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CaptainToonces
2011-Jan-18, 07:15 AM
Do people living at the North Pole live shorter lives than those living at the equator due to time dilation effects?

Jens
2011-Jan-18, 07:29 AM
Do people living at the North Pole live shorter lives than those living at the equator due to time dilation effects?

Yes, I'm sure they do. Here's (http://www.craigmayhew.com/blog/tag/time-dilation/) a calculation.

CaptainToonces
2011-Jan-18, 10:27 AM
Yes but what is your calculation of the effect of gravitational time dilation? On the north pole the Earth's gravity field is stronger because the surface at the pole is .1% closer than the surface at the equator, maybe more.

Stronger gravity causes time to go slower there, so it would work in the opposite way from the increased speed of those living at the equator.

caveman1917
2011-Jan-18, 12:12 PM
Though in all this it is important to realize that proper time doesn't change. Someone at the pole will see someone at the equator die sooner than himself, but both have lived equally long lives by their own reckoning, it's not like one of them will have 'missed out' on things.

Jens
2011-Jan-18, 12:55 PM
Yes but what is your calculation of the effect of gravitational time dilation? On the north pole the Earth's gravity field is stronger because the surface at the pole is .1% closer than the surface at the equator, maybe more.

Sorry, I'm not qualified to make the calculations. You'll need somebody who can do the dilation math.

Hornblower
2011-Jan-18, 05:55 PM
I find differences in elapsed clock time at the two locations of a millisecond or so over a typical human life span of some 2 billion seconds. Hardly worth the trouble of calculating it when compared to the real world variations in longevity.

I worked from equations found in Wiki articles about time dilation.

korjik
2011-Jan-18, 08:14 PM
I find differences in elapsed clock time at the two locations of a millisecond or so over a typical human life span of some 2 billion seconds. Hardly worth the trouble of calculating it when compared to the real world variations in longevity.

I worked from equations found in Wiki articles about time dilation.

SR or GR?

CaptainToonces
2011-Jan-19, 01:20 AM
I find differences in elapsed clock time at the two locations of a millisecond or so over a typical human life span of some 2 billion seconds. Hardly worth the trouble of calculating it when compared to the real world variations in longevity.
This question is not about "how small" a factor it is, the question is firstly to help understand that there is an effect at all, which is interesting, and secondarily the question is which causes more time dilation-- the stronger gravity at the pole, or the increased velocity at the equator?

Hornblower
2011-Jan-19, 12:52 PM
This question is not about "how small" a factor it is, the question is firstly to help understand that there is an effect at all, which is interesting, and secondarily the question is which causes more time dilation-- the stronger gravity at the pole, or the increased velocity at the equator?

In the case of the motion-related component, I do not think there is a simple absolute answer. Anytime there is relative motion between two people, each person would see the other person's clock running slower. A third party could see differences between the rates of the polar and equatorial clocks that would depend on the relative motions of all three.

CaptainToonces
2011-Jan-20, 07:40 AM
Still don't feel i have received an answer here. If my twin and i are born on the North Pole and my twin walks down to the equator in early childhood and lives out his entire life there, then returns at age 100, while I remained at the North Pole for those 100 years, and we then compare clocks, what do our clocks say, has he aged more than me, and how much of the difference is caused by gravitational time dilation compared to how much of any difference is caused by relative velocity time dilation?

Hornblower
2011-Jan-20, 01:25 PM
Still don't feel i have received an answer here. If my twin and i are born on the North Pole and my twin walks down to the equator in early childhood and lives out his entire life there, then returns at age 100, while I remained at the North Pole for those 100 years, and we then compare clocks, what do our clocks say, has he aged more than me, and how much of the difference is caused by gravitational time dilation compared to how much of any difference is caused by relative velocity time dilation?

Perhaps I prematurely gave up on a simple answer last time. See this article:

http://en.wikipedia.org/wiki/Time_dilation

Scroll down to Velocity and gravitational time dilation combined-effect tests.

I think your scenario would be similar to what Hafele and Keating found with commercial airliners. The gravitational effect of climbing just a few miles overwhelmed the velocity effect, with the net result that the flying clock ran slightly faster.