Scientists use the Tokyo Skytree to test general relativity | Hacker News Reader

Scientists use the Tokyo Skytree to test general relativity

phys.org

101 pointsdnetesn40 comments

There is something that has always bugged me about the space curving analogy and how it relates to relativity.

Gravity in a multi body system or in special cases of a two body system, has counteracting forces. If you found the Lagrange point between a binary black hole system, you could stay there. Or if you hollowed out the core of the Earth, you would float because you are being pulled in all directions at once (essentially the 2 body problem doesn’t “behave” for concave objects or distance less than diameter).

Is time slower or faster at the Earth’s core? Is it slower or faster at the Lagrange point of a three body system?

In the limit of weak gravity, gravitational time dilation depends only on the gravitational potential, and not at all on the local gravitational field. So going down to the center of the Earth just has the opposite effect of going up to space, i.e. the clock will run slower. Nothing special happens just because the field happens to cancel out. The equivalence principle essentially tells us that local gravitational field values don't have meaning, anyway.

You are claiming you can distinguish between freefall inside the center of the earth, from freefall traveling between the stars, solely by the effect on time dilation?

Yes, one can measure the difference in gravitational potential between two locations by comparing clocks. This is precisely what was done in the Skytree experiment.

By definition in free-fall there is no gravitational potential!

Of course there is. The gravitational potential does not depend at all on the (non-relativistic) velocity.

How would you measure this gravitational potential?

For example by comparing two extremely good clocks. Or the same way the earth's gravitational potential is mapped - by measuring the relative height and the gravitational acceleration in many points and numerically integrating along the way.

I feel like we are speaking different languages - you are in free fall.

There is no gravitational acceleration to measure. It's zero.

Yes, you seem to have a fundamental misunderstanding about what free fall means.

In the absence of other forces, a body in a gravitational field experiences a constant acceleration that only depends on the strength of the field. In the accelerating reference frame of the object, there are no net forces. You could for example measure the gravitational acceleration of earth by jumping from a plane and measuring how fast the ground is coming towards you.

You are inside a box, you do not see the ground, so how can you use it to measure anything (to measure "how fast the ground is coming towards you")?

Time dilation of a clock does not depend on the clock being able to reference some external object, like the earth. (I do recognize you can not measure time dilation until you compare to some other clock.)

So, let's reframe with a thought experiment and maybe you can answer:

A clock in the center of the earth, and a clock dropped from a tall tower on earth (ignore the rotation of the earth). Each clock sends two laser pules, exactly 1/100 of a second apart toward the other clock.

(The falling clock sends its pulses moments after being dropped, so it has essentially zero speed relative to the clock in the center of the earth.)

The partner clock then measures how far apart in time it received the two pules.

After that we collect the reports from the clocks and evaluate.

Will the two clocks each report the same time interval?

For an even better experiment lets add a third clock, this one resting on the surface of the earth.

Now you are confusing a number of different things.

Einstein used a free-falling sealed box to derive the equivalence principle. This does not imply that any free-falling system is a sealed box. Thinking about clocks makes absolutely no sense without having a way of comparing them.

In your example, the clock in the center of the earth will run slower than the one falling from the tower due to gravitational time dilation. Note that Einstein's "light clock" thought experiments do not capture this effect, since it stems from General Relativity, not Special Relativity.

> Is time slower or faster at the Earth’s core?

That is a more complicated question than is immediately apparent because it is not just the curvature of spacetime that is in play, it is also the fact that objects that are supported at the surface of the earth are effectively being accelerated upwards (through spacetime) by that support. An object at the center of the earth doesn't need any support to remain in place, so it is in an inertial frame. To really do an apples-to-apples comparison of the effect of spacetime curvature alone you'd need one clock at the center of the earth and another in orbit so that each clock would be in a locally inertial frame. But now you have special relativistic effects because the two clocks are in relative motion. So there is no absolute answer to the question. It depends on which frame of reference you use. The clock in orbit will think the one at the center of the earth is slow, the one at the center will think the clock in orbit is slow (this is essentially the classic twin paradox).

The essential observation/consequence of General Relativity is that is that everyone (in the absence of non-gravitational interactions) is just floating, or travelling in a straight line as-measured-locally. We travel in orbits because space is curved. (“Space-time tells matter how to move; matter tells space-time how to curve.” -- Wheeler)

A clock at the center of the Earth runs more slowly than a clock on Earth's surface.

The answer to your Lagrange point question is probably indeterminate. The differences in clock rates depend on the relative depths in potential not the magnitude of gravitational force (as measured by anyone).

Time is faster at earths core. I think it has been proven already.

I have a question for all the physics nerds here: The surface of the Earth is not quite flat. When you consider the sheer radius of it, it can be approximated as such, but it isn't. Do geographical features (massive mountains and deep oceans) impact the gravity of Earth, or are they truly irrelevant?

Yes. In the experiments in our lab, we are sensitive, through gravity-gradients, to the annual variation of the water table in the hill adjoining the instrumentation.

