Project GREAT (2005) General Relativity Einstein / Essen Anniversary Test. Tom Van Baak PTTI 2006 Washington DC
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1 Project GREAT (2005) General Relativity Einstein / Essen Anniversary Test Tom Van Baak tvb@leapsecond.com PTTI 2006 Washington DC
2 Introduction Project GREAT in 2005 Attempt to prove the theory of relativity Take cesium clocks up a mountain Do clocks really speed up or slow down? Celebrate 100 th anniversary of 1905 Albert Einstein s Annus Mirabilis Celebrate 50 th anniversary of 1955 Louis Essen s NPL cesium clock 06-Dec-2006 Project GREAT 2
3 Albert Einstein Who was Einstein? Need I say more Theory of relativity Time is not absolute SR, GR, space-time Bold predictions Later confirmed Enormous influence 06-Dec-2006 Project GREAT 3
4 Einstein and th anniversary of relativity: books, magazines, radio, TV, web sites, Physics Year, lectures 06-Dec-2006 Project GREAT 4
5 Louis Essen Who was Essen? First Cesium Clock Joint NPL USNO project to calibrate atomic time against astronomical time Hz Book: Famous for a second 06-Dec-2006 Project GREAT 5
6 Essen and th anniversary of atomic time NPL Caesium Jack Parry and Louis Essen Photo from 06-Dec-2006 Project GREAT 6
7 Cs Second How long is a second? 06-Dec-2006 Project GREAT 7
8 Louis Essen 10 years later Essen at NPL with a HP 5060A Flying Clock 06-Dec-2006 Project GREAT 8
9 Flying Clocks in the 1960 s Starting in 1964 with HP 5060A Portable transistorized cesium clock Hundreds of clock trips Remote synchronization to µs levels See HP Journals: 1964, 65, 66, world-wide time synchronization Paved the way for flying clock relativity experiments in the 1970 s 06-Dec-2006 Project GREAT 9
10 Relativity and Clocks High-level summary: Clocks run slower if they move at high velocity (SR) Clocks run slower in the presence of greater gravity (GR) Clocks lose time traveling East (Sagnac) This implies: According to general relativity, stationary clocks on mountains run faster. 06-Dec-2006 Project GREAT 10
11 And so 2005 General Relativity Einstein Essen Anniversary Test Project GRE 2 AT 06-Dec-2006 Project GREAT 11
12 Chapter 2 Flying clock experiments 06-Dec-2006 Project GREAT 12
13 1971 Hafele & Keating PTTI, vol 3, 1971 Time, Oct 18, 1971 Science, Jul 14, Dec-2006 Project GREAT 13
14 Hafele & Keating Round-the-world (EW/WE) flying clocks Hafele thought there would be effect Keating didn t (was open to finding out) Many scientists were certain Results were stunning: all 4 clocks showed difference between EW and WE Relatively simple, cheap experiment 06-Dec-2006 Project GREAT 14
15 1975 C.O. Alley Multiple flights P3C airplane Chesapeake Bay Environment Multiple clocks 3 Cs, 3 Rb, 2 HM L.C. 5061A Laser link 06-Dec-2006 Project GREAT 15
16 C.O. Alley 3 different altitudes (25, 30, ) 5 flights, 2 h, multiple clocks, 0.5% 06-Dec-2006 Project GREAT 16
17 1976 R.F.C Vessot & M. Levine H-maser up, up and away: 10,000 km! NASA, ground stations, up/down links GP-A amazing results, %, 70 ppm 06-Dec-2006 Project GREAT 17
18 1977 NTS-2 Navigation Test Satellite #2 First NAVSTAR GPS, cesium in space Verify relativistic effects 06-Dec-2006 Project GREAT 18
