[chris (OP)]

How does gravity alter the activity of a caesium clock? I gather than, owing to relativistic effects, identical - initially sync'd - clocks can show time disparities if one is flown at high speed aboard an aircraft. So what's actually changing about the way the caesium atom keeps time in each of the two conditions?

[Colin2B]

I gather than, owing to relativistic effects, identical - initially sync'd - clocks can show time disparities if one is flown at high speed aboard an aircraft.

Two separate effects, one due to speed as described by SR for inertal frames and the other due to difference gravitational potential difference as described for accelerating frames - equivalent to gravity in GR.
NIST have measured gravitational time differences as small as about 300cm in the lab. https://www.nist.gov/news-events/news/2010/09/nist-clock-experiment-demonstrates-your-head-older-your-feet

@Janus is very good at describing the detail,  but you might find this link helpful https://thecuriousastronomer.wordpress.com/2015/02/11/time-dilation-in-general-relativity/

[alancalverd]

So what's actually changing about the way the caesium atom keeps time in each of the two conditions?

Nothing! The essence of relativity theory is that the airborne clock has no idea of its constant speed since all motion is relative, but each appears to the other to be losing synchronisation because their separation is changing. Not to be confused with gravitational effects, where acceleration or a difference in gravitational potential warps spacetime: again each clock continues to work in the same way, but appears to run at a different rate from the point of view of the other.

[chris (OP)]

So the frequency of resonance of the caesium atoms is identical in both settings, but when viewed from the perspective of the other, it appears to have changed?

[jeffreyH]

A video explaining this may be useful with a very ingenious device.

[alancalverd]

So the frequency of resonance of the caesium atoms is identical in both settings, but when viewed from the perspective of the other, it appears to have changed?

That's relativity in a nutshell!  The electrons in the cesium atom have no knowledge of where they or you are, only that they are in the electric field of the nucleus, so the transition energy is independent of velocity. As it must be, since absolute velocity is meaningless.  The gravitational picture is more difficult to explain but a clock at point  A  in the universe can only transmit one tick at a time, so if observers at B and C  measure different frequencies  f_AB≠f_AC emitted from A, the difference must be due to their relative gravitational potentials.

[jeffreyH]

I have a question. Please refer to this Wikipedia page  https://en.m.wikipedia.org/wiki/Time_dilation and the section Simple inference of velocity time dilation. The diagram there shows the situation where the mirrors are moving to the right. What about when the mirrors are moving along the L axis?

[Halc]

What about when the mirrors are moving along the L axis?

In a frame where the mirrors move along the L axis, the time to go from mirror A to mirror B is different than going the other way.  In one case, light is trying to catch up to a receding mirror, and in the other, far less time is needed as the two are approaching from opposite directions.
The distance L is also contracted.  These effect couple together and the net result is the exact same dilation measured as a clock orientated a different way.

[syhprum]

Apart from SR and GR effects does a gravitational field have any effect on the actual frequency of the clock ?
I know that the strength of gravity is tiny compared to electrical or nuclear forces and may be too small for our technology to detect but is there a theoretical possibility?.

[Colin2B]

Apart from SR and GR effects does a gravitational field have any effect on the actual frequency of the clock ?.

Only if it’s a pendulum clock and it’s a bigger effect than GR. Otherwise all clocks are affected by relativistic effect - as viewed from another location.

[alancalverd]

Relativity says either there is no "actual" frequency, or it is always whatever you measure at that point! Interesting that a mechanical wristwatch with an escapement wheel will keep perfect time anywhere in the universe but a pendulum clock will stop if g = 0.  Thus a pendulum clock does not measure time, but gravity!

[Janus]

Relativity says either there is no "actual" frequency, or it is always whatever you measure at that point! Interesting that a mechanical wristwatch with an escapement wheel will keep perfect time anywhere in the universe but a pendulum clock will stop if g = 0.  Thus a pendulum clock does not measure time, but gravity!

However, while a pendulum clock sitting on the surface of the Earth and one sitting on the surface of a world with 4 times the Earth's mass and twice its radius would experience the same value of g, the one sitting on the more massive planet would tick slower when compared to the one on the Earth.

[jeffreyH]

What about when the mirrors are moving along the L axis?

In a frame where the mirrors move along the L axis, the time to go from mirror A to mirror B is different than going the other way.  In one case, light is trying to catch up to a receding mirror, and in the other, far less time is needed as the two are approaching from opposite directions.
The distance L is also contracted.  These effect couple together and the net result is the exact same dilation measured as a clock orientated a different way.

I go less for the length contraction and rather for the fact that any medium through which the light is traveling is also in motion. This will have a directional effect upon the light.

Of course if the moving object contained a vacuum then we are unable to rely upon a medium to explain the constancy of the speed of light.

That is the interesting part.

[evan_au]

any medium through which the light is traveling is also in motion.

This theory was put to bed over a century ago.

Shhhh! Don't wake it up!
See: https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment

[syhprum]

There are basically two kinds of clock those that depend on gravity a and those that depend on inter molecular forces such as crystals or balance wheel springs, these are affected by magnetic fields and to a lesser extent by gravity (of course the former is wholly dependent on gravity).
It is known that the intense magnetic fields of magnastars  distorts atoms would this screw up the caesium clock
 

[evan_au]

If we are going for extremes, the gravitational gradient around a stellar-mass black hole will tear apart any kind of clock - and "spaghettify" the person trying to read the clock and measure the degree of time dilation...

[alancalverd]

...or you could just extrapolate the gravitational red shift to infinity.

[Janus]

There are basically two kinds of clock those that depend on gravity a and those that depend on inter molecular forces such as crystals or balance wheel springs, these are affected by magnetic fields and to a lesser extent by gravity (of course the former is wholly dependent on gravity).
It is known that the intense magnetic fields of magnastars  distorts atoms would this screw up the caesium clock
 

It would likely screw up the electronics needed to get a reading from the clock, but I really don't see the point of this question.  Nobody claims that a cesium clock is perfect, only that they are very very accurate, and that any variation due to local conditions in normal situations (such as between sea level and a high mountain) are much much smaller than the effect we are trying to meaure ( time dilation).

If you could put a clock in orbit around the black hole at the center of our galaxy, it would be in free fall and experiencing 0g, and even orbiting just 1 AU from the BH, the tidal forces on it would be insignificant, in the order of  3 x 10^-8 g over 1 meter.   However, the time dilation factor would have such and clock losing nearly 3/4 of an hour per day as compared to a far distant clock.   You wouldn't need an cesium clock for this measurement, any reasonably priced watch would do to measure the effect.

[jeffreyH]

any medium through which the light is traveling is also in motion.

This theory was put to bed over a century ago.

Shhhh! Don't wake it up!
See: https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment

I guess you are alluding to that ether nonsense. That is why the vacuum bit was important. And yes I know I have invited every ether nut to jump into this thread. Let's see what happens ...

[jeffreyH]

This would be a useful review page for any sane enquirers.
https://www.doitpoms.ac.uk/tlplib/dielectrics/dielectric_refractive_index.php