Some physicists believe gravity is weakening. If true, then Earth won’t hold gases in its atmosphere. Lighter gases, like oxygen, will escape, and life on Earth will end. Robert H. Dicke predicted that gravity weakens by about 0.2% every year (I’m skeptical about this estimate). It must weaken by more than 90% for oxygen to escape our atmosphere.
Why is it weakening? Let’s first recall what gravity is. It is a force; it makes objects move. The apple fell to the ground because Earth’s gravity pulled it down. According to Newton, there is an attraction between any two objects that have a mass. This attraction is proportional to the masses and inversely proportional to the square of the distance between them. If we double either mass, the attraction doubles, if we double the distance, the attraction drops to a quarter. The constant of proportionality is called the universal gravitation constant and is denoted by G. When I say gravity is weakening, I mean G is dropping.
For over two and half centuries, Newton’s theory of gravitation triumphed. Then Einstein came along with the General Theory of Relativity. But Einstein’s theory cannot account for a G that changes with time, it violates the energy conservation principle (Ray 2007) – something sacred to physics.
This idea of a gravitational constant that changes with time is often credited to Paul Dirac. In this post, I’ll try to explain the basic idea behind Dirac’s reasoning.
Imagine a proton and an electron kept apart from each other. The ratio of their electrostatic attraction to gravitational attraction is a stupendously large number: 1 followed by 40 zeroes. This is a number coming from atomic constants like the charges and masses of electrons and protons. The age of the universe, as predicted by Hubble’s observations, is also close to 1 followed by 40 zeroes in Dirac’s system of units (Dirac 1937). Dirac marveled at this co-incidence and suspected a deep connection between the universe and the subatomic particles.
Dirac’s Large Number Hypothesis says that any two large numbers in cosmology, are related by a simple mathematical relation. From the previous example, the ratio between the electrostatic and gravitational force between a proton and an electron is equal to the age of the universe. The simple mathematical relation, in this case, is just equality. One immediate consequence of this hypothesis is that this ratio is always changing as the universe ages.
When combined with the Cosmological Principle, Dirac’s Large Number hypothesis predicts that the universal constant of gravitation, G, is inversely proportional to the age of the universe. As the age of the universe increases, the value of G decreases, and gravity weakens.
Now, what is the Cosmological Principle? It is the idea that humans don’t occupy a special place in the universe. This is very much in spirit with Copernican philosophy – we are not the center of the universe. On a large scale, the universe looks uniform. Dirac says the cosmological principle has “a great simplifying effect on the subject, and until there is more definite evidence of their inadequacy it does not seem worthwhile to try more complicated schemes.” (Dirac 1937).
Now coming back to gravity weakening. Although first proposed in 1937, this idea has continued to fascinate theoretical physicists. There are several theories where G is not a constant but changes with time. The Brans-Dicke theory (Dicke 1962) is a popular alternative to Einstein’s theory.
This might make you wonder; why are physicists looking for alternatives? Isn’t Einstein’s theory successful? So far, General Relativity agrees with all experiments. But ask anyone in the field and they’ll tell you that Einstein’s theory is not enough – it breaks down at some level. Similar to how Einstein generalized Newton’s theory, many physicists believe there is a bigger theory and General Relativity is a special case.
Although various alternatives are being pursued, there are stringent requirements these theories have to meet. On the one hand, they have to make testable predictions, and on the other, they have to encompass Einstein’s theory as a special case.
With amazing technological advances, we can now detect gravitational waves and photograph black holes. The recent two Nobel prizes in Physics (2019 and 2020) were awarded for work in the areas of Gravitation and Cosmology. The future holds promise.
References
(Ray 2007) Saibal Ray, Utpal Mukhopadhyay, Partha Pratim Ghosh. Large Number Hypothesis: A Review (2007). https://arxiv.org/abs/0705.1836 [gr-qc].
(Dirac 1937) Dirac Paul Adrien Maurice. 1938 A new basis for cosmology. Proc. R. Soc. A. 165: 199-208.
(Dicke 1962) Brans, Carl, and Robert H. Dicke. “Mach’s principle and a relativistic theory of gravitation.” Physical review 124, no. 3 (1961): 925.
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