According to Einstein's theory of General Relativity, gravity is a natural consequence of a mass’s influence on space.

I. Einstein, General Relativity and Gravity

Because mass and energy distort the shape of spacetime, the Euclidean geometry of standard textbooks cannot accurately describe it. Einstein’s general relativity uses more complicated math built on the non-Euclidean geometry devised in the 19th century by Bernhard Riemann. With help from his friend Marcel Grossmann, Einstein adopted further advances by the mathematicians Gregorio Ricci-Curbastro, Tullio Levi-Civita and Elwin Christoffel to describe spacetime geometry in terms of mathematical expressions called tensors. Tensors are similar to vectors — quantities, such as velocity, composed of two components (in velocity’s case, speed and direction). Tensors are similar but can encompass more than just two components. Einstein used tensors to develop his equation describing the gravitational field, known as the Einstein field equation.

**Gμν = 8πTμν**
On the left side of Einstein's Field Equation is a tensor describing the geometry of spacetime — the gravitational field. On the right is the tensor describing the matter and energy density — the source of the gravitational field. The equation shows that spacetime geometry equals mass-energy density when adjusted with the proper units and numerical constants. (Actually, the equation stands for a set of multiple equations owing to the complexity of tensors. So experts usually speak of the Einstein field equations, plural.)

**Gμν + Λgμν = 8πTμν**
When Einstein applied his Field Equation to the entire universe, Einstein found that the universe would be unstable, easily disturbed into a state in which spacetime would be either expanding or collapsing. So he added a term that came to be called the cosmological constant, symbolized by the Greek letter lambda. It represents a specific and constant amount of energy density throughout space that would supposedly keep the universe stable and changeless. Later, evidence that the universe was indeed expanding led Einstein to renounce lambda. But it has been revived by modern cosmologists to explain the apparent increase in the universe’s rate of expansion that was discovered in the late 1990s by Saul Perlmutter and his team.

In mid-1915 Einstein saw that there was a way to make relativity truly general. Rather than imposing energy-momentum conservation on the equations, he worked on devising equations that would impose the conservation law on the universe.

Einstein quickly realized that his new theory of gravity was really a theory of the cosmos. In 1917, he wrote a famous paper applying general relativity to the universe as a whole. Today that paper stands as the foundation for modern cosmology. But at the time, Einstein was troubled — his equations implied an unstable universe, either growing or collapsing. In those days, the universe was supposed to be eternal, everlasting and changeless. So Einstein altered his equation, adding a factor called the cosmological constant, representing a constant energy density in space that kept the universe static.

Others were not so sure. Alexander Friedmann, a Russian mathematician, developed a description of an expanding or contracting universe from Einstein’s original equations. Einstein first thought Friedmann to be in error, but then relented, although still viewing the “expanding universe” as of mathematical interest only. When Edwin Hubble’s analysis of light from distant galaxies confirmed the universe’s expansion, Einstein finally agreed to the principle. Despite his own reluctance to accept it, Einstein’s general relativity math did in fact imply what John A. Wheeler of Princeton later called the “most dramatic prediction that science has ever made” — the expansion of the universe.

For weak gravitational fields, the results of general relativity do not differ significantly from Newton’s law of gravitation. But for intense gravitational fields, the results diverge, and general relativity has been shown to predict the correct results. Even in our Sun’s relatively weak gravitational field at the distance of Mercury’s orbit, we can observe the effect. Starting in the mid-1800s, Mercury’s elliptical orbit has been carefully measured. However, although it is elliptical, its motion is complicated by the fact that the perihelion position of the ellipse slowly advances. Most of the advance is due to the gravitational pull of other planets, but a small portion of that advancement could not be accounted for by Newton’s law. At one time, there was even a search for a “companion” planet that would explain the discrepancy. But general relativity correctly predicts the measurements. Since then, many measurements, such as the deflection of light of distant objects by the Sun, have verified that general relativity correctly predicts the observations.

Rather than preventing the universe from collapse, the vacuum energy Einstein describes can explain why the universe now expands at an accelerating pace. General relativity, and it's cosmological constant, today forms the core science for analyzing the history of the universe and for forecasting its future.

But apart from its use in cosmology, general relativity was not widely applied to scientific problems in its first four decades. For the most part, general relativity languished in departments of mathematics, rarely studied in physics.

Shortly after Einstein introduced general relativity, Karl Schwarzschild calculated its implications for the gravity of a massive sphere. Schwarzschild determined that for any given mass there existed a “critical radius” — a limit, he believed, to how small that amount of mass could be compressed. In 1939, Einstein concluded that mass could not be compressed to within that “Schwarzschild radius.” But in the same year, J. Robert Oppenheimer, later to lead America's Manhattan Project for the development of the atomic bombs used against Japan during WWII, and Hartland Snyder, of Northwestern University and later Brookhaven Labs, calculated otherwise, claiming that a sufficiently massive object could indeed collapse within that radius, disappearing from view and leaving only its gravitational field behind.

