A Matter of Time: Part 3.
Mike Dziekan
VP Engineering, Connecticut Analytical Corporation
Part 2 appeared in the 14 July 2006 issue of The
Citizen Scientist and is available here.
Time and Calendars
A day is a day is a day. Actually, there are two days that
we must be aware of, a normal 24-hour solar day that we are
all accustomed to, and the sidereal day of 23 hours 56 minutes
4 seconds. To understand why there is a difference, look at
the image of the Earth orbiting the Sun.
Figure 1. A plot showing the rotational difference between
a sidereal day and a solar day.
As Earth rotates about its axis, we perceive that the Sun
is moving across the sky. If you were to measure the amount
of time from one local noon to the following day's local noon,
then we would measure 24 hours. This is known as a solar day.
However, if we were to use a different reference star instead
of the Sun as a measurement point, and repeat the same procedure
to measure the length of day, there will be approximately
a 4 minute difference. The day will now be 23 hours, 56 minutes,
4 seconds. This is known as a sidereal day.
On close examination of Fig. 1, one can see why the Earth
rotates slightly more than 360°, because the Earth has
moved in its orbital position around the Sun by the angle
α. If we use the Sun as an indication
for measuring a noon to noon period, then during this time,
the Earth has rotated about 361° instead of the expected
360° . This is only a slight difference, but after a while,
it will be noticeable.
A year is a year. Actually, there are also two main years
that we must be concerned with: a tropical year and
a sidereal year. A tropical year is determined by
the succession of the Sun between two vernal equinoxes, which
is equal to 356.2422 days. A sidereal year is the time required
for the Earth to complete one full orbit around the Sun, and
is equal to 365.2564 days, or just over 20 minutes longer
than a tropical year.
Since the tropical year is determined by the time it takes
for two consecutive passages of the Sun through the vernal
equinox, this conforms to our seasons. Thus, the tropical
year is the year that our calendars measure. If we tied the
sidereal year to our calendars, then, due to the precession
of the Earth, we would notice that the seasons (winter, spring,
summer, and fall) would slowly creep out of step with when
we expect them to happen. These minor differences can build
up over time, and it is interesting to note that in 1582 A.D.,
there were ten consecutive days stripped from the calendar.
In October of 1582 A.D., Pope
Gregory XIII removed the dates of 5-14 October to correct
for an error.
The calendar for October 1582 A.D. went from 4 October with
the following day being 15 October. Before this, people had
been using the Julian
calendar, credited to Julius Caesar in 46 B.C., and then
adopted the Gregorian
calendar (can you guess where the name came from?) The
days in the Julian calendar were slightly too long, which
caused Easter to arrive earlier and earlier.
Did you celebrate the start of the millennium on 1 January
2000? If you did, then you showed up at the party an entire
year too early! Think about this. A century is one hundred
years. If we start counting, we don't start at zero. If you
were starting a new calendar system, the first year would
be year 1. The following years would be year 2, 3, 4, etc.
up to 99. If you have pieces of paper numbered from 1 to 99,
then you have 99 of them, not 100. The second century starts
in the year 101, not 100.
The same rationale applies to the start of the 21st century.
Counting from 1901 to 1999, we have a total of 99 years, not
100. A century is 100 years long, not 99 years. On 1 January
2000, we started the 100th year, or the final year of the
20th century. The actual start of the 21st century was 1 January
2001. Even today, as educated as we are, and with global news
and instant internet communication, millions of people still
got it wrong and started celebrating the new millennium on
1 January 2000. The only celebrating in the year 2000 should
have been celebrating the last year of the millennium, not
the start of the next one.
Easter
Easter is a prominent religious holiday in many countries.
The exact determination of the day of Easter is done as follows.
In western Christianity, Easter always falls on a Sunday from
22 March to 25 April. Without going into the calculations
involved in establishing the exact date, the date of Easter
is the first Sunday following the first full moon that occurs
on or after the vernal equinox. There is more to this than
I want to get into now, so for those wishing to know more
details, see Date
of Easter.
Twilight
The time of twilight is specified according to the angle
of the Sun below the horizon. There are three twilight categories:
civil, nautical, and astronomical. Each corresponds to an
additional 6 degrees that the Sun dips below the horizon.
