# 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. Tanmayi says:

That is a very fascinating concept, especially for a high school senior who does not have much knowledge of this topic.
Kudos to those guys!

2. spyder says:

So, for the Tibetans living at 13,000 feet above sea level (and beyond), their lives are lengthened, just by where they live? Cool.

3. Bob says:

I once wanted to throw in special relativity and calculate how much older or younger fighter pilots would be. Thousands of hours at high altitude and speeds averaging 300+ mph.

4. Heidi says:

I’m wondering if this knowledge helps us to expand or develop possible theories/implementation of time travel…

5. paul says:

@spyder

their elevation from from earth would increase the rate of the passage of time rather than slow it, in other words their lives are shortened!

6. Katharine 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?

7. Sean says:

Katharine — every physical process is “slowed down” (or more correctly, “experiences less time”) in exactly the same way. That’s true from the subatomic level, to the mechanical level, to the biological level. A person bringing a clock with them wouldn’t notice anything out of the ordinary, because both they and the clock would be affected in precisely the same way; it’s only when comparing to clocks on other trajectories that you notice time dilation.

8. Katharine says:

But how is it slowed down? (Another terrible question, I suppose.)

9. Bob P. says:

But the perception of time by the person at a higher elevation, flying fast, in a strong gravitational field, etc., remains the same. So you may be younger than the people you left behind, but you would experience them as growing older faster, and your own lifespan running at the normal rate.

10. Katherine, This is a pretty good explanation of the process for an enthusiastic laymen.

As I understand it, it has to do with the speed of light being constant regardless of the motion of the observer. In order to experience the speed of light as a constant, regardless of the observer’s motion, time must become a variable in situations experiencing drastic forces due to acceleration or gravity.

Speed = Distance/Time since C (the speed of light) is constant, as is Distance, the variable of time must shift.

Someone who gets this better than me should really explain it, but I thought I’d take a crack at it just for the hell of it.

11. Rohan says:

After reading this I have now rearranged the contents of my refrigerator accordingly.

12. Lab Lemming says:

So if you are in orbit, does your speed slow you down more than your altitude speeds you up, or do they cancel out?

13. Bob P. says:

Rhacodactylus, yes indeed the speed of light is the constant of the universe, and not relative time, so time varies while the speed of light does not.

14. Chris Ho-Stuart says:

I’m distracted by the statement about a clock being “stopped” at the horizon of a black hole. I think that could be expressed better surely?

There are three ways to try and thing of what happens at the horizon of a black hole.

(1) What happens to a clock held stationary at the horizon?

This is unphysical. It can’t happen. However, in the limit as a clock is held at a small constant distance above the horizon, the dilation diverges to infinite. Yes?

(2) What happens to a clock falling past the horizon?

It keeps ticking just fine, all the way.

(3) What is observed from outside as a clock falls past the horizon?

Signals to outside become redshifted to infinite. If they could be physically observed indefinitely (also unphysical) then the clock would appear “frozen”, never ticking past a certain point (which is the proper time of the clock as falls past the horizon).

I find it a bit awkward to consider this as a clock being stopped; it gets into a mess of what co-ordinates to use.

However, I am an egg. If I’ve messed up the above, please put me right!

15. Joseph Smidt says:

Sean, that is incredible NIST people can make such measurements! Really cool.

@Chris:

These things only show up when you compare clocks at two different places. A clock sitting at the horizon of a black hole is only “stopped” relative to a clock at some arbitrarily large distance from the black hole. the contradictions you cite never show up, because the observer sitting at the horizon will never be able to compare notes with the observer far from the hole.

For what it’s worth, though, so long as the black hole is large enough that tidal forces are small, then the correct answer is that the clock just keeps ticking fine, all the way.

Regardless, the apparent contradictions arise from trying to compare observations near the horizon to observations far from the horizon.

17. Chris Ho-Stuart says:

My concern was with the statement “At the event horizon of a black hole, they [clocks] wouldn’t tick at all”. There are two cases I consider.

(1) Clock at rest wrt to the hole. (Not physically possible.)

The issue of “comparing notes with a clock sitting at the horizon” doesn’t arise, because a clock cannot sit at the horizon, in the same sense exactly that a clock cannot travel at the speed of light.

A clock sitting at rest a small distance above the horizon has an enormous gravitational force that must be counteracted by some force (like a powerful rocket engine) to keep it at rest.

In this case (clock at rest near to the horizon) the time dilation wrt to another clock can be measured simply as the redshift of the signal from the clock; and this is the gravitational time dilation effect, which diverges to infinite as the chose rest point is chosen closer to the horizon. In the same way, the clock that is sitting near the horizon sees a signal from a remote clock as enormously blueshifted.

