From: “Ken Smith” <>
Newsgroups: aus.religion.christian
Sent: Tuesday, June 21, 2005 9:37 AM
Subject: Re: How Are We Meant to Understand Genesis?

I have now had a chance to have a quick look through D. Russell
Humphreys’ book “Starlight and Time: Solving the Puzzle of Distant
Starlight in a Young Universe”.
I’m not surprised that assorted Christian cosmologists who have looked
at it are, to put it mildly, not impressed, and have produced lists of
errors they have found.

If Humphreys wants to impress those who know something about cosmology,
the first thing he will have to do is write using the language
cosmologists use in their technical writings. The book is clearly aimed
at creationist audiences who know nothing about non-Euclidean spaces,
and virtually nothing about observations of galaxies and various other
information which astronomers have accumulated over the years.

There will be various bits of mathematics in this post.
I apologise in advance for this, but if there are errors in a piece of
writing which involves general relativity this is inevitable.

I shall, however, attempt to illustrate the main point of modern
cosmology, the expansion of the universe and its satisfactory
explanation, by a drastic reduction of the number of dimensions of space
from three to just one. Then the development of this one-dimensional
“universe” with time can be illustrated by a two-dimensional surface,
with one dimension representing space and the other dimension time.
And two-dimensional surfaces can be visualised, without too much
difficulty, in a three-dimensional space.

If parts of this (apart from mathematical terminology) are difficult to
follow, please respond asking questions about those parts, and I will do
my best to provide answers.

Humphreys accepts the vast scale of the universe which has been
discovered by astronomers over the past 80 or so years.
The second paragraph on page 10 reads:

Some laymen pondering this question wonder if the astronomers’
estimates of distances might be greatly in error. I don’t think
so. Astronomers have dozens of methods for estimating such
distances, all of which generally agree with one another. Many of
the methods, especially for closer objects such as the Andromeda
galaxy, are based on very reasonable assumptions, such as the
overall size or brightness of a galaxy.

When I read the last sentence here I must admit I muttered a rude word
under my breath. Way back in the early months of 1953, as part of the
preliminary reading on cosmology (for my honours thesis) before getting
stuck into learning general relativity, I read Edwin Hubble’s classic
“The Realm of the Nebulae” (Yale University Press, 1936). I have just
taken this off my bookshelves and reread chapter 4, `Distances of
Nebulae’. The Andromeda galaxy is known to astronomers as M31, after
its number in the Messier catalogue (1784), which listed various fuzzy
objects observed by astronomers. On page 98 Hubble writes `The
discussion eventually settled down to a comparison of the galactic
system with M312, which was regarded as an exceptionally large spiral.’
“. . . exceptionally large . . .” compared with Humphreys’ comment about
“. . . overall size . . .” ?

The distance to M31 was, in fact, determined by using Cepheid variables.
Pages 92-96 in Hubble explain this, with the light curves of several
Cepheids and Plate VI showing these in M31. Since Hubble’s book may not
be readily accessible, “The Big Bang” by Joseph Silk (W. H. Freeman,
3rd edition, 2001), pages 33-38 may be consulted. Simon Singh’s “Big
Bang” (Fourth Estate, 2004) contains a lot of information about the
Andromeda Galaxy. Hubble’s distance measurements are explained on pages
219-229, and the correction to the distance when a second class of
brighter Cepheid variables was discovered is covered on pages 372-383.
These pages also show that this resolved the problem about the universe
being younger than the Earth, which had been a problem with Hubble’s
original observations.

So much for Humphreys’ comment about “overall size or brightness” being
used to estimate the distance to the Andromeda galaxy.
This does not inspire confidence in anything else Humphreys may write.

But it is when Humphreys talks about gravitational red-shift, and, in
particular in the section on pages 14-18 headed “What the Big Bang
Theorists Fail to Tell You” that things start to go haywire.
He correctly explains that the universe is assumed to have no boundaries
and no centre. He also illustrates the expansion of the universe by the
usual reduction to a two-dimensional analogue of the surface of an
expanding balloon.
But he then talks about additional dimensions in space, and claims that
cosmologists visualise the three-dimensional universe expanding into a
fourth spatial dimension.

This is simply wrong.
Since Don has quoted from “The Large Scale Structure of Space-time” by
Hawking and Ellis, I assume that he has at least glanced at the first
few pages of chapter 3, `General Relativity’, where the details of the
mathematics are expounded. In particular the first sentences of section
3.1, `The space-time manifold’ are important.
The term “manifold” is used since this is standard mathematical
terminology. Symbols have been translated into the nearest ASCII
equivalent. If any terms in the following need elucidation, the
preceding chapter, `Differential Geometry’, provides a concise
introduction to the topic in 45 pages.

The mathematical model we shall use for space-time, i.e. the
collection of all events, is a pair (M, g) where M is a connected
four-dimensional Hausdorff C^(infinity) manifold and g is a Lorentz
metric (i.e. a metric of signature +2) on M.
Two models (M, g) and (M’, g’) will be taken to be equivalent if
they are isometric, that is if there is a diffeomorphism
theta: M -> M’ which carries the metric g into the metric g’, i.e.
theta * g = g’. Strictly speaking then, the model for space-time
is not just one pair (M, g) but a whole equivalence class of all
pairs (M’, g’) which are equivalent to (M, g). We shall normally
work with just one member (M, g) of the equivalence class, but the
fact that this pair is defined only up to equivalence is important
in some situations, in particular in the discussion of the Cauchy
problem in chapter 7.

The authors then go on to produce reasons for assuming, in particular,
appropriate differentiability conditions on the manifold, and refer to
experiments on pion scattering as evidence of continuity down to
distances as small as 10^(-15) cm.