19 Recent relativity experiments 1996 NPL & BBC 25 th anniversary of H&K with London (NPL) to Washington DC (USNO) 2000 T. Celano, TSC military airplane, cesium clocks, comsat modems 2002 T. Celano, TSC similar but with two-way communication, real-time corrections 06-Dec-2006 Project GREAT 19
20 Recent relativity experiments CRL (NICT) measured GR time dilation when moving several 5071A between low and high altitude facilities Also, many non-atomic clock relativity experiments are in progress GP-B, black holes, LIGO, 06-Dec-2006 Project GREAT 20
21 Chapter 3 The Big Idea 06-Dec-2006 Project GREAT 21
22 Relativity at home? Theory of relativity well confirmed With planets, particles, atomic clocks But is it so extreme, so exotic, that only places like Harvard, USNO, JPL, or NASA can prove it? Or is it possible to perform a home experiment to confirm Einstein s prediction? This seems far-fetched. 06-Dec-2006 Project GREAT 22
23 Relativity at home Methods; take atomic clock At high speed, or To high altitude, or On long eastward or westward trip, or All the above Modes; transport using Airplane Rocket Satellite 06-Dec-2006 Project GREAT 23
24 Relativity at home None of those methods work for me: I don t have a plane Rocket or satellite is out of the question But I do have: Many atomic clocks Nearby mountains So, use a mountain? 06-Dec-2006 Project GREAT 24
25 Northwest Mountains (N) Mt Baker, Glacier Peak (S) Mt Rainer, Mt Adams, Mt St Helens (E) Olympic range, Cascade range 06-Dec-2006 Project GREAT 25
26 Back of Envelope Calculation According to GR, clock frequency changes approximately by: g h c 2 On earth, this is /meter That s really small! Too small for me (or anyone) to measure From NPL website 06-Dec-2006 Project GREAT 26
27 is too small, but Say, you go up 1 km instead of 1 m f = = 0.11 ps/s And stay a whole day T = f s = 9.5 ns 9 ns is huge ; so this looks possible! The key to detecting time dilation: go high and stay long Sign is + (blue shift) 06-Dec-2006 Project GREAT 27
28 The Big Idea Take our 3 kids and 3 cesium clocks up Mt Rainier See if Einstein was right about gravity and time See if clocks really run faster up there 06-Dec-2006 Project GREAT 28
29 Map: Seattle to Mt Rainier Just 100 miles away (~2½ hours) 06-Dec-2006 Project GREAT 29
30 Math Detail To a first approximation, small v, h Kinematic: f k ½v 2 c 2 Gravitation: f g g h c 2 Sagnac: f s R 2 cos 2 ( ) c 2 Net f f k f g f s Total T f T 06-Dec-2006 Project GREAT 30
31 Prediction: Sagnac Effect cos² factor is 0.5 for 45 vs. equator 200 ns for km round-the-world So 0.001x that for 40 km, or 200 ps No effect for N-S travel And no effect for same-path round-trip So ignore Sagnac effect 06-Dec-2006 Project GREAT 31
32 Prediction: Velocity Effect Automobile speeds are relatively low 65 mph 96 fps 100 kph 30 m/s Actual trip is 100 miles and 2.5 hours Average speed below 40 mph Worst case 30 m/s for 10 4 s so f = , and T = -50 ps. So ignore Velocity factor too! 06-Dec-2006 Project GREAT 32
33 Prediction: Gravitational Guess 40 to 48 hours Guess = 1340 meters f = This f is very measurable with 5071A 1340 m 40 hours T +20 ns This T is very measurable with 53132A 06-Dec-2006 Project GREAT 33
34 Time Dilation Examples Transport Speed (km/h) Altitude (km) f T Walking 5 0 ~0 ~0 ps/h Car ps/h 0.4 ns/d Balloon ns/d Plane ns/d +95 ns/d GREAT 2+2 h drive ps GREAT 40 h stay ns 06-Dec-2006 Project GREAT 34
