# Pair of aluminum atomic clocks reveal Einstein's relativity at a personal scale

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 www.physorg.com/news184517462.html) 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."

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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.

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**More information:***C.W. Chou, D.B. Hume, T. Rosenband and D.J. Wineland. Optical Clocks and Relativity.

*Science*. Sept. 24, 2010.

**Citation**: Pair of aluminum atomic clocks reveal Einstein's relativity at a personal scale (2010, September 23) retrieved 21 April 2019 from https://phys.org/news/2010-09-pair-aluminum-atomic-clocks-reveal.html

## User comments

rahgwarghNoumenonNo, they are comparing two clock rates that are separated by 33 cm. They are measuring the effect of a very large mass on space-time, not a quantum interaction of a "graviton" particle.

mertzjNoumenonThe gravitational force is 10^36 times weaker than the electromagnetic force, so no.

@ gwargh, time dilation is not invariant and so depends on the relative velocities of the two events, which in this case is zero.

El_NosesstrittWhile it is true, this effect (special relativity)is smaller and in addition to the general relativistic effect of the higher clock being in a weaker gravitational field (less space-time curvature)

sstrittMaxwellsDemonTime dilation increases closer to the center of mass (time dilation is proportional to the gravitational binding energy, which increases toward the center of a mass). So if the Earth were of uniform density, time dilation would be (sqrt of 1.5) times greater at the center than the time dilation at the surface. But since the density increases toward the center, the time dilation at the center would be slightly larger than that.

MaxwellsDemonsstrittHow does this jive with the fact that in Newtonian gravitation, the fractional mass of the earth above any mass located within the earth exerts no net gravitational force?

MaxwellsDemonThink of it this way: if I were to place an Earth-like planet directly above your head, you'd be weightless at the center of gravity between the two planets. But your time dilation wouldn't magically disappear, it would actually increase (relative to a distant observer), because you'd be immersed in an even more intense gravitational field.

The degree of time dilation can be easily calculated by taking the Lorentz transform of the escape velocity for any point in the gravitational field. It takes a greater velocity to escape from the center of a mass than it does to escape from the surface, so time dilation is always maximum at that point.

yOnsaHuskysstrittthanks. that makes sense!

braindeadNoumenonbraindeadbraindeadbraindeadSo how would this affect time at satellites parked in Lagrangian points?

AntAntMaxwellsDemonIn the weak field limit, which applies to Earth gravity and v much less than c, this equation is sufficient to combine the two effects:

dtE/dtc = 1 - U/c^2 - v^2/2c^2

Where U = the sum of local gravitational potentials GMi/ri

HuskyvisualActually, it does not. The magnitude of the field is the same thing as the net force, by definition. The fields of the planets on the two sides of you cancel out. Same thing is valid in terms of curvature - as curvature has direction, the two curvatures caused by the masses on your two sides cancel out, resulting in flat space at your point.

MaxwellsDemonThat’s false. The gradient flattens out at the center of mass, but the magnitude of the field is at maximum value there. It’s like the top of a hill – the center is flat but it’s displaced upward.

“Gravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the lower the gravitational potential (closer to the center of a massive object), the more slowly time passes.”

http://en.wikiped...dilation

For the interior Schwarzschild solution and explanations you can follow up here:

http://www.physic...t2147975

Brett_MorganAntThe reality is there are allowances that have to be made due to the satelite being in orbit, for which very acurate calculations have been made. What these are called is irelavent, but because you and others believe in time dilation (and even an entity "time") you have chosen to apply these links to the adjustments.

To dilate "time" there needs to be an entity "time", there isnt.

Remember occams razor

NoumenonMaxwellsDemonWith the unified matrix of spacetime, c isn’t simply the speed of light in a vacuum anymore; it’s also the conversion factor of time and space units. One second of time is equivalent to 3x10^8 meters of spatial separation.

So as you sit there experiencing one second of time, you’re moving through spacetime at the speed of light. One second per second is equivalent to 3x10^8 meters per second. Neat, huh?

