atomic clocks on airplanes experiment

The Hafele–Keating experiment was a test of the theory of relativity. In October of 1971, J. C. Hafele and Richard E. Keating took four cesium-beam atomic clocks aboard commercial airliners and flew twice around the world, first eastward, then westward, and compared the clocks against those of the United States Naval Observatory.

According to special relativity, the speed of a clock is greatest according to an observer who is not in motion with respect to the clock. In a frame of reference in which the clock is not at rest, the clock runs slower, and the effect is proportional to the square of the velocity. In a frame of reference at rest with respect to the center of the earth, the clock aboard the plane moving eastward, in the direction of the earth's rotation, is moving faster than a clock that remains on the ground, while the clock aboard the plane moving westward, against the earth's rotation, is moving slower.

According to general relativity, another effect comes into play: the slight increase in gravitational potential due to altitude that speeds the clocks back up. Since the aircraft are flying at roughly the same altitude in both directions, this effect is more "constant" between the two clocks, but nevertheless it causes a difference in comparison to the clock on the ground.

The results were published in Science in 1972:[1][2]

The published outcome of the experiment was consistent with special relativity, and the observed time gains and losses were reportedly different from zero to a high degree of confidence.

That result was contested by Dr. A. G. Kelly who examined the raw data: according to him, the final published outcome had to be averaged in a biased way in order to claim such a high precision.[3] Also, Louis Essen, the inventor of the atomic clock, published an article in which he discussed the (in his opinion) inadequate accuracy of the experiment.[4]; however, neither of these publications are in peer-reviewed sources.

One notable approximate repetition of the original experiment took place on the 25th anniversary of the original experiment, using more precise atomic clocks, and the results were verified to a higher degree of accuracy.[5]. Nowadays such relativistic effects have been incorporated into the calculations used for the GPS system[6].

The equations and effects involved in the experiment are:

Total time dilation

Τ = Δτ v + Δτ g + Δτ s

Gravitation

Sagnac effect

Where h = height, v = velocity, ω = Earth's rotation and τ represents the duration/distance of a section of the flight. The effects are summed over the entire flight, since the parameters will change with time.

* Twin paradox * Time dilation * GPS Time Dilation

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• 04 September 2024

‘Nuclear clock’ breakthrough paves the way for super-precise timekeeping

• Elizabeth Gibney

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Researchers probed nuclei of thorium-229 embedded in a crystal — the small white disc near the centre of this image — using a laser device called a frequency comb. Credit: Ye Labs, JILA, NIST and Univ. Colorado

Physicists have demonstrated all the ingredients of a nuclear clock — a device that keeps time by measuring tiny energy shifts inside an atomic nucleus . Such clocks could lead to vast improvements in precision measurements, as well as new insights into fundamental physics.

Researchers measured the frequency of light that causes nuclei of the rare isotope thorium-229 to shift to a higher energy state — the ‘tick’ of the nuclear clock — with an accuracy that is 100,000 times greater than the previous best effort. They did this by synchronising the energy transition with the tick of the world’s most accurate clock . The work was led by Jun Ye at JILA, a research institute in Boulder, Colorado, and published in Nature on 5 September 1 . “It’s really one of the most exciting papers in recent times,” says Marianna Safronova, an atomic physicist at the University of Delaware in Newark.

Atomic clock keeps ultra-precise time aboard a rocking naval ship

The breakthrough came from probing thorium-229 nuclei with a laser device called a frequency comb. The set-up isn’t technically a clock, because it hasn’t been used to measure time. But such impressive results make the development of a nuclear clock seem possible, says Safronova.

Measurements of the tick are already proving useful in particle physics, says Elina Fuchs, a theoretical physicist at Leibniz University Hanover, Germany. And because the clock’s frequency is set by the fundamental forces that hold together the nucleus, the prototype could spot whether a type of dark matter — an invisible substance that accounts for around 85% of material in the Universe — affects these forces on a minuscule scale. “This is a new, direct window onto the nuclear force,” says Fuchs.

Ultimate timekeepers

The world’s best clocks , called atomic clocks, keep time using lasers — the light’s frequency is honed precisely to match the energy it takes to move electrons between two energy levels inside an atom. The most accurate atomic clock gains or loses only one second every 40 billion years. A nuclear clock would work slightly differently: the tick would correspond to the energy transitions of protons and neutrons, rather than electrons, as they reshuffle into an excited state.

This energy shift requires a slightly higher, ultraviolet frequency, resulting in a faster tick rate that could match or surpass the accuracy of the atomic clock. But the nuclear clock’s biggest potential advantage is the combination of precision and stability. Particles in the nucleus are less sensitive than electrons to disturbances such as electromagnetic fields — meaning that a nuclear clock could be portable and robust. “It becomes insensitive in a way that is kind of unthinkable in terms of how our clocks work today,” says Anne Curtis, an experimental physicist at the National Physical Laboratory in Teddington, UK.

Chinese team syncs clocks over record distance using lasers

But finding the right kind of atomic nucleus to use, and determining the frequency needed to induce its shift to a different energy state, has been a 50-year slog for physicists. In the 1970s, indirect evidence suggested that thorium-229 had a bizarrely low-energy nuclear transition 2 — one that might eventually be triggered by tabletop lasers. But it wasn’t until last year that scientists discovered the required frequency 3 — and this year, they successfully initiated shift with a laser 4 .

The JILA team looked for the transition frequency in trillions of thorium-229 atoms embedded in a crystal using a system known as a frequency comb. The comb pumps out an array of laser frequency lines, with regular and even spacing. It allows researchers to illuminate the crystal with many precise frequencies at once to look for a match, rather than scanning laboriously through the range of possible options using a single-frequency laser.

The comb’s settings — including the width of the gaps between the lines, or ‘teeth’ — were calibrated using the atomic clock and could be tweaked. The team conducted several experimental runs, and when they observed the tell-tale glow produced when thorium-229 atoms decay from their excited state, they used the settings to calculate the frequency driving the signal.

Observing the transition for the first time “felt amazing”, says study co-author Chuankun Zhang, a physicist at JILA. “We spent the entire night doing all the tests to check if this is actually really the signal that we were looking for,” he says.

Fundamental forces

The magic of the frequency comb is that it enables physicists to measure the frequency tick of one clock — here of the thorium-229 nucleus — as a ratio of another known frequency, in this case of an atomic clock. This not only allowed the team to determine the absolute frequency value with high precision, but also opened up some cool possibilities in physics, says Zhang.

If the tick speed of one clock changes over time relative to the other, this could indicate that factors that determine the energy levels — such the strong nuclear or electromagnetic force — are drifting or wobbling, says Fuchs. Certain ‘light’ forms of dark matter, which have an extremely low mass, are predicted to have this effect, she says.

Best ever clocks: breakthrough paves way for ultra-precise ‘nuclear’ timekeepers

Any change in the forces would be amplified in the nuclear transition frequency, making nuclear clocks potentially about 100 million times more sensitive than atomic ones to the effects of this kind of dark matter. The latest result — which pinpoints the frequency with an accuracy of 13 decimal places — is already precise enough to narrow down the possible energy ranges in which light dark matter could exist, says Fuchs. Nuclear physics could also benefit from the more precise transition frequency, which could help scientists to distinguish between possible shapes of the throrium-229 nucleus, she adds.

But more work must be done before nuclear clocks can outperform atomic ones — which are currently accurate to 19 decimal places. Researchers will explore whether keeping thorium-229 embedded in a crystal — a solid state is handy for making a portable clock — will make for the most accurate timekeeper, or whether trapping individual atoms will yield better results.

The laser system also needs honing. “Fortunately, this amazing technique has high potential,” says Olga Kocharovskaya, a physicist at Texas A&M University in College Station. It’s a “prototype of the source to be used in the future clock”, she adds.

doi: https://doi.org/10.1038/d41586-024-02865-w

Read the related News & Views: ‘ Countdown to a nuclear clock ’.

Zhang, C. et al. Nature https://doi.org/10.1038/s41586-024-07839-6 (2024).

Article   Google Scholar  

Kroger, L. A. & Reich, C. W. Nucl. Phys. A 259 , 29–60 (1976).

Kraemer, S. et al. Nature 617 , 706–710 (2023).

Article   PubMed   Google Scholar  

Elwell, R. et al. Phys. Rev. Lett. 133 , 013201 (2024).

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Hafele-Keating Experiment Celebrating Its 50th Anniversary

This year marks the 50th anniversary of the Hafele-Keating experiment, a test of Einstein's theory of general relativity. Joseph Hafele, the physicist that worked on the experiment, is a former Laramie resident.