The end of civil twilight is when the Sun is 6 degrees below
the horizon. The end of nautical twilight is when the Sun
is 12 degrees below the horizon. Finally, the end of astronomical
twilight is when the Sun is 18 degrees below the horizon.
Atomic Time
There is an old horologists saying that states that if you
have one clock, you know what time it is, but if you have
two, you no longer know. If you look at Fig. 2, you will note
at the top one clock indicating 11:00. With just one clock,
you can be pretty sure about the time. If there are now two
clocks, with each one indicating a slightly different time,
you don't really know which one is correct. If you have three
or more clocks, then you can take an average result, but this
only works to a certain point!
Figure 2. How having a different number of clocks can help
or confuse the determination of time.
Mechanical clocks have come a long way and incorporated many
technological improvements to provide better accuracy, precision
and reliability. Electronics enabled a vibrating quartz crystal
to keep better time by maintaining an accuracy of about 1
millisecond in several days. Further improvements enabled
the resonant portion of a clock to shrink from that of a wafer
of quartz to individual atoms. Now
atomic clocks can keep time to about 1 second in 10,000,000
years!
Two main determining factors in specifying the quality of
a clock are accuracy and frequency stability. A clock can
be accurate to several hundredths of a nanosecond (10-9
second), but if it slowly drifts over time it loses accuracy.
If a clock is extremely stable over time, but determines each
second to be slightly less that a full second, then it is
stable but not accurate. A factor that closely relates to
both accuracy and stability is called Q or the Quality
factor.
Q is an inherent characteristic of an oscillator that influences
its stability. Basically, it's the resonant frequency divided
by the resonant width of the oscillator. With a very high
resonant frequency, and an extremely narrow resonant width,
a very high Q can be realized. The more narrow the resonant
width, the purer the frequency.
The following list shows the Q of various kinds of clocks:
Tuning Fork: Q ~ 103
Quartz Watch: Q ~ 104
Rubidium Clock: Q ~ 107
Cesium Beam Clock: Q ~ 108
Cesium Fountain Clock: Q ~ 1010
Even though the newer atomic clocks can keep time with extreme
accuracy, the average time of several master clocks is employed.
All these clocks have one thing in common in that they keep
track of time and tick away the seconds. But how long is a
second? The second was originally defined astronomically as
the period equal to 1/86,400 of a solar day. Remember the
slight differences in sundial time and the EOT? This was then
changed from a solar day (sundial time) to a mean solar day.
In 1956 the second was redefined in terms of the period of
revolution of the Earth around the Sun for a particular epoch.
This was later changed
in 1960 by the 11th General Conference on Weights and
Measures.
In 1967, during the 13th General Conference of Weights and
Measures (Conference Generale des Poids et Mesures)
with the greater acceptance of atomic clocks, the tie between
astronomical measurements for the determination of the second
was broken. The new, non-astronomical definition of the second
is 9,192,631,770 vibrations between two hyperfine levels of
the ground state of the cesium-133 atom.
Because we are able to measure time in increasingly smaller
increments, over the years it has been noticed that the Earth
does not rotate in a consistent manner. Sometimes it speeds
up a little, and sometimes it slows down a bit. Although the
Earth slowly speeds up and slows down, overall it is slowing
down, albeit very slowly. The International Earth Rotation
Service (I.E.R.S.) spends a lot of time and effort to measure
this slight deviation.
As the Earth speeds up and slows down over time, the I.E.R.S.
is responsible for determining when to add a leap second.
By international agreement, a leap second may be added to
the end of any month, but the preferred dates are at the end
of June and the end of December. Did you notice that 2005
was longer than normal? The I.E.R.S. added a leap second at
the end of December 2005.
The Bureau International des Poids et Measures (B.I.P.M.)
is an organization responsible for determining a time standard.
The B.I.P.M. is responsible for establishing UTC (Temps
Universel Coordonne) or Coordinated Universal Time.
After a meeting by the International Telecommunications Union
to recommend time scale notations, it was decided to make
the acronym UTC instead of CUT. This was supposed to make
it language independent. Where did UTC come from? I'm glad
you asked. It started out as GMT, or Greenwich Mean Time.
GMT was based upon mean solar time, and is therefore astronomically
derived.
GMT is kept by a physical clock at the Greenwich observatory
that would drop a ball at the defined time. UTC is an agreement
of time based on data from timing laboratories throughout
the world. There is no physical clock that determines UTC.
