Thursday, October 27, 2011

Ussher Effect, addendum

Two posts ago I asked; on what day of the year did the Big Bang happen? This proved to be relative to the observer’s state of motion; an uncertainty of 13,039 kph will make the universe’s birthday spread out over the entire year.
Now I ask; what day of the week? What hour of the day? What minute of the hour? And what second of the minute?

Let R = the relative difference of time rates between two frames, v = their relative velocity, and c = lightspeed = 299,792,458 meters/second. Then:

1 / sqrt(1–(v/c)^2)     =    1 + R
sqrt(1–(v/c)^2)          ~    1 - R
(1–(v/c)^2)               ~    1 - 2R
(v/c)^2                     ~    2R
(v/c)                        ~    sqrt(2R)
v                             ~    299,792,458 m/s * sqrt(2R)
v                             ~    1,079,252,849 km/hr * sqrt(2R)

This, the Ussher velocity, is an uncertainty of velocity that yields an uncertainty in time rates of R.

For the “what day in the year” question, R = 1 year/(13.7*10^9 year); so v = 13,040 kph;
For “what day of the week”, R = 1 /(52*13.7*10^9); so v = 1,856 kph;
For “what hour of the day”, R = 1 /(365.25*13.7*10^9); so v = 700 kph;
For “what minute of the hour”, R = 1 /(24*365.25*13.7*10^9); so v = 139 kph;
For “what second of the minute”, R = 1 /(60*24*365.25*13.7*10^9); so v = 18 kph;

On the equator, the birth-week-day of the universe changes every day; in an airplane, the birth-hour of the universe changes as it lands; in a race car, the birth-minute of the universe changes as it gets up to speed; and the birth-second of the universe changes for a fast jogger.

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