Time Dilation in Your Living Room

Einstein tells us that the time you experience between two events depends on the path you take through the universe. In particular, it can depend on the curvature of spacetime along your trajectory. At a quick-and-dirty level: clocks in a strong gravitational field tick more slowly than ones far away from any gravity. (At the event horizon of a black hole, they wouldn’t tick at all.)

Or not so far away: James Chin-Wen Chou and colleagues at NIST have measured the difference in clocks that are separated by 33 centimeters in elevation. That’s one foot for you Americans. (See NPR, Science News, press release. And because this is a blog rather than Old Media, I’ll even link to the research paper in Science.) As predicted, the elevated clock ticks faster by a factor of (1 + 4×10-17). If you stand on a chair, you’ll move into the future that much faster.

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!

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43 Responses to Time Dilation in Your Living Room

  1. PeteM says:

    “You must be this tall to time travel”

  2. Karen says:

    @Rohan LMAO

    Another reason why an underground bunker could be good for your long-term survival. 🙂

  3. Foster Boondoggle says:

    Actually, Sean, many of us have contact with GR on a more or less every day basis. Do you have a smartphone or car with GPS? The satellites’ timing computers include corrections for both GR and SR; the GR effect from being higher up the gravity well is considerably bigger than the SR effect due to orbital motion. Without the corrections, the location calculations would drift by something like 10km/day.

    I read somewhere that the DoD overseers of the project were skeptical about the GR correction and required the contractor to put in an on/off switch for it. Needless to say, the switch has been set to “on”. http://www.johnstonsarchive.net/relativity/einstein2.html.

  4. Pat Dennis says:

    So.. does the equivalence principle still hold? Did the scientists prove that the clocks are subject to a gravitational field, rather than being located in an elevator accelerating in the direction of the lab’s vertical axis?

  5. Milan pintar says:

    Tibetans like spyder says won’t live longer becAuse they have more mass under them, more gravity so time will go slower … Actually that does mean they will live longer :/

  6. spyder says:

    Thanking you Milan, that was part of my point. The other was that altitude has its own set of problems; these measurements were, afterall, made in a vacuum.

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  8. Fritts says:

    Time travel is easy. If you want to travel into the future, all you have to do is wait. To travel into the past, go hang out with the amish.

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  10. Jimbo says:

    Few of us trailer trash can afford a subscription, so the link to Science is irrelevant.
    However, arxiv is free:

    There is also a good story on this at physorg.com

    Wineland is way overdue for the Nobel prize.

  11. Raskolnikov says:

    So my brain stays younger than my legs. That explains a lot!

  12. Raskolnikov says:

    Damn, just read an article about it in the journal and suddenly realized that I made a mistake: the more intense the gravitational field, the slower time goes. Hence, my feet should be younger than my head instead.

    So I can’t blame relativity for feeling young in the head but old in the legs. :/

  13. waveforms says:

    I have trouble with explanations that rest on the abstraction of locations based upon distance. This is possibly an artifact of analytical (break things down and isolate them ) thinking. All points in space are connected by the collapse of the wavefunction of the universe, which may as well be called ‘now’. Sure, event A may not be able to influence event B because it is outside of it’s time horizon but there is always event AB which is inside the time horizon of both A and B. You say distances are so great that there is point AB between A and B which is outside both A and B time horizon? fine. split the distance again. My view is is that all spacetime locations are connected to each other, all connected to the collapse of the wavefunction of the universe, and connected to all it’s neighbor’s ‘now’. Therefore there can only be one collapse of the wavefunction, one ‘now’, so Time has to be an illusion. What happens in a black hole is just a different illusion from the one we know.

  14. Supernova says:

    Hmm, the NPR article appears to have it wrong: “The higher clock experienced a slightly smaller tug of gravity, and ticked more slowly than the lower clock.”