35 Summary Calculations Many, High, Long 3 best clocks (5071A/001) 1340 m ( ) altitude Weekend (40 h) & 1340 m & 40h & 3 Estimate ~20 ns Estimated accuracy ~2 ns, 10% Time dilating at about 500 ps / hour 06-Dec-2006 Project GREAT 35
36 Clocks on Mountains Climb or drive? Plus batteries 06-Dec-2006 Project GREAT 36
37 Clocks on Mountains Drive, of course This is America 06-Dec-2006 Project GREAT 37
38 One-way or Round-trip Clocks run slower on a mountain so: Measure frequency of clock at home Measure frequency of clock on mountain Measure against what? How about GPS time & frequency Need better than accuracy Not with my GPS receivers 06-Dec-2006 Project GREAT 38
39 GPS reference Direct frequency measurement (GPS) 06-Dec-2006 Project GREAT 39
40 Summary Big Idea 3 kids, 3 clocks, 1 family minivan To 5400 feet For 40 hours Expect +20 ns Sync time/rate before trip Measure time/rate after trip Against reference; my house standard 06-Dec-2006 Project GREAT 40
41 Chapter 4 Home time lab 06-Dec-2006 Project GREAT 41
42 Home Time Museum & Lab ~ 06-Dec-2006 Project GREAT 42
43 Where does it all come from? Local aero/mil-surplus electronics Ham conventions; flea markets Used test equipment dealers Demo or refurbished models Friends, strangers; other time-nuts Sympathetic T & F companies And, of course, ebay! 06-Dec-2006 Project GREAT 43
44 Surplus Time & Frequency 06-Dec-2006 Project GREAT 44
45 Surplus Time & Frequency 06-Dec-2006 Project GREAT 45
46 Surplus Time & Frequency 06-Dec-2006 Project GREAT 46
47 Surplus Time & Frequency 06-Dec-2006 Project GREAT 47
48 Surplus Time & Frequency 06-Dec-2006 Project GREAT 48
49 Surplus Time & Frequency 06-Dec-2006 Project GREAT 49
50 Surplus Time & Frequency 06-Dec-2006 Project GREAT 50
51 Surplus Time & Frequency 06-Dec-2006 Project GREAT 51
52 Surplus Time & Frequency 06-Dec-2006 Project GREAT 52
53 Surplus Time & Frequency 06-Dec-2006 Project GREAT 53
54 Surplus Time & Frequency 06-Dec-2006 Project GREAT 54
55 Surplus Time & Frequency 06-Dec-2006 Project GREAT 55
56 Surplus Time & Frequency 06-Dec-2006 Project GREAT 56
57 Surplus Time & Frequency 06-Dec-2006 Project GREAT 57
58 Home Time Lab Not just dirt cheap clocks, but Manuals, cables, connectors, power supplies, meters, GPIB, USB, software, GPS antennas, GPSDO, WWVB, Loran-C, clocks, displays, IRIG, TCG, frequency counters, TIC, phase comparators, etc. Most old, some new; possibly broken, often working. Buy 3, play Frankenstein. 06-Dec-2006 Project GREAT 58
59 Museum of HP Clocks 06-Dec-2006 Project GREAT 59
60 Requirements GR effect / m f = If we want 10% accuracy We need a reference good to Dec-2006 Project GREAT 60
61 Chapter 5 A Powers of Ten tour 06-Dec-2006 Project GREAT 61
62 Powers of Ten - Introduction A quick overview of clock accuracy What clocks keep poor time? What clocks keep best time? And many in between 06-Dec-2006 Project GREAT 62
63 10-0 drip, drip Leak in ceiling 0.57 s 9.9 s 1.7 Hz 0.1 Hz 06-Dec-2006 Project GREAT 63
64 10-1 heart beat 10-1, 0.1, 10% The original 1 PPS Sometimes 2x, even 3x Much higher stability at night < 10% accuracy possible 06-Dec-2006 Project GREAT 64
65 10-1 heart beat 12 h frequency plot (evening/night) ADEV floor is 10-1 from 10 1 to 10 4 s! (is this OK?) 06-Dec-2006 Project GREAT 65