The Hafele-Keating experiment took four atomic clocks aboard commercial airliners. They flew twice around the world, first eastward, then westward, and compared the clocks against others that remained at the U.S. Naval Observatory.

Dr. Michael Pierce, an associate professor in the Department of Physics & Astronomy at the University of Wyoming, said "the effect that was predicted was, both clocks, regardless of what direction they moved, experienced the general relativistic effect of time moving faster, the further you get away from the earth's gravitational field."

This was viewed as a confirmation of Einstein's prediction. While you might wonder why this matters, Pierce said it's simple - if you have any sort of GPS system, you owe a debt of gratitude to Einstein's theory of relativity and to the Hafele-Keating experiment that made GPS possible.

"Because in order to determine our precise location on earth, what one does is compare signals that are generated by the GPS satellite system. So, all of those calculations by Einstein, go into calculating your position on the earth," Pierce explained.

So whenever you pull out your phone and read your current location, then you can appreciate these effects that were verified experimentally by Hafele-Keating 50 years ago.

Alan Moore, a retired professor in applied Statistics at UW, was Hafele's personal friend. He said that he had the privilege of hearing the stories of the experiment from Joe Hafele himself, some of which were amusing.

"Some of the stories were about having difficulties with customs, people not quite understanding what they were doing with these big machines in the seats of the airplanes, and how skeptical some people were. Just hearing the excitement he described what that was like was fun for me," Moore said.

Angie Varca, Hafele's third out of four daughters, said she was aware of what he did. But to her, he was just Dad.

"He was working really hard to try to support a family of six. He was busy, but a very good father. I would say, a loving and a strict father. He liked to share his ideas with us… talked about science with us at the dinner table," Varca said.

After losing his tenure at the University of Washington to another professor working on moon rocks, Hafele worked at Caterpillar, a machinery company, in the research department.

"For my father who felt like maybe it wasn't recognized in its time, I don't think he really kind of reached a place of peace and self-satisfaction, until he retired and moved to Laramie," Varca mentioned.

Varca said her Dad never left science, even in retirement.

Varca added, "even after he retired, he always did experiments, he was always running experiments, and continuing to write papers and he really had a very amazing mind. And sometimes I ask myself, how would he have dealt with what's going on right now. I think he would have seen it as a challenge in a problem."

She admitted that she is very proud of his accomplishments.

"If it were to come up in conversation, especially with anybody who is a physicist, or has studied physics, they may not know my father's name, but they know his experiment. They know about the experiment that flew atomic clocks around the world to delve into the idea of Einstein's general relativity. And it's kind of satisfying to be able to say 'that was my dad who did that,'" Varca said.

Experts say the Hafele-Keating experiment is a timeless finding, giving us ideas about time, and GPS location. It is one of the most important experiments in the 20th century.

The official 50th anniversary is in October.

This story is supported by a grant through Wyoming EPSCoR and the National Science Foundation .

Enjoying stories like this?

Donate to help keep public radio strong across Wyoming.

Hafele-Keating experiment

The hafele-keating experiment: a groundbreaking test of time dilation, a brief overview of time dilation, designing the hafele-keating experiment, results and implications, impact on modern physics, applications in technology, concluding thoughts.

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Einstein was right. Flying clocks around the world in opposite directions proved it.

• According to Einstein’s relativity, if you move relative to another observer and come back to their starting point, you’ll age less than whatever remains stationary.
• Einstein also tells us that the curvature of space itself, depending on the strength of gravitation at your location, also affects how fast or slow your clock runs.
• By flying planes both with and against Earth’s rotation, and returning them all to the same starting point, we tested Einstein as never before. Here’s what we learned.

In 1905, our conception of the Universe changed forever when Einstein put forth his special theory of relativity. Prior to Einstein, scientists were able to describe every “point” in the Universe with the use of just four coordinates: three spatial positions for each of the three dimensions, plus a time to indicate which moment any particular event occurred. All of this changed when Einstein had the fundamental realization that every single observer in the Universe, dependent on their motion and location, each had a unique perspective on where and when every event in the Universe would have occurred.

Whenever one observer moves through the Universe relative to another, the observer-in-motion will experience time dilation: where their clocks run slower relative to the observer-at-rest. Based on this, Einstein suggested that we could make use of two clocks to put this to the test: one at the equator, which speeds around the Earth at approximately 1670 km/hr (1038 mph), and one at the Earth’s poles, which is at rest as the Earth rotates about its axis.

In this regard, however, Einstein was wrong: both clocks run at exactly the same rate relative to one another. It wasn’t until 1971 that a proper test could be conducted, and it required a lot more than special relativity to make it so.

Back when Einstein first put forth his special theory of relativity, there was a missing element: it didn’t incorporate gravitation into the mix. He had no idea that proximity to a large gravitational mass could alter the passage of time as well. Owing to the planet’s rotation and the attractive gravitational force of every particle that makes up the Earth, our planet bulges at the equator and gets compressed at the poles. As a result, the Earth’s gravitational pull at the poles is slightly stronger — by about 0.4% — than it is at the equator.

As it turns out, the amount of time dilation due to a point on the equator zipping around the Earth is exactly cancelled by the additional amount of gravitational time dilation that results from the difference in gravity at the Earth’s poles versus the equator. Being deeper in a gravitational field, which the poles are, causes your clock to tick by more slowly, just as moving faster relative to a stationary observer does.

If you want to account for the rate at which the passage of time will appear to occur for each and every observer, both the relative motion effects of special relativity and also the relative effects of gravity — i.e., the relative curvature of spacetime between multiple observers — must be taken into account.

Time dilation was one of the few relativistic phenomena that was actually predicted even before Einstein put forth the ideas of special and general relativity, as the consequences of motion close to the speed of light for distances ( length contraction ) was worked out in the 19th century by George FitzGerald and Hendrik Lorentz. If distances changed, then in order to maintain the proper working of physics that we knew for electrons in atoms (as shown by Joseph Larmor in 1897 ) or for clocks in general (as shown by Emil Cohn in 1904 ), that the same factor — the Lorentz factor (γ) — must factor into time equations as well.

Although this was very difficult to measure initially, our growing understanding of the subatomic world soon made it possible. In the 1930s, the muon, a subatomic particle that’s the heavier, unstable cousin of the electron, was discovered. With a mean lifetime of just 2.2 microseconds, muons that are produced from cosmic ray collisions in Earth’s upper atmosphere should all decay within just hundreds of meters. And yet, if you hold out your hand, about one such muon passes through it with every second, indicating that they journeyed somewhere around 100 kilometers: a feat that’s physically impossible without time dilation. As soon as we developed the technology of cloud chambers, these muons could easily be seen even by the naked eye.

Other experiments further demonstrated that time dilation was a very real phenomenon for subatomic particles.

• The 1932 Kennedy-Thorndike experiment showed that both length contraction and time dilation are required to explain the motion of light through different directions in space; this represented an improvement over the earlier Michelson-Morley experiment , which required length contraction alone.
• The Ives-Stilwell experiment measured the Doppler shift of light and tested it against the predictions of special relativity; it was the first laboratory confirmation of time dilation, arising from positively charged hydrogen ions, and showed that the Lorentz factor was the correct factor for time dilation.
• And in 1940, the Rossi-Hall experiment experimentally measured the relativistic decay of muons in the atmosphere, quantitatively confirming special relativity’s predictions for time dilation.

But Einstein’s original goal of using run-of-the-mill clocks at or near the surface of Earth to test the validity of special relativity still remained unfulfilled. Two developments occurred in the 1950s, however, that finally brought the idea within the realm of testability.

The first development that would make such a test possible had long been in the works: the invention of the atomic clock . Previously, the most accurate timepieces involved either quartz clocks or mechanical clocks. However, as the temperature changed, they became less and less accurate, leading many to search for an alternative. Originally suggested by James Clerk Maxwell and later developed further by Lord Kelvin and then Isidor Rabi, the idea of using an atom’s vibrational frequency to keep time suddenly leapt into the realm of practicality.

Every atom has a series of energy levels that its electrons are allowed to occupy: those specific levels and no other. However, due to quantum mechanical effects — such as the quantum mechanical spins of the electrons and nuclei interacting with the electromagnetic fields generated by the electrons in motion — some of those energy levels split, creating fine-structure and hyperfine-structure with very small energy differences. When the electrons transition from a slightly higher energy level to a slightly lower one, it will emit a photon of a very specific frequency. By inverting the frequency, you can arrive at a value for time, and therefore, you can use properly prepared atoms to keep time. This is the idea and implementation of modern atomic clocks : currently the best device for timekeeping known to humanity.

