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[Phys-l] The Biological effect of Proton Decay



Dr Vic Stenger is currently working on a book which will address the so
called fine tuning issue in cosmology. This has generated a lot of
discussion
on Dr Stenger's Atoms and Void list (which I manage) concerning the
question ;
what is the range that the dimensionless constants can vary and still
permit the
evolution of life. Below is a rather crude analysis on one particular
facet of
this question.




The Biological effect of Proton Decay.


Unfortunately the title above implies that this post will be something
more than actually provided. I won't make any attempt at a detailed
analysis
of the biological effect of proton decay. Rather I will make some
conservative assumptions to see where the limit might be for the existence
of life in
relationship to the stability of the proton. Of course those better
informed can alter these assumptions, so the exercise will be useful in
any case.
It should be noted that it is my assumption that the biological effects of

proton decay are the most limiting effect in relation to fine tuning
concerns.


In the recent paper mentioned "A dying Universe, the Long Term evolution
of
astrophysical Objects" by Adams and Laughin ( See Link at Bottom) there is
a section with a detailed discussion of the various mechanism of proton
decay. In this post I will look at one particular mode of Proton Decay,
known
as the Sphaleron proton decay process, because the probability of this
mode of decay occurring is constrained by the Dimensionless constant
Alpha_w
the weak field fine structure constant. This is being done to get some
idea
of how "fine tuned" this constant must be to allow the evolution of life.


In the paper mentioned above cosmic time is expressed as a log function
which simplifies the mathematical analysis. So we have;


eta= Log_10[ t(yr)]

So today

eta_0= Log_10[13.7E9]= approx 10.14


This illustrates this way of defining cosmic time.


The following assumption is made.

The maximum background radiation which will allow the evolution of life
is 1000 times the background radiation on earth (approximately 500
mrads/yr.) I will ignore radiation quality factors by assuming a quality
factor
of 1, throughout this.

Therefore the limit will be 500,000 mrads/yr or 1.58 E-5 rads/sec = approx

1.5 E-5 rads per second.


One rad is the deposit of .01 Joules in one KG of matter. Therefore

1.5 E-5 J/sec* .01 J/KG= 1.5E-5 J/sec KG which will be our
bio-limit.

We will assume 100 percent of the energy of the decaying proton is
deposited in the mass.

E_prot= 938 MEV

Therefore

938 E-6 ev/decay* 1.6E-19 J/ev= 1.5E-10 J/decay.

(Of course we would expect neutron decay via this process also but we
will assume that most of that energy is carried off as low interaction
neutrinos.)

In a given KG mass of biological matter (mostly water) we would expect
about 55.55 moles. or

3.34E25 molecules/KG

Which is about 3.34 E 26 protons/KG


The number of decays per second to reach our stated bio-limit is

1.5 E-7 J/KG-sec/ 1.5 E-10 J/decay = 1000 decay/sec


We can relate this directly to a half life by calculating the decay
constant.

Lamda= (dN/dt)*(1/N) = 1000 decays/sec * 1/3.34E26 protons/KG= 3E-24


t(1/2)= -ln[0.5]/lamda= .693/3E-24= 2.3E23 sec= 7.32E15 yrs

Going back to the Cosmic time equation


eta=eta_1 +eta_sup

Where eta_1 is natural time scale without suppression and eta_sup is
the weak field suppression factor.

eta_1 = -31 and eta_sup= 4*pi/(alpha_w*ln[10]

We get

eta= -31 + 4*pi/(alpha_w*ln[10] = log[7.34E15]= 15.86


Giving us a value of alpha_w at the limit of 1.16E-1


Given that Alpha_w = 3.17E-2 this represents


% change= 100 * delta[alpha)w]/ alpha_w= 266 %


So based on the given assumptions a change of this amount would be fatal
for the prospects of life in the Universe.


Bob Zannelli

))))))))))))))))))))))))))
_http://arxiv.org/PS_cache/astro-ph/pdf/9701/9701131v1.pdf_
(http://arxiv.org/PS_cache/astro-ph/pdf/9701/9701131v1.pdf)

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