Stan Zygmunt (and implicitly Glenn) wrote the following:
> Glenn wrote:
>
> ====================================================
> It is my understanding that the current candidates for GUT [Grand
> Unification Theories] have quite a number of arbitrary constants. So if a
> particular GUT, with particular arbitrary set of constants is able to
> explain why the mass of the electron is as it is and other physical
> constants are as they are, there is still the question of why the
> arbitrary GUT constants take on the values they do. There would have to be
> some logically prior theory in order to explain those constants. Even if
> you get the whole system back to one constant with a value of, say 42
> (which would prove the Hitchiker), one must still explain why that single
> constant took that value.
>
> All in all, it looks like a set of Russian Dolls to me.
>
> Is there any comment from either David Bowman or Stan Szygmunt?
>
> glenn
> Foundation,Fall and Flood
> http://members.gnn.com/GRMorton/dmd.htm
>
> ================================================
>
> I'll confine myself to a brief comment since Glenn asked for one :)
>
> I basically agree with what Brian and Glenn have written on the
> anthropic principle. It all comes down to initial conditions, I
> believe. Even if one day a "theory of everything" is achieved which
> explains why the electron mass is what it is (along with a whole raftload of
> other "fundamental parameters"), that theory will BY NECESSITY involve
> initial conditions. It is important to realize that a mathematical
> theory is distinct from and independent of the initial conditions which
> must be fed into it in order to predict how a particular system will evolve
> in time. So even if such a supertheory is achieved, the question will then
> be "Why THESE initial conditions which lead to the particular universe we
> live in?"
>
> Glenn, a question for you (since I'm not an expert in nonlinear dynamics):
> While chaos theory describes the way a system's time-evolution is quite
> sensitive to initial conditions, aren't there also mathematical equations
> of motion which lead to very similar time evolution no matter what the
> initial conditions? (Is this a "strange attractor"?) The existence of such
> systems could be appealed to by those who seek to blunt the force of an
> anthropic principle which depends on "fine-tuning" of initial conditions.
>
> What do you think? And you, Brian?
>
> Stan Zygmunt
> ^
> |
> |
> (note the spelling, Glenn! :) )
Although I am not an expert here, please let me say something (since at least
Glenn asked). Regarding Glenn's Russian Doll GUTs, it is my understanding
that he is correct that typical GUT theories have too many free unpredicted
parameters for them to be a truly fundamental theory. The GUT theories have
fewer of these parameters than for the "Standard Model" of the
U(1) X SU(2) X SU(3) gauge theory with the spontaneously broken SU(2) weak
interaction sector of the low energy limit, but I recall that the reduction
in the number of these parameters is not an impressive amount. However GUTs
don't pretend to be the final answer. They just unite the Weak, EM, and
Strong interactions into one natural framework. Very conspicuously they leave
out the gravitational interaction--the weakest and most complicated
interaction of them all.
This is not the only weakness of this class of theories. As I recall, GUTs
don't naturally explain the dynamical reasons for why the original GUT gauge
symmetry group should spontaneously breakdown to the separate gauge groups of
the individual interactions at the energy scales that they do. I think that
this symmetry-breaking is put in by hand via the Higgs mechanism rather than
being dynamically generated by the theory itself. This is one reason for some
of the residual parameters. The big reduction is that the Strong, EM and
Weak low energy coupling constants are all related to each other--but this
just reduces 3 independent constants to one. There are still too many other
free parameters. The biggest problem with GUTS is that they all predict that
all baryonic matter is radioactively unstable (i.e. protons eventually must
decay ultimately into such things as positrons). The simplest GUTS have
already been falsified because their predicted proton lifetime is too short.
Experimentally, no proton has been observed to decay despite many years of
looking in multiple experimental collaborations. The current lower bound for
a proton's half-life is, I think, something like 10^33 yrs. The simplest
GUTS predicted values around 10^29 to 10^31 yrs. Other GUTS are still in the
running but the race is not as exciting as it was before since the lack of
fundamentalness of GUTS has caused them to not be in vogue as before.
Superstring TOEs show more ultimate promise (not performance). They have far
fewer (hardly any) undetermined parameters and they have both GUTs and
quantized gravitation as appropriate limiting cases. It recently has been
shown that what formerly were thought to be different classes of superstring
theories are in fact just hidden versions of the same theory written in
different terms. It may be possible that there really is only one fully
self-consistent theory with the power to potentially explain "everything". In
principle, superstring theories predict the free parameters of the other more
well-known theories of particle physics. In practice they are so intractable
and complicated that they can't be solved sufficiently to hardly make a single
hard quantitative numerical prediction about such things.
Regarding Stan's comment about initial conditions, I think the hope of the
people in the field is that the ultimate theory will be so naturally
constrained by the requirements of maximal beauty, simplicity, and self-
consistency that only one boundary condition will be possible or compatible
with it. This is something like the motivation for Hawking's no-boundary
proposal for theories written in imaginary time. The idea is to have the
boundary condition as a natural part of the theory.
I'm not an expert on chaos theory either but let me comment on Stan's question
concerning it. The short answer to Stan's first question is *yes*, and the
answer to his second one is *no*. Hamiltonian systems cannot exhibit a
contractive dynamics where the initial conditions are irrelevant and the
system always converges to a common behavior because Liouville's Theorem
forbids it. Phase space volumes are conserved for Hamiltonian systems and
can't contract. The For *dissipative* systems then such behavior is the norm.
Any pendulum with friction will eventually end up hanging down still. This
state is the stable fixed point attractor for the system and all initial
states converge to it. *Driven* dissipative systems are more colorful.
Things can be attracted to sets in phase space more complicated than a single
fixed point like the damped pendulum. Various limit cycles, bounded surfaces,
etc., are possible for the motion to converge to. A *strange* attractor is
a an attracting set in phase space such that the motion converges to it for
a wide range of possible initial conditions, but this attracting limit set in
phase space is itself a rarified fractal and spread out all all through a
large region of phase space. Once the motion settles down onto the strange
attractor the motion still looks chaotic and is still very sensitive to slight
perturbations of the state as the system state seems to wander irregularly
throughout phase space (yet is confined to the attractor).
David Bowman
Georgetown College
dbowman@gtc.georgetown.ky.us