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Time - How Accurate Are Our Sums - 06/03/2011

I've just been watching good old Brain Cox, the trendiest physicist on our telly at the moment, talking about time. We currently believe our universe is 13.5 billion years old, give or take a few.

It raised a question. How are we measuring those years? 1 year comprises of 365.25 days. One day comprises of 24 hours. That's fine, but we do seem pretty sure that back when life was forming a day consisted of about 6 of our current measurements of an hour. The rotation of the earth is slowing, very very gradually, due to the friction of the water in our seas and the air on the surface. As such there would have been 1461 sunrises and sunsets every year, every time our planet circles the sun. It would seem fair to suggest that in another few million years there may be only 340 sunrises and sunsets to every time we circle the sun.

The slowing of the earths rotation itself should not have any bearing on how long it takes for the earth to circle our sun once. As such when a dendochronologist is counting tree rings, each ring represents one trip around the sun and this should represent a consistent amount of time, no matter how long each day was then, now or in the future. That is of course if we are certain that our speed of rotation around the sun is indeed constant.

There's no friction in space to slow us down. Or is there? What of the solar winds? What of the relentless bombardment of meteorites? What of the gravitational effects of the moon versus the sun? What of the inertial effects of plate tectonics? All these seem immeasurable in our timeframe of our lifespan, so tiny, so miniscule to be irrelevant. Yet with the passage of 4 billion "years" since the formation of our planet these effect may be cumulative. What of the ever-decreasing mass of our sun affecting our orbital path? If our sun is getting lighter and lighter then its gravitational pull must be decreasing, which means for us to remain in a stable orbit that orbit must increase.

The point is, has anyone ever calculated this? Are all our calculations based on our existing state, orbit, mass and velocity and therefore are these calculations incorrect. Chaos theory show us clearly that one single error or difference in the starting values of an equation can alter the outcome, the final result, hugely.

Not long ago a second, the smallest measurement of time, was fixed. Not by the measurement of the passing of the skies, but against what we believe is a known universal constant. According to Wikipedia...

Since 1967, the second has been defined to be the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

So now we no longer calculate the passage of time by the rotation of the earth, the sun and the night skies, but by the radioactive properties of an atom. This means that if the earth is indeed 13.5 billion years old, I hope it was measure by cesium 133 atoms and not by rotations of the earth around the sun...

Just as a matter of interest...if the universe is 13.5 billion years old then...

13,500,000,000 years * 365.25 = 4930875000000 days

4930875000000 * 24 = 118341000000000 hours

118341000000000 * 60 = 7100460000000000 minutes

7100460000000000 * 60 = 426027600000000000 seconds

426027600000000000 * 9,192,631,770 = 3916314850656852000000000000 cesium 133 transistions....

3, 916, 314, 850, 656, 852, 000, 000, 000, 000 since the start of the universe...give a take a few. I cannot even begin to name that number...but if there was one atom of cesium 133 at the start of the universe, it sure has made a hell of a lot of transitions between hyperfine levels. I wonder if there are the same number of stars in the universe.

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