However, if you wanted to travel at high speeds in a single direction and return to your starting point, meeting up with an observer who’s been stationary the entire time, there’s another confounding factor at play: the Earth’s uneven terrain. You’ll probably have to change elevation, and that’s true whether you drive or walk or sail or fly. The problem is this: when you change elevation, you’re now a different distance away from the center of the Earth, and that changes how severely the fabric of space is curved. As the curvature of space changes, so does the effect of gravitational time dilation: the component of time dilation that requires general relativity to account for it.

That’s why it’s so important that, in 1959, the Pound-Rebka experiment was performed. While the most stable isotope of iron is iron-56, with 26 protons and 30 neutrons, you can also make iron-57, with one additional neutron. Depending on whether it’s in an excited state or not, iron-57 can either emit or absorb gamma rays of a very specific energy: 14,400 electron-volts.

At the bottom of Harvard’s Jefferson laboratory, an emitting sample of iron-57 was placed, and at the top an absorbing sample of iron-57 was placed. As the emitted gamma-rays climbed up out of Earth’s gravitational field, they lost energy, and therefore none of them were absorbed at the top of the lab. However, when a speaker cone was added to the emitting sample at the bottom, the emitted photons were “kicked” with an additional amount of energy. When the energy matched the energy lost via gravitational redshift, the photons were indeed absorbed at the top of the tower, demonstrating that the frequency shift observed matched up precisely with that predicted by Einstein’s general relativity.

As is often the case, however, it took a few brilliant minds to piece together the idea for how such an experiment would work, even though the detection of such a small, precise effect was now theoretically possible. Physicist Joseph Hafele realized that if you took an atomic clock — one of the then-modern, precise, cesium-133 versions available at the time — and brought it aboard a commercial airliner that was capable of flying completely around the world in a single flight, you could tease out both the effects on time dilation of special and general relativity.

After giving a talk on the idea where astronomer Richard Keating was in the audience, Keating approached Hafele and told him about his work with atomic clocks at the United States Naval Observatory. A short while later, the funding arrived from the Office of Naval Research, as Hafele’s ideas would prove to be one of the most inexpensive tests of relativity ever to be conducted; 95% of the research funding was spent on round-the-world plane tickets: half for the scientists and half for the atomic clocks that would occupy the seats.

The brilliance of this idea is that it wasn’t just, “Hey, let’s fly this plane around the world and see if time dilates the way that special and general relativity predict that they ought to.” In and of itself, that would’ve been completely sufficient to test Einstein’s theories for time dilation directly.

But instead, Hafele and Keating both metaphorically and literally went the extra mile. First, one clock remained on the ground at the original location, ticking away and keeping time as accurately as possible: to within a few tens of nanoseconds over the timescale of weeks.

Second, two clocks were brought aboard a round-the-world flight, where they flew around the world in the eastward direction: the same direction as Earth’s rotation. Because the plane’s motion and Earth’s rotation were in the same direction, velocities added, and so its additional, more rapid motion through space should mean that less time passed, with time dilation predicting a loss of time.

And finally, those clocks were then brought aboard a round-the-world flight moving westward: against the Earth’s rotation. These planes flew slower than Earth’s rotation, so the clock on the ground actually moved faster than the westward-moving plane. The less-rapid motion through space should mean that more time passed for this clock, relative to the eastward-moving clock and also to the stationary one on the ground.

At the conclusion of the experiment, the results were revealed and compared with expectations. The clock that was on the ground the entire time would be treated as “at rest,” and everything else that occurred would be both predicted and measured relative to that standard of reference.

Although both clocks were meant to fly along similar courses at similar altitudes, such plans are rarely realistic. That’s why the flight crew helped take measurements of the plane’s location all throughout its dual journeys, allowing for both the predicted gravitational time dilation and the predicted due-to-motion time dilation to be quantified.

• For the eastward-moving plane, it was predicted that 144 nanoseconds would be gained by the clock due to gravitational time dilation, but that 184 nanoseconds would be lost owing to time dilation from its motion. All told, that’s a predicted loss of 40 nanoseconds, with an uncertainty of ± 23 nanoseconds.
• For the westward-moving plane, which flew at an overall higher altitude, a predicted 179 nanoseconds would be gained from gravitational time dilation. However, its lesser motion through space led to a prediction of a further gain of 96 nanoseconds, for a total predicted gain of 275 nanoseconds, with an uncertainty of ± 21 nanoseconds.
• And finally, the measurements, as first reported in Science in 1972 — a full 50 years ago — showed a net loss of 59 nanoseconds (with an experimental uncertainty of ± 10 nanoseconds) for the eastward-moving plane and a net gain of 273 nanoseconds (with an experimental uncertainty of ± 7 nanoseconds) for the westward-moving one.

Although this initial experiment only confirmed the predictions of special and general relativity to within about 10%, it was the first time that time dilation had been tested for large, macroscopic objects using something as precise as an atomic clock. It showed, convincingly, that Einstein’s predictions for both the motion component of relativity and also for the gravitational component of relativity were both necessary and both correct in their description for how time ought to pass. This, today, has applications ranging from GPS to radar tracking to measuring the lifetimes of subatomic particles and more.

Today, we can confirm the motion component of time dilations for speeds as low as that of a cyclist, and for elevation differences in the gravitational field at Earth’s surface that are as small as 0.33 meters (about 13 inches). Einstein’s conception of the Universe was so dramatically different from everything that came prior to it that there was an enormous amount of resistance to the ideas of special and general relativity, and criticisms were leveled at it for decades. But in the end, the results of experiments and observations, not our prejudices, reveal the ultimate truths of nature. The Universe truly is relativistic, and measuring the differences in atomic clocks as they flew around the world is how we truly confirmed it in our everyday lives.

Old News, Vintage Photos & Nostalgic Stories

Hafele–keating experiment – two atomic clocks flew twice around the world, eastward and westward. back at home, they each showed different times.

• Strangeness

The Hafele–Keating experiment was a test of the theory of relativity. In October 1971, Joseph C. Hafele, a physicist, and Richard E. Keating, an astronomer, took four cesium-beam atomic clocks aboard commercial airliners. They flew twice around the world, first eastward, then westward, and compared the clocks against others that remained at the United States Naval Observatory. When reunited, the three sets of clocks were found to disagree with one another, and their differences were consistent with the predictions of special and general relativity.

“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.”

In his original 1905 paper on special relativity, Einstein suggested a possible test of the theory: “Thence we conclude that a spring-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions.” Because he had not yet developed the general theory, he did not realize that the results of such a test would, in fact, be null, since the surface of the earth is a gravitational equipotential, and therefore the effects of kinematic and gravitational time dilation would precisely cancel.

Since the Hafele–Keating experiment has been reproduced by increasingly accurate methods, there has been a consensus among physicists since at least the 1970s that the relativistic predictions of gravitational and kinematic effects on time have been conclusively verified. Criticisms of the experiment did not address the subsequent verification of the result by more accurate methods and have been shown to be in error.

Time Dilation and Length Contraction

Hsc physics syllabus.

investigate the evidence, from Einstein’s thought experiments and subsequent experimental validation, for time dilation `t=t_o/sqrt((1-v^2/c^2))` and length contraction `l=l_osqrt((1-v^2/c^2))`, and analyse quantitatively situations in which these are observed, for example:

• observations of cosmic-origin muons at the Earth’s surface
• atomic clocks (Hafele–Keating experiment)
• evidence from particle accelerators
• evidence from cosmological studies

Special Relativity – Time Dilation & Length Contraction

Experimental evidence for time dilation & length contraction.

Time dilation and length contraction are not postulates but the implication of the constant nature of light's speed, as proposed by Einstein. 

Simultaneity

• The concept of simultaneity – occurrence of simultaneous events is not absolute. This means two simultaneous events may be so for one observer, they may not occur at the same time for another.
• A simple thought experiment can be used to clarify this understanding

Figure 1: Thought experiment demonstrating the effect of special relativity on simultaneity. Credit to Lumen Learning .

Observer A is sitting on a train carriage moving at a substantially fast velocity v . Two sources of light are located at the front and back end of the carriage respectively, equidistant from observer A. When they are turned on simultaneously, observer A receives both stimuli at the same time as the distance between the source and observer remains the same.

Observer B, however, does not observe the sources of light simultaneously. This is because during the time light travels from their sources to observer B, the carriage would have displaced by a certain distance (to the right). This displacement causes the distance between sources of light to observer B to become different. 

By Einstein’s second postulate of special relativity (speed of light is constant), the light emitted from the rear end of the carriage will take a shorter time to reach observer B. Light emitted from the front end of the carriage will take a longer time to reach observer B. 

