Hafele (seated) and Richard E. Keating aboard one of
||One of the
atomic clocks used in the experiments.
Four cesium beam clocks flown around the world on commercial jet flights during October 1971, once eastward and once westward, recorded directionally dependent time differences which are in good agreement with predictions of conventional relativity theory. 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 nanoseconds 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.
Their conclusion is described at the end of their "Observed" paper:
One of the most enduring scientific debates of this century is the relativistic clock "paradox" (1) or problem (2), which stemmed originally from an alleged logical inconsistency in predicted time differences between traveling and reference clocks after a round trip. This seemingly endless theoretical debate, which has flared up recently with renewed vigor (2, 3), begs for a convincing empirical resolution with macroscopic clocks. A simple and direct experimental test of the clock problem with portable atomic clocks is now possible because of the unprecedented ability achieved with these clocks (4).
Another key paper written by Hafele only: http://www.dtic.mil/dtic/tr/fulltext/u2/a489971.pdf
In conclusion, we have shown that the effects of travel on the time recording behavior of macroscopic clocks are in reasonable accord with predictions of the conventional theory of relativity, and that they can be observed in a straightforward and unambiguous manner with relatively inexpensive commercial jet flights and commercially available cesium beam clocks. In fact, the experiments were so successful that it is not unrealistic to consider improved versions designed to investigate aspects of the theory that were ignored in the predicted relativistic time differences (1). In any event, there seems to be little basis for further arguments about whether clocks will indicate the same time after a round trip, for we find that they do not.
In 1905 Einstein laid a radical new basis for the concepts of space and time. Though Newton's absolute time had proved adequate for most practical purposes, Einstein produced convincing arguments against it. Absolute time contains an element of mystery which is incompatible with precisely defined scientific quantities. Consequently, Einstein defined a new empirical basis for time by accepting a definition which states, in effect, that "time is that which is indicated by a clock," and then proceeded to develop his relativity theories on that basis. Einstein's relativity has proved to be completely compatible with all relevant observations; in fact, no definitive test ever performed has disproved it. The results of our flying clock experiments, at least at the present state of analysis, offer no exceptions.
Another consequence of Einstein’s theory is that clocks run more slowly near massive objects. In the range of speeds and length scales encountered in our daily life, relativistic effects are extremely small. For example, if two identical clocks are separated vertically by 1 km near the surface of Earth, the higher clock emits about three more second-ticks than the lower one in a million years.
Scientists have known for decades that time passes faster at higher elevations—a curious aspect of Einstein's theories of relativity that previously has been measured by comparing clocks on the Earth's surface and a high-flying rocket.
Now, physicists at the National Institute of Standards and Technology (NIST) have measured this effect at a more down-to-earth scale of 33 centimeters, or about 1 foot, demonstrating, for instance, that you age faster when you stand a couple of steps higher on a staircase.
Newsweek article: Portable Atomic Clocks can Measure the Height of a Mountain
Here, we report the first field measurement campaign with a transportable 87Sr optical lattice clock. We use it to determine the gravity potential difference between the middle of a mountain and a location 90 km away, exploiting both local and remote clock comparisons to eliminate potential clock errors.
The Washington Post: Scientists take an atomic clock on the road and use it to measure the height of a mountain
“Time passes with different speeds depending how far you are away from large masses,” Christian Lisdat, co-author of the study and physicist of Germany’s National Meteorology Institute, told Newsweek. That large mass is Earth.
“Time really changes,” he added, explaining that “if you go up, time passes more quickly.” The gravity further above sea level at the top of a mountain is weaker, so time literally moves slightly faster. The difference, however, is tiny.
Scientists have described a major step forward in using time to determine height above sea level. For the first time, they took an optical atomic clock out of the lab. Their liberated device was brought into the French Alps.
By comparing the tick rate of the portable atomic clock on a mountain with a similar clock in a lab in Torino, Italy, the researchers showed that the altitude difference between the two locations was about 1,000 meters, or 3,280 feet. Their work was published in Nature Physics.
According to Einstein's theory of relativity, time moves differently depending on where you are in a gravity field.
For example, a clock on top of a tall mountain — far from the center of the Earth — will move a tiny bit faster than a clock at the base of that mountain, where the gravity is stronger.
It's not a mechanical error. Time itself actually passes faster at the top of the mountain.
