1. LIGO- G050656-00-W About Time by Dr. Fred Raab LIGO Hanford Observatory December 17, 2005

2. LIGO- G050656-00-W About Time 2 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?”

3. LIGO- G050656-00-W About Time 3 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

4. LIGO- G050656-00-W About Time 4 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 Earth’s rotation »Sundials measure Earth’s rotation in the daytime using shadows »At night we can use any bright star Calculating Earth’s movements »Earth makes one rotation each day »Earth makes a circular orbit around the sun each year »Earth’s 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 1/24 th of circle)

5. LIGO- G050656-00-W About Time 5 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 1/12 th 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)

6. LIGO- G050656-00-W About Time 6 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”

7. LIGO- G050656-00-W About Time 7 The “Longitude Problem” Columbus (1492) opened up exploration and trade routes that ventured far to the West of Europe and by the late 1500’s, 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 today’s 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.

8. LIGO- G050656-00-W About Time 8 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 (Roemer’s 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”

9. LIGO- G050656-00-W About Time 9 Atomic clocks Ever since Harrison’s 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”

10. LIGO- G050656-00-W About Time 10 Atomic clocks are very good Today’s 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.

11. LIGO- G050656-00-W About Time 11 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 Sun’s 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 Earth’s 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

12. LIGO- G050656-00-W About Time 12 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 Earth’s 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