66 10-2 tuning fork oscillator 0.01, 1% General Radio Type 213 Audio Oscillator 1 kc ; f = ~992.8 Hz ±1.3 mhz (60 x 1 s) Accuracy < 1% Count those 9 s ADEV is Dec-2006 Project GREAT 66
67 10-2 tuning fork oscillator plots 06-Dec-2006 Project GREAT 67
68 10-3 precision tuning fork 0.001, 0.1%, 1 ms/s General Radio Type kc tuning fork f = ~999.4 Hz ±400 Hz (60 x 1 s) Accuracy < 0.1% ADEV is Dec-2006 Project GREAT 68
69 10-3 precision tuning fork plots 06-Dec-2006 Project GREAT 69
70 10-4 mechanical oscillator 0.01%, 100 ppm Mechanical oscillator Four 9 s 06-Dec-2006 Project GREAT 70
71 10-5 mains 0.001%, 10 ppm 60± Hz 06-Dec-2006 Project GREAT 71
72 10-5 mains plots 06-Dec-2006 Project GREAT 72
73 10-6 quartz watch (RC) %, 1 PPM, 1 s/s +160 ms/d = ppm 06-Dec-2006 Project GREAT 73
74 10-6 quartz watch (RC) Nightly WWVB radio sync (60 khz) Look closely at 01:30 AM PST +1h +30m +15s Plot of 9 days Rate variations Sync variations 06-Dec-2006 Project GREAT 74
75 Aside: Quartz Wall Clock Quartz crystal and divider/driver IC Stepper motor (180 per step) 06-Dec-2006 Project GREAT 75
76 Quartz Wall Clock 32 khz oscillator 1 Hz stepper 06-Dec-2006 Project GREAT 76
77 Quartz Wall Clock Polarity alternates Pulse size: 1.5 V x 50 ms 06-Dec-2006 Project GREAT 77
78 Quartz Wall Clock Coil current: 1.5 V / ma Oscillator current: <1 µa Pulse power (V x A): 4.5 mw Pulse width: 50 ms Clock Energy (P x T): 4.5 mw x 50 ms = 225 µj = 60 pico kwh AA battery (2850 mah) = ~2 years 06-Dec-2006 Project GREAT 78
79 10-7 chronometer 0.1 ppm Rated ¼ sec/day deviation 06-Dec-2006 Project GREAT 79
80 10-7 chronometer ~55 hour runtime 200 ms phase residuals ADEV Dec-2006 Project GREAT 80
81 10-7 chronometer From 1940 s USN manual Phase Dial error Frequency Daily rate Drift Deviation in rate 06-Dec-2006 Project GREAT 81
82 10-8 pendulum clock 0.01 ppm, 10 ppb 10 ns/s, 864 s/d Shortt, Fedchenko, Riefler, Littlemore 06-Dec-2006 Project GREAT 82
83 10-8 pendulum clock Amazing astronomical pendulum clocks Several centuries of understanding and perfection. Limitations addressed: Temperature, humidity, mass, friction, metallurgy, escapement, master/slave, vacuum, isochronous suspension, etc. When all factors solved, the best pendulum clock is just a good gravimeter 06-Dec-2006 Project GREAT 83
84 10-8 pendulum clock plots 06-Dec-2006 Project GREAT 84
85 10-9 earth ppm Slow by ~2 ms per day Also somewhat irregular ADEV 10-8 ~ 10-9 Limited by core, weather, climate Also lunar/solar tides 06-Dec-2006 Project GREAT 85
86 10-9 earth plots 06-Dec-2006 Project GREAT 86
87 10-9 earth Earth as a frequency standard Suggested improvements: Thoroughly clean, and dry with cloth Remove surrounding gas and water vapor Wait for core to cool before use Re-align axis of rotation (wobbling) Keep away from nearby moon (tides) Keep away from sun (tempco) Re-adjust rate (avoid leap seconds) 06-Dec-2006 Project GREAT 87
88 10-10 ocxo 0.1 ppb, 100 ps/s, 8.64 s/d short /d drift 06-Dec-2006 Project GREAT 88
89 10-11 good ocxo 0.01 ppb, 10 ps/s, 864 ns/d (~1 s/d) short ~10-11 /d drift 06-Dec-2006 Project GREAT 89
90 10-12 excellent ocxo 1 ppt, 1 ps/s, 86.4 ns/d (~100 ns/d) ~10-13 short/mid ~ /d drift 06-Dec-2006 Project GREAT 90
91 10-13 rubidium 8.64 ns/d (~10 ns/d) ~10-13 mid-term ~ /m drift 06-Dec-2006 Project GREAT 91
92 10-14 cesium 864 ps/d (~1 ns/d) ~10-13 mid-term ~1 1 day 06-Dec-2006 Project GREAT 92