So for this clock at rest, it cannot be at the horizon, and it runs arbitrarily slow wrt to a remote clock for rest points arbitrarily close to the horizon. This dilation effect can be measured by the remote clock (as a redshift of the near horizon clock) and by the near horizon clock (as a blueshift of the remote clock).

(2) Clock falling through the horizon. (Does not stop ticking)

The clock keeps ticking all the way, but a remote observer can only observe signals from above the horizon. The falling clock appears “frozen” in time, with the signal from the falling clock being redshifted without limit so that the falling clock is eventually invisible.

In this case, however, the falling clock does not see an equal and opposite blue shift in the remote clock. In fact, the remote clock would appear redshifted to the falling observer, if it is on the same side of the hole. A remote clock on the other side would be blueshifted.

The point is that in this case it is wrong (IMO) to say that a clock stops ticking at the horizon. A falling clock does not stop ticking at the horizon, and a clock cannot be at rest on the horizon.

I think we agree on this, and this is the reason I balked at the statement in the blog post… but I don’t know how it could be best worded for a simple introductory post.

18. Dogg says:

@paul
But the higher the mountain, the stronger the gravity(since there is more mass on that direction)….. so maybe their life is longer?

19. Chris Ho-Stuart says:

Doesn’t follow, Dogg. The gravitational acceleration is greater on the mountain than at the same altitude above a plain; but both are less than at the surface on the plain. (A satellite can measure the gravitational anomaly with a mountain; because it is at the same altitude as when above the plain.) Hence you live faster and die sooner on the mountain than back home on the plain. (Though of course you experience the same time in either case, so there’s no loss of experience; you die sooner only from the remote perspective of another fixed observer.)

My favorite example: a Dad demonstrates time dilation for kids by taking them on a weekend trip up Mt Rainer with three atomic clocks! Mum stayed home with reference clocks in the kitchen. See Clocks, Kids, and General Relativity on Mt Rainier.

The conclusion of a letter to Physics Today about the experiment:

Instead of fanciful stories of rocket ships and twins, the kids got a hands-on introduction to general relativity with real clocks and a family road trip. Furthermore, by being at high altitude for the weekend, we experienced more time together, relatively speaking. It was the best extra 22 nanoseconds I’ve ever spent with the kids.

So, yes, not only do we live in a time when atomic clocks are altimeters, but when relativity is child’s play.

20. Is it actually correct to say that time slows down?

The way I understand it, being in a gravitational field or far away from it makes no difference to whoever is there themselves. One’s own time only appears to slow down or speed up to an outside observer (ie. seen from a different frame of reference).

(Ie. something that happens inside a gravitational field affects the outside world in slow motion; something that happens far away from any such field affects the outside world in closer to absolute speed. With the limits being 0 and c respectively.)

(Or in yet other words: it takes two for an Einstein tango.)

What gives?

21. James says:

@ Lab Lemming,

A quick calculation suggests to me that for orbits where the orbital radius is less than 1.25 the Earth’s radius, time will slow down (ie. The speed is more important). For larger orbits, time will speed up.

22. Chris Ho-Stuart says:

Aristotle, consider the case of family that went for a holiday up Mt Rainer for the weekend, and came back down again. They have now experienced about 22 nanoseconds more elapsed time than the one family member who remained at home.

This is real. It’s measured. If you have a conference phone call between family members up in the lodge at Mt Rainer and family members back home nearer to sea level, and ANY other third observer at some fixed location on the Earth, that third observer can, in principle, identify without ambiguity the party on top of the mountain because they are speaking very slightly faster, as long as they can make the measurements with sufficient accuracy.

The clocks really do run faster up the mountain than at sea level. This is a comparison of two clocks, of course. You can only see the effect by comparison with another clock; you don’t experience time slowing down or speeding up yourself.

But the effect is real, and as the post indicates, it can now be measured so accurately that differences in speed of clocks at less than a meter altitude difference, and less than 10 m/s relative velocity, can be observed in a lab setting.

Cheers — Chris

23. Darcy says:

Great to have you back Sean! Truly no blogger compares. 🙂

24. Katharine, you asked how the clock mechanism is affected and no-one really answered that. It isn’t affected at all – the clock is accurately measuring time, which continues as normal (at exactly 1 second per second, if that makes any sense) in the clock’s frame of reference. It’s time itself that appears to be slowing, not the clock. Similarly with the contraction of space – there’s no force on a 1 metre ruler that makes it shorter, it’s still accurately measuring 1 metre but space itself appears smaller.

So now you’re going to ask what mechanism is causing time to be slower where the clock is, and the answer to that is essentially “what made you think it would be the same?”. It’s simply a fundamental property of the universe that time isn’t constant everywhere, it depends on velocity and acceleration, and always has done, but we didn’t realise it.