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
of Dr Stenger's the Atoms and Void list (which I manage) concerning over
what range of 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