93 10-14 more cesium not! Cesium clocks differ by 2x 50x E.g., old 5060A vs. new 5071A 06-Dec-2006 Project GREAT 93
94 10-14 another cesium Not even close to 1 day FTS 4010 Portable Clock Old, tired 06-Dec-2006 Project GREAT 94
95 10-14 one more cesium About 2 1 day FTS 4050 See variety of Cs beam cavities 06-Dec-2006 Project GREAT 95
96 10-14 BVA quartz But can you get to high altitude and measure in 1 to 100 seconds? short drift 06-Dec-2006 Project GREAT 96
97 10-15 active h-maser 86.4 ps/d Near 1 Cavity auto-tuned 06-Dec-2006 Project GREAT 97
98 10-15 cesium, long-term High-perf units Pair near at a day Floor near in weeks 06-Dec-2006 Project GREAT 98
99 Powers of Ten summary 10% to orders of magnitude 06-Dec-2006 Project GREAT 99
100 Chapter 6 Experimental setup 06-Dec-2006 Project GREAT 100
101 Key Parameters How high How long How stable How many How precise you measure Cartoon by Dusan Petricic Scientific American column Wonders by Philip and Phyllis Morrison 06-Dec-2006 Project GREAT 101
102 Ingredients Portable clocks, hp Check against base clock (home) Check against themselves (away) Base clock (passive H-maser) Check against active H-maser) Check against Measurement system hp 53132A TIC (~150 Laptop 06-Dec-2006 Project GREAT 102
103 Portable Clock(s) Many Cs tested (5060,5061,4050,4060) Three good 5071A/001 chosen Color coded clocks, cables, TIC, kids Deliberate phase offset of +1, +2, +4 s 1 PPS cables kept with clocks HP 53132A TIC per clock Data logged at 1 Hz; 5 min averages 06-Dec-2006 Project GREAT 103
104 5071A Pick best ones 06-Dec-2006 Project GREAT 104
105 Data collection RS232 interface PC serial port logger MJD time-stamps 8 port serial-to-usb 53132A ti,mean,sdev 5071A stats GPS NMEA 06-Dec-2006 Project GREAT 105
106 Base Clock, House standard Master 1 PPS, CH1-76 passive H-maser 1PPS distribution system (8x) 1PPS vs. HP 58503B GPSDO 1PPS vs. CNS-II (sawtooth-less M12+) 1PPS used as ref for 5071A (x3) Deliberate phase offset of -4 s 5 MHz vs. active maser 06-Dec-2006 Project GREAT 106
107 AC / DC power Engine tap from minivan 12 VDC 2 batteries in parallel for 12 V 4 batteries in series/parallel for 24 V 12VDC/120VAC inverters AC power for clocks AC power for laptop(+batt) and TIC Triple backup for clocks (AC,DC,+batt) Power, voltage, and current monitors 06-Dec-2006 Project GREAT 107
108 Comment on Clock Accuracy Need to predict time 2 days in future Not accuracy, but stability ADEV ( =2d) 5071A/001 is ~ Three clocks: Redundancy (single point of failure) Self-checking (one clock, two clocks ) Lower uncertainty ( 3 = 1.7x better) 06-Dec-2006 Project GREAT 108
109 Carrying the Time How to measure clocks when at home? Compare with house reference Compare amongst themselves How much to trust clocks when away? What do clocks do when you re not looking? Guess future behavior = known past Paststatistics give future predictions Certainty replaced with confidence 06-Dec-2006 Project GREAT 109
110 Stability: Measurements Phase measurements: p0, p1, p2, Frequency calculations (tau T): f1 = (p1 p0)/t, f2 = (p2 p1)/t, 06-Dec-2006 Project GREAT 110
111 Stability: Predictions Predict (extrapolate) future phase: p2 = p1 + f1 T = p1 + (p1 p0) Later, check prediction error: e2 = p2 p2 = p2 2p1 + p0 06-Dec-2006 Project GREAT 111
