Physicists Show Einstein's Relativity Bending Time Over the Span of Just 1 Foot

By Andrew Moseman | September 24, 2010 11:41 am


That’s the minuscule factor by which time speeds up if you’re elevated just one foot higher from the surface of the Earth, according to new study in Science that cleverly demonstrates Einstein‘s general relativity on a human scale. Don’t rush to move into the basement to extend your life, though: That tiny speck of a difference would account for just about a billionth of a second over the span of the year.

Gravity is the key player in this time variance:

According to Einstein’s theory of general relativity, big objects with lots of gravity — planets or stars — bend the fabric of time and space, like bowling balls on a trampoline. The closer you get to these objects, the stronger the pull of gravity and the slower time moves. An astronaut watching a clock fall into a black hole, for example, would see its hands gradually slow down as the pull of gravity increases. []

The researchers led by James Chin-Wen Chou recorded tens of thousands of seconds ticking by on atomic clocks placed at the two different heights to capture the minute difference.

As DISCOVER blogger Sean Carroll notes at Cosmic Variance:

Not a surprise, of course; it’s a straightforward application of general relativity. Still, we need to look pretty hard to find GR showing up on human scales. These guys worked very hard!

Indeed, while it’s cool to show relativity at work on scales accessible to people, the more important part of the study might be the tools, not the findings.

With further refinement, ultraprecise clocks such as the ones used in the new study could one day allow scientists to measure geographic variations in Earth’s gravitational field—a science called geodesy—with unprecedented precision. Geodesy is important for calculating Earth’s mass distribution, which can help determine, for instance, the distribution of water on the planet and how that water moves. [National Geographic]

Related Content:
DISCOVER: 20 Things You Didn’t Know About… Time
DISCOVER: 20 Things You Didn’t Know About… Relativity
DISCOVER: Time May Not Exist
80beats: Einstein Proven Right (Again!) by the Movements of Galaxies
Cosmic Variance: Time Dilation in Your Living Room

Image: flickr / Robbert van der Steeg

CATEGORIZED UNDER: Physics & Math, Top Posts
MORE ABOUT: Einstein, relativity, time
  • Nemesis

    If I lived in the nucleus of an atom at the center of the earth, I’d be immortal!

  • Lance

    Now there’s a good question. If you’re down a well (let’s say half way to the center) will there be more gravitational pull or will the mass above you decrease the effect of the mass below you? Or more directly, does gravity increase as one moves towards the center of a massive object or do you achieve maximum force on the surface?

  • Wayfarer

    Actually as you go deeper down a hole the gravitational acceleration pulling you down will be less as there’s less mass beneath you. You can look at Fig. 5 in my name link. I used to remember how to derive this in A-level physics but that was almost a decade ago…

  • Sundance

    @Lance, and @Wayfarer;

    Even though this article is about General Relativity, we can use the Newtonian inverse-square-law. The acceleration due to gravity is proportional to m*1/r^2, where r is the distance from the centre of the planet, star, or whatever is creating the gravity you’re concerned about, and m is its mass. At any point inside a hollow sphere, the mass of matter on one side of you is proportional to r^2, with r the distance you are from it. So the acceleration you feel from one side is proportional to (r^2)*(1/r^2)=1 (i.e. it’s constant), while the acceleration from the other side is also constant, with exactly the same value (although a different value of r). So the acceleration from both sides cancels out.
    If you do a google search for “gravitational force inside a hollow sphere”, you’ll get more detailed answers than I can fit in here. The end result is that if you are beneath the surface of the Earth, you only feel a gravitational force from the matter closer to the centre of the Earth than you are.

  • scribbler

    Actually, it’s a bit short sighted to think of the hollow sphere as stationary since the earth goes around the sun, the sun goes around something else and so on and so forth.

    Good thought puzzle is that the closer we get to the speed of light the slower time goes to an outside observer until theoretically it stops at light speed. Well, since we can’t get to the speed of light, we can’t test whether time stops or not.

    However, coming to a complete stop IS doable, at least hypothetically. Theory then dictiates that whatever comes to a complete stop has time accellerated infinitely, right?

    Would it then disappear from our space/time?

    Interesting thought puzzle…

  • Medisoft

    Wow, crazy article! Just a *little* above my head though!

  • mba student

    that’s a trip and where can i buy that clock!

