About Time by Dr. Fred Raab

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About Timeby Dr. Fred Raab

• LIGO Hanford Observatory
• December 17, 2005

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About Time

• Humans have a sense of time
• Do all people sense time in the same way?
• Do other animals sense time?
• How do we measure time?
• Astronomical clocks
• Mechanical clocks
• Atomic clocks
• Coordinating time
• Connections between space and time
• Navigation
• Relativity
• Different ways to answer, What time is it?

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A Sense of Time

• People perceive a sense of time
• Ice cream melts in a short amount of time on a
  summer day
• It will be a long time before summer vacation
• People perceive an arrow of time
• If we see a movie of someone diving into a
  swimming pool and splashing water about, it seems
  normal
• If we see a movie of water droplets jumping into
  the center of a swimming pool and then a person
  rising feet first out of the water and landing on
  a diving board, it seems funny and weird
• Do all people experience time the same
• We share many impressions of time, but we also
  sometimes disagree on whether something took a
  long time or not
• Since animals cannot talk, we do not know if they
  experience time like we do

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Astronomical measures of time are ancient

• Movement of the sun, moon and stars in the sky
• First way time was measured by humans
• Sky only appears to move actually we are seeing
  Earths rotation
• Sundials measure Earths rotation in the daytime
  using shadows
• At night we can use any bright star
• Calculating Earths movements
• Earth makes one rotation each day
• Earth makes a circular orbit around the sun each
  year
• Earths rotation axis is tilted relative to its
  orbit about the sun
• This tilt causes the seasons and also causes the
  positions of the constellations to appear to
  rotate about the North Star each year
• This gave rise to dividing circles into 360
  degrees (close to the 365 days in a year) and 24
  hours (time to rotate 1/24th of circle)

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Motion of the Moon

• Earth rotation causes sun and stars to drift by
  15 degrees per hour ( 360 degrees / 24 hours)
• Earth orbit causes the constellation positions at
  midnight to drift toward the West by 1 degree/day
• But the Moon drifts from constellation to
  constellation and from day to night making
  roughly 12 circuits each year
• So a month is 1/12th of a year, or roughly 30
  days
• This effect is caused by the orbit of the Moon
  around Earth
• These numbers 360, 30, 24 and 12, became the
  basis for calendars and clocks because they could
  be obtained from each other by multiplication and
  division
• However they are not the exact numbers
• For instance there are 365 days in a year and it
  takes 29 days for a lunar orbit (bankers
  calculate interest on a 360-day year)

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Mechanical time

• Astronomical timekeeping is OK if you stay in the
  same place, but if you move East or West on
  Earth, then your astronomical time changes
• So, a city that is 15 degrees East of us
  (Cheyenne, Wyoming) would be 1 hour ahead of us
  in time
• As long as it takes much longer than 1 hour to
  get a message between Pasco and Cheyenne (before
  1861) this is not a problem
• But there was a problem measuring space that
  could take advantage of a new way to measure
  time the Longitude Problem

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The Longitude Problem

• Columbus (1492) opened up exploration and trade
  routes that ventured far to the West of Europe
  and by the late 1500s, Earth had been
  circumnavigated
• World-wide trading companies were becoming the
  economic basis of power for Spain, England and
  France
• But world-wide shipping losses in money and lives
  were huge, because ships could not determine
  their longitude and were lost at sea
• The British Parliament set up the Longitude
  Prize (worth more than todays Nobel Prize) to
  encourage the invention of a way to measure
  longitude
• This required that a clock be invented that
  could be carried on a ship and kept
  synchronized to a clock in England comparing
  astronomical time to the English time (now
  Greenwich time) to about 5-10 minutes accuracy, a
  captain could obtain his longitude with
  sufficient accuracy to avoid wrecking his ship.

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Solving the Longitude Problem

• Galileo, Newton, Cassini, Halley and many other
  scientists worked on the Longitude Problem
• This work led to advances in astronomy (accurate
  orbits for our Moon and the moons of Jupiter) and
  physics (Roemers first measurement of the speed
  of light)
• Ultimately, John Harrison won the longitude prize
  for the invention of a portable mechanical clock,
  which Captain Cook demonstrated on a famous
  voyage to the Pacific
• Harrison developed both a ship-board clock
  (called a chronometer) and the pocket watch

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Atomic clocks

• Ever since Harrisons invention, timekeeping and
  navigation have been intertwined
• As we traveled farther and needed more
  navigational accuracy, the demand for precision
  in timekeeping accuracy has become more and more
  important
• Eventually, quantum physics would lead to the
  discovery of ultra-stable and unimaginably
  reproducible clocks Atoms
• Today, the second is defined as 9,192,631,770
  cycles of microwave radiation corresponding to a
  particular hyperfine splitting of energy levels
  in the ground state of an atom of Cesium with
  atomic number 133.
• Devices that measure and count these atomic
  seconds are called atomic clocks

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Atomic clocks are very good

• Todays best atomic clocks will lose or gain less
  than 1 second of time in 1,000,000 years!
• Atomic time is broadcast across the US from
  Colorado and from the Global Positioning System
  (GPS) satellites.
• GPS navigation on Earth is accurate to within
  20-ft
• Differential-GPS surveying was used to position
  LIGO foundations to a precision of 3/8 inch over
  5 miles
• You can buy radio-controlled wristwatches for
  under 50, that receive broadcasts of atomic time
  and synch to them.

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General Relativity the laws of space and time

• Einstein developed Relativity from 1905-1916
• Time and Space are stretched and shrunk by
  motion and matter
• Theory first confirmed by detection of Suns
  space warp in 1919
• Atomic clocks on GPS satellites tick more
  rapidly than the same atomic clocks on the ground
• The orbiting GPS clocks are becoming younger than
  us because of the high speed of motion of the
  satellites
• This causes the GPS clocks to look slower
  (dilation)
• But Earthbound clocks are slowed down because of
  the stronger time warp due to Earths mass
• This causes the GPS clocks to look faster
• Time warpage is stronger than time dilation at
  the height of the GPS orbits, so GPS clocks
  appear to gain about a second per century,
  relative to atomic clocks on the ground
• General relativity is used to correct accurately
  for these time dilations and time warps

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Coordinating Astronomical and Atomic Time What
time is it?

• Universal time (UT) is astronomical time, counted
  from 0 hours at midnight, with duration of a Mean
  Solar Day, defined to be as uniform as possible
  despite variations in Earths rotation rate
• International Atomic Time (TAI) is based on
  combining data from a large number of atomic
  clocks around the world
• Coordinated Universal Time (UTC) differs from TAI
  by introduction of occasional leap seconds to
  bring it closer to UT, so that over the millenia
  we will not have sunrise at midnight
• This is the time displayed in the LIGO control
  room, derived from GPS satellites and compared to
  atomic clocks at Hanford Livingston
• Sidereal time is important to amateur
  astronomers it measures Earth rotation relative
  to distant stars as opposed to the Sun
• Barycentric time has the duration of sidereal
  time, but is calculated at the center of mass of
  the solar system, rather than at Earth. It is
  important for measuring incoming signals from
  space (like radio signals from pulsars), because
  it is more immune to accelerations from orbiting
  planets and asteroids