112 Stability: Allan Deviation Stddev of prediction errors gives you estimate of future accuracy of clock This [p2 2p1 + p0] thing is ADEV 06-Dec-2006 Project GREAT 112
113 Map home clocks 06-Dec-2006 Project GREAT 113
114 Map mobile clocks 06-Dec-2006 Project GREAT 114
115 Map mobile power 06-Dec-2006 Project GREAT 115
116 Map Paradise, Mt Rainier ~ 06-Dec-2006 Project GREAT 116
117 Chapter 7 Photos of the trip 06-Dec-2006 Project GREAT 117
118 The GREAT Trip, day 1 Carrying clock downstairs. Limited time; car is a mess, but it works. 06-Dec-2006 Project GREAT 118
119 The GREAT Trip, day 1 Kids in the rear, clocks in the middle, and instrumentation in the front. 06-Dec-2006 Project GREAT 119
120 The GREAT Trip, day 1 Dad making final clock BNC connections to TIC; Mom says goodbye. 06-Dec-2006 Project GREAT 120
121 The GREAT Trip, day 1 Detail of TIC s and laptop in front seat and clocks in middle seat. 23:33:48 UTC 06-Dec-2006 Project GREAT 121
122 The GREAT Trip, day 1 Kids drink stop costs me $8 and 125 ps (¼ hour x 500ps/h). 06-Dec-2006 Project GREAT 122
123 The GREAT Trip, day 1 Final gas stop and evening arrival in Rainier National Park. 06-Dec-2006 Project GREAT 123
124 The GREAT Trip, day 2 Paradise Inn is at 5400 elevation. Large parking lot to hide in. 06-Dec-2006 Project GREAT 124
125 The GREAT Trip, day 2 Classic old Northwest inn; you should visit sometime. 06-Dec-2006 Project GREAT 125
126 The GREAT Trip, day 2 Wonderful hiking trails and climbing. 06-Dec-2006 Project GREAT 126
127 The GREAT Trip, day 2 Good, the car is still there. Hike to Glacier Vista (6300 ) 06-Dec-2006 Project GREAT 127
128 The GREAT Trip, day 2 Oh no. The sun is really strong and the A/C isn t working as well as I hoped. 06-Dec-2006 Project GREAT 128
129 The GREAT Trip, day 2 Avoid a ticket and move the car again. Ouch, running low in fuel. Now what. 06-Dec-2006 Project GREAT 129
130 The GREAT Trip, day 2 Kids are fine. Trip is long. Looking for GPS location for next time. What! Valet shuts car off for an hour. 06-Dec-2006 Project GREAT 130
131 The GREAT Trip, day 2 Air is thin; little sleep; ponder Time; spend an hour; why are we doing this; Harrison; GPS. That s 500 ps/beer. 06-Dec-2006 Project GREAT 131
132 The GREAT Trip, day 3 Got gas at 6 AM. Used gal in 34 h = 0.46 gph; ~2h/gal, so about 1 ns/gal. Cost me $51 and 745 ps. 06-Dec-2006 Project GREAT 132
133 The GREAT Trip, day 3 More hiking, exploring, playing. It s a fun place for a while. 06-Dec-2006 Project GREAT 133
134 The GREAT Trip, day 3 42 hours is up; time to leave. We re all tired. Can this really work? Go home. 06-Dec-2006 Project GREAT 134
135 The GREAT Trip, day 3 Carry clocks & TIC s back inside, reconnect same cables, resume phase comparison, unpack car. Sleep. 06-Dec-2006 Project GREAT 135
136 Chapter 8 Analysis of GPS data 06-Dec-2006 Project GREAT 136
137 GPS Log Serial NMEA data stream (0.5 Hz) $GPGGA (time/lat/lon/alt) $GPRMC (time/date/lat/lon/speed) $GPRMC,120454,A, ,N, ,W,26.8,272.6,190905,17.8,E,A* $GPGGA,120454, ,N, ,W,1,03,2.2,727.7,M,-18.8,M,,*77 Software tool calculates time dilation , ,728,14, Generated plots 06-Dec-2006 Project GREAT 137
138 Plots from GPS Log Latitude, Longitude 06-Dec-2006 Project GREAT 138
139 Plots from GPS Log Altitude, Velocity 06-Dec-2006 Project GREAT 139
