Physics: good vibrations show how Big G is inCONSisTANT
Oscillating beams can improve our understanding of a hitherto uncertain fundamental constant of nature.
Anyone who has studied physics at high school will have been taught that the force of attraction between two massive objects is proportional to their masses, and inversely proportional to the square of the distance between them. This is known as Newton’s inverse square law. Introduce the physical constant, ‘Big G’, and we have an equation to calculate the gravitational force exactly.
Or maybe not exactly, if there’s uncertainty in the value of Big G. Experimental measurements of this constant show a relatively large spread of values, which suggests that the sources of uncertainty are not fully understood. This leads us to seek new ways of measuring the weakest of the four fundamental forces of nature.
In an ultra-quiet and temperature stable laboratory housed in a former military bunker in the Swiss Alps, Zürich-based physicist Tobias Brack and others have come up with a way of using oscillating beams to determine G at much higher frequencies than the millihertz regimes of previous experiments. The researchers suspend two 1m-long, 4kg beams in parallel, set one of them vibrating at around 42Hz, and measure motion induced by gravity in the second beam. The arrangement minimizes reaction forces at the beam supports, and maximizes the gravitational effect.
What is particularly clever about this setup is that the relative path length change generated by an astronomical gravitational wave is of order 10 to the power –20 or less, which would result in Brack’s bar changing by only a hundredth of an attometer (10 to the power –18). The measurement of such a tiny change is possible as the vibration is amplified when the resonant frequency of the bar matches that of the vibration-inducing signal, with the degree of amplification determined by the bar’s quality factor: a mechanical engineering property. In this case the amplification factor is around 10 million, corresponding to a movement of 25 picometers.
Brack and his colleagues derived a value for G some 2.2% higher than that recommended by the Committee on Data for Science and Technology, but the most important take from this study is the potential afforded by mechanical amplification of gravitationally-induced motion. We’ve come a long way from the torsion balance first used by Henry Cavendish in 1797 to measure the force of gravity.