precise time: from cpu clocks to hacking the...

Precise Time: from CPU clocks Precise Time: from CPU clocks to hacking the Universeto hacking the Universe

Tom Van BaakFOSDEM’15

Brussels, 1 February 2015

v1.7

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Outline

• Part 1 – computers and timekeeping• Part 2 – time and frequency• Part 3 – amateur timekeeping• Part 4 – powers of ten• Part 5 – kids, clocks, and relativity

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1. computers and timekeeping

• A long ago:– computers were calculators, not clocks– time was for people, not programs, and– it came from astronomers, not atoms

• Photos/influences from the early days:– first leap second, 1972– my first 3 computers– a CPU test program that deeply affected me

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1972 computer: NCR 200

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1974 computer: GE 635

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1976 computer: Honeywell 6620

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Instruction timings (GE 636)• computers, clocks, precision, accuracy, measurement

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1980 timekeeping was simple

• UNIX timekeeping (System-III, PDP11/34)– time(), sleep(), (gtime: stime: alarm:)

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2015 timekeeping is complex

• clock(), gettimeofday(), TIME-TAI, TIME-UTC, TIME-MONOTONIC, TIME-THREAD, TIME-PROCESS, TIME-DURATION, tv_sec, tv_usec, tv_nsec, POSIX, TOY, TAI, TAI64, leap second, ISO 8601, granularity, resolution, drift, precision, jitter, adjtime(), NTP, PTP, QueryPerformanceCounter, RDTSC

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Engineers get timekeeping

• Software and hardware timing:– kHz, MHz, GHz (rate, speed, frequency)– ms, µs, ns, ps (duration, period, time interval)– time_t, tv_sec, tv_usec, tv_nsec, ticks, jiffy– disk storage: data rates, latency– network communication speeds, ping times– cpu instruction times, cache misses, OOE– video frames, USB packets, SPI, I2C

• Makefiles, databases, synchronization

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2. time and frequency

• What is time?– so obvious we don’t usually ask– so mysterious we don’t actually know

• Some cute (but circular) definitions…– “Time is what clocks measure”– “Space is what prevents everything from

being in the same place”– “Time is what prevents everything from

happening at once”

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Basics: time, time interval

• Seems like two kinds of time?– date & time, time-of-day, when (earth)– duration, time interval, how long (timer)

• Time interval: time(A) to time(B)– distance “space interval”: point(A) to point(B)

• Time-of-day = time interval: then to now– people simply agree on “then” (aka epoch)– 1 AD, 1858-11-17, 1970-01-01, 1980-01-06

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Basics: frequency, clock

• Frequency = periodic events over time– count the events (e.g., 51.0 cycles)– measure elapsed time (e.g., 1.004 seconds)

• Units: “per second”, 1/second, s-1, Hz– frequency is a ratio (as length, mass, etc.)– period = 1 / frequency (20 ms : 50 Hz)

• Clock = frequency plus counter– analog (hands) or digital (symbols)

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Chronometer adjust (time, rate)

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Frequency adjust

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Time adjust (20 ns)

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What (where) time is it?

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Basics: clock comparison

• Compare clock time– difference: (t1–t0) seconds, ms, µs, ns, ps

• Compare clock frequency– ratio: (f1/f0) or relative (f1-f0)/f0 [unit-less]– measure slow time drift between clocks

• No two clocks are identical!– are you looking close enough?– or, are you waiting long enough?

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Astronomy and clocks

• Earth/sun orbit is a clock (unit: year)– 365.24219265 d/y (ratio)

• Moon/earth orbit is a clock (unit: month*)– 27.321662 d/m (ratio)

• Earth rotation is a clock (unit: day)– 86400.002117 s/d (ratio) today*

• Pulsar 1937+21 is a clock (unit: blink)– 0.0015578065 s = 641.92825 Hz

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Basics: clock stability

• Don’t care about time (can set)• Don’t care about frequency (can adjust)• We care about consistency of frequency

– stability, or instability (lower is better)– a standard deviation* called sigma

• Stability is measured by sampling– the sampling time interval is called tau

• Allan deviation, log-log sigma(tau) plot

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Basics: summary

• Time• Time interval• Frequency• Clocks• Clock comparison• Offsets/adjustments, time & frequency • Frequency Stability• Time Accuracy

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3. amateur timekeeping

• Two kinds of clocks(1) My own clock; with precise oscillator

– wide variety of DIY clock projects– set once, then occasionally compare

(2) My own clock; but “borrow” the time– radio clocks (WWVB, DCF77, GPS)– power line (50/60 Hz mains) wall clocks– network clocks (telephone, cellular, NTP)

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A DIY quartz analog/LED clock

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How to keep time?

