[fsh]

A decent frequency counter can resolve a frequency difference of 1E-15 in a few minutes of averaging. Modern GPS-based frequency comparisons (dual-band, post-processed using precise point positioning) are also accurate to the 1E-15 level with around one day of averaging. Note that these counters operate with radio frequencies. The best atomic clocks use optical transitions and are accurate to around 1E-18. In this case, one gains around 6 orders of magnitude in frequency resolution by translating the laser frequency into a radio frequency using an optical frequency comb. The accuracy of the relative frequency measurement is not limiting at all.

The gravitational redshift amounts to around 1E-16 (not 1E-15) when moving the earth one meter closer or further from your clock. You standing next to it is going to have absolutely no effect.

[rcxdude]

> when moving the earth one meter closer or further from your clock. You standing next to it is going to have absolutely no effect.

Maybe GR messes this up, but at least with newtonian gravity the difference is not as stark as this comparison would imply: a 1m change in elevation is about 300ugal, while an 80kg person 1m away is about .5ugal, so still not going to show up on a 1e-18 clock, but it's pretty close.

[fsh]

The gravitational redshift is proportional to the gravitational potential (~1/distance), not to the gravitational acceleration (~1/distance²). This suppresses the effect of small masses nearby a lot compared to the effect of the earth.

[rcxdude]

ah, gotcha, that makes a big difference

[pclmulqdq]

This is pretty much entirely a GR effect, not a Newtonian effect.