Remember how I started this series? I wrote, “In reality,
you cannot simply state the time without an awareness of some
reference.” Think about that, for there is no reference for
atomic time. If you were to make an atomic clock that was
accurate to within 1 second in 1,000,000 years, what time
would it be when you started it? You would have to reference
it to some agreed to standard. Sure, you can accurately count
off tiny fractions of a second, but does an atomic clock know
when it is noon? It doesn't, and in all actuality, only a
sundial indicates noon. An atomic clock in its most basic
form is an extremely precise and accurate oscillator that
drives an electronic counter.
Any clock is only as precise as when you started it. If you
started an atomic clock at 12:55 P.M. and a dime store, battery
powered wall clock at 1:00 P.M., when the actual time was
1:00 P.M., then which clock is correct? Even though the atomic
clock will greatly outperform the dime store clock in every
measurable sense, it is off by five minutes. The better clock
in this instance would be the dime store clock! This is not
because it is functionally better. In fact, it is grossly
inferior, but it was started at a known reference for the
correct time.
You could always argue that if you know the atomic clock
is off by five minutes, then you could simply add five minutes
every time you look at it. My point is that it doesn't matter
how precisely you can measure time. What really matters is
how precisely you can compare the time being measured to a
standard! It doesn't really matter if that standard is correct
or not. What matters is that it is agreed to by everyone.
This is the job for many scientists and engineers throughout
the world.
International Time Services
How can we use atomic time to our benefit? Many electronic
devices take advantage of a radio signal transmitted by NIST
(National Institute of Standards and Technology). The US radio
signals are WWV
, WWVH
, and WWVB
. Some of those “atomic” wall clocks utilize one of more
of these radio signals to adjust their time to conform to
an atomic clock standard. There is a great PDF
article written by NIST that details how to utilize these
signals to make radio controlled “atomic” clocks. Keep in
mind that these radio controlled clocks (RCC) that utilize
WWVB or any of the other signal formats, will most likely
update your clock only once a day. Some may do it more often,
but I suspect most use the signal to resync with atomic time
once a day.
The NIST PDF article gives important information on how to
properly utilize and sync to the signal transmitted from the
atomic clock in Colorado. This is information for manufacturers
and consumers who make or use those LCD “atomic” clocks that
are widely available. Keep in mind that these Wal-Mart, K-Mart,
and BJ's brand radio controlled clocks (RCC) that
utilize WWVB or any of the other signal formats, will most
likely update your clock once a day. The LCD clocks are
marketed as being an “atomic” clock, but are obviously not.
They just make use of a standardized radio signal (WWV, WWVH,
or WWVB) to synchronize the digital clock to a true atomic
standard. A true atomic clock would sell for a good deal more
than $29.95.
In addition to the US sources of time standards, there are
several additional international ones.
JJY ( Japan ) – http://jjy.nict.go.jp/index-e.html
DCF77 ( Germany ) – http://www.eecis.udel.edu/~mills/ntp/dcf77.html
MSF ( UK ) – http://www.npl.co.uk/time/msf.html
BPC ( China ) – http://time.ewha.net/
HBG ( Switzerland ) – http://www.metas.ch/en/labors/4/4.html
These time standards are each based on atomic references.
The correct time is nothing more than an agreed to standard.
That time standard is currently UTC. UTC is the culmination
of years of increasingly precise measurements. GMT (Greenwich
Mean Time) was at one time the world time scale, but was found
to fluctuate too much when compared to newer, more accurate
clocks. Later came UT0, UT1 and UT2. The UT0, 1,2 time scales
were attempts to correct for seasonal and random variations
in the Earth's rotational spin and seasonal polar wobble.
Today, UTC is the accepted universal time. GMT, UT0, UT1,
and UT2 are all astronomically based “Earth” times, while
UTC is “Atomic” time.
Conclusion
In conclusion, I hope this series made you stop and think
about how time influences many things we take for granted
so often in our daily lives. I have either given you more
questions, a headache, or answered some questions, and possibly
answered some questions you didn't know you had. The next
time someone asks you what time it is, pause to reflect upon
everything we covered in this series before you answer the
question!
This concludes Mike Dziekan's three-part series on his
journey through the world of time. Editor. 
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