# Experimental sticky (Hafele-Keating experiment)

• edpell
In summary, the experimenters flew atomic clocks on commercial airliners around the world in both directions and compared the time elapsed on the airborne clocks with the time elapsed on an earthbound clock. Their results were in agreement with general relativity's predictions, showing that the eastbound clock lost time and the westbound clock gained time due to their different speeds relative to the Earth's rotation. The Earth's rotation causes a non-inertial frame of reference, and the use of four atomic clocks reduced systematic errors due to clock drift. This experiment highlights the difference between the predictions of general relativity and special relativity, as the latter does not account for the effects of non-inertial frames.
edpell
In the experimental sticky it says

"They flew atomic clocks on commercial airliners around the world in both directions, and compared the time elapsed on the airborne clocks with the time elapsed on an earthbound clock (USNO). Their eastbound clock lost 59 ns on the USNO clock; their westbound clock gained 273 ns; these agree with GR predictions to well within their experimental resolution and uncertainties (which total about 25 ns). By using four cesium-beam atomic clocks they greatly reduced their systematic errors due to clock drift."

But it seems this does not match SR. Two planes take off from say New York City. One flies at a speed of a commercial airliner on some path, the other flies at the same speed on a different path. They both return to the starting point each having traveled the same distance at the same speed as seen by the observer that stayed on the ground in New York. But the two clock do not show the same time dilation! What does this mean?

They are moving at different speeds wrt to the Earth clock because of the Earth's rotation.

Edit: I didn't get that quite right. I think the Earth clock is not inertial due to the Earth's rotation, so what one should do is set up a global inertial frame, in which all three clocks should be moving with different velocities (or something like that, am not getting this straight off the top of mu head, but the Earth's rotation is important).

The speed of the two planes is it measured with respect to the ground? If so, they travel at the same speed with respect to the stay behind clock. If not, how is the velocity of the planes measured?

The sun rises in the east, so the Earth spins eastward relative to a particular inertial frame.

To fly eastward, one must fly even faster relative to the inertial frame.
So the eastward clock will run slow.

To fly westward, one must fly slower relative to the inertial frame.
So the westward clock will run fast.

Did I get that right?

Dave, that measures only the GR effect, not the SR effect.

atyy said:
The sun rises in the east, so the Earth spins eastward relative to a particular inertial frame.

...which is often called the Earth Centered Inertial (ECI) frame.

So if we had a flat Earth (say a box full of air 48 thousand miles long) and the box is moving at the velocity 1000 miles per hour (about the Earth rotational speed) call it frame X. We start at the middle with two planes one flies "East" in the direction of the boxes velocity and one flies "west" opposite the boxes motion. After 24,000 miles of flight they stop and look at their clocks what do they see? If the box is an inertial frame then both planes traveled at the same velocity (opposite directions but same speed) in that frame and both should experience the same time dilation. If one the other hand we consider a frame in which the box is moving (frame Y) then one plane flies faster and one flies slower in that frame. So in frame Y one plane flies faster (more time dilation) but flies a longer distance and the other flies slower (less time dilation) and a shorter distance. So they both arrive at the same time in frame Y and in Frame X and both pilots have aged the same amount. No twin paradox. So how come the clocks in the experiment differ? How does going from a "flat Earth" to a round Earth change the physical measurement?

Last edited:
Thread title edited to make it more specific.