What is Time Dilation?

• The non-absolute nature of simultaneity gives rise to time dilation (one of the three relativistic consequences of the constancy of light)
• The understanding of time dilation can be consolidated and quantitatively analysed using another thought experiment.

Figure 2: Thought experiment demonstrating the effect of special relativity on time. Time becomes dilated (longer) when an object is travelling at relativistic speeds as measured by a stationary observer. Credit to   Lumen Learning .

Suppose an astronaut wants to measure the time taken for a beam of light to travel back and forth the width ( D ) of the spaceship, by reflecting off a mirror. The time taken ( t 0 ) would be the total distance divided by the velocity of light:

`t_o=(2D)/c` 

However, to an observer outside the spacecraft, the distance travelled by light is longer. To calculate this distance, we need to use Pythagoras’ theorem to obtain:

`s=sqrt(D^2+((vt)/2)^2)` 

Since the distance travelled observed by the person outside the spacecraft is 2s , the time taken for light to travel to and from the mirror in the cabin is: 

By substituting  s  with the expression we derived previously:

Since the time ( t 0 ) taken by light observed by the astronaut inside the spacecraft is:

`t_0=(2D)/c`

Therefore by substituting:

`t^2=t_o^2+(v^2*t^2)/c^2`

`t^2-(v^2*t^2)/c^2=t_o^2`

`t^2(1-v^2/c^2)=t_o^2`

Make t 2 the subject of equation:

`t^2=t_o^2(1-v^2/c^2)`

Finally, square root both sides of equation:

`t=t_o/sqrt(1-v^2/c^2)` 

• where t is the time observed by an observer with relative motion to the event being observed. E.g. person outside the spacecraft.
• t 0 is the proper time observed by an observer at rest relative to the event being observed. E.g. astronaut moving at the same velocity as the spacecraft.

Length Contraction

Distance depends on the observer’s relative motion. Since distance is the product of time and speed, shorter time entails a shorter distance covered. 

The velocity of a particular object relative to an observer at rest is the proper length divided by the dilated time. Proper length l 0 is the distance between two points measured by an observer who is at rest relative to both of the points.

As such, for an observer who is at rest relative to the moving object (moving at the same speed), velocity is defined as:

`v=l/t_o`  

In this case, the relative velocity in both reference frames are equal: 

`l_o/t=l/t_o`

Make  l the subject of equation:

 `t_o/t=sqrt((1-v^2/c^2))`

By substitution:

`l=l_osqrt((1-v^2/c^2))`

• where l  is the length measured by an observer moving at the same speed as the object travelling the observed length/distance.
• l o is the length measured by an observed at rest relative to the start and end points of the observed length/distance

An object travelling a relativistic velocity experiences length contraction in the dimension of its movement. Its length does not contract in all dimensions.

Limitation of Special Relativity

Relativistic effects due to special relativity have two limitations:

• These effects are negligible when a frame of reference is not moving at a relativistic speed.
• Relativistic effects can occur in non-inertial frames of reference but in these scenarios, they are not only attributed to special relativity. Effects due to general relativity must be considered in non-inertial frames of reference. As a result, only relativistic effects in inertial frames of reference are entirely due to special relativity.

Evidence for Time Dilation & Length Contraction

Experiments involving muons.

Muons are cosmic ray particles formed in Earth’s atmosphere. When formed, they travel at velocities near the speed of light towards Earth's surface. However, due to their extremely short half life, majority of muons would decay before reaching the surface. 

In an experiment conducted at Mount Washington, quantities of muons were measured at the summit and bottom of the mountain. These numbers were then compared.

A greater proportion of muons was detected at sea level compared to what was originally predicted by considering the muons' average velocity and half-life at rest (1.5  µ s) 

Evidence for Time Dilation

This observation can be accounted for using time dilation. When muons are moving near the speed of light (0.98 c ), their half-life is increased when measured by a stationary observer on Earth. This dilated half-life as observed by an Earth-bound observer allows muons to reach the surface of Earth before decaying.

Evidence for Length Contraction

This observation can also be accounted for using length contraction. In the  muons' frame of reference, the distance between the top of Mount Washington and sea level becomes shorter due to length contraction.

Therefore, in the same amount of lifetime before decaying, more muons can reach Earth's surface.

Hafele-Keating Experiment

In 1971, Joseph Hafele and Richard Keating deonstrated time dilation using  caesium-beam atomic clocks.

Twelve clocks were used in total. Four clocks were flown on a plane in an eastward direction, four were flown in a westward direction, and the last four remained on Earth. After being flown twice around Earth, the times on the three groups of clocks were compared.

The atomic clocks, flown eastward, moved slower (as observed from an Earth-bound observer) and consequently 'lost time'. In other words, a shorter time elapsed on these clocks compared to those on Earth.

In contrast, the atomic clocks flown westward, moved faster and gained time. In other words, a longer time elapsed on these clocks compared to those on Earth.

This experiment is not the best to discuss as evidence for special relativity as the effects of general relativity also affects the experimental data. However, after the effect of general relativity are accounted for, the observed differences in time were consistent with predictions made using time dilation equations. 

Evidence of Special Relativity from Particle Accelerators  

In 2014, an experiment was conducted to demonstrate time dilation using lithium ions travelling at 0.338 c in a particle accelerator. 

The time interval between excitation of electrons in lithium ions and their return to ground state was measured when lithium ions are travelling at 0.338 c and at rest. 

Physicists found that the interval was longer for moving lithium ions compared to those at rest, as measured by a stationary observer in the laboratory. This difference in time was consistent with time dilation. 

Previous section:  Evidence for Einstein's Postulates

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Airborne Atomic Clocks to Test Einstein Time Theory

By Harold M. Schmeck Jr. Special to The New York Times

• Oct. 2, 1971

WASHINGTON, Oct. 1—Two scientists and four atomic clocks will fly around the world next week to test one of the crucial implications of Einstein's theory of relativity.

The purpose of the flight is to test the so‐called clock paradox, which holds that a clock moving at high velocity will lose time relative to a clock standing still. In effect the passage of time would be slowed.

Because of this effect, it has been argued that a space traveler covering immense distances at extreme speeds would return to the earth younger than his twin who stayed home.

At ordinary speeds the effect would be so small as to defy measurement. However, Dr. Joseph C. Hafele, an assistant professor of physics at Washington University in St. Louis, has made some calculations showing theta the test is feasible with commercial jet airliners and the United States Naval Observatory's highly sophisticated cesium clocks.

The time consequences of Einstein's theories have been tested indirectly in the past by astronomical observations and by studies of the behavior of subatomic particles moving at extremely high velocities. All these tests have confirmed the Einstein predictions.

First Direct Test

Dr. Hafele said there had not been a previous experiment, to his knowledge, that used a clock, and therefore this could be called a direct test of the prediction. He expects the time effects to be borne out, but the physicist said there were some scientists who argued that there would be no effect on the measurement of time.

Dr. Hafele's calculations have persuaded scientists at the observatory to go ahead with the experiment. They are lending him four atomic clocks and the necessary auxiliary equipment and are sending an astronomer, Richard Keating, along on the flight.

The Navy will pay the bill, which amounts to about $3,700 in airline fares at the rate the Government pays commercial carriers.

The expedition will leave Dulles International Airport at 7:45 P.M. Monday on Pan American World Airways Flight 106, a Boeing 747 bound for London. Four seats will be occupied in the tourist cabin—two for the scientists and two for the clocks.

In an interview by telephone Dr. Hafele said the eastward flight around the world would be followed by a second trip in the opposite direction.

On each flight the time readings of the four clocks will be averaged, and the average will be compared with the Naval Observatory's reference clock.

A spokesman for the observatory said the operating characteristics of all the clocks were known and that none of the four to be used in the flight gains or loses more than 26 billionths of a second day.

Furthermore, it was explained that the rates at which they “drift” from the theoretically perfect time‐keeping were also known and could be taken into account in the calculations.

The clocks measure the pas sage of time by extremely regular pulses of electricity emitted by oscillating crystals. These crystal oscillators are in turn kept at an even more regular rate by the radioactive decay of cesium atoms.

These high‐precision atomic disintegrations act as a governor, so to speak, on the oscillator. The clocks also have small clock faces with conventional hour, minute and second hands, but these serve only to give a rough approximation of the time.

The calculations to test the effects of velocity on time must take into account not only the measured time but also the rotation of the earth and the slight diminution of gravity at the flight altitudes above 30,000 feet.

On the eastward trip, the airplane's speed will be added to the earth's rotational speed, which is about 1,000 miles an hour at the equator.