• “Timebase” required (quartz oscillator)– how accurate is it?– how to measure it?

• Use frequency counter– how accurate is it?– how to measure it?

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Accuracy

• 0.01/10.00 MHz = 0.1% (~86 sec/day)• 0.0001/10 = 10 ppm (~0.8 sec/day)

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More accuracy

• Better timekeeping needs better timebase– better measurement requires better counter– better counter requires better reference

• What does it mean to “keep” time?– who’s time are we actually keeping?– WWVB, DCF77, NTP, Loran-C, GPS time– what is UTC; how good are atomic clocks?

• This time stuff is all so interesting

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The quest for better oscillators

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The quest for more digits

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Slippery slope

• More oscillators, more test equipment– quartz, rubidium, cesium standards– microseconds, nanoseconds, picoseconds

• Most modern technology depends on:– precise time synchronization– stable frequency references

• Books, articles, op/svc manuals, HPJ– danger: catch the “time bug”

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Home time & frequency lab

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Museum of hp clocks

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HP quartz

105B 107BR 106B 104AR 103AR 101A 100ER

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HP clocks

HP01 571B 5321 117A 114BR 115BR 113AR

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HP cesium & rubidium

5071A 5065A 5062c 5061B 5061A 5060A

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Vintage hp 5061A (eBay)

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FYI: cesium (caesium)

• Cesium atomic clocks are not radioactive• They use a natural, stable Cs133 atom, not

the scary man-made radioisotope Cs137

• Analogy: C12 vs. C14

• K39 vs. K40 (banana)• “hyperfine transition”

9,192,631,770 Hz• Solid / liquid [28 °C]

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First radioactive cesium clock!

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What is the best clock?

• Quartz: inaccurate and drifts• Rubidium vapor: more stable but still drifts• Cesium beam: better still and no drift• Hydrogen maser: most stable, small drift• UTC is “average” of 364 clocks [w1412]• Exotic ion, “fountain”, optical clocks• No one best clock, no perfect time

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“Keeps perfect time”

• quartz • art deco

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Which watch is best?

• You go shopping for watches at lunch…

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Which clock do you want?

• Checking each day, at precisely noon:• (a) (b) (c) (d)• 12:00:00 12:01:30 12:03:30 12:06:11• 12:00:00 12:01:40 12:03:25 12:07:22• 12:00:00 12:01:20 12:03:30 12:08:33• 12:00:00 12:01:10 12:03:35 12:09:44• 12:00:00 12:01:40 12:03:30 12:10:55• Which one do you want to buy?

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Which clock do you want?

• Answer:– (a) is probably a stopped watch– (b) is most accurate, but more variable– (c) is less accurate, but less variable– (d) is least accurate, but very stable

• Watch (d) is exactly 1:11 fast per 24h– regulate (or simply apply a math correction)

and then you have the best watch

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Best wristwatch

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4. powers of ten

• Any periodic event is can be a clock– not all clocks are super accurate

• How regular the occurrence determines:– how good or bad the clock is

• How continuous the events determines:– how reliable the clock is

• The range of accuracy/stability is huge!– all you have to do is measure it

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“Powers of Ten” – inspiration

• Mr Charles and Ms Ray Eames (1977)– “the effect of adding another zero”

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Fractional units

• 1 second / day = ~1.2 × 10-5

• 3 seconds / month = 10-6 = 1 ppm• 1 second / month = ~3.8 × 10-7

• 1 second / year = ~3.2 × 10-8

• 1 ms [millisecond] / day = ~10-8

• 1 µs [microsecond] / day = ~10-11

• 1 ns [nanosecond] / day = ~10-14

• 1 sec / 3 000 000 years = ~10-14

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10-0 drip, drip• Leak in ceiling• 0.57 s … 9.9 s• 1.7 Hz … 0.1 Hz

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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

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10-1 heart beat• 12 h frequency plot (evening/night)• ADEV floor is 10-1 from 101 to 104 s!