At the time, nobody paid any attention. But in the 1960s, newfound astrophysical anomalies suggested that gravitational collapse was at work in the cosmos, and Oppenheimer and Snyder’s idea was revived as what came to be known as black holes. Famous for swallowing anything they encounter and allowing nothing to escape, black holes are probably the most bizarre astrophysical consequences of general relativity and gravity. Small black holes have been detected throughout space and supermassive black holes reside in the cores of most galaxies. And we now suspect that smaller black holes, even orbiting pairs of black holes, circle super massive black holes at the center of galaxies.

More recently black holes (schematic of one shown) have been used as thought-experiment laboratories for investigating several outstanding mysteries about the nature of space, time and gravity.

In creating general relativity, Einstein’s had to envision physical processes governing matter, space and time, while at the same time formulating abstract mathematical expressions corresponding to that reality. As a student, Einstein testified, he neglected mathematics. His intuition was not strong enough to guide him to the most profound of math’s many subfields. But in the physical realm of natural phenomena, “I soon learned to scent out that which was able to lead to fundamentals and to turn aside from … the multitude of things which clutter up the mind and divert it from the essential.” At first he didn’t realize that “a more profound knowledge of the basic principles of physics is tied up with the most intricate mathematical methods.” He learned that from his pursuit of general relativity.

Fantastic physical phenomena were first discovered not through the lenses of telescopes, but within the squiggles Einstein had scratched out on paper to make the world make sense — to him. And now physical nature makes sense to modern science only because of Einstein’s insights through thought experiments.

“Einstein’s ideas,” his friend the physicist Max Born wrote over half a century ago, “have given the physical sciences the impetus which has liberated them from outdated philosophical doctrine, and made them one of the decisive factors in the modern world of man.”

See:

University Physics Volume 1, Einstein's Theory of Gravity, Rice University.

"Einstein's genius changed science's perception pf gravity" by Tom Siegfried, 10/4/2015, ScienceNews

"An improved test of the strong equivalence principle with the pulsar in a triple star system⋆"

G. Voisin (1,2), I. Cognard (3,4), P. C. C. Freire (5), N. Wex (5), L. Guillemot (3,4), G. Desvignes (6,5), M. Kramer (5,1), and G. Theureau (2,3,4).

- Jodrell Bank Centre for Astrophysics, The University of Manchester, Manchester, UK

e-mail: guillaume.voisin@manchester.ac.uk, astro.guillaume.voisin@gmail.com
- LUTH, Observatoire de Paris, PSL Research University, Meudon, France
- Station de Radioastronomie de Nançay, Observatoire de Paris, CNRS/INSU, Université d’Orléans, 18330 Nançay, France
- Laboratoire de Physique et Chimie de l’Environnement, CNRS, 3A Avenue de la Recherche Scientifique,

45071 Orléans Cedex 2, Franc
- Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
- LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, 5 Place Jules Janssen, 92195 Meudon, France

Received 6 April 2020 / Accepted 28 April 2020

II. Is Gravity Quantized?

In 2015, however, theoretical physicist James Quach, now at the University of Adelaide in Australia, suggested a way to detect gravitons by taking advantage of their quantum nature. Quantum mechanics suggests the universe is inherently fuzzy—for instance, one can never absolutely know a particle's position and momentum at the same time. One consequence of this

uncertainty is that a vacuum is never completely empty, but instead buzzes with a “quantum foam” of so-called

virtual particles that constantly pop in and out of existence. These ghostly entities may be any kind of quanta, including gravitons.

Decades ago, scientists found that virtual particles can generate detectable forces. For example, the

Casimir effect is the attraction or repulsion seen between two mirrors placed close together in vacuum. These highly reflective surfaces move due to the force generated by virtual photons winking in and out of existence. Previous research suggested that

superconductors might reflect gravitons more strongly than normal matter, so Quach calculated that looking for interactions between two thin superconducting sheets in vacuum could reveal a gravitational Casimir effect. The resulting force could be roughly 10 times stronger than that expected from the standard virtual-photon-based Casimir effect.

