Monday, October 24, 2011

The Ussher Effect

Yesterday I noted:

"The exact calendar date of the Big Bang is indefinite, due to the relativity of time-rates. Pick any day of the year, including leap-day, and the Big Bang occurred on that day in some reference frame. (Hour and minute are also adjustable.)"

To be specific:
The universe is about 13,700,000,000 years old; for two reference frames to differ on the exact value by one full year, they would have to have a relative time dilation factor of 1 + 1/13,700,000,000; so if v is their relative velocity, and c = lightspeed = 299,792,458 meters/second, then:

1 / sqrt( 1 - (v/c)^2 )   ~     1  +   7.3 * 10 ^ -11

sqrt( 1 - (v/c)^2 )       ~     1  -   7.3 * 10 ^ -11

( 1 - (v/c)^2 )           ~     1  -   1.46 * 10 ^ -10

(v/c)^2                   ~     1.46 * 10 ^ -10

(v/c)                     ~     1.208 * 10 ^ -5

v                         ~     3622 meters/second   ~   13039 kph

Thirteen thousand and thirty-nine kilometers per hour?  Call it the Ussher speed; a velocity uncertainty sufficient to make the birthday of the universe spread out over the entire calendar year.

The Ussher speed is slow, in cosmic terms. The spin speed of the Earth's equator is about 1670 kph; Earth's orbital speed is about 107,000 kph; respectively about one-eighth and eight times the Ussher speed. I calculate that at the Earth's equator, the cosmic birthday shifts two and a half months each day; and for the entire Earth the cosmic birthday shifts 875 years each year; which is about a year for every ten hours.

This does not include the solar system's orbit of the Galaxy, and the galaxy's motion relative to the microwave background.

Therefore the birthday of the universe is spread out over the entire calendar year; so you can take it as any day whatsoever. Call this the Ussher Effect.

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