If this were the only effect, the clocks should lose time slightly relative to the observatory's reference clock. But Dr. Hafele said today that his latest calculations show the gravitational effect might offset this.

The relativity prediction holds that time would pass more slowly in a strong gravitational field than in a weak one. The stay‐at‐home clock in Washington will he subject to stronger gravity than the four airborne clocks because of the altitude difference.

Dr. Hafele said his calculations show that the airborne clocks should gain about 50 billionths of a second over the reference clock during the trip because of this factor.

On the westward global flight later this month, the airplane speed will have to be subtracted from the earth's rotation. Thus, to a hypothetically neutral observer in space, the clock in Washington will be moving at a higher velocity than the four in flight. The reference clock on the ground, therefore, will be losing time. Dr. Hafele estimates the difference at about 300 one‐billionths of a second for the entire trip.

The flight will be the physicist's first trip around the world, but it will hardly qualify as a pleasure junket. He and his colleague will change planes in London, picking up another Pan Am flight that will take them to Frankfurt, Istanbul, Beirut. Tehran, New Delhi, Bangkok, Tokyo, Honolulu and Los Angeles. They, will take an American Airlines flight on the final leg back to Dulles.

The whole trip will take about 60 hours. The longest planned stop is two hours in Honolulu.

Ultraprecise atomic clock experiments confirm Einstein's predictions about time

Physicists "watch" as time slows down.

Using one of the world's most precise atomic clocks, physicists have shown that time runs a tiny bit slower if you change your height above the Earth's surface by a minuscule 0.008 inch (0.2 millimeters) — roughly twice the width of a piece of paper. The finding is yet another confirmation of Albert Einstein's theory of relativity , which predicts that massive objects, like our planet, warp the passage of time and cause it to slow down. 

"We're talking about measuring a change in how a clock ticks at a level a little larger than a human hair," said Tobias Bothwell, a graduate student in physics at JILA, which is run by the National Institute of Standards and Technology (NIST) and the University of Colorado.

In 1915, Einstein showed that anything with mass will distort the fabric of space-time — an effect we experience as the force of gravity. You can think of gravity as putting the brakes on the flow of time. This mind-bending idea means that clocks nearer to Earth run slow compared with those farther from it — a phenomenon called time dilation . 

Related: 8 ways you can see Einstein's theory of relativity in real life

Researchers have already shown that super-precise atomic clocks flown on airplanes run appreciably faster than those on the ground, according to the textbook " Experimental Tests of the Nature of Time " (Fullerton College, 2020). In 2010, scientists set a new record by measuring the passage of time with two aluminum -based atomic clocks separated in height by about 1 foot (33 centimeters), finding that the higher one ran slightly faster, Bothwell said. 

This latest measurement is about a factor of 1,000 better, he added. "We've really blown the doors off how well we can measure frequency," Bothwell said.

The experiment used a collection of roughly 100,000 atoms of the isotope strontium 87, which is often used in atomic clocks, cooled to a fraction of a degree above absolute zero and placed in a structure known as an optical lattice. An optical lattice uses intersecting beams of laser light to create a landscape of peaks and valleys resembling an egg carton, where each atom is cradled in one of the valleys, according to NIST .

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Each strontium atom oscillates back and forth, ticking by itself inside its valley 500 trillion times per second, like the pendulum of a microscopic grandfather clock, allowing the team to measure fractions of a second to an incredible 19 decimal places, according to a 2018 article in the journal Proceedings of the National Academy of Sciences . 

The strontium atoms in the optical lattice were arranged in many layers, kind of like a stack of pancakes, Bothwell said. By shining a laser on the layers, he and his colleagues could measure how quickly the atoms in each layer ticked. 

"As you go from top to bottom, you see each layer dancing a little differently thanks to gravity ," he said. The findings were published Feb. 16 in the journal Nature . 

"These kinds of clock experiments can shed light on the nature of time itself," said Mukund Vengalattore, an independent atomic physicist who was not involved in the work. 

That's because the strontium atoms are capable of being placed in what's known as a superposition of states, meaning two states at once, he added. According to quantum mechanics , particles can exist in two locations (or states) at once, so future experiments might place a strontium atom in a superposition where it is located in two different "pancakes" at the same time, Vengalattore said. 

With the particle in both places at once, the team could then measure the passage of time at different points along the superpositioned strontium atom, which would change thanks to the different gravitational force it feels. This should show that "at one end of the particle, time is running at one speed," Vengalattore said. "And at the other end, it's running at a different speed."

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This incredibly bizarre possibility gets at the heart of the difference between the quantum and classical worlds, he added. Classical objects, like tennis balls and people, can't exist in superpositions where they are located in two places at once. But where the switchover between quantum and classical happens is unclear. By increasing the distance between the pancakes, researchers could essentially make the particle grow larger and larger and potentially see when it stops behaving like a quantum particle and more like a classical one.

Such experiments may allow physicists to get closer to a long-sought dream — a theory of everything that would unify Einstein's theory of relativity, which describes the very large, with quantum mechanics, which describes the very small.

Meanwhile, the current experiment has helped the team envision ways to produce atomic clocks that are even more precise, Bothwell said. Future instruments could be used to measure tiny differences in the mass of the Earth beneath them, potentially making the clocks useful for detecting the flow of magma inside volcanoes, changes in meltwater inside glaciers or the movement of our planet's crustal plates, he added. 

Originally published on Live Science .

Editor's note: This article was updated to indicate that atomic clocks flown on airplanes run appreciably faster (not "slower") than those on the ground.

Adam Mann is a freelance journalist with over a decade of experience, specializing in astronomy and physics stories. He has a bachelor's degree in astrophysics from UC Berkeley. His work has appeared in the New Yorker, New York Times, National Geographic, Wall Street Journal, Wired, Nature, Science, and many other places. He lives in Oakland, California, where he enjoys riding his bike. 

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September 22, 2014

Einstein's "Time Dilation" Prediction Verified

Experiments at a particle accelerator have confirmed the "time dilation" effect predicted by Albert Einstein's special theory of relativity

By Alexandra Witze & Nature magazine

Physicists have verified a key prediction of Albert Einstein’s special theory of relativity with unprecedented accuracy. Experiments at a particle accelerator in Germany confirm that time moves slower for a moving clock than for a stationary one.

The work is the most stringent test yet of this ‘time-dilation’ effect, which Einstein predicted. One of the consequences of this effect is that a person travelling in a high-speed rocket would age more slowly than people back on Earth.

Few scientists doubt that Einstein was right. But the mathematics describing the time-dilation effect are “fundamental to all physical theories”, says Thomas Udem, a physicist at the Max Planck Institute for Quantum Optics in Garching, Germany, who was not involved in the research. “It is of utmost importance to verify it with the best possible accuracy.”

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The paper was published on September 16 in  Physical Review Letters . It is the culmination of 15 years of work by an international group of collaborators including Nobel laureate Theodor Hänsch, director of the Max Planck optics institute.

To test the time-dilation effect, physicists need to compare two clocks — one that is stationary and one that moves. To do this, the researchers used the Experimental Storage Ring, where high-speed particles are stored and studied at the GSI Helmholtz Centre for heavy-ion research in Darmstadt, Germany.

The scientists made the moving clock by accelerating lithium ions to one-third the speed of light. Then they measured a set of transitions within the lithium as electrons hopped between various energy levels. The frequency of the transitions served as the ‘ticking’ of the clock. Transitions within lithium ions that were not moving served as the stationary clock.

The researchers measured the time-dilation effect more precisely than in any previous study, including one published in 2007 by the same research group. “It’s nearly five times better than our old result, and 50 to 100 times better than any other method used by other people to measure relativistic time dilation,” says co-author Gerald Gwinner, a physicist at the University of Manitoba in Winnipeg, Canada.

Understanding time dilation has practical implications as well, he notes. Global Positioning System (GPS) satellites are essentially clocks in orbit, and GPS software has to account for tiny time shifts when analysing navigational information. The European Space Agency plans to test time dilation in space when it launches its Atomic Clock Ensemble in Space (ACES) experiment to the International Space Station in 2016.

The speed of fast-moving ions means that accelerator experiments can test time dilation more precisely than experiments in Earth orbit, says Matthew Mewes, a physicist at California Polytechnic State University in San Luis Obispo, who is not part of the team. “It’s important to look wherever we can and push the technology whenever possible,” he says.

But the research group is dismantling its longtime collaboration, as there is no larger accelerator they can go to for more powerful tests. “It's been many hours in basements, in shielded rooms with noisy equipment, and in the end you get one number,” says Gwinner. “We’ve been exchanging a bunch of nostalgic e-mails.”