In fact, as you acquire speed in any direction and of any magnitude, you’re still moving at the speed of light, because as your spacelike motion increases, your timelike motion decrease in perfect proportion so that your total spacetime velocity equals c. This concept is called “four-velocity” (because it includes the time dimension with the three spatial dimensions): http://en.wikiped...velocity

braindeadSpooky action at distance and time.

gwredeAaarrghhhhhh.....

yOnsaSometimes people need things explained in other ways to reach that eureka moment. People not understanding initially what is written here is precisely why it should be on the net. The people here want to learn and are interested in these ideas. You must have felt this way at some point before you became all knowing and condescending.

This is an interesting topic and I am happy to see all of these comments. I come to this website for the comments as much as the articles themselves.

braindeadmg1Time as such started at 0 when the big bang happened, after that every particle has its own age so relating time between particles is pointless, no two are the same. The only true time would still exist at the origin(big bang) and would in some metric sense given no gravity or other effect be happily increasing in a linear fashion. If we were able to know the current time at the origin and our current time, we could deduce the rough offset of the universe based on distance from the centre.

Time is useful only to us to measure something and is quite relative. Meaning it is not absolutely right but right enough for us to understand and work with.

I believe entangled pairs are still subject to data travelling at c between them.

genastropsychicallstAntAntMarcoPolo2010Quantum_ConundrumHowever, since Everest is massive, the gravity actually may be slightly stronger than expected at the real summit as compared to say the same elevation above a plain or ocean.

At any rate, Everest's summit has aged by about 5 seconds less in the past 2000 years as compared to it's base...

Quantum_Conundrum2 Peter 3:8 "...one day is with the Lord as a thousand years, and a thousand years as one day..."

DonRTabulaMentisThe interferometer in the video used vertically makes an impressive gravity detector.

MaxwellsDemonBut I just checked up on the details of the Pound-Rebka experiment (aka the Harvard tower experiment...and it turns out that Herr Grusenick's apparatus generated a -false positive- (probably from a subtle flexing of the components as the gravitational stress shifted under rotation). Basically he built a 'gravitational redshift/blueshift detection simulator'...only the effect it shows shouldn't be visible at that wavelength at that scale!

The gravitational redshift at that degree of separation would only be a fraction of a wavelength of a high-energy gamma photon...there's just -no way- any shift would be visible to the naked eye at a green photon wavelength over that distance:

http://en.wikiped...periment

http://hyperphysi...tim.html

Next time I'll check the math *before* posting, mea culpa! Sorry for the misdirection!

daywalk3rYep MD. Watched the video and my eyes were rolling @ how many wavelengths it was shifting, which gave me some instant chuckle :)

Too bad that the allu rails are bending because of asymetric distribution of weight on the board, aswell as expanding/contracting due to temparature shifts in the room (the "time of day" differences mentioned by the author).

But every effort pays off - actually almost all of the YouTube commenters have no objections whatsoever and jump the train without questions ;-D

Was just about to post a reply, but then refreshed and saw your last comment, which in bulk mentions most of the other points I had on mind, so kudos to you :)

getgoahttp://blogs.mysp...37454303

Isaac Newton was not correct, Einstein is not correct they are relatively correct meaning they will never be able to understand the correct answer. This is usually called in the bible snakes craft--the winding routes of humans.

Here is a male defying centre of gravity:

http://www.youtub...bnMeOtMs

BrianFraserhttp://fqxi.org/d...Time.pdf

http://fqxi.org/c...opic/294 (discussion)

Another article shows what relationship time has to space:

http://scriptural...maFactor

WarrensnMaxwellsDemonActually, if you lived at the top of Mt. Everest you'd age one billionth of a second more each year compared to someone at sea level.

Source: http://www.cfa.ha...tare.htm

This is backwards and incorrect: time moves faster further away from the center of mass, slower closer to the center of mass. Over the last 2000 years the top of Mt. Everest has aged 2 millionths of a second more than a position at sea level.

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