Viewed another way, the hill beside our lab deflects the direction of "down" by about 50 nanoradians for every meter you move vertically in the lab. (If you kept the hill, and got rid of the earth, a satellite would orbit the hill.)

The really crazy thing about the experiments described in the article is that they depend on the difference in potential, which is much harder to estimate. As these clock-based experiments reach still-higher sensitivities, we're going to see improved and interesting tests of gravity emerge alongside the increasingly-difficult problems of time-transfer at these levels of precision.

This was really interesting to read, thank you. The "a satellite would orbit the hill" and " direction of "down" parts of the comment, in particular, really helped understand/visualize what you were describing. Also, I immediately went into the next room and told my wife about it, because I thought it was that interesting. Thanks for chiming in.

Thanks -- it's so cool!

(We care about this difference-in-the-direction-of-down because we need to lock one of our turntables to "local vertical" with nanoradian stability. It was initially a surprise, before my time, when it was realized that it was impossible to do so simultaneously for two sensors on the same turntable but at different locations on the turntable axis.)

Also, if you think that's cool, depending on your latitude, the "down" you experience doesn't point in the direction of the center of the earth. The earth is rotating, so there is a substantial centrifugal contribution to the acceleration you experience. Off the top of my head, I believe the effect here in Seattle is about 14 milliradians. It is zero at the pole and equator (the apparent centrifugal acceleration makes you effectively lighter!), though :).

> by about 50 nanoradians for every meter you move vertically in the lab.

Holy moly. Just what kind of measurements are you doing in your lab?

Precision tests of gravity: https://www.npl.washington.edu/eotwash/node/1

Our most-recent measurement: https://news.ycombinator.com/item?id=22797729

Once you know how, it's not as hard as you'd expect to measure a nanoradian ;).

That looks like all kinds of fun! Thanks for the links.

It is fun -- it requires an interesting blend of patience and impatience. Each individual step in the measurement process is slow, but those who are most successful at it are very hungry to get at reliable answers quickly.

Gravity is, by most measures, our oldest force, and while GR is a very successful theory, we know essentially nothing about the underlying mechanism. This is very much unlike the rest of the Standard Model, where we have very-successful quantum theories.

Yes, the mass of the earth was estimated in 1774 by measuring how much a nearby mountain deviated measurements.

https://en.wikipedia.org/wiki/Schiehallion_experiment

Mason and Dixon reported a systematic error in their measurements of the border of Maryland and Pennsylvania to the Royal Society. This was suspected to be the mass of the Allegheny Mountains and eventually led to subsequent experiments. https://en.m.wikipedia.org/wiki/Mason%E2%80%93Dixon_line

I learned about that when I was reading the novel by Pynchon. I can't remember whether it was actually in the novel or if I stumbled across it while cross referencing.

Gravity is used by the oil and mining industry to find deposits.

https://www.hartenergy.com/exclusives/gravity-and-magnetic-g...

The geoid deviates from the ellipsoid by an amount on the order of tens of metres - from -106m in southern India, to +85m in Iceland. This has effects on satellite orbits as well as on ocean surface, although that is affected further by ocean circulation (meaning it is not locally flat) and subsequently by tides.

Relevant link: https://en.wikipedia.org/wiki/Geoid

There was an experiment done to measure the gravity of a mountain in Scotland before the United States was even a thing:

https://en.wikipedia.org/wiki/Schiehallion_experiment

"The Royal Society formed the Committee of Attraction to consider the matter, appointing Maskelyne, Joseph Banks and Benjamin Franklin amongst its members"

Their effect is minuscule, but measurable: https://svs.gsfc.nasa.gov/11234

If memory serves, there’s a spot over the Marianas Trench where gravity is about 1% lower. Said that way, it doesn’t sound like much, but 0.1 m/s² sounds pretty substantial to me.

Navy used gravity measurements to help inertial navigators.

https://www.navy.mil/submit/display.asp?story_id=31940

Which Way Is Down?

https://www.youtube.com/watch?v=Xc4xYacTu-E

Down is towards enemy.

General info is available here: https://en.wikipedia.org/wiki/Gravitational_time_dilation

Does time run faster at night time when you are further away from the sun?

> The scientists from RIKEN and their collaborators took up the task of developing transportable optical lattice clocks that could make comparably precise tests of relativity, but on the ground. The ultimate purpose, however, is not to prove or disprove Einstein.

What they are testing is their ultraprecise clocks, not the theory of general relativity like the headline says.

Sure, but all of these things are always interlinked. It's entirely possible that the first deviation we ever find from general relativity will come in the form of just trying to make better and better clocks, but then finding some funny systematic effect that prevents different atomic clocks from properly syncing up, and then ruling out all other explanations. This kind of discovery is not without precedent in physics.

The clocks were of course compared in previous experiments with no height difference between them.

The Skytree experiment is directly measuring gravitational time dilation which is a central prediction of General Relativity. Combined with an accurate measurement of the height difference and local gravitational acceleration, this makes it a very accurate test of GR.

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