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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 10-6…10-4

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10-2 tuning fork oscillator• plots

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10-3 precision tuning fork• 0.001, 0.1%, 1 ms/s• General Radio Type 813

single vacuum tube• 1 ‘kc’ tuning fork• f = ~999.4 Hz• ±400 µHz (60 x 1 s)• Accuracy < 0.1%• ADEV is 10-7…10-4

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10-3 precision tuning fork• plots

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10-4 mechanical oscillator• 0.01%, 100 ppm• Mechanical oscillator

transistorized• “Four 9’s”

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10-5 mains (line frequency)• 0.001%, 10 ppm• 50/60± Hz

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10-5 mains (line frequency)• plots

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10-6 quartz watch (RC)• 0.0001%, 1 ppm, 1 µs/s• +160 ms/d = +1.85 ppm

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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

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10-7 chronometer• 0.1 ppm• Rated ¼ sec/day deviation

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10-7 chronometer• ~55 hour runtime• 200 ms phase residuals• ADEV 610-7

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10-7 chronometer• From 1940’s USN manual…• Phase

– Dial error• Frequency

– Daily rate• Drift

– Deviation in rate

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10-8 pendulum clock• 0.01 ppm, 10 ppb

10 ns/s, 864 µs/d• Shortt,

Riefler,Fedchenko,Littlemore’

• T ≈ 2π√(L/g)

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10-8 pendulum clock• plots

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10-8 pendulum clock• Fedchenko AChF-3 clock (Nov 1969)

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10-9 earth• 0.001 ppm• Slow by ~2 ms per day• Also somewhat irregular• ADEV 10-8 ~ 10-9

• Limited by core, weather, climate• Lunar/solar tides, periodic variations• Tidal friction, long-term drift

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10-9 earth (40y of data)• plots

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10-9 earth clock• Long-term plot (300 years)• Length of day (LOD) is 86,400 seconds ±

a few milliseconds

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10-9 earth clock• Short-term plot (3 recent years)• LOD is about 86,400.002 seconds

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10-9 earth clock

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10-9 earth 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)

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10-10 ocxo• 0.1 ppb, 100 ps/s, 8.64 µs/d• 10-10…10-13 short• 510-10/d drift

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10-11 good ocxo• 0.01 ppb, 10 ps/s, 864 ns/d (~1 µs/d)• 10-11…10-13 short• ~10-11/d drift

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10-12 excellent ocxo• 1 ppt, 1 ps/s, 86.4 ns/d (~100 ns/d)• ~10-13 short/mid• ~310-12/d drift

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10-13 hp 106B quartz• Best hp quartz• ~410-13/d drift

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10-13 rubidium• 8.64 ns/d (~10 ns/d)• ~10-13 mid-term• ~110-11/m drift

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10-14 cesium• 864 ps/d (~1 ns/d)• ~10-13 mid-term• ~110-14 @ 1 day

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10-14 more cesium• 10-14 not!• Cesium clocks differ by 2x – 50x• Vintage 5060A

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10-14 another cesium• Not even close to 10-14 @ 1 day • FTS 4010• Portable clock

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10-15 hp 5071A cesium• High-performance model• Pair ~210-14 at a day• Flicker floor ~510-15 in weeks

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10-16 active H-maser• 8.64 ps/d• Under 110-15 @1d• Most stable

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Summary – powers of ten

• 17 orders of magnitude– from a billion times

worse than earth– to a billion times

better than earth

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5. kids, clocks, and relativity

• What to do with atomic clock hobby?• Einstein said time itself is not fixed

– S.R. predicts higher speed slows time– G.R. predicts stronger gravity slows time

• Is this only abstract theory in textbooks?– fast moving rocket ships and aging twins– objects getting too close to black holes

• Can this be tested for real on earth?

