Water-Born Ideas

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Surely, the oldest and greatest water-born idea came to Archimedes.

Most of us get our inspiring ideas while sitting comfortably undisturbed in the loo.

[Aside: My sister with her husband and two kids was visiting us at Qrs. B-140 at IIT KGP. That was a spacious Heaven with 3 bedrooms and three attached bathrooms. Only one of them was 'Western' with a commode; but it was deeply hidden in a nook of the apartment. All were using the other two happily. But one fine morning when my brother-in-law wanted to use a loo, the other two were 'occupied'; so I showed him the potty. He went in with his 'Economic Times'. After half an hour my sister was looking for her husband all over and getting worked up. I told her he must be in the third loo: upon which she scolded me: "I wanted to keep the thing a secret from him. Now he won't return till the whole paper is read twice over!"

When I was in our Faculty Hostel, I had an attached bathroom all for myself with a commode. Many of my Ph. D. issues were settled while woolgathering there. Also, I used to have a pen and paper with me. Our X-Ray Professor was reputed to have a whole book-rack installed there handily].

Apparently his King gave Archimedes a fine new crown of gold and asked him to tell him if it was pure gold or the goldsmith cheated him adulterating it with copper, which mixes with gold rather like water with milk.

And Archimedes had a sensitive balance and maybe a meter scale.

Now, the density of gold is almost double of copper. If it was a regular object like a sphere or a cube, the solution is trivial: measure its weight and volume and divide one by the other.

But a crown is a weird irregular object mostly hollow (like the head of its customer) and full of holes for ventilation. No scale can get its volume. So, Archimedes had to act quick with the aid of only his balance.

Rest is history: While jumping and settling down in his swimming pool, he felt the usual buoyancy. But now he suddenly realized that the weight apparently lost by him gives him the volume of the dipped 'article'.

This meant that all he had to do was to weigh the crown in air and again in water and divide the true weight by the loss of weight.

No wonder he jumped out of water and ran home shouting "Eureka!".

To this day I am amazed at this wonderful Nobel-deserving idea.

Let us fast-forward a couple of millennia to the swimming pool at Stanford in the 1960s, maybe. Schiff and his colleagues entered the pool on a summer afternoon for their usual swimming bout. And while fooling around with its water, he had his brilliant idea:

Schiff was worked up to invent an 'experiment' that could verify a strange prediction of Einstein's General Relativity. This says that when a massive body moves about, it sweeps the spacetime around it somewhat. And this 'gravity-current' acts on other bodies nearby and disturbs them from their usual motion. We know that a wire carrying an electrical current attracts or repels a nearby wire carrying its own current. To Schiff this was known as 'gravitomagnetism'.

The point is that the effect is too tiny to detect in the laboratory. While in water, playing around with his hands, he realized that an eddy that he made traveled in the water outwards and 'spun' a nearby floating object.

That was it: We do have a massive spinning object called the Earth and we can put another one in 'orbit' in an orbiting satellite. Suppose we install an extremely sensitive gyroscope in the satellite. If Einstein is right, the spin of the Earth should act on the orbiting gyro and disturb it by tilting its axis a weeeeee bit. The effect is cumulative; the longer the satellite lives, the more the tilt.

Schiff perhaps straight went to his Office in the nood to calculate the tilt and found as usual that it is on the 'periphery of the possible' with the technology available: Perfectly smooth sphere of stainless steel supercooled to avoid any thermal effects, near-perfect vacuum to get rid of air-currents etc. The proposal was approved and a few million dollars granted. The thing was ready in a few years.

But not the rocket and the satellite. Those days, GR got the least priority and all rockets were busy launching military and commercial vehicles.

I first read about this in Chapter 11 or so of Weinberg's tome and gave the involved calculation as an M Sc Project to Porus. And I told him that in that Chapter there are 2 printer's devils: In 2 important Equations, two 'numbers' were missing (like 3 and 1.5). His Project was to find which Equations and what missing numbers. He reported his results in 3 months and was through.

I was watching for its verification till I retired in 2005. Nothing happened: no rocket and satellite available. Only the other day, it seems they could get one and the result, after correcting for a dozen others, was verified indeed to within 15%, making it a brand-new 6th (?) test of Einstein's GR.

It is known as the 'spin-precession' in a gravity probe satellite.

So, there you are: the spinning Earth sweeps the nearby spacetime along with it and this acts on other nearby objects: a clue that the 'ghost' forces of Newton may after all be due to this gravitomagnetc effect of the entire Universe!


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