I”ve mentioned my 60-foot putt at St. Andrews on more than one
occasion in these columns. If you”re a regular reader you no
doubt will say, “Enough already!” But now my friend Dan in
Hawaii has questioned the truthfulness of my claim, even going so
far as to suggest I used a rubber ruler to measure it. This, I
strongly deny. The measurement of distance is relatively
straightforward, although I will grant that measuring my putt with
my own foot-long foot may have introduced an error of plus or
minus a foot in my measurement.
The measurement of time is more complex. Perhaps you saw the
recent A&E production of, or read the book “Longitude”. Both
deal with the efforts of clockmaker John Harrison in the 1700s to
come up with a clock that, when taken to sea, would only gain or
lose a few seconds in a month. This may not seem a sufficiently
exciting subject to warrant a book or movie. However, in the
18th century the matter of determining a ship”s position at sea was
quite often a matter of life or death. Sometimes it was even the
life of a crewmember, hanged for disagreeing with the captain”s
opinion of the ship”s location!
For those of you like myself who are nautically or geographically
challenged, it might be well to establish the nature of latitude and
longitude. Latitude is a fairly straightforward concept,
designated by those parallel lines on the globe parallel to the
equator. The equator is a natural zero point of reference, with
the sun appearing virtually directly overhead at some time of the
day. Even back in Columbus” time, the measurement of latitude
was relatively simple by sighting on the sun ”s position or by
knowing the length of the day (time between sunrise and sunset).
In 1492, Columbus just set himself on a course at a certain
latitude, “sailing the parallel” it was called, and he would have
sailed straight to India if other landmasses hadn”t gotten in the
way. He was able to find his way back to Spain by following the
same strategy.
Longitude, however, was a different kettle of fish, especially if
you were the British Navy sailing in the island-infested waters and
along the rocky coasts around Britain, France and Spain. The
lines of longitude run from the North to the South Pole, are not
parallel to each other and there is no particular natural place to
put the zero reference line. A sailor could arbitrarily measure the
longitude taking his homeport as a reference. How does
Harrison”s clock come into the picture? The earth rotates once
every 24 hours. One rotation is 360 degrees. If you do the math,
this corresponds to 15 degrees every hour. Now, suppose you
know the time difference between your position at sea and the
time at your homeport. If the difference is half an hour, this
means you”re 7.5 degrees (half of 15) east or west of your
homeport. You might still be uncertain and want to know how
many miles away. It all depends on your latitude, as you can
readily see by looking at your globe. At the equator, one degree
is about 69 miles while at the poles a degree is virtually zero miles
since all the lines of longitude come together.
The time difference we use to calculate our longitude is not the
accustomed difference due to being in different time zones, where
you are either hours ahead or hours behind. Rather this is the
actual time referred back to the time at your homeport reference.
This time at your location at sea, I”m assuming, is calculable from
observations of the sun and knowledge of your latitude in the
hands of a knowledgeable nautical type. The trick is that, to
know the time back home, you must have a clock that was set
properly back home and that does not gain or lose a significant
amount of time over an extended stay at sea. In the early 1700s,
that wasn”t easy.
Spurred on by a prize that today would be equivalent to millions
of dollars, Harrison worked for decades to finally perfect clocks
that met the test of going to sea and keeping remarkably accurate
time. Even then, he was only awarded half the prize. The A&E
movie took liberties in filling in some of the unknown personal
aspects of Harrison”s life, as well as in the life of a 20th century
fellow portrayed as being obsessed with bringing Harrison”s
clocks back to working order. Astronomers controlled the Board
of Longitude, which was responsible for awarding the prize.
They not only weren”t impressed with Harrison”s lack of academic
credentials but also had a natural bias towards astronomical
solutions to the longitude problem. Astronomical solutions were
possible but were quite unwieldy at sea.
