Resolving the Clock Paradox: The Hafele and Keating Experiment

[tkm2002]

"During October, 1971, four cesium atomic beam clocks were flown on regularly scheduled commercial jet flights around the world twice, once eastward and once westward, to test Einstein's theory of relativity with macroscopic clocks. From the actual flight paths of each trip, the theory predicted that the flying clocks, compared with reference clocks at the U.S. Naval Observatory, should have lost 40+/-23 nanoseconds during the eastward trip and should have gained 275+/-21 nanoseconds during the westward trip ... Relative to the atomic time scale of the U.S. Naval Observatory, the flying clocks lost 59+/-10 nanoseconds during the eastward trip and gained 273+/-7 nanosecond during the westward trip, where the errors are the corresponding standard deviations. These results provide an unambiguous empirical resolution of the famous clock "paradox" with macroscopic clocks."

Eastward Journey Westward Journey
Predicted -40 +/- 23 ns + 275 +/- 21 ns
Measured -59 +/- 10 ns + 273 +/- 7 ns



I don't know why the time gained 273+/-7 nanosecond during the westward trip?

 

[CFDFEAGURU]

See Benjamin Crowell's book.

Here is a link to it.

http://www.lightandmatter.com/genrel/

Thanks
Matt

 

[atyy]

See Benjamin Crowell's book.

Here is a link to it.

http://www.lightandmatter.com/genrel/

Thanks
Matt

What's wrong with eating mashed potatoes?

 

[sylas]

Eastward Journey Westward Journey
Predicted -40 +/- 23 ns + 275 +/- 21 ns
Measured -59 +/- 10 ns + 273 +/- 7 ns



I don't know why the time gained 273+/-7 nanosecond during the westward trip?

Another very clear description is at hyperphysics. See Around-the-World Atomic Clocks.

Basically, the clocks are affected by gravitational dilation (higher up in Earth's gravitational field they run more slowly) and velocity dilation (due to their speed of movement around the Earth).

The clock that remains at the same place on Earth's surface is also moving with Earth's own rotation, and this needs to be considered.

Both clocks have similar gravitational dilation. The clock flying westward is flying towards the setting Sun, and so it is flying against Earth's rotation. It moves the most slowly with respect to the center of the Earth, and so has the least time dilation with respect to the center of the Earth. The clock at one place on the surface is moving faster wrt to the Earth's center, and hence it runs slow. The west flying clock should be expected to record more time when the clocks come to the same position again. The east flying clock is going faster that the "fixed" clock, and so it will lose time.

Both clocks gain time because of the gravitational effects, but the east flying clock loses more than it gains, and so runs slightly slow. The west flying clock gains both because it is slower than the fixed clock, and also higher.

All velocity calculations are done in the more or less inertial frame of Earth's center.

Cheers -- sylas

 

[vin300]

http://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment" also mentions sagnac effect, but how do you get the formula

 

[sylas]

http://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment" also mentions sagnac effect, but how do you get the formula

That wikipedia page looks dubious, and the discussion page indicates (as is often the case) a lot of cranks who think they understand relativity and don't. Handle with care.

I recommend the hyperphysics page that I cited previously. However, the link didn't work because of the way frames are handled. Here's a better link to the hyperphysics description.

Hafele and Keating Experiment at hyperphysics​

The Sagnac effect is simply an alternative way to handle the motion of the reference point fixed on the surface of the Earth. You don't need to use it if you calculate velocities with respect to the center of the Earth. The page above explains the formulae used, and they way they do it, using the center of the Earth as the reference point, means you don't have to use the Sagnac effect.

The wikipedia page is a bit confused on that, and some of the people discussing it in the wikipedia discussion are completely mistaken about it. It might be a good project for someone with an interest in wikipedia to try improving the article. Seriously. I edit wikipedia from time to time and its easy.

Cheers -- sylas

 

[yano108]

Sylas, is it my imagination, or does the hyperphysics page claim that the time measured w.r.t. the Earth's surface is greater than that measured w.r.t. the Earth's center? This goes against what I thought the case was, and what you appear to be saying. It has also been awhile, and I may be misreading.Thanks!