
Scientists use the Tokyo Skytree to test general relativity - dnetesn
https://phys.org/news/2020-04-scientists-tokyo-skytree-einstein-theory.html
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hinkley
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?

~~~
knzhou
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.

~~~
ars
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?

~~~
fsh
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.

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

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

~~~
ars
How would you measure this gravitational potential?

~~~
fsh
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.

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

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

~~~
fsh
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.

~~~
ars
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.

~~~
fsh
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.

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grenoire
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?

~~~
ISL
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.

~~~
RHSeeger
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.

~~~
ISL
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 :).

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mcnamaratw
General info is available here:
[https://en.wikipedia.org/wiki/Gravitational_time_dilation](https://en.wikipedia.org/wiki/Gravitational_time_dilation)

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

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DeusExMachina
> 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.

~~~
knzhou
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.