  15. Nullius in Verba says:

    “So, being the biologist and mechanistically-oriented sort that I am, how does this go from time dilation to affecting the actual clock mechanism? Or is this an entirely terrible question to ask, being that relativity and related topics are topics that require some suspension of your preconceptions about How Things Work?”

    Easiest approach is to first explain basic time dilation from Moving Fast.

    Imagine we are walking across a flat, open field, which has two dimensions called Forwards and Sideways. We’re going to relabel them so Forwards is Time and Sideways is Space. There is a rule that says we must both walk at the same, constant speed, and the time we personally experience is the same as the distance we walk. So we’re both walking Forwards at the same speed parallel to one another, and we both experience the same personal time walking from one place on the field to another.

    Now we separate and walk in different directions at an angle to one another across the field. Forwards and Sideways are now different directions, and we each have our own definition. In my coordinates, my companion not only drifts sideways, becoming further away in Space as we get further forward in Time, but also slowly falls behind me, apparently going through Time more slowly. But in my companion’s coordinates, it is me that is falling behind. We each see the other’s clock running slow, even though each of us is walking at the same constant rate, and locally everything looks normal. It’s simply because we are walking in different directions, and so have different definitions of Forwards and Sideways.

    Now imagine that instead of a flat field, it instead has bumps and dips in it – it is curved. I walk between the bumps and because my path is clear, I make good progress. My companion walking parallel to me has to go up and down the hills, and so walks further. She slowly falls behind me, and I creep ahead of her, even though we are both walking at the same speed. Since ‘Forwards’ is time, this curvature results in people apparently moving through time at different rates with respect to one another.

    The analogy gets two things wrong. One is that rather than each person being a point moving along the line, they instead ‘exist’ constantly along the entire line. If our paths should cross again, rather than seeing only my footprints, my companion meets me at an earlier time (from my point of view). The other is that the geometry of the plane is a bit wrong. Normal plane geometry is based on Pythagoras’ theorem, that the square of the diagonal length is the sum of the squares of the lengths Forwards and Sideways. In spacetime, the length squared is not the sum, but the difference – i.e. Forwards squared minus Sideways squared. It is this peculiarity of the geometry that makes time different from the three dimensions of space, and also causes the speed of light limit. (If you walk at 45 degrees, what happens to the length?) But that’s pretty brain-twisting, and the basic principle is the same.

    Time dilation (and length contraction) isn’t anything mysterious or complicated, it’s just basic 2D geometry. And apart from the twisted Pythagoras rule, easily accessible to the intuition.

  16. Yair says:

    Dear Prof. Carroll,

    Can you please comment/blog about Erik Verlinde’s GR-as-Thermodynamics suggestion.


  17. bittergradstudent says:


    I know how to interpret classical General Relativity very well. I know nothing about quantum gravity, and I REALLY know nothing of what it would mean to ‘collapse the universe’s wavefunction’. That’s going to have to depend on the theory of quantum gravity we’re discussing.

  18. waveforms says:


    I’m not saying what is right or wrong in the current theories, or in your calculations. I’m saying it is a problem for me to accept. Not because of the limitations of the human brain, but because it isn’t logical.

    I am referring to the moment when the future becomes the present. We can call it ‘collapse of wave function of the universe’ or ‘now’ or ‘decoherence’, whatever works. I am saying that that moment has to be instantaneous and pervasive throughout the universe. It spreads faster than light, similar to the expansion of space, which it may be related to.

    At every given moment, the possibilities of any given point in space is recalculated based partly upon it’s neighbors possibilities, partly on it’s expansion (not sure) and partly upon it’s own possibilities. Since it’s neighbor’s possibilities are part of the calculation, all neighbors possibilities are part of that calculation and Time has to be an emergent phenomena. If Time is different inside a black hole ( I believe it is) it is because the emergence of Time is different, not because the ‘nows’ are different.

    Yes, I’ve reached this conclusion via meditation and not mathematics, but if I were a theoretical physicist, I would be looking at that “not sure” part above.