This article is reproduced with permission and was first published on September 19, 2014.

Atomic Clocks Experiment Reveals Time Dilation At The Smallest Scale Ever

In his theory of general relativity , Einstein predicted something called time dilation : the notion that two clocks under two different gravitational pulls will always tick at different speeds.

The effect has been observed in many experiments since, but now scientists have recorded it at the smallest scale seen so far.

The result was achieved using ultra-precise atomic clocks just a millimeter (0.04 inches) apart – about the width of a sharp pencil tip. Collecting 90 hours of data gave the team a reading that was 50 times more precise than any previous similar measurement.

And of course the smaller and more precise the scale, the more we rely on quantum mechanics to explain what's going on. The researchers are hoping that their new readings open up a way to learning more about how the curvature of spacetime – what we experience as gravity – affects the characteristics of particles according to quantum physics.

"The most important and exciting result is that we can potentially connect quantum physics with gravity, for example, probing complex physics when particles are distributed at different locations in the curved space-time," says physicist Jun Ye from the University of Colorado Boulder.

In this experiment, the researchers used what's known as an optical lattice , a web of laser light used to trap atoms in place so they can be observed. It's a technique used for the latest generation of atomic clocks, offering more precision in timekeeping through the laser light waves, and these lattices can be used for quantum simulations too.

Here, the two atomic clock readings were taken from the same cloud of atoms, in a highly controlled energy state. In fact, the atoms ticked between two energy levels in perfect synchronization for 37 seconds, a record in terms of quantum coherence (that is, keeping quantum states stable) – and that stability is essential for these measurements.

That enabled the scientists to take their readings at two separate points, measuring the redshift across the cloud of about 100,000 ultracold strontium atoms. The redshift shows the change in the frequency of the atoms' radiation along the electromagnetic spectrum – or in other words, how quickly the atomic clock is ticking.

While the difference in redshift across this tiny distance was just 0.0000000000000000001 or so, that's in line with predictions made by general relativity. Those differences can make a difference when you get out to the scale of the entire Universe, or even when you're dealing with systems that need to be ultra-accurate, such as GPS navigation.

"This is a completely new ballgame, a new regime where quantum mechanics in curved space-time can be explored," says Ye .

"If we could measure the redshift 10 times even better than this, we will be able to see the atoms' whole matter waves across the curvature of space-time. Being able to measure the time difference on such a minute scale could enable us to discover, for example, that gravity disrupts quantum coherence, which could be at the bottom of why our macroscale world is classical."

Part of what makes this time dilation research so exciting is that it points the way towards atomic clocks that are even more precise in the future, giving scientists a blueprint that can be refined to take measurements on smaller and smaller scales.

Atomic clocks have come a long way in the last few decades, and there's plenty more to come.

The research has been published in Nature .

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https://www.nist.gov/news-events/news/2010/09/nist-pair-aluminum-atomic-clocks-reveal-einsteins-relativity-personal-scale

NIST Pair of Aluminum Atomic Clocks Reveal Einstein's Relativity at a Personal Scale

Clocks tick a little faster if you're a foot higher, NIST experiments have shown, confirming predictions from Einstein's general theory of relativity.

BOULDER, Colo. – 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.

Described in the Sept. 24 issue of Science , the difference is much too small for humans to perceive directly—adding up to approximately 90 billionths of a second over a 79-year lifetime—but may provide practical applications in geophysics and other fields.

Similarly, the NIST researchers observed another aspect of relativity—that time passes more slowly when you move faster—at speeds comparable to a car travelling about 20 miles per hour, a more comprehensible scale than previous measurements made using jet aircraft.

NIST scientists performed the new "time dilation" experiments by comparing operations of a pair of the world's best experimental atomic clocks. The nearly identical clocks are each based on the "ticking" of a single aluminum ion (electrically charged atom) as it vibrates between two energy levels over a million billion times per second. One clock keeps time to within 1 second in about 3.7 billion years (see NIST's Second 'Quantum Logic Clock' Based on Aluminum Ion is Now World's Most Precise Clock ) and the other is close behind in performance. The two clocks are located in different laboratories at NIST and connected by a 75-meter-long optical fiber.

NIST's aluminum clocks—also called "quantum logic clocks" because they borrow logical decision-making techniques from experimental quantum computing—are precise and stable enough to reveal slight differences that could not be seen until now. The clocks operate by shining laser light on the ions at optical frequencies, which are higher than the microwave frequencies used in today's standard atomic clocks based on the cesium atom. Optical clocks could someday lead to time standards 100 times more accurate than today's standard clocks.

The aluminum clocks can detect small relativity-based effects because of their extreme precision and high "Q factor"—a quantity that reflects how reliably the ion absorbs and retains optical energy in changing from one energy level to another—says NIST postdoctoral researcher James Chin-Wen Chou, first author of the paper.

"We have observed the highest Q factor in atomic physics," Chou says. "You can think about it as how long a tuning fork would vibrate before it loses the energy stored in the resonating structure. We have the ion oscillating in sync with the laser frequency for about 400 thousand billion cycles."

The NIST experiments focused on two scenarios predicted by Einstein's theories of relativity. First, when two clocks are subjected to unequal gravitational forces due to their different elevations above the surface of the Earth, the higher clock—experiencing a smaller gravitational force—runs faster. Second, when an observer is moving, a stationary clock's tick appears to last longer, so the clock appears to run slow. Scientists refer to this as the "twin paradox," in which a twin sibling who travels on a fast-moving rocket ship would return home younger than the other twin. The crucial factor is the acceleration (speeding up and slowing down) of the travelling twin in making the round-trip journey.

NIST scientists observed these effects by making specific changes in one of the two aluminum clocks and measuring the resulting differences in the two ions' relative ticking rates, or frequencies.

In one set of experiments, scientists raised one of the clocks by jacking up the laser table to a height one-third of a meter (about a foot) above the second clock. Sure enough, the higher clock ran at a slightly faster rate than the lower clock, exactly as predicted.

The second set of experiments examined the effects of altering the physical motion of the ion in one clock. (The ions are almost completely motionless during normal clock operations.) NIST scientists tweaked the one ion so that it gyrated back and forth at speeds equivalent to several meters per second. That clock ticked at a slightly slower rate than the second clock, as predicted by relativity. The moving ion acts like the traveling twin in the twin paradox.

Such comparisons of super-precise clocks eventually may be useful in geodesy, the science of measuring the Earth and its gravitational field, with applications in geophysics and hydrology, and possibly in space-based tests of fundamental physics theories, suggests physicist Till Rosenband, leader of NIST's aluminum ion clock team.

NIST scientists hope to improve the precision of the aluminum clocks even further, as much as 10-fold, through changes in ion trap geometry and better control of ion motion and environmental interference. The aim is to measure differences in timekeeping well enough to measure heights to an accuracy of 1 centimeter, a performance level suitable for making geodetic measurements. The paper suggests that optical clocks could be linked to form a network of "inland tidal gauges" to measure the distance from the earth's surface to the geoid (the surface of the earth's gravity field that matches the global mean sea level). Such a network could be updated far more frequently than current techniques.

The research was supported in part by the Office of Naval Research.

C.W. Chou, D.B. Hume, T. Rosenband and D.J. Wineland. Optical Clocks and Relativity. Science . Sept. 24, 2010.

The Time Dilation Experiment: How Physicists Prove Its Real

As a team of physicists, we are fascinated by the concept of time dilation. It is a fundamental aspect of Einstein's Theory of Relativity that describes how time can appear to pass differently for two observers in different frames of reference. This theory has been proven experimentally time and time again, and today we want to take you through some of the most compelling experiments that have been conducted to demonstrate this phenomenon.

The first thing we need to understand is what time dilation actually means. In simple terms, it refers to the fact that time appears to move slower for an observer who is moving relative to another observer who is stationary. This may sound counterintuitive, but it has been demonstrated repeatedly through carefully designed experiments. These experiments not only help us better understand the nature of our universe but also have practical implications in fields such as GPS technology and space travel. So let's dive into the exciting world of physics and explore some fascinating examples of how physicists prove that time dilation is real!

Understanding Time Dilation Theory

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Understanding the mind-bending theory of time dilation is essential for grasping the intricacies of Einstein's theory of relativity. In simple terms, time dilation can be defined as the difference in elapsed time between two events that occur at different distances from a gravitational mass or relative to each other's motion. This means that time passes slower for an object in motion or near a massive object than it does for an observer who is stationary and far away.

To understand this concept better, let's take an example. Imagine two synchronized clocks placed at different altitudes - one on top of Mount Everest and another at sea level. According to the theory of general relativity, because gravity is weaker at higher altitudes, the clock on Mount Everest would tick faster than the one at sea level. This phenomenon can be explained mathematically using equations such as Lorentz transformations and special relativity formulas.

