Timekeeping:
From the Sun to the Atomic Second
Dr E Anne Curtis
National Physical Laboratory, Teddington, UK
Celebration of Science
17 October 2015
Our History
“I believe that in the National Physical Laboratory we have
the first instance of the State taking part in scientific
research. The object of the scheme is, I understand, to bring
scientific knowledge to bear practically on our everyday
industrial and commercial life; to break down the barrier
between theory and practice; to effect a union between
science and commerce.“ - HRH the Prince of Wales 1902
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universities of Strathclyde
and Surrey
• 400 laboratories, state of
the art facilities
Metrology
SI base units:
electrical
quantity
time
thermodynamic
temperature
luminous
intensity
length
mass
amount of
substance
How did we get from the sun
to the atomic second?
The second is 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 caesium 133 atom
Overview
 Historical overview of timekeeping
• what drives our need for clocks
• the technology of metrology
 Current state-of-the art
• how to make an atomic clock
• what do we need it for today
Accuracy vs Precision
Increasing accuracy
- averaging data
can give a more
precise result
Systematics
- understanding
the offset
Increasing precision
Stability
Inaccurate
Imprecise
Accurate
Imprecise
Inaccurate
Precise
Accurate
Precise
Reproducibility
- same results?
For clocks:
 accuracy – getting to work on time
 stability/precision – measuring heart beat
 reproducibility – do you trust your clock?
What is a clock?
Oscillator
Counter
something periodic - repeating
(pendulum, electromagnetic radiation)
something that can measure the oscillations
3
2
1
rf counter
Reference
for accuracy and reproducibility from place to place
(how do you check your clock is still “on time”?)
Measuring Time
Two questions:
Why do people need to know what time it is?
How do these needs change over time?
Oscillator
Counter
Reference
Local solar time
• based on the motion of the sun across the sky
• Egyptian obelisks (3500 BC), portable shadow clocks (1500 BC)
Systematics:
• changes throughout the year
• overcast days
• ~12 hours a day without a clock!
Measuring Time
Water clocks
• Among the first timekeepers that didn’t depend on
the motion of celestial bodies
• Simple Egyptian clocks (1500 BC), more elaborate
Greek & Roman clocks (100 BC to 500 AD)
• Inflow and outflow types
• Invented to measure time at night
• timing of the night watch
• night time religious ceremonies
• also used to time debate in court
• portable version to measure pulse rate
Systematics:
• sloping sides only give near constant drip/flow
• temperature and humidity affect flow rate
• evaporation
Calibrate with sundial
Measuring Time
Egyptian Waterclocks
Innovations:
 markers to measure the
passing of time
 gears to enable mechanical
readout mechanism
Elaborate Su Song Chinese Waterclock (1088 AD)
Measuring Time
Pendulum Clocks
• Concept credited to
Galileo (1582)
• First clock constructed
by Huygens (1656)
Systematics:
Period of a pendulum
(small oscillation amplitude)
l
T~2p
√g
l = length of pendulum
g = acceleration due to gravity
• change in temperature/humidity (length of pendulum)
• change in air pressure (friction on pendulum)
To compensate temperature changes:
• mercury pendulums (1721) maintains centre of mass
• bimetal construction (1726) compensates length change
Error to less than 10 seconds / day
Measuring Time
Navigation in the 17th century
• Founding of the Royal Observatory by
King Charles II in 1675
• Purpose – to solve the problem of
longitude at sea
What is the longitude problem?
• Latitude is measured by the
sun’s angle at noon
Earth circumference
360o
24 hour day
15o = 1 hour
• Easy to measure local time by
the sun, but to find your
horizontal position (longitude)
you need to know the time at a
Pendulum clocks were accurate enough
known reference point
on land, but problematic at sea
• Large variation in humidity and temperature
• Rocking of the ship (storms)
• Corrosion from the sea air
Measuring Time
Longitude Act of 1714
• £20,000 prize for measuring
longitude to 0.5° (> £2 million)
• error of 35 miles at equator
• equivalent to an accuracy of
3 seconds per day
Prize won by John Harrison
But how accurate
are your seconds?
• Sea-going clock H4 accurate
to 0.2 seconds / day
• ~30 km over the 7-week trip
Measuring Time
Greenwich Mean Time
• Noon is not the same as the sun being
directly overhead (±15 min over year)
• Instead use mean annual average of the
non-uniform motion of the real sun
• 1 second = 1 / 86400 of the mean solar day
• Established as the global standard in 1884
Any standard based on the rotation of the earth was
going to run into problems, as measurement technology
and timing needs became more sophisticated.
