the universe to

increase over time is that there is a direction, an arrow of

time, a time asymmetry to distinguish past from future,

which corresponds with our own perception of time.

This is clear at the macroscopic level, however, on a

microscopic scale, since the amount of energy involved

in the process is so small, it is more difficult to assert

that entropy is increasing, and that therefore time is

moving forward (toward the future), rather than back-

ward (toward the past).

In the macroscopic world, how can we explain the

obvious time-asymmetry of the universe if the funda-

mental laws of physic are time-symmetric? Physicists

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

impossible to find any time-asymmetry.

The set of irreversible processes that began in an un-

stable non-equilibrium state constitute a branch system

[1,2]. That is to say, every one of these processes began

in a non-equilibrium state, which state was produced by

a previous process of the set.

Once I have understood the origin of the initial un-

stable state of each irreversible process within the uni-

verse it is not difficult to obtain a growing entropy, in

any subsystem within the universe. Alternatively, taking

into account the enormous amount of information con-

tained in the subsystem we can neglect some part of it

[3,4]. I can use more refined mathematical tools [5,6].

With any one of these tools I can solve this problem.

It remains only one problem: why the universe began

in an unstable low-entropy state? If I exclude a miracu-

lous act of creation we have only three scientific answer:

a) The unstable initial state of the universe is a law of

nature.

b) This state was produced by a fluctuation.

c) The expansion of the universe (coupled to the nu-

clear reactions in it) produces a decreasing of the (mat-

ter-radiation) entropy gap.

The third solution was sketched by Paul Davies in ref-

erence [2], only as a qualitative explanation. The expan-

R.O. Aquilano / Journal of Bioph ysic al Ch emistry 2 (2011) 49-52

sion of the universe is like an external agency (namely:

external to the matter-radiation system of the universe)

that produces a decreasing of its entropy gap, with re-

spect to de maximal possible entropy, max

S (and there-

fore an unstable state), not only at t = 0 but in a long

period of the universe evolution. We shall call this dif-

ference the entropy gap ΔS, so the actual entropy will be

maxact

SS S.

In the microscopic world Feng and Crooks created a

method to accurately measure the time asymmetry of the

microscopic. In fact have found that, on a microscopic

scale and for some intervals, entropy can actually de-

crease. And that while the general entropy increase on

average, each time the experiment does not, that is, time

is not always a clear direction. My work aims at under-

standing the relation between time asymmetry and en-

tropy, which would also be crucial for the development

of future molecular and cellular studies.

2. THE ENTROPY

We know that the universe isotropic and homogeneous

expansion is a reversible process with constant entropy

[7]. The matter and the radiation of the universe are in a

thermic equilibrium state *()t



at any time t. As the

radiation is the only important component, from the

thermodynamical point of view, we can chose *()t



as a black-body radiation state.

Let us consider an isotropic and homogeneous model

of universe with radius a. From the conservation of the

energy-momentum tensor and radiation state equation,

we know that -1

aT, we can verify that S const.

The irreversible nature of the universe evolution is

not produced by the universe expansion, even if ρ

*()t



has a slow time variation. Therefore, the main

process that has an irreversible nature after decoupling

time is the burning of unstable H in the stars (that pro-

duces He and, after a chain of nuclear reactions, Fe).

This nuclear reaction process has certain mean life-time





 and phenomenologically we can say the state

of the universe, at time t, is:

()()0[() ]

tte t



 



  (1)

where 1



is certain phenomenological coefficient

constant in time, since all the time variation of nuclear

reactions is embodied in the exponential law t





. I can

foresee, also on phenomenological grounds, that 1



must peak strongly around 1



the characteristic en-

ergy of the nuclear process.

All these reasonable phenomenological facts can also

be explained theoretically: Eq.1 can be computed with

the theory of paper [9] or with rigged Hilbert space the-

ory [5]. In reference [10] it is explicitly proved that 1



peaks strongly at the energy 1



. The normalization

conditions at any time t yields:

()() 1,...0tr ttrttr







 (2)

The last equations show that 1



is not a state but

only the coefficients of a correction around the equilib-

rium state *()t



. It is explicitly proved in paper [10],

that 1



has a vanishing trace.