140 Predictions from GPS Log SR (velocity): 50 ps Sagnac effect: 150 ps (net 1 ps) 06-Dec-2006 Project GREAT 140
141 Predictions from GPS Log GR (gravitational): ns 06-Dec-2006 Project GREAT 141
142 Composite plot - beginning Trip start 06-Dec-2006 Project GREAT 142
143 Composite plot - middle More gas 06-Dec-2006 Project GREAT 143
144 Composite plot - end Trip end 06-Dec-2006 Project GREAT 144
145 Composite plot (net ns) 06-Dec-2006 Project GREAT 145
146 Chapter 9 Analysis of clock data 06-Dec-2006 Project GREAT 146
147 Worked example Raw data 3 clocks 06-Dec-2006 Project GREAT 147
148 Worked example Red only 5.85 s 5.55 s -220 ns 10 days 06-Dec-2006 Project GREAT 148
149 Worked example Slope (freq) Pre/post ns/d Dec-2006 Project GREAT 149
150 Worked example Remove fixed ~5.8µs offset 06-Dec-2006 Project GREAT 150
151 Worked example Line fit Phase offset No freq diff 06-Dec-2006 Project GREAT 151
152 Worked example More fit Dec-2006 Project GREAT 152
153 Worked example Best fit Dec-2006 Project GREAT 153
154 Worked example Expand scale ~1 ns/d match Huge time jump! 06-Dec-2006 Project GREAT 154
155 Results Raw clock phase, with mean 06-Dec-2006 Project GREAT 155
156 Results 1 Red 20.3 ns 06-Dec-2006 Project GREAT 156
157 Results 2 Green 17.5 ns 06-Dec-2006 Project GREAT 157
158 Results 3 Blue 26.3 ns 29.7 ns 06-Dec-2006 Project GREAT 158
159 Results 4 Mean 23.2 ns 06-Dec-2006 Project GREAT 159
160 Results 5 Composite 4 ns(?) 06-Dec-2006 Project GREAT 160
161 Analysis Methods Frequency before extrapolated forward Frequency after extrapolated backward Both before and after; mean frequency Continuous or hourly/daily averages? One day; or ±3 days; -n +m days? Mean phase or last/first phase? Calculated removal of phase jump until optimal least squares fit? 06-Dec-2006 Project GREAT 161
162 Phase Jump Simulation Artificially remove time dilation Stddev improves to a point 06-Dec-2006 Project GREAT 162
163 Ambiguity Gap in time is clear, but Precise magnitude depends on both pre- post-trip rate precision, which is Influenced by frequency averaging time 1 hour? 1 day? 2 days? 7 days? Might be a bit subjective, but All methods seem to agree to a few ns 06-Dec-2006 Project GREAT 163
164 Ambiguity 3+3? 3+5? 3+10? 1+1? 3+3? 06-Dec-2006 Project GREAT 164
165 Chapter 10 Base & portable clock performance 06-Dec-2006 Project GREAT 165
166 Base Clock House ref is passive H-maser Ref vs. GPS; phase (12-days) 06-Dec-2006 Project GREAT 166
167 Base Clock Ref vs. GPS, ADEV (decade) Near/below at 1 d 06-Dec-2006 Project GREAT 167
168 Base Clock Ref vs. GPS, ADEV (many tau) Note 1 d, 2 d better than 1.5 d 06-Dec-2006 Project GREAT 168
169 Base Clock Composite ADEV 06-Dec-2006 Project GREAT 169
170 Base Clock Passive H-maser ref vs. active H-maser at 1 day means no worries 06-Dec-2006 Project GREAT 170
171 Base Clock But weird short-term stability Probably OK (20 ps jumps, 10 ps noise) 06-Dec-2006 Project GREAT 171
172 Portable Clock(s) ~2 days before trip + ~10 days after tip 06-Dec-2006 Project GREAT 172
173 Portable Clock(s) ~3 week trip would work even better 06-Dec-2006 Project GREAT 173
174 Confidence Summary Base clock is good to ~ Portable clocks are good to ~ Relativistic effect is ~ GPS log is much better than 1% No show-stopper glitches So experiment accuracy is ~15% 15% of 22 ns is ~3 ns 06-Dec-2006 Project GREAT 174