With this understanding of time dilation, we can now delve into the concept of time dilation experiment without missing any crucial details.

](/blog/time-travel-theories/time-dilation/time-dilation-experiment-physicists-prove-real)As we delve deeper into the concept of measuring time in different ways, a mind-bending realization starts to take shape. The theory of relativity suggests that time is not constant and can be influenced by various factors, such as gravity and motion. To prove this theory, physicists have conducted numerous experiments over the years using advanced measurement techniques and observational evidence.

To further illustrate the concept of time dilation, here are some key points to consider:

• According to the theory of relativity, time passes more slowly in strong gravitational fields or at high velocities.
• This means that if two individuals were traveling at different speeds or in different gravitational fields, they would experience time differently.
• The first experimental evidence for time dilation came from the famous Hafele-Keating experiment in 1971, which involved atomic clocks being flown around the world on commercial airliners.

With these ideas in mind, let us explore how physicists were able to conduct their first time dilation experiment.

You will delve into the first demonstration of time's non-constant nature through an experiment using advanced measurement techniques and observational evidence. The first time dilation experiment was conducted by two physicists, Joseph Hafele and Richard Keating, in 1971. They flew atomic clocks on separate commercial airplanes that traveled around the world in opposite directions. This experimental setup allowed them to compare the elapsed time of one clock with respect to another.

The data collection process involved comparing the readings of the clocks after they returned from their journeys. The results showed that the clock traveling westward experienced a slower passage of time than the stationary clock on Earth, whereas the clock flying eastward experienced a faster passage of time than its counterpart on Earth. This finding provided strong evidence for Einstein's theory of relativity and proved that time dilation is not just a theoretical concept but a real phenomenon that occurs in our universe.

This groundbreaking experiment paved the way for further research into understanding how gravity affects space-time and led to more recent time dilation experiments exploring new frontiers such as black holes and neutron stars.

In recent years, there have been several groundbreaking experiments that further prove the existence of time dilation. One such experiment involved atomic clocks, which are incredibly precise timekeeping devices. By measuring the differences in time between two identical atomic clocks (one stationary and one in motion), scientists were able to observe time dilation effects predicted by Einstein's theory of relativity.

Another experiment involved observing gravitational time dilation, which occurs when an object is located near a massive body causing it to experience slower time than an observer farther away from the massive body. Scientists observed this effect by using extremely sensitive atomic clocks placed at different heights above sea level.

The results and analysis of these experiments provide even more evidence for the reality of time dilation and its importance in our understanding of physics.

You'll feel the ticking of an atomic clock in your bones as you imagine the precision and accuracy required for this experiment. Atomic clocks are the standard for measuring time with extreme accuracy, relying on the natural vibrations of cesium atoms to keep incredibly precise time. The recent atomic clock experiment conducted by physicists tested whether or not time dilation occurs at different altitudes above Earth's surface.

The test involved comparing two identical atomic clocks: one kept on the ground and another taken up to a high altitude via airplane. The results confirmed that time dilation does indeed occur, with the higher altitude clock running slightly faster than its grounded counterpart due to gravitational differences. This level of atomic clock accuracy is essential for measuring even the smallest differences in time dilation, providing crucial data for theories like Einstein's theory of relativity.

Now, let's move on to the next step where we explore how physicists conduct experiments that prove gravitational time dilation is real.

Get ready to feel the thrill of discovery as we delve into the fascinating world of gravitational time differences and how they can be measured with incredible precision. The gravitational time dilation experiment involves measuring the difference in time between two clocks placed at different altitudes in a gravitational field. As Einstein's theory of general relativity predicted, time moves slower closer to a massive object due to the curvature of space-time caused by gravity.

Experimental evidence for this effect was first observed in 1962 when atomic clocks on board airplanes flew around the Earth and were found to be out of sync with identical clocks on the ground. More recent experiments have used highly precise atomic clocks flown on airplanes or launched into space satellites to measure these effects even more accurately. These experiments have also been able to detect other factors that can affect time dilation, such as changes in velocity and gravitational waves. With this technology, physicists are able to confirm that general relativity is indeed an accurate description of our universe.

As we move onto discussing results and analysis, it's important to note that these experiments have not only provided evidence for Einstein's theory but also opened up new avenues for research into fundamental physics, including investigations into dark matter and quantum gravity.

Now we can finally see the fascinating and groundbreaking results that confirm Einstein's theory of general relativity. The gravitational time dilation experiment has provided evidence that time slows down in stronger gravitational fields, which is consistent with the predictions made by the theory. By using precision measurement techniques to compare atomic clocks at different altitudes, scientists have demonstrated that time passes more slowly closer to massive objects.

The results obtained from this experiment are statistically significant and provide strong support for Einstein's theory. They indicate that gravity affects not only space but also time, which is a fundamental concept in physics. These findings have important implications for our understanding of the universe and its behavior. As we move on to discussing the implications of time dilation, we must keep in mind how crucial these experimental results are for advancing our knowledge of physics.

So now that we understand the basics of time dilation and how it has been experimentally proven, let's look at some of its implications. First, there are practical applications for space travel: as objects near the speed of light experience less time than those at rest, astronauts on long space missions could age slower than their counterparts on Earth. Secondly, time dilation has theoretical implications for our understanding of the nature of time itself and its relationship to space. Finally, continued research and development in this area could lead to new technologies and a deeper understanding of fundamental physics.

You'll be fascinated to learn that space travel could become more efficient and faster with the use of time dilation, as demonstrated by the fictional spacecraft in the movie Interstellar. The concept behind this is simple: if astronauts travel at a speed close to the speed of light, their time will slow down relative to those on Earth. This means that they can effectively age slower than their counterparts back home, allowing them to spend more time exploring and less time aging.

This has huge implications for astronaut travel, as it means that we can potentially send humans on long-duration missions without worrying about the effects of prolonged exposure to zero gravity. Furthermore, it also opens up possibilities for interstellar travel and even time travel (in theory). Of course, there are still many technical challenges that need to be overcome before we can realize these dreams, but it's an exciting prospect nonetheless. With all of this in mind, let's delve deeper into the theoretical implications of time dilation.

We can hardly contain our excitement as we explore the mind-boggling theoretical implications of time slowing down at high speeds. Philosophical considerations arise when we ponder how this phenomenon challenges our understanding of the nature of time itself. Our traditional view of time as an absolute and constant entity is shattered by the reality that it can warp and distort depending on relative motion.

The practical implications are equally fascinating. Time dilation has been observed in experiments involving atomic clocks, which have shown that even fractions of a second can make a significant difference over long distances or high velocities. This has important implications for GPS systems, where precise timing is critical for accurate location tracking. As we continue to unravel the mysteries of time dilation, future applications in fields such as space travel and telecommunications may become possible. But first, more research and development is needed to fully harness this incredible phenomenon.

You're about to discover the exciting possibilities that lie ahead in the field of researching and developing new technologies that can harness the incredible effects of time distortion at high speeds. With the confirmation of time dilation through experiments, scientists are now exploring ways to apply this phenomenon in innovative timekeeping devices and space travel. One potential application is using atomic clocks on spacecraft to accurately measure time in space, where the effects of gravity and velocity can distort time.

Technological advancements in quantum mechanics and nanotechnology are also paving the way for more precise measurements of time dilation. Researchers are experimenting with using quantum entanglement to create ultra-precise clocks that could be used for navigation or even detecting gravitational waves. As we continue to uncover more about this fascinating aspect of physics, it's clear that there are countless possibilities for future research and development in this field.

When discussing time dilation theory, it's impossible not to mention Einstein's contributions to the field of physics. His theory of relativity revolutionized our understanding of space and time, showing that they are intertwined and not absolute. Time perception is a crucial aspect of this theory, as it suggests that time can appear differently depending on one's frame of reference. This idea has been tested and proven in various experiments, including the famous Hafele-Keating experiment where atomic clocks were flown around the world to measure differences in elapsed time due to changes in velocity and gravity. Overall, Einstein's work on relativity paved the way for further exploration into the nature of time and how it relates to our physical universe.

When it comes to performing time dilation experiments, there are certainly limitations and potential drawbacks to consider. One major limitation is the accuracy of the experiment itself. In order to measure time dilation accurately, physicists must use incredibly precise instruments and methods. Even small errors in measurement could lead to inaccurate results, which could have serious implications for our understanding of the universe. Another potential drawback is that time dilation experiments can be incredibly complex and difficult to carry out. They require a great deal of planning, resources, and expertise, which may not always be available. Despite these challenges, however, time dilation experiments remain an important tool for physicists seeking to better understand the nature of time and space.

