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08/21/2001
Baking Raisin Bread
My friend Dan in Honolulu is concerned about my three recent
choices of subject matter, notably the male sexual organ,
flatulence and spitting out spiders. He has urged me to get things
back on a higher plane. When challenged in that manner, what
choice do I have but to return to questions concerning our
universe, my favorite topic?
For a number of years now, scores of new planets have been
discovered outside our own solar system. These planets are in
orbits that aren''t at all like the orbits of the planets in our solar
system. However, just the other day, I heard a report on the
radio that some researchers have found two Jupiter-size planets
orbiting a star in orbits similar to those of our own planets. Who
knows? Perhaps further study will reveal a solar system that
does resemble ours and possibly answer the question as to
whether there just might be life out there.
In an era of many such profound questions, it''s nice to know that
some of them are being cleared up. On a personal note, old
Bortrum finally thinks he understands what happens when you
bake a loaf of raisin bread - and how it may relate to our
expanding universe. Lest you think I''m off my rocker, hear me
out.
In a recent publication (I''ve forgotten the name), I saw the
answer to a question from a reader. It was a question I''ve
pondered myself. When we see the light from a distant galaxy a
few billion light years away we see it as it was those billions of
years ago. How far away is the galaxy now? The answer was
that it is much farther away today. I don''t remember the figures
but do recall a remark that the reader shouldn''t worry if the
answer implied motion greater than the speed of light. That
would violate Einstein''s fundamental law that nothing can move
faster than light. However, it was stated that Einstein''s limit does
not apply to space itself. I concluded that this meant that it was
space expanding that caused that galaxy to move away from us
so rapidly.
Well, for me this is pretty deep stuff. There was also a remark
tossed in that the farther away a galaxy is, the faster it''s moving
away from us. I have heard or read this point many times before
and have just taken it as gospel. However, at 4 AM recently, I
woke up and wondered why this was true. Unable to go back to
sleep, I harked back to an article I read a few years ago. Until
then, I had thought the expansion of the universe after the Big
Bang was like blowing up a balloon - I thought that all the stars
and galaxies were more or less on the surface of the balloon.
This was very nanve of me, to say the least. The article said the
expanding universe was actually more like a loaf of bread.
So, at about 4:15 AM, I decided that I should be able to figure
out for myself why distant objects move away faster than the
closer ones. It turned out to be quite simple! Let''s assume we
are baking a perfectly round loaf of raisin bread - hard to do
maybe, but let''s pretend. Let''s look at three raisins - one in the
center of the ball of dough, another on the surface and a raisin
exactly halfway between the two in line with them. Let''s say our
ball of dough is 2 inches in diameter. That means the distance
from the center raisin to the surface raisin is 1 inch and the
distance from the center to the middle raisin is a half-inch. Now
take a peek at our bread an hour later. It''s ten times bigger in
diameter, 20 inches. Ok, that''s a big loaf of bread but it makes
the math easier. The distance from the center raisin to the
surface raisin is now 10 inches.
The way my bread rises as it bakes, the middle raisin will still be
halfway between the center and the surface raisins. So, if we''re
on the center raisin, we''ve seen the middle raisin move out from
a half inch away to 5 inches away. In other words, it''s moved 4.5
inches in that hour. The surface raisin has moved from 1 inch
away to 10 inches away from the center raisin. It''s moved 9
inches in an hour. Voila! The farther away the raisin, the faster it
moves away. In our case, the distant surface raisin moved away
from the center twice as fast as the middle raisin. Of course, the
next step is to say the raisins are galaxies, the bread is the
universe and the distances are in millions or billions of light-
years. By the time it was 5 AM, I could go back to sleep, totally
satisfied with my keen mathematical insight. As you probably
know by now, it doesn''t take much to make me happy! Let''s
hope I''m right!
If you want to know some actual numbers for how fast galaxies
are moving away from us, the September 2001 issue of National
Geographic has a neat article by Carl Zimmer. The article
actually deals with how the ages of things ranging from the
deaths of recent crime victims to the pyramids to the universe are
determined. However, the article gives a simple formula to
calculate what we''re after. Our calculation requires us to know
the value of the so-called Hubble Constant. The article gives the
current value of the Hubble Constant as 72. If you know how far
away a galaxy is, you just multiply that distance by 72 and you
get how fast that galaxy is moving away from us Milky Way
types.
I should mention that you must know the distance in
megaparsecs (a megaparsec is 3.26 million light-years) and that
the answer comes out in kilometers per second. For example,
the galaxy M100 is some 15 megaparsecs (50 million light-years)
away and it''s moving away from us at 1,275 kilometers (over 700
miles) a second. That doesn''t seem to me to be a mind-boggling
speed. But, if that same formula holds for a galaxy 10 billion
light-years away, about 200 times farther away than M100, the
more distant galaxy is moving away 200 times faster than M100.
That''s roughly 140,000 miles a second. That''s zipping right
along and approaching the speed of light of 186,000 miles a
second.
Back to that loaf of raisin bread, you more skeptical types may
say that the dough near the center would initially be more gooey
than the surface crust and that the center and middle raisins
might fall a bit off positions. A pox on you! I was talking theory
and a theorist can assume anything he or she wants! But I''ll
probably wake up at 4 AM pondering your point!
Allen F. Bortrum
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