Astronomy & Celestial Mechanics
the sky, computed
Concept

Time dilation — where it appears

The slowing of a clock as seen by an observer from whom it is moving, or across an expanding universe. A process at redshift z is seen to take 1 + z times as long, so supernova light curves and quasar flicker both stretch with distance.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

TCB has gained 23.5 seconds on TT since 1977. How far four of the solar system's time scales have drifted apart, against years since they were set equal. TT is the time a clock on the Earth's geoid keeps, and it is flat here by definition. TCG is the time a clock at rest just outside the Earth's gravitational well would keep, and it runs faster by seven parts in ten thousand million — 0.0220 seconds a year. TCB is the time a clock at rest outside the Sun's well would keep, and it runs faster by fifteen parts in a thousand million, or 0.4893 seconds a year. TDB is TCB with that rate divided out so that it stays within milliseconds of TT, which is what makes it usable as an ephemeris argument and what makes it a coordinate rather than a proper time. The differences are constants and they are not corrections: an ephemeris tabulated against one of these and evaluated against another is wrong by the whole of this plot.

A second that depends on where the clock is

A clock in orbit runs fast, a clock at the bottom of a gravity well runs slow, and a clock at rest far from the Sun runs faster than anything on Earth by fifteen parts in a thousand million. Astronomy therefore has four different seconds, two of them longer than the others, and an ephemeris has to declare which one it is tabulated against.

sky · Timescales Three reasons the flicker slows with redshift, only one of them cosmology. The observed flicker timescale of the faintest quasars a flux-limited survey can see, relative to its value at redshift 0.2, logarithmic, separated into its causes: time dilation alone (a factor 5.0 by redshift 4); the bluer rest-frame wavelength a fixed band samples at higher redshift, which shortens the timescale (×0.78); and the heavier black holes the flux limit selects (×15.3). Together, ×49.9. Read as a power of (1+z) the total has exponent 2.74 where dilation alone has 1.00: a test that does not hold mass and wavelength fixed measures the selection, not the expansion.

A clock that flickers without a tick

If the universe expands, every process seen at redshift z runs (1+z) times slow. A supernova carries a calibrated clock and shows it. A quasar's light wanders with no period at all, and its characteristic timescale grows with the mass of its black hole and shrinks with the colour it is seen in, both of which change with redshift in any real survey. Reading the dilation from quasars means holding those fixed first, and on a short enough baseline the measurement hides the effect it is looking for.

cosmology · Expansion

Named alongside it

The objects these essays reach for when they reach for this one.

Barycentric coordinate timeClock rateCoordinate timeDamped random walkEphemeris timeGeoidGravitational redshiftLuminosity distanceMalmquist biasProper timeQuasarQuasars

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