[net.astro.expert] simplicity and symmetry in cosmology

ethan@utastro.UUCP (Ethan Vishniac) (05/17/84)

[Eat this header]

There is a recurring thread which runs through Mr. Gwyn's arguments
on cosmology to which I take strong exception.  I am *not* referring
to his favorite unified theory (although I am not sure how it is
supposed to relate to the current experimental and theoretical work
to particle physics).  What bothers me are his comments about symmetry
and simplicity in a physical theory.  Any one of a number of quotes
from him would serve to illustrate my point.  Let me confine myself to
one. ( I don't think Mr. Gwyn would regard this one as unfair or taken
out of context.)

>The closed, bounded, perfect-cosmological-principle cosmology is
>actually simpler in any measurable sense of which I am aware than
>the expanding "big bang" universe.

Now, Mr. Gwyn is clearly referring to simplicity in the sense that a
mathematician would i.e. devoid of complications, maximizing the internal
symmetries of the universe.  This has nothing to do with simplicity in
the sense of being the most economical explanation of the facts.  The
fundamental laws of physics may have many symmetries, none of which are
realized exactly, or even approximately, in any real situation.  Given
that the laws of physics are rotationally invariant do we conclude
that ferromagnets do not exist?  As for translational invariance, the
same laws of physics apply everywhere, but if you think that translates
to translational invariance of our environment, then I invite you to test
this by casting yourself off the nearest roof.  I could go on, but I think
that you all must see my point.

A successful model of the universe should account, as simply as possible,
for our observations.  I have discussed elsewhere what these are.  Mr.
Gwyn seems to be willing to take only one of them seriously, the Hubble
law.  I think this is completely unjustified, but even on this one point
his comments leave me unsatisfied.  I have been left with the impression
that he regards any ad hoc explanation as "simple" if it allows him to
continue with his prejudices intact.  I would prefer to base any explanation
of this (or any other) observation on the laws of physics as we know them, or
at least some recognizable expansion of them.  I cannot say if the E-S theory
falls into this category or not (anybody out there wish to comment?), but
I haven't heard Mr. Gwyn say that the E-S theory can explain the  Hubble
law in any natural way.

One final comment, the most symmetric possible metric (i.e. structure
of space-time) is the DeSitter space mentioned by Mr. Gwyn.  It has
the interesting property of satisfying the perfect cosmological principal
(homogeneity in space and time).  For this reason it was used as the
basis for the steady-state theory of Bondi, Gold, and Hoyle.  It does
indeed account for the Hubble flow, *because* it is an expanding universe.
Particles following geodesics (i.e. not being influenced by nongravitational
forces) diverge exponentially from one another at late times.  The theory
has been discarded within the astrophysical community because of its complete
failure to address the other observational points I have mentioned.  Even
before these points became generally accepted it was already necessary to
allow matter to be spontaneously produced from the vacuum in order to make
the model logically consistent.

                     "Just another Cosmic Cowboy"
                         
                         Ethan Vishniac
                         {ut-sally,ut-ngp,kpno}!utastro!ethan
                         Department of Astronomy
                         University of Texas
                         Austin, Texas 78712

gwyn@brl-vgr.UUCP (05/17/84)

There is no way I am going to convey the meaning of simplicity etc. in
a reasonable number of words, but let me at least give a practical guide
to comparing two competing theories of the fundamental laws of physics,
in order to convey something of what I have in mind.

Theory A consists of:
	(1) acceptance of several common mathematical ideas;
	(2) postulation of seven fundamental properties (charm, etc.?);
	(3) adoption of four principles of quantization, renormalization,
	    and so forth;
	(4) acceptance of a Lagrangian with three independent coupling
	    constants, of fourth order in the fundamental entities;
	(5) a 20-dimensional space;
	(6) a preferred frame of reference;
	(7) one principle of variation.

Theory B consists of:
	(1) acceptance of several common mathematical ideas;
	(2) postulation of one fundamental property;
	(3) adoption of two operational principles;
	(4) acceptance of a second-order Largrangian with no added constants;
	(5) a 4-dimensional space;
	(6) no preferred reference frame;
	(7) one principle of variation.

Then I would certainly claim that Theory B is the "simpler" theory,
since it has considerably fewer things put into it a priori.  This
of course does not mean that Theory B is guaranteed to describe
reality better than Theory A, although if it is comparable in
accuracy one should be strongly inclined to prefer it over Theory B.

(Note:  Theories A & B are meant to remind one of certain real
candidates, but the detailed counts of the basic enities, assumptions,
etc. do not necessarily correctly reflect those of any actual theories.)

There is even a quantitative method of assigning a measure to the
degree to which a field theory constrains its basic entities (the
basic idea is the asymptotic degrees of freedom of the higher-
order Taylor coefficients of the fields).  It is amusing that the
measure number for the Einstein-Straus-Kaufman unified field theory
(which I do NOT support) is precisely "42".  Now we know what the
ultimate question was (Life, the Universe, and Everything).

Einstein preferred a "stronger" theory to a "weaker" (i.e. less
asymptotic freedom) in the absence of any other criterion for
choosing between competing theories.  I prefer the "weaker" on
the intuitive grounds that it is less of a special-case theory...
Of course we assume that the theories in question agree with
reality sufficiently well; otherwise the choice is trivial.

gwyn@brl-vgr.ARPA (Doug Gwyn ) (05/17/84)

Under the particular formulation of the Einstein-Schr"odinger theory
that is most similar in form to General Relativity, and using the
traditional (but not unquestioned!) identification of the entities in
the formalism with aspects of the actual physical world, then it is
indeed the case that a particularly symmetric special solution of the
field equations is a deSitter universe.  This means that the extended
theory is certainly capable of "predicting" the Hubble effect.  Whether
this is the only reasonable cosmology one can have for this theory is
another matter.  I am not very familiar with the "diverging geodesic"
argument Ethan has stated but I do know that geodesics do not mean
quite the same thing in a pure affine theory.  I would like to look
into this further.

I do not relate the theory to current developments in cosmology
since in those cases where General Relativity is expected to be
sufficiently valid (low energy density, medium scale of distance,
and so forth) the extended theory should give comparable predictions
if one uses the same methodology for the non-General Relativistic
considerations (quantization or what have you).  However, it is not
the aim of the E-S theory to apply only in a limited problem domain
with other methods imposed outside that domain.  It is supposed to
be complete (although I will certainly admit that the formulation
of the theory does not guarantee that all relevant factors have
been included; I consider that an open question although most
theorists would disagree).