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What if Einstein was wrong?

by Miguel A. S. Pinto

Yes, I have asked the question: what if the most widely recognized physicist ever was actually wrong? Perhaps wrong is too hard of a word, especially in science, but let us say, partially incorrect. Allow me to elaborate. Physical theories, like any other scientific theories, are not perfectly exact descriptions of reality but approximate representations of the human perception of reality. Of course, this is absolutely normal, as the phenomena that happen in our world may be much more complex than we can imagine due to our biological and intellectual limitations.

Indeed, from a historical point of view, we have seen that, sooner or later, physical theories start to be incapable of explaining some observations. It happened, for example, with the famous law of universal gravitation introduced by Sir Isaac Newton (1643-1727), which was the first scientific theory to successfully describe how gravity works. Although Newton achieved an incredible feature, that is to describe both the free fall motion of objects on our planet and many celestial orbits with the same underlying physics (bear in mind that in the period he lived, the Earth and the skies were taken to be totally disconnected), his theory was not a match for the closest friend of our Sun, Mercury. You see, unlike the orbits of other planets in our solar system, Mercury’s orbit shifts over time (see Figure 1 for more context), and this contradicted both Newton’s and Kepler’s laws because, in such a framework, it should not happen. One of the scientists who tried to come up with a solution was Urbain Le Verrier (1811-1877), who predicted the existence of the planet Neptune. Le Verrier hypothesized the existence of a hidden planet close to Mercury that could provoke this particular phenomenon that was undetected on the other planets. However, such a planet was never observed, and despite many tentatives, no one could find the reason behind this strange behavior. Therefore, by the beginning of the 20th century, the scientific community looked at this problem as a limitation of Newton’s theory.

Figure 1: A slightly exaggerated representation of the perihelion precession of Mercury, a phenomenon in which the orientation of the elliptical orbit of the planet Mercury gradually shifts over time. Image taken from

Then, who was the brilliant mind that solved this issue? Well, I bet you already know the answer: our beloved Albert Einstein (1879-1955)! With his theory of General Relativity, Einstein began a revolution in the paradigm of gravitational physics because we started to look at gravity as a geometric dance between the union of space and time and the matter within it rather than an instantaneous force acting at a distance as considered by Newton. In fact, Einstein could also predict other wonders in our Cosmos, with the most evident examples being black holes and gravitational waves. Although we still have some questions regarding the existence of black holes, the truth is that with our most recent observations, we have a clear indication that certain extremely massive objects exist at the center of galaxies, including ours, whose general appearance coincides with such astrophysical objects. In addition, gravitational waves were detected for the first time in 2015, curiously 100 years after Einstein formulated his theory. Since this detection, we have had a new window of opportunities to study the very early stages of the Universe. On top of that, General Relativity continues to pass test after test, which cements its status as the consensual scientific understanding of gravity.

Figure 2: A representation of gravitational waves, space-time ripples created when a very strong gravitational event happens, such as two neutron stars orbiting each other. Image taken from

Nonetheless, we may be entering a peculiar time in history in which General Relativity faces similar difficulties as Newton’s theory in the first few years of the 20th century. By observing distant supernovas, cosmologists know that the Universe is experiencing an accelerated expansion now. However, such an expansion indicates that something is exercising an anti-gravitational effect, as gravity tends to attract objects towards each other. In principle, this may not be a problem, as we can incorporate this behavior into Einstein’s equations (which we assume describe gravity in large cosmological scales) through a form of energy called the cosmological constant, an exotic fluid that repels objects. (As a matter of fact, Einstein was the first to do so in 1917.) Although we do not find any substance like this in our everyday world, if we dig enough into the very short quantum scales, we find an intriguing form of energy that also tends to repel objects called vacuum energy, an energy related to entities known in physics as quantum fields. Yet, while the cosmological constant and the vacuum energy share the same property, the experiments suggest they are somehow two separate things. This problem, commonly referred to in the scientific literature as the Cosmological Constant Problem, is the seed of a perhaps more serious issue: if the only manner we can provide insight into what leads to the current cosmic acceleration is by assuming the existence of a cosmological constant and this entity is not the vacuum energy, then it could be that General Relativity may be incomplete, at least at cosmological scales. There are other (mostly theoretical) problems with Einstein’s masterpiece, but this has been the primary driver of an alternative line of research that aims to answer the accelerated expansion: modified gravity theories.

Modified gravity theories are alternatives (or extensions, depending on the theory/point of view) to Einstein’s theory. Indeed, the first modified theories were primarily motivated by intellectual ambitions and not by a particular observation. The first one was carried out by Hermann Weyl (1885-1955) in 1918, only three years after Einstein published the final version of General Relativity. At the time, Weyl tried to unify gravity with electromagnetism, in the sense that these two interactions would be somehow interconnected, pretty much of what Newton did with the “Earth” and “Sky” Physics in the 17th century. While Weyl could not fulfill his desire, his contributions had an incredible impact on particle physics, demonstrating that sometimes we start somewhere and finish in a place we could not imagine. For the remaining of the 20th century, other physicists also tried their luck in modifying the gravitational laws. Right after Weyl, Theodor Kaluza (1885-1954) and Oskar Klein (1894-1977), proposed a theory that aimed to unite gravity and electromagnetism as well. Whereas Weyl altered the geometry on which General Relativity is based, Kaluza and Klein added an extra spatial dimension to the three we encounter in our everyday lives to account for new physics. Furthermore, they postulated that this 5th dimension should be compactified (sort of curled up) so that we could not notice it. For this reason, it is widely regarded as a precursor of string theory, one of the current candidates for a “theory of everything”. Interestingly enough, another physicist who worked in modified gravity was Einstein himself! Alongside Elie Cartan (1869-1951), they developed a theory that interprets gravity as a geometrical effect, identical to General Relativity, but with the remarkable advantage that can be, to a certain extent, related to quantum mechanics. Later, in the 60s, following the works by Pascual Jordan (1902-1980), Robert Dicke (1916-1997) and his PhD student Carl Brans (1935-present) came up with a gravitational theory later known as Brans-Dicke theory. This alternative theory combines the equivalence principle, a pillar of General Relativity, with Mach’s principle, which states that “the gravitational constant should be a function of the mass distribution of the Universe”. A noteworthy mention goes to Hans Adolf Buchdahl (1919-2010), whose groundbreaking work involved formulating a theory capable of generalizing Einstein’s equations. This theory, now identified in the literature as f(R) (reads f of R) gravity, remains a significant contribution to our understanding of gravity.

Nowadays, everyone who works in modified gravity is doing their best to theoretically describe the cosmic acceleration, following in the footsteps of these precursors. Either by altering the principles of General Relativity, adding extra contributions or dimensions, there is a taste for everyone. I do not know what the future holds, but if the upcoming data from novel telescopes, such as Euclid, contradicts the Standard Cosmological Model and, thus, General Relativity, my bet is on the modified gravity scenario. Otherwise, I guess Einstein was right after all.

February 8, 2024