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Comment by WitCanStain | Hacker News Reader

What could we do with more accurate atomic clocks that we cannot do with current ones?

The article points to a use I wouldn't have thought of.

The deeper you go into a gravitational field, the slower time goes. Therefore comparing clocks in different places gives a way to measure gravity. These clocks could be sufficiently precise to find mineral deposits underground from their gravity signature.

> These clocks could be sufficiently precise to find mineral deposits underground from their gravity signature.

We've been doing that since the 1960s at least with such things as the LaCoste & Romberg gravimeter (1936).

You can download, see online the "Geoid"

https://americanhistory.si.edu/collections/nmah_865074

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

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

Magnetic anomalies also highlight inteesting places for minerals, the issue with both magnetic and gravity fields variations lies with determining the "true" depth to target (medium sized shallow target, or massive deep taget?) which is known as an inversion problem.

Yes, but a better clock means more precise measurements, means we can locate smaller masses to higher precision.

Does it?

Inversion is rarely unique, and it's not due to the precision with which the field is measured.

https://earthsciences.anu.edu.au/study/student-projects/nove...

https://inside.mines.edu/~rsnieder/snieder_trampert_00.pdf

Epilogue:

    Linear inverse problem theory is an extremely powerful tool for solving inverse problems. Much of the information that we currently have on the Earth’s interior is based on linear inverse problems

    Despite the success of linear inverse theory, one should be aware that for many practical problems our ability to solve inverse problems is largely confined to the estimation problem.

Yes, inverse problems are hard. And not always possible in practice. See, for example, https://www.ams.org/publicoutreach/feature-column/fcarc-1997... for a case where one isn't possible.

That said, the gravity technique is one that actually gets used today. With better precision, it can be even more useful than it already is.

The problem is that the planet could be hollow and produce the same gravitational measurements on the surface and outside. It needs to be coupled with a model that introduces constraints for the inverse problem to be defined.

Since mining is only concerned with material that's within maybe 0.1% of the distance from the surface to the core, seems like you'd just need to move the sensor around and make sure the signal changes about where you'd expect for a mass of X Kg at a depth of Y meters instead of a supermassive chunk of dense material much deeper. Or, to put it another way, build a grid map of the area and subtract any background signal. Would that not work for some reason?

Consider the special case of a spherical deposit. You can find the center and mass of the deposit, but not its volume or density.

But now that you know it is there, you can use other techniques, like seismic measurements, to nail that down.

In practice, that's what would happen. Move around until seeing some larger gravitational pull, likely indicating some deposit. However, formally, this is not correct due to the mere fact that the gravitational force is proportional to 1/R^2, just like a Columb force. Thus, there are infinite numbers of mass distributions that produce the exact same gravitational field on the surface. The planet could be hollow, and we would not know it only from the field measurements.

A practical constraint is mass density, which has maximum and minimum values. We can make a crude approximation that the planet's density is constant, evaluate the field on the surface from the planet's shape and compare it with measurement. This would be more useful, but still, it wouldn't tell us whether there is a combo of water reservoir and a large massive deposit below it.

Thats why you generate typical geologic formations and add a few drillhole constraints.

Sure this isnt going to be a star trek scanner but for practical purposes theres a bunch of other techniques to constrain the results

For interest, Precision Vs Accuracy, Atomic Clocks Vs Sapphire Oscillator

https://news.ycombinator.com/item?id=28232645

Detecting gravity waves with large laser triangles required a few advances in technology - precision clocks was one.

Not so long ago had you asked your question the answer would have been "detect gravity waves".

Most units of measurement are derived from the second, so the more precise our frequency standards, the more precise everything else can be. Things like interferometry and spectroscopy depend directly on very precise frequency standards.

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