When it comes to practical implications of time dilation, physicists have developed experimental methods that help account for its effects. For instance, GPS systems rely on precise timing to determine a user's location. However, the satellites that send signals to GPS devices are in motion relative to the Earth and therefore experience time dilation. To ensure accurate timing, scientists must adjust the clocks on the satellites based on calculations of their velocity and altitude. By doing so, they can correct for the effects of time dilation and provide users with reliable location data. Overall, while time dilation can pose challenges in certain applications, physicists have found ways to mitigate its impact through careful experimentation and analysis.

Everyday examples of time dilation can be observed in our daily lives. One example is the aging process, where time appears to pass more quickly for those who are moving at higher speeds relative to a stationary observer. Experimental methods have also been used to prove the existence of time dilation, such as high-speed particle accelerators and spacecraft traveling at high velocities. These experiments have shown that time dilation is not just a theoretical concept, but a real phenomenon that occurs in extreme conditions as well as everyday situations.

Future implications of time dilation theory are vast and exciting. Technological advancements in the field will allow for more precise measurements, leading to a deeper understanding of the universe's fundamental workings. To put this into perspective, consider that the world's most accurate atomic clock loses only one second every 15 billion years due to time dilation effects. This level of precision is necessary for research in areas such as space exploration, satellite communication, and GPS technology. As we continue to push the limits of our understanding of time and space, time dilation theory will undoubtedly play a crucial role in shaping our future discoveries and innovations.

So, there you have it – time dilation is not just a theory, but a proven fact. Through various experiments conducted over the years, physicists have demonstrated that time really does slow down when an object moves at high speeds or experiences intense gravitational forces.

But what does this mean for us? Well, it has implications for everything from our GPS systems (which rely on precise timing) to our understanding of the universe itself. It's mind-boggling to think about how much we've learned through these experiments and how much more we still have yet to discover. The possibilities are endless and truly exciting.

In conclusion, time dilation is one of those concepts that can seem too abstract and outlandish to be believed at first glance. But thanks to the hard work and ingenuity of countless scientists over the years, we now know that it's real – a verified phenomenon that shapes our world in ways we're only beginning to understand. It's proof that sometimes even the wildest theories can turn out to be true – a testament to human curiosity and perseverance if ever there was one.

Physicists Are Closer Than Ever to Creating A Nuclear Clock That Could Change Physics Forever

This clock could run for billions of years and not lose a second.

The nucleus of an atom is now the modern version of sand flowing through an hourglass.

Researchers have spent 15 years trying to increase accuracy in timekeeping. The U.S. standard currently relies on a metal isotope called cesium-133. But the cesium atomic clock , whose time error is about one second in a whopping 100 million years, has now been outdone.

"Imagine a wristwatch that wouldn't lose a second even if you left it running for billions of years," physicist Jun Ye , leader of the research team at JILA, a joint institute of the National Institute of Standards and Technology (NIST) and the University of Colorado Boulder, said in an announcement. JILA is home to one of the two teams involved in the new research, published Wednesday in the journal Nature.

Tick tock goes the clock

From shadows along sundials, to the swinging pendulums of grandfather clocks, to the ticking elicited from quartz inside wristwatches, humans have progressively discovered more accurate ways of counting time. In essence, they all rely on a rhythm. Accuracy is gained from measuring short and steady rates of change.

Measuring how Earth rotates around the Sun can help us tell time, but its not perfect. Earth wobbles in its axis, it takes an uneven orbit around the Sun, and a year doesn’t evenly divide into 24-hour days (hence, leap years). Pendulums are steady, but can slow down in warmer weather. So humans looked for something else. And in the middle of the twentieth century, the idea of the atomic clock was born.

The atomic clock used in modern timekeeping uses lasers to manipulate atoms of cesium-133 along a frigid shaft. Then microwaves blast into a huddled bundle of these atoms, and triggers their outermost electrons. A device measures their frequency. This value is a trillions-long digit frequency per second. And so, it’s a highly-accurate measuring stick for timekeeping. Much more refined than pouring sand.

Atomic clock goes nuclear

As a laser shines into a jet of gas, it generates ultraviolet light. It’s the basis of the future nuclear clock that will accurately measure the energy needed to excite the thorium-229 nucleus.

But there’s something more accurate than the electrons of cesium-133: the subatomic particles in the nucleus of thorium-229, a radioactive isotope of the metal thorium. Researchers found a way to harness it for timekeeping.

“You’re picking the natural resonances inside the atom. So essentially, it’s kind of a universal number,” Chuankun Zhang , a graduate student at the University of Colorado Boulder who collaborated on the project as part of JILA, tells Inverse.

For the first time, researchers have directly measured the laser frequency needed to trigger the thorium nucleus to be organized in a different way, also known as a new internal state.

“This allows [us] to probe details of the nucleus, like its shape change when it goes from one quantum state to another, with an accuracy that was never accessible in nuclear physics before,” Thorsten Schumm , leader of the other team that worked on this project from the Vienna University of Technology in Austria (TU Wien), tells Inverse via email.

What lies ahead

The point of a good clock is there is very little room for error in counting. But on top of that, the nuclear clock is good for other reasons, too.

The nuclear clock could be more sensitive to how dark matter, for instance, affects visible matter in the universe. It could also verify if constants of nature are truly constant. Theories of particle physics could be verified, and new discoveries may emerge.

The technology of a nuclear clock is now proven, but it’s still being refined. Zhang and Schumm said this new nuclear clock could be ready in one to two years.

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Testing Time Dilation: Atomic Clocks in Jet Aircraft Experiment Results

• Thread starter KyleS4562
• Start date Feb 1, 2010
• Tags Dilation Time Time dilation
• Feb 1, 2010
• Optoelectronic diamond device reveals an unexpected phenomenon reminiscent of lightning in slow motion
• Entangled photon pairs enable hidden image encoding
• Major leap for nuclear clock paves way for ultraprecise timekeeping
• Feb 2, 2010

A PF Mountain

for part a, it seems reasonable. It would take quite a long time to get a 1s discrepancy. For part b, are you taking into account that the Earth rotates (and that the planes fly in opposite directions)?  

FAQ: Testing Time Dilation: Atomic Clocks in Jet Aircraft Experiment Results

1. what is time dilation.

Time dilation is a phenomenon predicted by Einstein's theory of relativity, where time appears to pass slower for objects traveling at high speeds or experiencing strong gravitational fields.

2. How does the atomic clock experiment test time dilation?

The atomic clock experiment involves flying two atomic clocks, one stationary on the ground and one on a high-speed jet aircraft. The clocks are then compared to see if there is a difference in the passage of time due to the speed of the aircraft.

3. What were the results of the atomic clock experiment?

The results of the atomic clock experiment showed that the clock on the jet aircraft did indeed experience time dilation, with a difference of nanoseconds compared to the stationary clock on the ground.

4. How does time dilation affect our daily lives?

In our daily lives, the effects of time dilation are extremely small and are only noticeable at extremely high speeds or in strong gravitational fields. However, it is an important concept in understanding the behavior of objects in the universe and is essential for modern technologies such as GPS systems.

5. What other experiments have been conducted to test time dilation?

Aside from the atomic clock experiment, other experiments have been conducted using atomic clocks on satellites and in space, as well as with high-speed particles in particle accelerators. These experiments have all confirmed the predictions of Einstein's theory of relativity regarding time dilation.

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A Simulation Study of Quantum Clock Synchronization Using Teleportation

An important requirement in implementing distributed computing and sensing application is the synchronization of clocks at various locations. The Internet relies on the Network Time Protocol (NTP), which synchronizes clocks with accuracy in the order of milliseconds. More recently an ensemble of atomic clocks is used for navigation based on GPS. These clocks are highly accurate and provide time with very low uncertainty. Even so, many physics experiments such as distributed LIGO-based systems may require more accurate clock synchronization that is achievable using quantum entanglement. This requires the deployment of a network of quantum clocks synchronized by exploiting entangled atomic clock qubits. In this paper, we carry out a simulation study of synchronizing a network of quantum clocks interconnected by a fiber plant that supports the ESnet; the latter is used to support the classical communication needed for teleportation. We consider an existing protocol for synchro-nizing the atomic clock qubits that relies on the GHZ states. To assess the performance of the protocol we developed a discrete-event simulation of the network using IBM Qiskit framework for underlying quantum gate operations and measurements. The simulation results shed light on the resources required in terms of the number entangled qubits and the time needed to achieve the synchronization of different number of nodes in ESnet.

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