175 3-Hat, phase (home) Cs i Cs j via lab reference 06-Dec-2006 Project GREAT 175
176 3-Hat, phase (away) Cs i Cs j via mutual-comparisons 06-Dec-2006 Project GREAT 176
177 3-Hat, phase (combined) Cs i Cs j continuous 06-Dec-2006 Project GREAT 177
178 3-Hat, resid (home) Cs i Cs j via lab reference 06-Dec-2006 Project GREAT 178
179 3-Hat, resid (away) Cs i Cs j via mutual-comparisons 06-Dec-2006 Project GREAT 179
180 3-Hat, resid (combined) Cs i Cs j 06-Dec-2006 Project GREAT 180
181 Final Graph; days 06-Dec-2006 Project GREAT 181
182 Final Graph; +kids +mountain 06-Dec-2006 Project GREAT 182
183 Chapter 11 Conclusion 06-Dec-2006 Project GREAT 183
184 What went wrong Difficult physical clock transfers Direct morning sunlight temperature Unexpected out-of-gas event, OK Hotel turned minivan off, OK GPS battery ran out, OK One TIC was 53131A (500 ps vs. 150 ps) Minivan A/C has poor algorithm Parking lot hassles, OK More exhausting than expected 06-Dec-2006 Project GREAT 184
185 What went right No loss of clock No loss of any data Relativity effects obvious and stunning Three clocks was good idea Mean closer than hoped for Standard deviation wider than expected Good input for another run Not bad for a first try Kids had a great time! 06-Dec-2006 Project GREAT 185
186 Conclusions Experiment worked rather well We now believe what we know Fun technical challenge Echo of historical experiments Useful precise time teaching example A fitting 2005 PTTI celebration Came back much* older and wiser Relativity is now child s play Best 22 ns of my life! 06-Dec-2006 Project GREAT 186
187 Thank you For years of inspiration and support More info: Patience from wife & kids Time for questions General Relativity Einstein / Essen Anniversary Test 06-Dec-2006 Project GREAT 187
188 06-Dec-2006 Project GREAT 188
189 Chapter Extra material 06-Dec-2006 Project GREAT 189
190 Einstein & Atomic Clocks Verifying GR with atomic clocks Did Einstein know? (he died in 1955) NBS Cs 1953, Essen 1955, Naumann & Stroke article 06-Dec-2006 Project GREAT 190
191 Project GREAT 2007? Make minivan a lab not just a transport 2+ week pre-trip, 1+ week post-trip Single switch: ext Maser vs. int Rb ref Careful solar and thermal insulation Use park/inn power instead of car engine Proper air con solution in vehicle Real-time plots; wireless status & alerts! More kids; more clocks (5?) Test 1970 s H&K-era 5061A s for contrast Try direct GPS frequency measurement 06-Dec-2006 Project GREAT 191
192 Humor cesium wristwatch Bill s watch Atomic Bill first true atomic wrist watch 06-Dec-2006 Project GREAT 192
193 Humor portable cesium clock Tom s backpack (Project GREAT, ver 1) Atomic Tom climbing with atomic clocks 06-Dec-2006 Project GREAT 193
194 Humor Glimmer Twins GR says high clocks run faster 1965: Keith gets high (for 40 years) 2005: looks much older 06-Dec-2006 Project GREAT 194
195 Humor relativity Time flies while you re having fun Stay young: fly fast and low How to spend more time with your kids How to make your wife younger 06-Dec-2006 Project GREAT 195
196 Humor make time go faster Charlie and the Chocolate Factory 06-Dec-2006 Project GREAT 196
197 Chapter 1 Introduction 06-Dec-2006 Project GREAT 197
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