Hello jtbell in the ECI the west going plane has a lower speed on the night side of the planet and a faster speed on the day side of the planet. Likewise but opposite the east going plane has a high speed on the day side and a lower speed on the night side. So it seems in the ECI both have the same average speed. So why is there a difference in the two clocks?

edpell said:
So if we had a flat Earth (say a box full of air 48 thousand miles long) and the box is moving at the velocity 1000 miles per hour (about the Earth rotational speed) call it frame X. We start at the middle with two planes one flies "East" in the direction of the boxes velocity and one flies "west" opposite the boxes motion. After 24,000 miles of flight they stop and look at their clocks what do they see? If the box is an inertial frame then both planes traveled at the same velocity (opposite directions but same speed) in that frame and both should experience the same time dilation. If one the other hand we consider a frame in which the box is moving (frame Y) then one plane flies faster and one flies slower in that frame. So in frame Y one plane flies faster (more time dilation) but flies a longer distance and the other flies slower (less time dilation) and a shorter distance. So they both arrive at the same time in frame Y and in Frame X and both pilots have aged the same amount. No twin paradox. So how come the clocks in the experiment differ? How does going from a "flat Earth" to a round Earth change the physical measurement?

In X, the planes fly in opposite directions with the same speed, so they will land at the same time. Frame Y is moving relative to X, so the planes will not land at the same time.

A concrete way to get at this is that the three clocks have different accelerations. If the west-going clock could fly fast enough to cancel out the Earth's rotation, it would have zero acceleration. In reality it doesn't quite fly that fast, but it does have the smallest acceleration of the three. By the equivalence principle, these accelerations are equivalent to gravitational fields, which cause time dilation.

There is also an effect from real gravitational time dilation, because the planes are flying at a certain altitude. This is the reason for the asymmetry between the results of the east-going and west-going planes, relative to the one back in Washington.

In the case of a GPS satellite, the gravitational effect is actually bigger than the SR effect.

Would it be correct to say this is a general relativity effect (accelerations) as opposed to a special relativity effect (velocities)?

bcrowell said:
A concrete way to get at this is that the three clocks have different accelerations. If the west-going clock could fly fast enough to cancel out the Earth's rotation, it would have zero acceleration. In reality it doesn't quite fly that fast, but it does have the smallest acceleration of the three. By the equivalence principle, these accelerations are equivalent to gravitational fields, which cause time dilation.

There is also an effect from real gravitational time dilation, because the planes are flying at a certain altitude. This is the reason for the asymmetry between the results of the east-going and west-going planes, relative to the one back in Washington.

In the case of a GPS satellite, the gravitational effect is actually bigger than the SR effect.
This depends on the orbit.

edpell said:

Would it be correct to say this is a general relativity effect (accelerations) as opposed to a special relativity effect (velocities)?

Just because you have an acceleration, that doesn't mean you need GR. You only need GR if there are gravitational fields. It's just useful to think about the accelerations because it shows that you don't have three different inertial frames; someone in one of the frames can tell which one he's in from local measurements.

This experiment has two effects, one of which can be understood purely using SR, the other requiring GR.

## 1. What is the Hafele-Keating experiment?

The Hafele-Keating experiment was a landmark experiment conducted in 1971 that tested the theory of relativity proposed by Albert Einstein.

## 2. How was the Hafele-Keating experiment conducted?

The experiment involved flying atomic clocks on commercial airplanes in opposite directions around the world. The clocks were synchronized on the ground and then compared to determine if time dilation occurred as predicted by Einstein's theory.

## 3. What were the results of the Hafele-Keating experiment?

The results of the experiment showed that the clocks did experience a difference in time, with the clock that traveled eastward gaining time and the clock that traveled westward losing time. This supported the theory of relativity and showed that time is relative to the observer's frame of reference.

## 4. What is the significance of the Hafele-Keating experiment?

The Hafele-Keating experiment provided direct evidence for the theory of relativity and helped to further solidify it as a fundamental theory in physics. It also demonstrated the concept of time dilation, which has since been confirmed by numerous experiments and is a crucial aspect of many modern technologies, such as GPS systems.

## 5. Are there any criticisms of the Hafele-Keating experiment?

Some critics have pointed out that the experiment was not precise enough to fully support the theory of relativity, as there were potential sources of error that could have affected the results. However, subsequent experiments have further validated the findings of the Hafele-Keating experiment, making it a significant contribution to our understanding of the universe.

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