Alternative Gravity Theories
By Vasiliki Karanasou, PhD Candidate, Laboratory of Theoretical Physics, University of Tartu
We all remember the schoolbook story of Newton, who was supposedly sitting idly under an apple tree when an apple fell on his head, leading him to discover the law of gravity. Things probably didn’t happen exactly that way, but according to Newton, gravity is a force that one body exerts on another, causing attraction between them. This force is responsible for apples falling from trees, for people being held to the ground instead of floating away, and for planets orbiting the Sun. Newton’s theory managed to describe our world very effectively—or did it?
Although Newtonian gravity explains many macroscopic phenomena, an early sign that it is incomplete is its inability to fully describe Mercury’s orbit around the Sun. Moreover, when studying phenomena involving speeds close to that of light, Newtonian theory proves to be entirely inadequate. In 1915, Einstein introduced a new theory—general relativity—which radically reshaped our understanding of space, time, and gravity.
Space is no longer a passive backdrop where events unfold and time flows uniformly. In relativity, space and time are combined into a four-dimensional entity known as spacetime. We can imagine this entity like a stretched-out sheet held taut at the corners. If we place a ball on this sheet—or, analogously, planets, stars, or galaxies in spacetime—their mass causes the sheet to bend. The greater the mass, the deeper the curvature.
Since objects in the universe are not stationary, they don’t simply fall into heavier bodies but instead move along curved paths around them. That’s why planets in a solar system orbit their star. So gravity is no longer considered a force, but rather the curvature of spacetime caused by the presence of mass.
Gravity is geometry. But what kind of geometry? Our first thought might be Euclidean geometry—the kind we learned in school—where the shortest distance between two points on a plane is a straight line. But what if spacetime isn’t flat? What if it’s curved like a sphere?
Imagine the Earth and suppose we want to travel from Estonia to Argentina. Even if we follow the shortest path, it won’t be a straight line but a curve due to the Earth’s shape. The type of geometry Einstein proposes for spacetime is called Riemannian geometry.
Although general relativity has successfully explained many phenomena that classical Newtonian theory could not, it may still not be the final answer.
Observations indicate that the universe is expanding. If we could observe the night sky with the naked eye in enough detail, we would see all other galaxies moving away from ours at a uniform speed. This expansion is not yet fully understood, and several hypotheses have been proposed.
One of the most well-known theories involves dark matter and dark energy. If there is something that doesn’t interact with light—hence “dark”—it might explain the universe’s accelerating expansion.
Another approach is to modify the theory of gravity itself. But what does that mean? As we’ve said, gravity is geometry. So can we assume a different geometry?
Mathematically speaking, besides curvature, we can define two more properties of spacetime: torsion and non-metricity. In Einstein’s theory, only curvature is non-zero; torsion and non-metricity are assumed to be zero. But if we allow all three to coexist—or at least two of them—then spacetime no longer follows Riemannian geometry, and the theory of gravity must change as well.
The following diagram illustrates what happens to a vector (an oriented line) when it is subjected separately to curvature, torsion, and non-metricity while being parallel transported in spacetime—that is, moved without changing it deliberately.
So, could an alternative theory of gravity be the final answer?
Although such a theory might explain the expansion of the universe, that is not the only phenomenon we must account for.
Many alternative theories of gravity have already been developed. Some have been ruled out based on experimental data, and among those that remain, each one explains certain phenomena but fails to account for others—none stands out as the most likely.
Maybe none of them are correct because we’re still missing something fundamental. Perhaps we need a radical shift in how we perceive gravity. Perhaps we need a new relativity.
In the second case, two vectors are parallel transported in a geometry with torsion. The result is that the parallelogram we would expect them to form does not “close.”
In the third case, a vector is parallel transported in a geometry with non-metricity. The result is that the length of the vector changes.
References
- https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation
- https://en.wikipedia.org/wiki/General_relativity
- E. Albert, “Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie”, Sitzungsberichte der Preußischen Akademie der Wissenschaften: 142 (1917)
- Supernova Search Team Collaboration, A. G. Riess et al., “Observational evidence from supernovae for an accelerating universe and a cosmological constant,” Astron. J. 116 (1998) 1009–1038
- E. J. Copeland, M. Sami, and S. Tsujikawa, “Dynamics of dark energy,” Int. J. Mod. Phys. D 15 (2006) 1753–1936
- J. Beltrán Jiménez, L. Heisenberg, and T. S. Koivisto, “The Geometrical Trinity of Gravity,” Universe 5 (2019) no. 7, 173