Today, of course, your battery-powered wristwatch would be
more than sufficiently accurate to have won the prize. Which
brings me back to cesium. You may recall that a couple weeks
ago, I mentioned the breaking of the speed of light barrier. The
chamber through which the light propagated was filled with vapor
of the element cesium. It also turns out that for quite some time
the world has depended on a fountain of cesium atoms as the
ultimate standard of time. In this fountain clock, a couple of laser
beams are used to form a cloud or fountain of cesium atoms,
which then falls through a microwave cavity where the resonant
frequency is measured. Today, the second is defined as “the
duration of 9,192,631,770 periods of the radiation corresponding
to the transition between the two hyperfine levels of the ground
state of the cesium 133 atom.” Either you understand the last
two sentences or you don”t. In either case, not to worry. The
important thing is that certain cesium fountain clocks, one in
Boulder, Colorado, another in Paris, are accurate to
0.15 seconds. This is 1.5 femtoseconds, a
femtosecond being one millionth of a billionth of a second.
According to an article in the June issue of Discover magazine by
Verlyn Klinkenborg, if this clock ran for 20 million years it would
not gain or lose a second! That”s what I call a timepiece! (I
checked Klinkenborg”s math and get a maximum error of 0.6
seconds after 20 million years.) This fountain clock is not one
made for travel at sea, however. The whole thing occupies a
small room, the fountain chamber is about six feet high and the
170 optical components are mounted on a heavy optical bench
designed to damp the slightest vibrations.
This being the most accurate clock in the world you might think
logically that it is the standard clock by which all timepieces are
set. But no, this clock is only turned on for a few days at a time
for test or experimental purposes and to check the accuracy of
other clocks. It seems that the actual world standard time is
generated in Paris by comparing the times of over 200 clocks of
different varieties around the world. Strangely, according to the
Discover article, there is a repeated comparison of the times at all
the metrology labs around the world using the Global Positioning
System (GPS) to do the comparisons. The data are fed to Paris
and some weeks later Paris sends a notice telling each of the labs
how far from the average their clocks were. The individual labs
then maneuver their computer software to “steer” their clocks to
the average value. The rationale for this approach seems
ridiculously obvious, if not scientifically sophisticated. The
approach is that with one clock you can”t be sure you”re on the
money. If you have two clocks and they differ, which one is
correct? So you bring in a third and a fourth etc. Finally, you get
an average of some 220 clocks and you”re reasonably sure you
have a good average idea of the time.
Why all the fuss? For one thing, the GPS system depends on the
precision of the time signals to calculate your position, be it at sea
or on land trying to steer your car to an unfamiliar address. Even
more important for the financial health of the world is that the
transmission and translation of the messages and data zooming all
over the world via the Internet and such depends on the time
signals being spot on target; otherwise chaos would result. So,
when you realize that your checks or stock transactions are being
electronically routed in pulses from one bank or brokerage firm to
another, it all depends on meshing these pulses exactly in the
timing sequences.
Last year”s Nobel Prize in chemistry was directly related to time in
very small femtosecond increments. The prize was awarded to
Ahmed Zewali, the Linus Pauling Professor of Chemical Physics,
and director of the Laboratory for Molecular Sciences at the
California Institute of Technology. Zewali got the award because
he has managed to actually study chemical reactions as they occur
in real time. The real time of Zewali”s work is in the femtosecond
and picosecond (1,000 femtoseconds) range. He and his
colleagues have been able to follow chemical reactions by first
hitting the compounds with a laser pulse to sort of pump them up
and get the reaction going. Then, at intervals of perhaps tens or
thousands of femtoseconds, follow with another laser “probe”
pulse. By following what happens to that probe pulse, Zewali can
detect the state of a particular molecule. He and his coworkers
can vary the interval between the pulses and map the reaction as it
occurs. It”s sort of like a superfast camera that allows you to
follow the reaction in slow motion and actually see what actually
happens during the all-important first stages of the reaction.
This may sound pretty esoteric and of not much use to us average
guys or gals but collaborations between femtosecond types and
other workers in a wide variety of fields have blossomed and the
results are beginning to pour out. Some of the work involves
biological studies involving DNA and how charges are transferred
in a DNA molecule. The ability to follow such reactions might in
the future allow the interception or modification of deleterious
biological reactions in tumor growth, for example. Or, drugs
might be designed to intervene in an appropriate manner in the
reactions associated with various diseases. All this due to the
ability to control and utilize time in fantastically small increments.
I liked the way the Discover article ended, quoting a question
concerning the nature of time posed by St. Augustine over a
thousand years ago. “While we are measuring it, where is it
coming from, what is it passing through, and where is it going?”
Allen F. Bortrum
