Newton and Einstein: Two Visions for the Same Mystery

From attraction to curvature: a conceptual revolution

Gravity is the most familiar of the fundamental forces, but also the most mysterious. From Newtonian universal attraction to the curvature of spacetime described by Einstein, the concept has evolved profoundly. Understanding gravity means following an intellectual adventure spanning more than three centuries, marked by two great physical theories that have transformed our vision of the universe.

Newton: the universal force

In 1687, Isaac Newton (1643-1727) formalized the law of universal gravitation in his Philosophiæ Naturalis Principia Mathematica. He postulated that an attractive force acts between two massive bodies:

$$ F = G \frac{m_1 m_2}{r^2} $$

where \( F \) is the gravitational force, \( m_1 \) and \( m_2 \) are the masses, \( r \) is the distance between the centers of mass, and \( G \) is the gravitational constant. This law explains the motion of planets, projectiles, and tides, and remains valid in most everyday cases.

Newtonian Limit

Newton recognized a philosophical flaw in his own theory: how can a mass "know" that another mass exists at a distance to attract it instantaneously, without any mediating support? This "instantaneous action at a distance" was criticized, particularly by supporters of a mechanical space, such as Huygens or later Einstein.

Einstein: gravity is geometry

In 1915, Albert Einstein (1879-1955) proposed a radically different vision with his theory of general relativity. It is no longer a force but a deformation of spacetime caused by mass and energy. Massive objects "bend" spacetime, and other objects follow these curvatures, like a marble following an inclined track:

$$ R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8 \pi G}{c^4} T_{\mu\nu} $$

This Einstein equation relates geometry (Ricci tensors, scalar curvature, metric) to the matter-energy content of the Universe (\( T_{\mu\nu} \)). It predicts phenomena unknown at the time: black holes, gravitational waves, cosmic expansion...

Einsteinian Limit

Incompatibility with Quantum Mechanics

General relativity is a continuous geometric theory, while quantum mechanics is based on discrete fields and probabilities. These two descriptions of the world are fundamentally incompatible. When attempting to unify gravity and quantum mechanics, current mathematical tools lead to divergences and inconsistencies. This is why there is still no fully accepted quantum theory of gravitation.

Singularities and Loss of Predictability

Under certain extreme conditions, such as at the center of a black hole or at the moment of the Big Bang, Einstein's equations predict singularities, where the curvature of spacetime becomes infinite. These areas elude any physical description and signal a breakdown of the model. General relativity, although extremely precise, then becomes inoperative, as it ceases to predict deterministic results.

Absence of Mediating Particle

Unlike other fundamental interactions that are expressed within the framework of the standard model using mediating particles (photon, W/Z bosons, gluon), gravity does not have a confirmed gravitational boson. The graviton, a hypothetical particle with spin 2, is suggested by certain theoretical approaches (strings, loops), but has never been detected or integrated into a coherent quantum framework.

Unresolved Cosmological Problems

General relativity is not sufficient to explain certain modern cosmological observations. It is necessary to introduce dark matter (to explain the dynamics of galaxies) and dark energy (to account for the acceleration of the expansion of the universe). These entities represent about 95% of the content of the universe, but their physical nature remains unknown, suggesting that the current theory of gravity is incomplete.

Comparative Table of Gravity Theories

Today's Gravitational Mysteries

Gravity Still Not Quantized

Despite the phenomenal success of general relativity in describing gravitational phenomena on a large scale, we still do not have a coherent quantum formulation of gravity. Unlike other fundamental forces, described within the standard model by quantum fields and mediating particles (such as the photon for electromagnetism), gravity eludes this quantization.

Unification attempts—such as string theory or loop quantum gravity—propose promising mathematical frameworks, but none have yet produced verifiable predictions or direct experimental evidence. The existence of the graviton, a hypothetical spin-2 boson associated with gravity, remains purely theoretical and undetected.

Black Holes and the Limits of Relativity

Black holes are extreme objects where density becomes such that the curvature of spacetime diverges. They represent both a triumph and a limit of general relativity. Although their macroscopic properties (event horizon, Schwarzschild radius, tidal effects) are well described, the interior of black holes—particularly the central singularity—eludes any coherent physical description.

Furthermore, the paradoxes associated with these objects, such as the information paradox (loss of information in Hawking evaporation), highlight the conflict between general relativity and quantum mechanics, reinforcing the need for a theory of quantum gravity.

Dark Matter: An Invisible Gravitational Effect

Measurements of the rotational speed of galaxies, gravitational lenses, and the formation of large-scale structures reveal gravitational effects inexplicable by visible matter alone. To account for these anomalies, astrophysicists postulate the existence of dark matter: a form of non-baryonic, invisible matter, interacting only through gravity.

Despite several decades of research, no dark matter particles (axions, WIMPs, etc.) have been detected. It is possible that these effects are due to a modification of the laws of gravity on a large scale, as suggested by alternative theories such as MOND or TeVeS.

Dark Energy and Cosmic Acceleration

In 1998, observations of Type Ia supernovae revealed that the expansion of the universe is not simply continuous, but accelerating. This unexpected phenomenon is attributed to a mysterious form of energy, called dark energy, responsible for a dominant negative pressure on a cosmological scale.

According to the standard cosmological model (ΛCDM), this dark energy represents about 68% of the total energy content of the universe. It is often modeled as a cosmological constant \( \Lambda \), but its deep nature remains unknown: is it a property of the quantum vacuum, a new particle, an unexplored interaction, or a manifestation of modified gravity?

Towards a Unified Gravity

All these mysteries suggest that general relativity, although very precise, is only an approximation of a deeper theoretical framework. The ultimate goal of fundamental physics remains the unification of the four interactions—gravitational, electromagnetic, weak, and strong—into a theory of everything (TOE, Theory of Everything).

Approaches such as superstring theory, loop quantum gravity, non-commutative geometry, or holographic models (holographic principle, AdS/CFT correspondence) attempt to address this challenge. But none have yet allowed experimental validation. One of the major challenges of the 21st century will be to uncover the true gravitational laws that govern the extreme regimes of the universe.

References:
• Newton I., Philosophiae Naturalis Principia Mathematica, 1687.
• Einstein A., Die Feldgleichungen der Gravitation, Preussische Akademie der Wissenschaften, 1915.
• Misner, Thorne, Wheeler, Gravitation, W.H. Freeman (1973).
• Will, C.M., The Confrontation between General Relativity and Experiment, Living Reviews in Relativity, 2014.

Source: Gravitation, Misner, Thorne & Wheeler (1973) – Princeton University Press; C.M. Will, The Confrontation between General Relativity and Experiment, Living Reviews in Relativity (2014); S. Carroll, Spacetime and Geometry, Addison-Wesley (2004).