Rob, the Magic Elastic

dearest nightowls,
our surprise daily blog
from none other than
our "whabby"

pull up a chair, and enjoy!


Thanks so much, cpgem8, for asking me to post a blog on the Owl’s Nest. I like it here, and was delighted to accept!

Wow, Owl Nesters. You’re probably hoping I’m going to take this opportunity to spill some nasty cyberspace secrets and juicy gossip. Ha! When cpgem8 asked me if I’d do this, her request acted like a kick in my pants, motivating me to finish off one of a trilogy of "blogs" that I’ve been working on for my MySpace page (sadly, more off than on) since last March. Ouch! I beg your indulgence in letting me post that blog here. It means that I’m going to hopefully amuse you… and maybe even engage you, if I’m lucky… in a really big topic this morning. Gigantic, in fact, because it’s no other than… the expansion of the universe itself!! Yep… I’m going to try to convey some of my understanding of what it means when you hear on a science show that the universe is growing bigger over time.

Let’s begin with one of my favorite blog devices: that pesky old visualization exercise! Imagine you are in your kitchen and are pulling out three ordinary items from one of your drawers: a 12 inch ruler, with all the ordinary colored markings delineating inches and fractions of inches along one side; a nice stout (thick and wide) four- inch long elastic band; and a thin-tipped black magic marker.

I love that elastic band, because it’s so amazingly useful as an explanatory device. I love it so much, I’m going to call it Rob. Rob the Elastic.

Now, imagine you take the elastic band and align one of the curved ends with the "bottom" of the ruler (the "zero" point on the ruler’s scale). Then, you gently lay the rest of the elastic lengthwise along the business (marked) edge of the ruler. Be sure you’re not stretching the elastic, at all. You just want to be straightening it out to its full (but still limp) length, so that the other curved end is exactly aligned with the four- inch marker on the scale.

Easy, right? Next, pretend you take your magic marker and draw three narrow vertical lines along the side of the elastic closest to you, producing three black stripes. Please carefully select specific positions along the elastic to make these stripes. One should be exactly at the 1-inch mark on the ruler, the second one exactly at the two-inch mark, and the third exactly at the three-inch mark.

Now comes the really exciting part of the exercise (LOL!). I want you to imagine grasping the bottom of the elastic band and wrapping it around the bottom edge of the ruler, right inside the marked edge. Carefully lock down and immobilize the bottom of the elastic by pushing it against the ruler with your left thumb, on one side, and your left index finger, on the other.

You’re almost there! The only remaining thing I want you to imagine doing is grasping the other curved end of the elastic with the thumb and forefinger of your right hand, and in one smooth motion, a motion that takes exactly one second, stretching the elastic until it just fits over the other (top) side of the ruler.

Let’s consider what you’ve accomplished with this little "wrap-around" action. Literally one second ago, Rob the Elastic was limp, only four inches long, and a little embarrassed, to tell you the truth. Now, as a result of your rather firm handling, Rob is a proud 12 inches long, stretched comfortably between the top and bottom edges of the ruler.

Simple, huh? So simple, you’re probably wondering why we’ve even bothered to imagine getting Rob stiff at all. Well, remember when we had Rob in his original (unstretched) version and you marked him with stripes at the one, two, and three-inch locations? The thing I want to draw your attention to now is where those stripes ended up along the ruler following the stretch. The answers are totally intuitive. Rob stretched from four inches to 12 inches, exactly three times his original length. The stripe that was originally one inch from Rob’s base was originally ¼ of the way to the end of the elastic. That’s still true after the stretch; that stripe is still ¼ of the distance to Rob’s tip, so it is now three inches from the origin. Similarly, the stripe at the original half-way point (two inches from the origin) will be right smack in the middle of the stretched version, at the six inch point on the scale. Finally, the stripe that was originally at the three-inch marker willbe ¾ of the way to Rob’s tip, at the 9-inch marker on the ruler.
But hold on a minute, everybody. The most intriguing aspect of these black stripes is not their absolute distance away from the point of origin. It’s determining how fast the stripes moved during the one second that you were manhandling (!) Rob. The stripe that was originally at the one-inch location moved to three inches. Since speed is simply distance divided by time, and the stripe moved a total of two inches, it moved at a speed of two inches/second. But, the stripe that was originally at the two inch location moved from there to the six inch mark, and so it had to be moving at a speed of four inches/second. The three-inch marker moved to nine inches, for a speed of six inches/second. Rob’s tip, originally four inches away from the origin, moved all the way to 12 inches (eight inches/second).

Things are starting to get a little weird! You were playing with a single object. Yet, different parts of the object were moving at different speeds during the one second that you stretched it out. For every additional inch that the stripe on the elastic was originally displaced from the point of origin, an addition two inches per second was added to its speed. One inch away, the stripe traveled at two inches per second, its initial distance from the origin (1 inch) multiplied by the two inches per second expansion rate; two inches away, the stripe traveled at (2 * 2 inches/second) = four inches/sec; three inches away, the three-inch stripe traveled (3*2 inches/sec) = 6 inches per second.

Notice the power we suddenly have with this clear, breathtakingly simple mathematical relation, nesters! We can use it to calculate the speed that any arbitrary stripe would travel, at any arbitrarily distance from the point of origin along a ruler of any arbitrary length, as long as this "mega-Rob" elastic was stretched at the same 2-in/sec rates. For example, suppose you had used elastic that was six inches in original length instead of four. If you stretched it out at this same rate of 2 inches/second, the end of this elastic would travel out to (6*2) + 6 = 18 inches in the first second, moving smartly along at 12 inches/sec.

OMG, though. What if we pretended that Rob was infinitely elastic, and you are all superwomen with the capability and stamina to just keep stretching him? Where would the original one-inch marker be located at the end of the second second (get it?) of stretch time? Well, we know it was at the three-inch point at the end of the first second. During the second second, then, it would be traveling at (3 *2) = six inches/sec, which would place it at the ninth inch point on the ruler. Notice the increase in the speed that this mark was experiencing over time; originally at 2 inches/sec during the first second of stretching, it’s speed increased threefold in only the second second!! Imagine (and go ahead and calculate, if you like) its speed, and how far away it would be after 10 seconds. After 1000 seconds. After one million trillion seconds!

The universe behaves in EXACTLY this way, owl nesters! It’s just constantly stretching out at an expansion rate, not of 2 inches/second per inch, like Rob, but at 72 kilometers per second per megaparsec. What that means is, every second that goes by, there is 72 kilometers of additional space between us and objects that are one "megaparsec" away (a megaparsec is 3.26 million light years, about a million light years further than the Andromeda Galaxy). For objects that are twice that distance away (two megaparsecs, or about 6.5 million light years), there is 144 kilometers of additional space separating them from us with every elapsed second.

The Universe is far, far larger than these paltry numbers, of course. Estimates are that there are objects as far as 36 billion light years from us. However, there is so much space being created every second between us and galaxies that far away, that the light from these objects will never reach us. Light travels at "only" 300,000 kilometers per second. When we get far enough away that 300,000 kilometers or more of additional space is being created between us and the object every second, it’s equivalent to the light being frozen!

What I’ve been describing here is what happens to the universe as time progresses. The reverse is also fascinating, that is, what the expansion rate means for the universe as we run time backwards. But that’s a topic for another blog!

Thanks so much for your attention to me and to Rob the elastic. This has been totally fun!!

Rob, the Magic Elastic