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While answering the question http://physics.stackexchange.com/questions/126867/gps-satellite-special-relativityGPS Satellite - Special Relativity it occurred to me that time would run more slowly at the equator than at the North Pole, because the surface of the Earth is moving at about 464m/s compared to the North Pole. The difference should be given by:

$$\frac{1}{\gamma} \approx 1 - \frac{1}{2}\frac{v^2}{c^2}$$

and at $$v$$ = 464m/s we get:

$$\frac{1}{\gamma} \approx 1 - 1.2 \times 10^{-12}$$

This is a tiny difference - about 4 days over the 13.7 billion year lifetime of the universe - but according to Wikipedia the accuracy of current atomic clocks is about 1 part in 10$$^{14}$$, so the difference should be measurable. However I have never heard of any measurements of the difference. Is there a flaw in my reasoning or have I simply not been reading the right journals?

While answering the question http://physics.stackexchange.com/questions/126867/gps-satellite-special-relativity it occurred to me that time would run more slowly at the equator than at the North Pole, because the surface of the Earth is moving at about 464m/s compared to the North Pole. The difference should be given by:

$$\frac{1}{\gamma} \approx 1 - \frac{1}{2}\frac{v^2}{c^2}$$

and at $$v$$ = 464m/s we get:

$$\frac{1}{\gamma} \approx 1 - 1.2 \times 10^{-12}$$

This is a tiny difference - about 4 days over the 13.7 billion year lifetime of the universe - but according to Wikipedia the accuracy of current atomic clocks is about 1 part in 10$$^{14}$$, so the difference should be measurable. However I have never heard of any measurements of the difference. Is there a flaw in my reasoning or have I simply not been reading the right journals?

While answering the question GPS Satellite - Special Relativity it occurred to me that time would run more slowly at the equator than at the North Pole, because the surface of the Earth is moving at about 464m/s compared to the North Pole. The difference should be given by:

$$\frac{1}{\gamma} \approx 1 - \frac{1}{2}\frac{v^2}{c^2}$$

and at $$v$$ = 464m/s we get:

$$\frac{1}{\gamma} \approx 1 - 1.2 \times 10^{-12}$$

This is a tiny difference - about 4 days over the 13.7 billion year lifetime of the universe - but according to Wikipedia the accuracy of current atomic clocks is about 1 part in 10$$^{14}$$, so the difference should be measurable. However I have never heard of any measurements of the difference. Is there a flaw in my reasoning or have I simply not been reading the right journals?

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Does time move slower at the equator?

While answering the question http://physics.stackexchange.com/questions/126867/gps-satellite-special-relativity it occurred to me that time would run more slowly at the equator than at the North Pole, because the surface of the Earth is moving at about 464m/s compared to the North Pole. The difference should be given by:

$$\frac{1}{\gamma} \approx 1 - \frac{1}{2}\frac{v^2}{c^2}$$

and at $$v$$ = 464m/s we get:

$$\frac{1}{\gamma} \approx 1 - 1.2 \times 10^{-12}$$

This is a tiny difference - about 4 days over the 13.7 billion year lifetime of the universe - but according to Wikipedia the accuracy of current atomic clocks is about 1 part in 10$$^{14}$$, so the difference should be measurable. However I have never heard of any measurements of the difference. Is there a flaw in my reasoning or have I simply not been reading the right journals?