Recently, Richard Norte of Delft University of Technology in the Netherlands and his colleagues developed a microchip to perform this experiment. This chip held two microscopic aluminum-coated plates that were cooled almost to absolute zero so that they became superconducting. One plate was attached to a movable mirror and a laser was fired at that mirror. If the plates moved because of a gravitational Casimir effect, the frequency of light reflecting off the mirror would measurably shift akin to the red shift detected from far off celestial objects due to expanding space. As detailed online July 20 in

*Physical Review Letters*, the scientists failed to see any gravitational Casimir effect. This null result does not necessarily rule out the existence of gravitons—and thus gravity’s quantum nature. It may simply mean that gravitons do not interact with superconductors as strongly as prior theories and work postulated, says quantum physicist and Nobel laureate Frank Wilczek of the Massachusetts Institute of Technology, who did not participate in this study and was unsurprised by its null results. Even so, James Quach says, this “was a courageous attempt to detect gravitons.”

Although Norte’s microchip did not discover whether gravity is quantum, other scientists are pursuing a variety of approaches to find gravitational quantum effects. For example, in 2017 two

independent studies suggested that if gravity is quantum it could generate a link known as “entanglement” between particles, so that one particle instantaneously influences another no matter where either is located in the cosmos. A

tabletop experiment using laser beams and microscopic diamonds might help search for such gravity-based entanglement. The crystals would be kept in a vacuum to avoid collisions with atoms, so they would interact with one another through gravity alone. Scientists would let these diamonds fall at the same time, and if gravity is quantum the gravitational pull each crystal exerts on the other could entangle them together.

The researchers would seek out entanglement by shining lasers into each diamond’s heart after the drop. If particles in the crystals’ centers spin one way, they would fluoresce, but they would not if they spin the other way. If the spins in both crystals are in sync more often than chance would predict, this would suggest entanglement. “Experimentalists all over the world are curious to take the challenge up,” says quantum gravity researcher Anupam Mazumdar of the University of Groningen in the Netherlands, co-author of one of the entanglement studies, which was written by Ryan J. Marshman, Peter F. Barker and Sougato Bose (University College London, UK), Gavin W. Morley (University of Warwick, UK) and Steven Hoekstra (University of Groningen, the Netherlands). Instead of the current multi-kilometer-sized LIGO and VIRGO detectors, the physicists working in the UK and in the Netherlands proposed a table-top detector. This device would be sensitive to lower frequencies than the current detectors and it would be easy to point them to specific parts of the sky – in contrast, the current detectors only see a fixed part.

Another strategy to find evidence for quantum gravity is to look at the cosmic microwave background radiation, the faint afterglow of the big bang, says cosmologist

Alan Guth of M.I.T. Quanta such as gravitons fluctuate like waves, and the shortest wavelengths would have the most intense fluctuations. When the cosmos expanded staggeringly in size within a sliver of a second after the big bang, according to Guth’s

widely supported cosmological model known as inflation, these short wavelengths would have stretched to longer scales across the universe. This evidence of quantum gravity could be visible as swirls in the polarization, or alignment, of photons from the cosmic microwave background radiation.

However, the intensity of these patterns of swirls, known as

B-modes, depends very much on the exact energy and timing of inflation. “Some versions of inflation predict that these B-modes should be found soon, while other versions predict that the B-modes are so weak that there will never be any hope of detecting them,” Guth says. “But if they are found, and the properties match the expectations from inflation, it would be very strong evidence that gravity is quantized.”

Another way to find out whether gravity is quantum is to look directly for quantum fluctuations in

gravitational waves, which are thought to be made up of gravitons that were generated shortly after the big bang. The Laser Interferometer Gravitational-Wave Observatory (LIGO) first detected gravitational waves in 2016, but it is not sensitive enough to detect the fluctuating gravitational waves in the early universe that inflation stretched to cosmic scales, Guth says. A gravitational-wave observatory in space, such as the Laser Interferometer Space Antenna (

LISA), could potentially detect these waves, Wilczek adds.

In

a paper recently accepted by the journal

*Classical and Quantum Gravity*, however, astrophysicist Richard Lieu of the University of Alabama, Huntsville, argues that LIGO should already have detected gravitons if they carry as much energy as some current models of particle physics suggest. It might be that the graviton just packs less energy than expected, but Lieu suggests it might also mean the graviton does not exist. “If the graviton does not exist at all, it will be good news to most physicists, since we have been having such a horrid time in developing a theory of quantum gravity,” Lieu says.

Still, devising theories that eliminate the graviton may be no easier than devising theories that keep it. “From a theoretical point of view, it is very hard to imagine how gravity could avoid being quantized,” Guth says. “I am not aware of any sensible theory of how classical gravity could interact with quantum matter, and I can't imagine how such a theory might work.”

See:

"Is Gravity Quantum" By

Charles Q. Choi on August 14, 2018,

*Scientific American*
"A stepping stone for measuring quantum gravity" University of Groningen, 18 August 2020.