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Relativity at home

• We have many atomic clocks at home• No planes or rockets (high speed)• But we have mountains (high altitude)

From NPL website

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Big idea

• Take our 3 kids withportable cesium clockshigh up Mt Rainier

• See if Einstein wasright about gravityand time

• See if clocks reallyrun faster up there

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Einstein and 2005

• 100th anniversary of relativity: books, magazines, radio, TV, web sites, “Physics Year”, lectures…

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Louis Essen (UK) and 2005

• 50th anniversary of cesium clock (NPL)• “famous for a second” 9 192 631 770 Hz

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Project GRE²AT

• General Relativity Einstein/Essen Anniversary Test (2005)– 100th anniversary (Einstein) theory of relativity– 50th anniversary (Essen) first cesium clock

• Combine atomic clock hobby, physics, history, technology, math, computers, children, car trip, vacation, and family fun

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Clock equations

• To a first approximation, small v, small h• Kinematic: fk ½v2c2 (redshift)

• Gravitation: fg ghc2 (blueshift)

• Sagnac: ts R2cos2()• c2

• Net freq f fk fg• Total time T fT ts

– these corrections are usually infinitesimal– 1/c2 ≈ 1.1×10-17 = 0.000000000000000011

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Magnify the effect

• Go as highas possible

• Stay as longas possible

• Measure asprecisely aspossible

Cartoon by Dusan PetricicScientific American column Wonders by Philip and Phyllis Morrison

http://www.sciam.com/1998/0298issue/0298wonders.html

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Time dilation calculation

• Turn infinitesimal into measurable• Frequency change f/f gh/c2

f/f 1.09×10-16 s/s/meter• But if you go up 1 km instead of 1 m, then

f/f = 1.1×10-13 = 0.11 ps/s• And if you stay up there 24 hours, then

T = f/f 86400 s = 9.5×10-9 s = 9.5 ns• Gravitational time dilation 10 ns/day/km

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The GREAT trip, day 1

• Carrying clock downstairs. Limited time; car is a mess, but it works.

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• Clocks in the middle, batteries (200 kg) on the floor, and instrumentation in the front.

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• Kids in the back. Dad making final clock BNC connections; Mom says goodbye.

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• Detail of TIC’s and laptop in front seat and clocks in middle seat. 23:33:48 UTC

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• Final gas stop and evening arrival at Rainier National Park.

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• Paradise Inn is at 5400 ft (~1650 m) elevation. Large parking lot to hide in.

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• Classic old Northwest inn; you should visit sometime.

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• Wonderful hiking trails and climbing. Lucky to have clear weather.

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• Avoid a ticket and move the car again. Ouch, running low in fuel. Now what.

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• Got gas at 6 AM. Used 15.78 gal in 34 h = 0.46 gph; ~2h/gal, so about 1 ns/gal.

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• More hiking, exploring, playing. It’s a fun place for a while.

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• 42 hours is up; time to leave. We’re all tired. Can this really work? Go home.

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The GREAT trip

• Home clock and mountain clock elevations (1650 m − 310 m = +1340 m)

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Back home, re-measure clocks

• Results are unknowable until the return(1) Did we see any time dilation?

– requires before/after time-rate comparison– comparison against stable “house” clock

(2) Did the results match prediction?– requires record of altitude and duration– used Garmin GPS NMEA log– approx +1340 m for 42 hours (integrate)

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Elevation and predicted dilation

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Clock results (measured)

• Red20.3 ns

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Mean clock results

• Mean23.2 ns

• ±4 ns• Predict

22.4 ns

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3-hat, residuals (home)

• Csi – Csj via lab reference

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3-hat, residuals (away)

• Csi – Csj via mutual-comparisons

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3-hat, residuals (combined)

• Csi – Csj

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GRE²AT experiment worked

• Gravitational time dilation is real!– we came back 22 ns older (wife −= 22 ns)– hacked hidden secret of the universe– ”relativity is now child’s play”

• Unexpected press– Physics Today, WIRED magazine

• No perfect clock, no perfect time– even atomic clocks are gravimeters

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Thanks for your time

• Poul-Henning Kamp, FOSDEM / Gerry Demaret, time-nuts mailing list

• Contact: [email protected]• Web: www.LeapSecond.com

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