As a young Associate Professor on Sabbatical Leave from UT, I was working at the Nobel Institute in Stockholm. I was interested in a problem in Astrophysics. Evidence had recently been obtained for the presence of silicon ions in light from quasistellar radio sources (called Quasars - objects that are billions of light years from earth, moving away from us at close to the speed of light). I had just been studying silicon ions by observing their in-flight radiation in a beam from a particle accelerator. I was intrigued by the possibility to determine the amount of silicon in the Quasar if I only knew the right rate constant (or orbit lifetime).
However, an atom has an infinite number of possible orbits, and electrons cascade down from orbit-to-orbit in a veritable death spiral. Thus light from each orbit contains a mish-mash of an infinite number of rate constants. Accurate interpretation was incredibly complicated - some had claimed impossible. I later made a Historical study using the libraries of Europe, and found that this problem had frustrated scientists in many different applications since at least 1795! Gaspard Riche de Prony had described the problem just after the French Revolution. Fortunately, I was much too naïve then to realize that the problem was insoluable.
One Saturday morning my friend Indrek Martinson and I were at the Institute. There had been a going-away party for friend the previous night, and we had slept over in the Guest Rooms there. I sat sleepily at my desk with this great spiral of orbits cascading down in my head. Suddenly a new picture coalesced in my fantasy. I saw vividly that the only way this cascade death spiral could reach the last step was for the whole infinity to funnel through the next-to-last step. Instead of considering a chain of infinite length, I could look at only the last two links. The last step would distort the next-to-last in a characteristic way, and my ignorance of the infinities would pass through like a smart sieve, and yield to a stimulus-response analysis.
For a particular time of decay, I could add the light from all the next-to-last steps with properly adjusted coefficients, find the rate-of-decrease of last step, and plot it as point on a graph. If I did this correctly for a lot of different decay times, the points should all line up with each other. All the points would be on right side of the graph because the left side is experimentally impossible - it corresponds to the cascades being totally unpopulated. This can't happen in the lab, but it's my fantasy - anything I want can happen in my head! All I had to do was to lay a ruler along the points, and the intersection with the axis would give me the rate constant. So, instead of relating my measurements to an i nfinite number of math functions inexactly, I had a way to relate my measurements to my other measurements exactly. At that moment I looked Mother Nature straight in the eye and said "Gotscha!"
Indrek came into the room and asked who I was talking to. I said "I think somebody was talking to me, but I'll let you know in a few minutes." I ran to the lab, did the math to make the graph, and found that the points formed a perfect straight line, just as I had fantisized. I laid a ruler along the points and found the lifetime. I checked the uncertainties and verified that this measurement was the most accurate that had to that time been obtained. Then I applied the results to the astronomical data. With a 30 centimeter ruler (1 foot in the US) I had measured the abundance of silicon in an object that is billions of light years away, and moving further away at nearly the speed of light. I recalled than that Archimedes had said "give me a lever long enough and I will move earth." I had found that 1 foot may be long enough. Today powerfully rugged computor algorithms have been developed to replace the ruler, but it's still the same method.
That night as I rode home on the Stockholm subway I felt a tingle in my spine, because I knew something that no one else in the world knew. This discovery has been very good to me. My technique is now used in atomic lifetime laboratories all over the world. Some years later I was talking to a colleague in Carlson Library, and my gaze fell on the big rotating globe of the earth in the lobby. I suddenly noticed that, as it turned, I could always see a continent that has a lab that uses my method. Literally, the Sun never sets on the use of something that happened inside my head! It is a modest discovery - neither the globe nor the earth began to shake because of this, but it became my very satisfying little secret and made all my hard work and study worthwhile. It's even more satisfying to know that people at the University of Lund have now noticed this little secret.