Monday, July 25, 2022

[asrkbeeb] historical events with precise times

what historical events do we know to a precision of 1 second or better?

if the historical date+time is recorded in UTC (or a local time zone defined as an offset from UTC), then, to calculate the amount of time that has elapsed since then, one needs to know how many leap seconds have occurred since then.  this is awkward.

better would be to record historical events using a time system without leap seconds, for example TAI or Terrestrial Time (TT).  even better would be a time system that counts up simply, rather than doing minutes, hours, days, leap days, months, etc.  then, simple subtraction yields the time elapsed between two dates.

to that end, we propose JD(TT), the Julian Date using the Terrestrial Time system, as a way to record and express precise historical dates and times.

previously, how to convert between local time and JD(TT).  unfortunately, the easiest way to get TT is to start with the widely disseminated UTC and adjust for leap seconds, so you still need an accurate record of leap seconds.

for example, on JD(TT) 2458737.710222037037 , rms sent to csail-related the email (about Marvin Minsky and Jeffrey Epstein) that ended his career (possibly).  perhaps it will end the Free Software Foundation; perhaps it will end the free software movement (hopefully not).  the acrimonious thread that his email was part of also caused all alumni to get kicked off of csail-related.

$ echo -n 'JD(TT) = '; echo 'scale=12;('$(date --date='TZ="right/America/New_York" 2019-09-11T01:01:34-04:00' +%s.%N)'-(946728000-10-32.184))/60/60/24+2451545' | bc
JD(TT) = 2458737.710222037037

even though our input precision was only 1 second (about 1e-5 day), we compute to 12 digits past the decimal point so that if one forgets the 32.184 second offset when converting from TT to TAI or UTC, one will get a time whose seconds decimal digits starts curiously .1840000 or .1839999 .  computing to 12 decimal digits (19 significant digits total) exceeds double precision, so we use the bc arbitrary precision calculator above.  128-bit long double in C (internally only 80 bits on x86) also works.  (printf requires the "%Lf" formatting string.  C++ cout requires <iomanip> and setprecision(19).)

aircraft crashes of September 11, according to Wikipedia:
JD(TT) 2452164.033150277777 : WTC north tower, American Airlines flight 11.
JD(TT) 2452164.044516018518 : WTC south tower, United Airlines flight 175.
JD(TT) 2452164.068636388888 : Pentagon, American Airlines flight 77.
JD(TT) 2452164.086286851851 : Pennsylvania, United Airlines flight 93.

is it only under special circumstances that the public can learn the precise times of aircraft incidents?

it probably takes considerable effort to determine precisely what offset (if any) a timekeeping system recording an event had from a time standard.  there has to be incentive either for the timekeeping system to be kept constantly in sync, or for later investigators to determine how off its clock was.

JD(TT) 2446459.193694375000 : Space Shuttle Challenger Solid Rocket Booster ignition command, T-0.000, "liftoff", (IMHO, the point of no return).  note that the UTC time is 0.01 seconds past an integer second.  the subsequent destruction consisted of many events over the next 74 seconds or so.  although spacecraft operations are typically recorded to high precision, it's generally hard to pick which moment was the historic moment.

JD(TT) 2453365.541634074074 : 2004 Indian Ocean earthquake.  the long fault ruptured over the course of many minutes, so I don't know what the time given on Wikipedia, precise to 1 second, represents.  both the shaking and destructive tsunami reached places around Indian Ocean seconds, minutes, and hours later, so it's hard to define a precise time the event impacted humans historically.

JD(TT) 2455631.741321574074 : 2011 Tohoku earthquake (Japan).  same caveats as above regarding the precise time according to Wikipedia.  the subsequent events at the Fukushima nuclear power plant were also likely recorded at high precision (though what records are public?), but it's also likely hard to pick precise historical moments.

JD(TT) 2457279.911032222222 : first direct observation of gravitational waves (GW150904).  the chirp lasted 0.2 seconds, followed by a ringdown.  (I could not find how long the ringdown was observed).  again, I don't know what the time given on Wikipedia, precise to 1 second, represents.  start of the chirp?  peak of the chirp?  perhaps the historic event is the moment the event horizons touched, which is probably immediately after the chirp.

there was a 7 ms delay between the two LIGO observatories, the time it took for the gravitational wave to travel between them.  simultaneity is difficult with relativity.  (does anybody really know what time it is?)  earthradius/c is 0.021 s, so perhaps it doesn't generally make sense to define the time of a historical event (on earth) to precision better than that.  or maybe better precision is OK if you are willing to also travel to the location of the event.  astronomers like to use one of several barycentric time systems, but those mark time at locations far from any human (center of the earth or solar system), so that time will be "off" according to the speed of light.

other historic astronomical events: neutrinos from SN 1987a (observed over an interval of about 15 seconds, future post phthecix), solar flares.

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