soft question - Would a sea level rise (on the other side of the Earth) if you would dip your finger into the ocean?

(I'm not a physicist & I hope this question isn't too basic/lame)

The question says it all & assuming:

• No atmosphere


• No Earth rotation


• Not a single object in the ocean(s)



• Ignore all other disturbances (earthquakes, etc.)


• The ocean is 'perfectly' still

If (due to-me-unknown reasons) the level wouldn't rise, how big an object had to be, so the sea/ocean level rise would be measurable?

Answer

a rough, back of the envelope computation you can do: Find out the surface area of the earth in your proposed thought experiment, find out the volume of a finger. Compare the number of water molecules in each case.

Now look at the compressibilty of water (its not 0) and determine whether it would be less energy to push all the water molecules on earth up a small amount or to compress a small amount. I'm assuming the region of compression would decay as you moved further away from the perturbation (so your finger doesn't do work against the whole world's water body, just a local region.

I presume it would be more likely to compress locally than move globally. Doing work against water means not only work against gravity, but work also against surface tension.