I am now able to compute the entropy gap S



with

respect to the equilibrium state *()t



at any time t. It

will be the conditional entropy of the state ()t



with

respect to the equilibrium state *()t



[3]:

[ log()]Str







 (3)

Using now Eq.1, and considering only times





 I can expand the logarithm to obtain:

()

Setr







 (4)

where I have used Eq.2. I can now introduce the equilib-

rium state i for T



. Then:

13 2

()

SZTetre









 (5)

where et



is a diagonal matrix with this function as

diagonal. But as 1



is peaked around 1



we arrive to

a final formula for the entropy gap:

3tT

SCTee







 (6)

where C is a positive constant.

3. EVOLUTION OF THE ENTROPY GAP

∆

I have computed of S



for times larger than decoup-

ling time and therefore, as 2/3

at and 1



,

where t0 is the age of the universe and T0 the present

temperature. Then:

()

SCete







 (7)

where C1 is a positive constant. The curve ()St it has

a maximum at 1



and a minimum at 2

tt. Let us

compute these critical times. The time derivative of the

entropy reads:

St S

tT t



















 

















(8)

This equation shows two antagonic effects. The uni-

verse expansion effect is embodied in the second and

third terms in the square brackets an external agency to

the matter-radiation system such that, if we neglect the

second term, it tries to increase the entropy gap and,

therefore, to take the system away from equilibrium (as

we will see the second term is practically negligible). On

the other hand, the nuclear reactions embodied in the

R.O. Aquilano / Journal of Biophysical Chemistry 2 (2011) 49-52

5151

y-term, try to convey the matter-radiation system to-

wards equilibrium. These effects become equal at the

critical times tcr such that:

cr cr

ttTt











(9)

For almost any reasonable numerical values this equa-

tion has two positive roots: 12

0cr cr

ttt .

For the first root we can neglect the y 0

tterm and I

obtain:









(10)

(this quantity, with minus sign, gives the third unphysi-

cal root).

And for the second root I can neglect the

2( /)

tt term, and I find:

ttTT









(11)

If I chose appropriate numerical values we can see

that it probably produces also a growing order, and

therefore the creation of structures like clusters, galax-

ies and stars [12].

Also I have a growing of entropy, a decreasing order

and a spreading of the structures: stars energy is spread

in the universe, which ends in a thermic equilibrium

[13]. In fact, when t the entropy gap vanishes

(see Eq.7) and the universe reaches a thermic equilib-

rium final state.

Since 414

101.5 10t years after the big-bang all

the stars will exhaust their fuel [13], so the border be-

tween the two periods most likely have this order of

magnitude and must also be smaller than this number.

This is precisely the result of our calculations.

In the molecular world, we can associate this with the

stem cells, seeing that the gap of entropy is close to

zero or zero. Feng and Crooks [14] contributed to de-

veloping a measure of the time-asymmetry of recent

single molecule RNA unfolding experiments.

With the previous calculations but consistent with the

body temperatures of animals, we see that the equations

are reduced almost naturally to zero entropy, and spread

over time, reaching the level of Feng and Crook, pro-

ducing the possibility that this occurs also mentioned

that the cells could become immortal.

4. CONCLUSIONS

We see that nature, at the macroscopic level, has a ten-

dency to mess up, which in physics called entropy effect.

However, on a microscopic scale, since the amount of

energy involved in the processes is very small, it is very

difficult to say that entropy is increasing, and therefore

time to move forward rather than backward.

Feng and Crooks say have a method to accurately

measure time asymmetry at the microscopic level. They

found that during some intervals the entropy may de-

crease. And, although the overall entropy increases at

each moment of the experiment does not, then the time

has no clear direction and time asymmetry is not secured,

but time has a symmetrical (not unlike this past or fu-

ture). As time progresses in the macroscopic world, it is

unclear at the level of a single molecule, and if we asso-

ciate this phenomenon to stem cells, as these remain

unchanged we could say that would be the only natural

case of detention of the arrow of time, which could be

associated with natural perennial or cell immortality.

5. ACKNOWLEDGMENTS

I wish to thank to Jack Szostak of Howard Hughes Medical Institute

to fruitful discussions. This work was supported by grant of National

University of Rosario (UNR), PID 1ING198.

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