Is gravity related to other forces in nature?, says S.Ananthanarayanan.

The force of gravity, which we feel and take for granted from the moment we are born, is apparent to us thanks to large masses, like the earth, the sun and heavenly bodies. Between ordinary objects, however, gravity is imperceptible. Ordinary things, even atoms, are held together by electrical forces. While there is another set of forces within the atomic nucleus, the masses at this scale are so small that the effects of gravity would vanish.

Tobias Westphal, Hans Hepach, Jeremias Pfaff and Markus Aspelmeyer, from the Austrian Academy of Sciences, Vienna and the University of Vienna, describe in the journal, Nature, their sally into measuring the faintest effects of gravity between objects down to milligrams. Measuring gravity forces between smaller masses could elucidate the role of gravity at the sub-nuclear distance scale, the authors say.

Our understanding of gravity, thanks to Einstein’s General Theory of Relativity, is sophisticated, and seemingly exact. As the sub-atomic scale too, we have unparalleled precision. A bridge between the theory behind gravity and the understanding of other forces, however has been elusive.

We are aware of the force of gravity because of our weight, which keeps us rooted to the ground, and because we see that things tend to fall earthward. It took the genius of Isaac Newton to connect gravity as the force which kept heavenly bodies in their courses and to formalize a mathematical framework. The other force that the ancients knew, and we now understand, is the electrical force. The huge difference in the magnitude of these two forces, however, keeps them separate - gravity acts at the scale of the cosmos and it is irrelevant in the domains where electrical forces dominate.

When the structure of the atom was discovered, a question to answer was how positively charged protons could be packed within the atomic nucleus, as electrical forces should drive them apart. This led to the discovery of a new kind of very strong, attractive force, that acted only when distances were very small, which is the case within the atomic nucleus. Once outside the nucleus, these forces fall to zero, and only electrical forces stay relevant.

Electrical and gravitational forces do not abruptly disappear, in this way. When the distance increases, they get weaker, but do not fall to zero. The electrical force is pretty strong too, but electric charges, the source of the electrical force, cannot accumulate. This is because electrical charges mutually repel. And then, they get neutralized by equal positive charges, which cannot be kept away for long. Electrical effects are hence strong, but measurable only over distances of millimeters. The case of gravitational forces is the opposite. The force is feeble and can hardly be made out between ordinary objects. But the cosmos does consist of very huge objects, like planets, suns and galaxies, and, despite the long distances, gravitational forces are powerful.

The comparison of how the mass of objects and the force of gravity varies over dimensions is instructive. As we know, the volume, and hence mass, of an object, say a sphere, increases according to the cube of its dimensions. This is to say that a sphere that is twice the size of another would weigh eight times as much. And one that is twice the size of the second sphere would weigh 64 times as much as the first sphere. The force of gravity, however, falls only according to the square of the distance. Thus, the force between objects would fall just to a fourth, if they are drawn twice as far apart, and by a factor of only 16 if the distance is doubled.

Over larger differences of size, say a million, the mass changes by a factor of 10¹⁸. But going the same million times further apart reduces the force of gravity only by a factor of 10¹². The force of gravity is still a million times stronger! The same thing applies the other way about. If the distance was reduced by a factor of a million, the force of gravity would get 10¹² times stronger. But if the dimensions of the object were a million times less, the mass falls by a factor of 10¹⁸. The net force is hence a million times weaker!

The force of gravity has hence been challenging to measure while using objects that it would be practical to handle. Following suggestions by scientists who had developed a sensitive method to measure weak electrical forces, Henry Cavendish, in 1798, set up an arrangement to detect the weak gravitational force that acts between objects at the everyday scale of masses.

Cavendish

The arrangement was of a pair of heavy balls of lead at the ends of a long baton, which was suspended from its middle by a thin fibre, like a silk thread. Next to the two balls, at the ends of the baton, were placed a pair of much larger lead balls, to attract the smaller balls by gravity. The force is feeble indeed, but the arrangement is so sensitive that the force causes a deflection – just a tiny deflection, balanced by the torsion of the silk thread.

The torsion balance can be calibrated using known forces, so that the angle through which the balance deflects measures the force applied, and hence gravitational attraction that causes the deflection. Cavendish compared the force by which the balls were attracted with their weight, which is the force of attraction by the earth. As the mass of the larger balls was known, Cavendish could get the mass of the earth, and a mean density, or the mass per cm³, of 5.48 grams, which is close to the modern figure—5.5153 grams.

Coming back to how gravity and the other forces known to us could be explained by a unified theory, the authors of the paper in Nature say that measuring how gravity behaves when dimensions get really small could help finding answers. As a first step towards lesser dimensions, the group has adapted the Cavendish method with gold particles just one millimeter across, in place of the lead balls. The particles are at the ends of a thin, 40 mm-long, glass capillary, suspended at its middle by a 35 mm-long, 4 micron- diameter silica thread. A similar particle of gold is placed next to one of the particles, and is moved back and forth, to provide a rhythmic acceleration to the test ball. This affects the pattern of oscillation of the arrangement, from which the feeble gravitational effect can be worked out.

An important requirement of the method, as of the Cavendish method, is to eliminate external disturbances. The arrangement was hence elaborately insulated from vibrations, seismic and acoustic and conducted inside a vacuum chamber, to eliminate effects of molecules of air. The result of the trials was a value of the gravitational constant, the factor that connects the masses and the gravitational force, that was 9% off the best-known value. Given the uncertainties that are intrinsic, the paper says, this is demonstration that we can measure gravitational effects of small objects to within 10%.

As the sources of error are known, improvements could make it possible to study gravity at the sub-atomic scale, the paper says. If we understand how gravity behaves at this scale, it would set the course for explaining puzzling aspects of the cosmos, and gravity, the nature of dark matter, being one.

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