Variation in the earth’s rotation
What causes changes in earth’s rotation?
Conservation of angular momentum
• weather patterns, tidal patterns
• changes in mass distribution of the earth
(fluid core, earthquakes)
• moon and earth getting farther apart
The difference between
Earth rotational time (UT1)
and the mean solar day.
seconds
Milliseconds
Variability of Earth’s Rotation Length of Day – 86400 seconds
Calendar year
Need a better reference
than the earth
The introduction of atomic time
1955: First caesium atomic clock
produced by Essen & Parry
at NPL, accurate to 1 part in 1010
1958: International Atomic Time (TAI) began,
following the development of further
caesium clocks at NBS (USA) and
ON (Switzerland) Reproducibility
1967: Caesium clock adopted as the basis
for the international definition of time
1 part in 1010 is ~1 second error in
300 years compared to 0.2 s per day,
(a few parts in 106) for the Harrison clock
The second is 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 caesium-133 atom.
1972: GMT was replaced as the international time
reference by Coordinated Universal Time (UTC)
maintained by an ensemble of atomic clocks
around the world (40 countries, ~260 clocks)
Leap seconds
keep UTC and
earth rotational
time consistent
Mircowave atomic standards today
Caesium fountain clock
Accuracy ~ 1  10 -15
(with several days averaging time)
error of 1s in 3 billion years….
How do atoms take us from errors of
second/day to second/billion years?
Atoms as references for clocks
Quantum Mechanics
- quantized energy levels
excited
ground
The atomic clock
Energy
visible/optical
UV/X-ray
frequency (f)  Energy (E)
radio/IR
precision of the
atomic reference
feedback
atomic signal
to oscillator
atoms are identical
reproducibility
“counter”
measures
radiation
oscillator
produces
radiation
atomic
reference
What is driving modern day clock development?
Navigation
- GPS + satellite control
- missile guidance systems
- deep space missions
Synchronisation
- very long base-line interferometry
and arrays (radio telescopes)
- global economy
Standards
- economic and public needs
Global Navigation
Satellite Systems
Image courtesy of ESA
1. How does satellite
navigation work?
2. What do clocks have
to do with any of this?
Proposed constellation of
Galileo satellites in space
Time of Arrival (TOA)
Ranging
Foghorn example
Dx2
Dx
speed of sound
v ~ 335 m/s
Dx
v=
Dt
Dx3
(meters)
(seconds)
Dx = v Dt
Time of Arrival (TOA)
Ranging – timing error
e
Foghorn example
Dx2
e
timing offset = 1 s
Dx
speed of sound ~ 335 m/s
e = v toffset
e = 335 m error!
Dx3
e
Timing errors reduce the
accuracy of the
position measurement
Satellite Navigation
Satellite
Dx = v Dt
Dx
Receiver
speed of sound
v ~ 335 m/s
speed of electromagnetic radiation
v ~ 300000000 m/s
for e ~ 0.3 m (1 ft), nanosecond timing is necessary
What’s next?
Clocks keep getting better and better
- optical clocks – would not lose 1 second in the lifetime of the universe
Earth-based clocks start to run into problems
- gravitational redshift (frequency of clock changes depending
on its distance from the geoid)
- atmospheric effects (communicating from satellites to earth)
Solution?
Put your optical clocks in space!
Space-based optical clocks
Optical master clock in space
Necessary for intercomparison of ground-based optical clocks
Fundamental physics
Tests of general relativity, e.g. STE-QUEST mission
Geoscience
Direct measurement of earth’s geopotential with high resolution
Tracking tectonic plate movement
Navigation
Upgrade of GPS/Galileo to optical clocks
VLBI
Very Long Baseline interferometry (LISA gravity wave detection)
VLA
Very Large (telescope) Arrays (Radio astronomy – timing)
Deep space missions
Communications
What has history shown us?
The better the clock, the longer the list…
Title of Presentation
Name of Speaker
DateThe National Measurement System delivers world-class
measurement science & technology through these organisations
NPL Open House
17 May 2016
2pm - 8pm
www.npl.co.uk/openhouse
The National Measurement System is the UK’s national infrastructure of measurement
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The former National Engineering Laboratory, and the National Measurement Office (NMO).
SI-bot. The Movie.
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1 second
1 minute
1hour
1 day
1 month
1 year
10 years
100 years
1000 years
1 million years
10 million years
100 million years
1 billion years
10 billion years
1
60
3600
86400
2626560
31536000
3.15E+08
3.15E+09
3.15E+10
3.15E+11
3.15E+12
3.15E+13
3.15E+14
3.15E+15