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Comment by lisper | Hacker News Reader

This article leaves so many unanswered questions, starting with the elephant in the room: how accurate is it? (Or how accurate do they expect it to be?)

I found the answer here:

https://en.wikipedia.org/wiki/Atomic_clock#Accuracy

It turns out that the current state of the art is 10^-15. Which immediately raises the second question: how do they measure this? 10^-15 is an error of roughly a nanosecond a year. GR causes that kind of time difference between your head and your feet when you stand up.

https://www.nist.gov/news-events/news/2010/09/nist-clock-exp...

I haven't done the math, but I'm guessing that just standing next to a 10^-15 clock would have noticeable effects due to the effects of your gravitational field.

Also: why does thorium-229 in particular have such a low-energy atomic transition? That seems kind of random.

Mind-boggling stuff.

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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.

> 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.

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

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.

ah, gotcha, that makes a big difference

An increase, but those effects are noticed with traditional atomic clocks too. The simple act of moving them between biuldings results in detectable GR effects: time dilation from acceleration as someone pushes the cart. A more accurate measure of such things could yield a functional GR-based accelerometer/gyroscope.

> Mind-boggling stuff.

This and the recent advances in clock precision. In the last few years cryogenic sapphire clocks have achieved short-term stability on the order of 10s of attoseconds.

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