Measuring the Size of the Universe
Date: Fall 2012
I have heard that the universe is approximately 13.7 billion years old. I guess this would leave me to believe that the universe is 13.7 billion light-years across. I know it must need more than that because seeing light 13.7 billion years ago was, well, 13.7 billion years ago. However, I have heard it is over 46,000,000,000 light years? Why is it not 27.4 light years? Could it have something to do with the amount of time it took light to get to us?
Excellent observation, Ingrid!
Yes, it does have to do with the length of time it took the light to be observed by us! Let us look at that a bit more closely.
Think about tossing a ball on a football field while your friend has a stopwatch. You toss the ball straight out forward of you and watch it carefully. Your friend sees the ball from the side, starting the watch exactly when you toss it. You watch how the ball changes size, getting smaller as it leaves you. When the ball crosses the 10 yard line, your friend records the time at 10 yards but keeps the watch running. Your friend stops the watch when the ball finally strikes the surface. Your friend saw the ball go the full distance. You friend saw the ball as the same size. You saw the ball get smaller and smaller.
You may now estimate where the ball was anywhere between the toss and the landing, simply by knowing how long it took the ball to get to the 10 yard line. Let us assume the ball is gaining speed after you threw it. You know how long it took to get to 10 yards so you can use math to find out how long it gets to 40, 50 yards. You may also know how far it goes in 5 seconds, 15 seconds. It is math.
Now the crucial jump in logic: You may also use how small the ball appeared to you to determine how far it is. The ball became elongated, very slightly as it left your hand. If you took a picture of it, it would appear elongated. When it stopped, it no longer changed size, you could prove that also with a photograph.
The example is overly simplistic, but the point is well made. Size, time, and points of measurement may be made using different means. The size of ball, its elongation and the lines of yardage may allow us to estimate things we cannot easily measure directly.
Same for the Universe.
For light, we may measure cosmic radiation and the light waves, how long the waves are and the frequency. When light becomes elongated, the color spectrum shifts toward the red. When light moves away from us, we see it just like the ball, light waves become elongated and lower frequency. In science we measure that as a shift toward the red part of the spectrum, the waves become elongated. Hence, we call it the red shift.
The size of the Universe is 46 billion light years in distance and if measured directly as you so well noted, would take 46 billion years for the measurement to get here. We have no way to directly measure that. However, using measurements for red shifting, we may measure the elongated, lower wavelength light that has traveled only 13 billion years. Just like we can measure the distance of the ball you threw.
I understand the 27 billion years of light distance that you calculated and that may be reasonably close if the Universe had stopped. It did not stop, it expanded, very rapidly.
The Universe is still moving and not at a steady rate. It is accelerating, becoming faster and faster. The Universe is expanding. So your 27 billion light years distance expanded to 46 billion light years.
The mathematics used for red shift calculations are a bit rigorous. You will slowly be exposed to it and hopefully will enjoy it as much as I do.
Thank you for your interesting observation and question! It is so exciting to see such insight in someone your age!
Peter E. Hughes, Ph.D. Milford, NH
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Update: December 2011