Thursday, March 04, 2010

[czdaoolt] Alternatives to the Clock of the Long Now

By synchronizing with local noon, the Clock of the Long Now attempts to be accurate to the day for at least 10000 years.  This is a worthy goal, especially because the length of the day is unpredictable and not constant (e.g., Chilean earthquake).

What other practically relevant questions of the passage of time can one ask, and how might we construct devices to answer them?  I can think of two.

The first is, how many years have passed?  Where a year is defined by the seasons.  Because of the chaoticity of the N-body problem, the length of the year is not constant. Losing track of what year it is leads to odd theories such as Fomenko's New Chronology.  We need a device that will count the warm-cold cycles of the seasons, or the long days-long nights cycles in the polar regions.  Interestingly, the reason we care about this question is because life on earth cares about seasons: if the climate should radically change (Earth becomes constant fire or constant ice or the axis tilt becomes zero) which breaks the clock, life on earth will no longer care.  Less extremely, if we suffer another Year Without A Summer, it's OK if the clock loses a year, from the point of view of life.  One way to implement this clock is a collection of designated trees around the world.  Cores are taken and rings counted at the start of the clock to determine their ages.  New trees replace old trees over the centuries, and we keep track of the offset age of each new tree.

Unlike human-made clocks, we can be confident that the "moving parts" of this clock (the trees) will remain functional for millions of years.  The hard part will be keeping records: which trees are the designated trees, and where are they?  What is the age offset of each tree from the start of the epoch? Attach durable markers to the trees.

The second question is, how much absolute time has passed?  Absolute time is measured in, say, metric seconds (though probably not to the accuracy of a second), and not time-varying quantities like solar days or seasonal years.

Here again we can rely on moving parts of highly reliable, natural design, rather than of human construction.

The first design is a modern implementation of a water clock:  A set of carefully prepared radioactive samples.  Their composition and radioactivity is measured at the clock start.  At any point in the future, someone can again measure a sample, and, knowing the half-life and records of when the clock was started, determine the absolute time that has passed.  This is simply radioisotope dating, e.g., carbon-13 dating, except with carefully prepared and recorded initial samples.  I don't know how precise this clock can be.

Humorously, we note that, because of the quantum nature of radioactivity, the clock will slow down whenever it is observed.

The second design is inspired by the orrery to be constructed over the Clock of the Long Now.  We reverse the design, making the actual solar system the clock, and calculating the date by measuring the location of the planets.  Although each planet has an orbital period of at most 165 years, the collection of the locations all planets probably defines a unique signature of a point in time over a very long period.  We benefit that no planet is in orbital resonance with another (Pluto is not a planet.).

Earlier we had said the N-body problem is not solveable, but contradictorily assuming it is, positions of the planets for dates in the future can be calculated.  Gravitational interactions like Uranus-Neptune (responsible for Neptune's discovery) and Jupiter-everything else must be incorporated, as must the perihelion precession of Mercury.

It's kind of a modern astrology: the question, what time is it, or what day is it, is answered by precisely specifying the locations of the planets in the sky.

For astronomical measurements, note that celestial coordinates right ascension and declination are not so great: the length of the day and the north pole changes.  A more apocalypse-resistant method would be to record positions relative to slow-moving (proper motion) distant stars or galaxies.

A third design uses another stellar system: a binary pulsar.  Two are known.  We measure and record absolute time by the orbital period decay due to gravitational radiation.  Neutron stars are extremely massive, nearly point objects, so the system is less likely to be significantly perturbed than our own solar system.  Or insidiously, a sci-fi adversary will have great difficulty destroying or altering this clock.

Finally, we can consider a human-made clock.  If we drop the requirement that the clock must be transparent and fixable, but require that the clock operate without any need for human maintenance, how long-lived a clock can we make?  I'm imagining a radioactive power source and quartz oscillator.  How good of a clock can we make cheaply enough to mass produce? The idea is to deploy a great many clocks (unlike the single-point-of-failure Long Now), hoping a few will survive the millennia.

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