How Do We Know That Newton’s Gravitational Constant is Really Constant?

In his “banned” TED talk, Rupert Sheldrake claims that the uncertainties in the measurements of Newton’s gravitational constant (“big G”) imply that it might vary with time. This constant determines the strength of all gravitational attractions in the universe, from an apple falling to the orbit of the sun around the center of our galaxy.

He further claimed scientists unfairly and dogmatically assume that G is constant without real proof. Both of these claims are demonstrably false; however, he asks a very interesting question, what if this constant did change?

After a bit of thought, I realized that if G varied with time, we could detect these variations as instabilities or anomalies in the orbit of the moon, since G is one of the factors determining the period and shape of the moon’s orbit. This is actually true for any orbiting objects we can observe, but thanks to the laser reflectors left by the Apollo and Lunokhod spacecraft, we know the distance to the moon to within 2 cm. This is so precise that even tiny variations in G would be detectable.

In the course of my research for this question, I discovered that many scientists have, in fact, tested for the stability of G using the moon’s orbit! Müller and Biskupek find that G has varied less than 0.2 parts per trillion per year over the course of the 35 years we have been making lunar ranging measurements.

Furthermore, multiple astrophysical methods are used to constrain the variability of G over much longer timescales. Mould and Uddin use distant supernovae to “set an upper limit on its rate of change” in G “of 0.1 parts per billion per year over 9” billion years. See also Table 1 of their paper for a nice collection of other methods and their results.

These constraints are at least ten thousand times smaller than the errors about which Dr. Sheldrake is speaking. They also show, contrary to his accusation, that scientists are actively testing the hypothesis that these constants of nature are actually constant. So far, for G, the hypothesis has been validated.

References

Jürgen Müller and Liliane Biskupek, “Variations of the gravitational constant from lunar laser ranging data” (2007) Class. Quantum Grav. vol. 24 p. 4533

Jeremy Mould and Syed A. Uddin, “Constraining a Possible Variation of G with Type Ia Supernovae” (2014) Publications of the Astronomical Society of Australia vol. 31

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