  • Rodney McDonell

    If you wanted to be imortal, the only way to do it would be to insert yourself into a singlearity… the center of the earth still ages. Though i’m not sure what you’d acheive… who knows what a singlearity holds… from our specific it is one thing but to be in it or rather it, would be another thing completely i’d imagine – that is, perceptions would never have been so relative.

  • BMGolley

    Actually, it’s not possible to come to a complete stop. One of the fundamental tenets of Special Relativity is that there is no rest frame. That is, there is no “not moving”, because you are always moving relative to something else. Therefore, we can define whatever frame we want as “stationary” (as long as its velocity is constant). So it’s perfectly acceptable to think of the hollow sphere as stationary.

  • Russ H

    The formula for the mass of an object is E=MC^2. The formula for the velocity of an object is E=MV^2. Because C is so large, a small decrease in C as an object gets closer to the earth causes a larger increase in V to balance the equation. The object decreases in mass because C is smaller, but increases in speed. The sum of the energy of the mass of an object plus the energy of it’s motion stay the same as an object falls to the ground. This is where ‘potential’ energy comes from. This also implies that gravity is caused by the time dialation and that there’s no force carrying particle for gravity. . . . in my humble opinion. :-)

  • scribbler

    There has to be a “not moving” state just as there is a “speed of light” state…

    We observe things traveling at the speed of light all the time (uh, light ;-). According to Einstein, then, time has stopped for the particles that are traveling at the speed of light. It is only reasonable to conclude then that since we observe things traveling at the speed of light that we could then observe things that don’t move at all.

    IF we knew where to look…

    I agree that since we are in motion that then the thing that is still would APPEAR to move. That in no way prevents it from having a velocity of zero, does it?

    My point is then that if Einstein is correct, then time for that object which has a velocity of zero accelerates to the infinite. So I posed the question about what it would look like and whether we would be able to see it at all. More interesting still is whether it would still have mass that affects it’s surroundings.

    There are afterall two speed limits in the OBSERVABLE Universe, are there not? Those being the speed of light and no speed at all. We think about the speed of light all the time (though wrongly presuming nothing goes that fast since well, light does) but spend very little thought on zero velocity at all…

    Since they’ve ruled out tacheons as dark matter/dark energy, why not examine matter that is stationary, or nearly so?

  • Ron F

    “Actually as you go deeper down a hole the gravitational acceleration pulling you down will be less as there’s less mass beneath you”

    Not necessarily. For that to be totally true, you would have to be assuming that the earth is uniformly dense. If you have a very dense core surrounded by a not-so-dense material, then (since gravity falls off at the square of distance), getting closer to the denser material may increase gravity more than enough to offset the increasing gravity from the matter above you.

    If you think this isn’t true, then let me ask you one question: is gravity greater on the surface of the earth, or at the edge of the atmosphere? At the edge of the atmosphere, you have the entire mass of the planet below you. On the surface of the earth, you have tons of mass above you in the form of gasses. Those gasses have mass, and thus there is gravity pulling you up. However, obviously the atmosphere is much less dense, therefore there is very little mass and thus little gravity pull you up. The increase in upward gravity is minuscule compared to the increase in downward gravity that you get by decreasing your distance to the more dense matter.

    Thus, descending into a hole will increase gravity up to a point. I have no idea at what depth you would achieve maximum gravity.

  • Keith

    Bending of objects in the universe is strictly dependent on the bodied matter that attracts it. Newton’s law of gravitation states a body attracts another body with a force that is inversely proportional to the square of the distance that separates the 2 bodies.

    Inevitably, in the space-time theory, where time is considered as a dimension, the euclidean distance between 2 matters (say 1 foot above the ground), actually bends in accordance to the force of the gravity.

    So far, that’s true – even for the lightest particle exists.

  • Guy Dudeman

    Step 1 : Get stoned out of your mind.
    Step 2 : Read this article.
    Step 3 : ???????

  • Ross

    So I wonder what the time difference would be between the top of Mt. Everest and the bottom of the Marianas trench. Especially over the course of millions of years.

  • peteyG

    All I know is, if space is infinite then I am the center of the Universe and paradoxically, so are you. Copernicus was right.

  • stan

    ….I wonder what this difference is on the moon

  • Emily

    So if I gain weight, ugh um, mass, I will slow down space time….

  • scribbler

    We are at the center of the known universe. So what if we travel around the sun. We’re still dead bang center, are we not?

  • troll

    what a shower of know-it-alls replying in the comments.


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