= 1.22
/(mirror separation). In the
case of Betelgeuse, the fringes disappeared when the mirrors were about
ten feet apart, giving an angular diameter of 0”.047 arcseconds.
One of the best and most beautiful things about Astronomy is the way its study has shed light on the mysteries of the world in which we live. Astronomy has given us ordinary things, like helium balloons (an element first seen in spectrographs of, and named for, our nearest star, Helios), and it has given us larger things, like the understanding that we are not the center of the Universe, and that the laws which govern us here on Earth also extend to the farthest points we can see.
One of Astronomy’s first applications was economic in nature. It provided a schedule for successfully planting and harvesting crops in ancient Sumer (the Biblical land of Shem), after populations grew too large to be supported by hunting and gathering. Along with Geometry, Astronomy enabled the priests of that country to re-establish property lines after the yearly river floods washed away the stone markers.
The Sumerians, prodigious writers and record-keepers, drew a direct line between astronomy and the laws of men. They believed that all of the laws governing behavior which could be made, and that means all laws, contradictory or not, resided in Heaven, and it was the duty of the God of each City to go to the celestial Library and select the set of laws which would govern that city and hence make it prosper.
We’re still trying to find those laws today.
In the Middle Ages, Galileo’s discovery of the moons circling Jupiter destroyed the Earth-centered view of the world, and, because society’s order on Earth was seen as a reflection of the order in God’s Universe, threatened the central authority of the Church. The resulting conflict led to a better understanding of the limits on the application of science, and eventually to the widespread use of the Scientific Method. It is to this that we owe our present prosperity, and to which three billion people owe their existence.
Astronomy may not be governing society’s laws anymore (not, at least, since Nancy Reagan’s astrologer left the White House), but it is still telling us about the very large and the very small in the world in which we live. Dark matter and dark energy were discovered with telescopes, not particle accelerators. Astronomy is even a window into the mysterious world of Quantum Mechanics.
In 1920, Michelson mounted four six-inch flats on a twenty foot beam at
the end of the 100” Hooker telescope on Mount Wilson, to
increase the effective diameter of the telescope’s primary mirror
and thus interferometrically measure the diameter of Betelgeuse.
The two flats on the ends of the beam were movable, and redirected the
starlight to two other flats, positioned over the primary.
These mirrors then directed the light down into the telescope, where the
two beams combined at the telescope’s focus. When the
outer mirrors were close together, interference fringes formed at the beam’s
focus. When they were moved apart, the interference
fringes disappeared. The star’s angular diameter was calculated from
the well-known formula, = 1.22/(mirror separation). In the
case of Betelgeuse, the fringes disappeared when the mirrors were about
ten feet apart, giving an angular diameter of 0”.047 arcseconds.
Why does this work? Light beams form stable interference fringes only when their wavelengths and, more importantly, their phases, are identical. A star is a copious emitter of photons, but they are not coherent, as in a laser beam. In a laser, all of the photons are marching in lock step. In a star’s photosphere, they are about as random as can be, having been generated by thermal sources arrayed across the star’s surface.
The answer lies in quantum mechanic’s uncertainty principle, which states that the product of a photon’s position and its momentum must be greater than a finite value. The smaller the one is, the larger the other must be. Michelson’s interferometer was actually forming interference fringes between single photons. If you were to ask yourself, “What is the uncertainty in the value of the lateral momentum of a photon that originates on Betelgeuse and still enters my eye?” you would come up with a very, very small number. That means that the photon’s lateral position must be very large. Ten feet wide, in this case. When Michelson’s mirrors were farther apart than this, they couldn’t capture single photons between them, and the interference patterns vanished.
Photons from smaller, more distant stars can be as large as the state of Texas. The uncertainty in their forward momentum makes them the thickness of a piece of paper. Thus, stellar photons resemble giant pancakes, or circular blankets, raining down on us from the sky.
So, the next time you’re out under the stars, realize that you’re walking around inside of single photons.