However the most important point is that all the work is based on a
four-dimensional manifold, with three space and one time dimensions (the
Lorentz metric in the above quotation from Hawking and Ellis).
Nowhere in books on cosmology will one find mention of the three
dimensional space which we inhabit expanding into a fourth spatial
dimension.

Humphreys is simply wrong when he writes on page 16

Now hang onto your hats, because it’s really impossible for anyone to
actually imagine a fourth dimension, but the equations of GR seem
to require that space have an extra dimension. (One more than
length, breadth and width — and I’m not referring to time as the
extra dimension).

What happens is that the three-dimensional spatial sub-manifold of the
four-dimensional space-time changes along the time axis.

Let me try to explain this using something which I don’t remember seeing
in any popular book on cosmology. Instead of considering the surface of
a balloon, we will drastically simplify things and consider a
one-dimensional space.

The circumference of a circle is a one-dimensional space: it needs only
one label to specify position on it.
This is one dimension down from the surface of a sphere: you need two
labels, such as latitude and longitude, to specify where you are on the
surface of the Earth, and if you are in an aircraft you need a third
label, such as altitude, to describe exactly where you are in the
atmosphere.

Now you can easily imagine an expanding circle – try stretching a rubber
band by rolling it over the surface of a drink bottle.

We want to illustrate what a two-dimensional space-time might look
like.
There are many things around which are shaped like cones: ice-creams,
dunce’s hats, witches hats as road warnings, and so on.
A cross-section of one of these is a circle, and the size of the circle
is different at different positions on the cone.

Now imagine measuring time along the surface of the cone, from the
vertex of the cone, and distance (one-dimensional) around the cone.
Then the surface of the cone could serve as a model for space-time,
provided that we remember that there is only one space dimension
involved.
At the vertex of the cone there is a singularity, with zero size for the
spatial dimension.
As we move away from this initial point with increasing time the size of
the circle increases.
And if you have a vase of appropriate shape you can see the size of the
(one-dimensional) universe increase at different speeds, or even
decrease.

And if you want a model of a universe starting with a “big bang” and
finishing with a “big crunch”, try the surface of the earth.
Start at a point like the North Pole, and measure time along the
meridians of longitude. The (one-dimensional) space will be the
parallels of latitude, and as time increases this space will expand,
reaching a maximum size at the equator. The “universe” then starts to
shrink, and finally collapses to a point in the “big crunch” at the
South Pole.

And various other shapes, which have circular cross-sections, could be
used to illustrate other rates of change of the “size” of the “universe”
as time increases.

Now none of us can visualise a curved three-dimensional space (which
would require a six-dimensional “flat” space to contain it), much less
to appropriate extra dimensions to visualise how it was changing in
time. And this is the reason that only a mathematical approach is
satisfactory.

However it is in the next section, `Why No Boundary?’, that Humphreys
makes his biggest error. And since the whole of the rest of the book is
based on this error, some time must be spent on it.

Humphreys seems to be somewhat confused over the distinction between an
“unbounded universe” and a “universe without a boundary”.
He starts this section with the paragraph

Why do Big-Bang cosmologists use as their starting point the
assumption (which seems quite contrary to common sense) that the
universe has no boundary? Is there some good scientific reason, or
is it perhaps demanded or even suggested by well established,
experimentally-backed theory, like general relativity?

The answer is no. It is an arbitrary assumption, called the
“cosmological principle,” or more recently the “Copernican
principle.” This assumes that (whether the universe is finite —
like that of the ant on the balloon — or infinite) there is no
edge and no center. On a large enough scale, matter is evenly
distributed around us. Therefore, it is asked, if there were an
edge, than why don’t we see more galaxies on one side of us than on
the other?

After two paragraphs of rather special pleading Humphreys goes on

Why have I spent so much time on this belief in an unbounded
universe? In such a universe, every galaxy is surrounded by an
even distribution of other galaxies, and there is no net
gravitational force (on a large enough scale). However, if the
universe is bounded, then there would be a center of mass and a
net gravitational force, and we could begin to consider the
time-distorting effects of gravity on a massive scale.

Humphreys starts with “. . . the universe has no boundary . . . ” which
agrees with his discussion about the expanding balloon analogue just
three pages earlier. But here he wrote “But this space is nevertheless
not infinitely large . . . “. In other words, it is bounded.
And just as the circumference of a circle is bounded (it has a finite
length), and the surface of a sphere is bounded (it has a finite area),
so it is perfectly possible that the three-dimensional space in which we
find ourselves is bounded (it has a finite volume). Whether this is so
or not is a matter for scientific investigation, and cannot be imposed
in advance.

Now both the circumference of a circle and the surface of a sphere have
no boundaries. In like manner, if space is bounded then it, too, will
have no boundaries.

But by the final paragraph I quoted Humphreys has changed the words he
uses to ” . . . this belief in an unbounded universe”, which simply does
not follow.

But one of Humphreys’ biggest blunders is in the final sentence quoted
“However, if the universe is bounded, then there would be a center of
mass . . . “
As mentioned above, the circumference of a circle is bounded. If this
were made of uniform wire it would have a mass, but would certainly not
have a centre of mass anywhere on the wire.
The surface of the Earth is bounded, but the surface does not have a
centre.
(A number of years ago I read an article which purported to show that
Jerusalem was the “centre” of the surface of the Earth, but could see no
point in this and didn’t follow up the work.)

And if the universe is spatially bounded, so that its volume is finite,
there is no reason for it to have “a center of mass”, and, in fact, the
very concept of such a centre seems to have no reasonable meaning.

And since virtually all the rest of the book relies on this “center”,
there is no need to look any further in the work.

However I shall continue reading and see just how many more errors I can
pick up.

Salaam

Ken Smith