# Time Dilation in Your Living Room

By Sean Carroll | September 23, 2010 1:07 pm

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!

CATEGORIZED UNDER: Science
• http://tanmayisai.blogspot.com Tanmayi

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!

• spyder

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

• Bob

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.

• Heidi

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

• paul

@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!

• Katharine

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?

• http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

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.

• Katharine

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

• Bob P.

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.

• http://Untitledvanityproject.blogspot.com Rhacodactylus

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.

• http://www.rohanmedia.co.uk Rohan

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

• http://lablemminglounge.blogspot.com Lab Lemming

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

• Bob P.

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.

• Chris Ho-Stuart

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!

• http://theeternaluniverse.blogspot.com/ Joseph Smidt

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.

• Chris Ho-Stuart

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.

• Dogg

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

• Chris Ho-Stuart

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.

• http://plasmasturm.org/ Aristotle Pagaltzis

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?

• James

@ 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.

• Chris Ho-Stuart

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

• Darcy

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

• http://www.mckerracher.net Phil McKerracher

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.

• PeteM

“You must be this tall to time travel”

• Karen

@Rohan LMAO

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

• Foster Boondoggle

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.

• Pat Dennis

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?

• Milan pintar

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 :/

• spyder

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.

• Fritts

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.

• Pingback: 24 September 2010 posts « blueollie()

• Jimbo

Few of us trailer trash can afford a subscription, so the link to Science is irrelevant.
However, arxiv is free:
http://arxiv.org/abs/0911.4527

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

Wineland is way overdue for the Nobel prize.

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

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. :/

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.

• http://www.physics.du.edu/ Supernova

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.”

• Nullius in Verba

“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.

• Yair

Dear Prof. Carroll,

Yair

@Waveforms:

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.

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.

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