That means your friend who lives in the Rockies is aging just a tiny bit faster than your friend who lives on the beach in Malibu.
"Your body and your biological experience exist in the real time of whatever place you are in," said Christian Lisdat, a physicist at Germany's National Metrology Institute who worked on the study. "And that is no different than clocks."
Most clocks aren't accurate enough to register the difference in the speed of time at different altitudes. After all, in 10 years, two clocks that are 1,000 meters apart from each other in height will be off by just 31-millionths of a second, Agnew said.
Quote from page 703:
The concept of proper time in relativity is really central to the whole subject. The proper time is the ordinary time actually kept by a clock, its own time, or, in German, eigenzeit. The high stability that has been achieved by the time keeping community with modern atomic clocks allows the effects of motion and gravity to be actually measured, with results in agreement with Einstein's predictions. Einstein's ideas are no longer just a matter of great scientific interest, actually forming the basis of the view of the universe that we now have from modern astronomy, but also a matter of practical engineering concern,
A clock will run faster the higher it is, and it will run slower the faster it moves. The primary curvature for slow speeds and weak gravitational fields is the curvature of time, not the curvature of space, as you read in so many of the popular books.
According to the theory of general relativity, the gravitational red shift causes a clock placed at a lower altitude, where gravity is strong, to run more slowly than a clock placed at a higher altitude, where gravity is weaker.
It can be shown that as the gravitational potential decreases - that is, as its absolute value increases with respect to the infinitely remote zero potential point of gravity in Equation (11) - time passes more slowly. This phenomenon is known as the gravitational red shift.
Now we present the results of our measurements of the altitude effect carried out on the basis of the height difference between the CNR cosmic-ray laboratory at Plateau Rosa, 3500 m, and Turin, 250 m above s.l., for which the equivalence principle predicts the relative time variation -- AU/ez~ At]t = 3.54.10 -18, corresponding to the gain Attl = 30.6 ns/d of the clock at mountain altitudes.
On return to NPL the travelling clock was predicted to have gained 39.8 ns, including an additional geometric factor. This compared remarkably well with a measured gain of 39.0 ns. We estimated the uncertainty due to clock instabilities and noise to be around ±2 ns. This short flying clock experiment therefore provided a clear demonstration of relativistic effects.
The combined flight times of 14 hours and mean height in excess of 10 km resulted in a predicted clock gain of 53 ns. This followed the principle that a clock in a weaker gravitational field (higher altitude) will run faster.
The effect of the aircraft’s speed relative to the Earth’s surface resulted in a predicted clock loss of 16.1 ns. This followed the principle that a moving clock runs slow.
According to Einstein, fast-moving clocks run slow (special relativity), and high-elevation clocks run fast (general relativity). Clocks that run fast gain time, so given our high elevation and how long we stayed, the prediction was that these clocks would gain about 22 nanoseconds. This, not because the clocks were moving (they were in a parked minivan), but simply because the clocks experienced a lower gravitational field by being 5400 feet above sea level for two days.
Of course, the predicted effect is incredibly small, but with clocks accurate enough, elevations high enough, the stay long enough, and time interval counters precise enough, the effect becomes measurable. The goal of this fun experiment was to measure, or at least to demonstrate, relativistic time dilation using equipment I had at home.
In June 2010 one of NPL's atomic clocks was flown [westward] around the world as part of a rare experiment to test Einstein's theories of Relativity. The results demonstrate that Einstein's theories are correct, as NPL was able to measure a clear time-shift of 230 ± 20 nanoseconds between the two clocks involved in the experiment. This agrees with the time-shift predicted by Einstein.
General Relativity effects are caused by the altitude of the flying clock - space time near the surface of the Earth is more steeply curved than at the height of the aircraft, so the airborne clock (and everything else on the aircraft) is travelling through space-time that is slightly less 'stretched' than it is at the Earth's surface. This stretching of space-time is what makes time run slower on the ground relative to on the aircraft.
Conceptually, the experiment is very simple. We take one accurate clock the top of the mountain and we take another accurate clock to a hotel at the base of the mountain and let them sit there for a day. Then we bring the clocks together again and compare. If time dilation is false then the clocks should still agree. If time dilation is real then we would expect the clock that was at the hotel to be a little behind the clock that was at the summit.