Mathematician David Hilbert developed general relativity equations before Einstein

To develop general relativity, Einstein relied on his college friend, Marcel Grossman

Recognizing the mathematical complexities of generalizing special relativity with a new picture of gravity and acceleration, Albert Einstein had Grossman introduce him to tensor calculus. Years before developing the precursor to GR together, Einstein would use Grossman's lecture notes to prepare for his exams.

Albert Einstein's theory of gravity arose from what he described as 'the happiest thought of his life': realizing that a person who fell off the roof of their house would not feel their own weight as they fell.

Visualizing Einstein's special relativity

Before Einstein developed his theory of general relativity, he worked out what is known as special relativity—or why time is experienced different for different observers. The breakthrough rests on his theory that light travels at a constant...

Explore Albert Einstein's Zürich notebook and review his notes on relativity

Within the pages are calculations, sketches and his first attempts at deriving what would be the field equations for gravity. It also documents some dead ends and the difficulties Einstein encountered as he describes part of the mathematics of what would become general relativity, describing it as "too involved."

A breakdown of the experimental test results supporting the general theory of relativity

Besides accurately explaining the slight wobble observed in Mercury's orbit, general relativity predicted that light would bend around massive objects by an amount matching what was observed when background starlight bent around the sun during an eclipse. The theory also predicted the existence of gravitational waves and black holes decades before they were found.

Scientists validated Albert Einstein's theory of gravity by measuring the apparent positions of stars via their starlight as it traveled near the sun on its way to Earth during a total solar eclipse.

Einstein created a mathematical term for anti-gravity to keep the universe static

General relativity predicted that the gravity of all the matter in the universe would cause it to collapse, contradicting the belief at the time that the universe was constant and unchanging. Albert Einstein added the cosmological constant to his equations, which acted like anti-gravity, to "fix" his math.

Nearly 50 years before the first observational evidence, a soldier fighting on the Eastern Front in World War I found a mathematical solution to Einstein's equations that suggested the existence of black holes.

Quantum mechanics and general relativity—two of the most successful explanations of the physics seen across the universe—are logically incompatible with one another because they use contradictory models for space and time.

Discoveries in electromagnetism, which suggested that light traveled at a single speed, became the catalyst for overturning Isaac Newton's view that all speeds are relative and could appear to change based on one's perspective.

One of Einstein's papers challenged quantum theory but helped confirm entanglement

In 1935, Einstein suggested that quantum mechanics was incomplete due to its strange implications about entangled particles. Their challenge led to decades of experiments that eventually proved distant particles could affect each other instantly.

While special relativity describes motion along a flat underlying fabric of the universe called spacetime, general relativity extends this theory to explain motion through curved spacetime.

Explore a simplified breakdown of the Einstein field equations

Often depicted as one formula, Einstein's equation represents a suite of 16 nonlinear partial differential equations, which can be simplified to six unique ones, that relate the geometry of spacetime to the presence of mass and energy.

Gravitational waves—ripples in spacetime that result from the motion of objects—were detected a century after Albert Einstein predicted their existence upon developing his theory of gravity.

During his 'miraculous year,' Einstein published four groundbreaking papers

The 1905 "annus mirabilis" papers explained the photoelectric effect, Brownian motion, the absolutism of the speed of light, and mass-energy equivalence, revolutionizing scientists' understandings of space, time, mass, and energy. For the discovery of the photoelectric effect, Einstein won the 1921 Nobel Prize in Physics.

Special relativity shows how motion at high speeds reshapes time, space, and energy

Einstein’s 1905 special theory of relativity revealed that the speed of light is absolute in the universe, forcing time and space to vary with one's speed. This idea led to the famous equation E=mc2, which shows that mass and energy are interchangeable.

Einstein’s theory of special relativity

Special relativity, formulated by Einstein, describes how space and time are linked for objects moving at constant speeds. It states that the speed of light is constant for all observers, leading to time dilation (moving clocks run slower), length contraction (moving objects shrink), and mass-energy equivalence (E = mc²). This video breaks down how motion and time are fundamentally related.

How neutron stars serve as laboratories for testing Einstein's theory of gravity

Data from a 16-year study of an orbiting pair of spinning neutron stars showed that measurements of gravitational wave energy and the bending of light around the system were consistent with predictions made by general relativity to an accuracy of at least 99.99% across seven tests. (Some readers may experience a paywall.)

The mathematics of general relativity does not rule out the existence of wormholes

Such objects, also known as Einstein-Rosen bridges, would resemble funnel-like tunnels connecting two regions of spacetime, allowing for instant travel across the universe. However, such structures would be incredibly unstable and require undiscovered materials with negative energy to keep them open.

Einstein and the fourth dimension

How Einstein's greatest theoretical achievement contains a simple but mind-bending proposition—the dimension of time is physically connected to the three observable spatial dimensions.

Experimenting with space-time

Einstein's theory of general relativity—that mass literally bends space and time—can be difficult for the human brain to imagine. This interactive resource lets you create celestial objects, imagine their effect on space-time, and see how they interact with each other (best viewed on desktop).

The first interferometric gravitational wave detector was invented in 1972

Robert Weiss completed the designs after his students asked about an earlier apparatus that used stretched aluminum cylinders to detect passing gravitational waves. Unfamiliar with general relativity and hoping to keep the course focused on experimental tests rather than mathematics, Reiss later asked his students to consider his device for homework. (Some readers may experience a paywall.)

Observations of colliding neutron stars by the Laser Interferometer Gravitational-Wave Observatory in 2017 confirmed that gravity travels at the speed of light.

General relativity describes a singularity as the final moment in time

Using Penrose diagrams—mathematical structures that compress all of space and time—physicists can observe the path of light and which events can affect one another. The space-time maps help visualize the structure of black holes and describe what happens when objects fall in.

Uncertainties in measurements make finding gravity's Newtonian limit unclear

Although Newton's "universal" law is unreliable in strong gravitational fields when compared with the field equations of general relativity, it is still taught for its accuracy on everyday scales. However, gravity's effect on small scales is too weak to be measured reliably, its accuracy at atomic scales remains unknown.

Within Einstein's picture of the universe, gravity is technically not a force because forces cause accelerations that deviate objects from their natural path, and moving solely due to gravity is natural.

Understanding how gravity works at the quantum scale is physics's greatest challenge

While the theory of general relativity explains how gravity works and quantum mechanics explains interactions at the subatomic scale, the two frameworks contradict one another. Developing a model of gravity mediated by particles can help complete the Standard Model.

Stephen Hawking's biggest discovery—Hawking radiation—came from a major mistake

Hawking radiation may not have been discovered without Jacob Bekenstein first convincing Stephen Hawking that black holes follow the laws of thermodynamics. The graduate student showed that black holes could shrink, setting the stage for Hawking's most significant contribution.

Albert Einstein taught courses in Davos

This silent video from the 1920s shows footage of Einstein at Davos. The famous scientist spent time there, delivering public lectures on his theory of relativity as part of the town’s university courses.

Explore a visualization of curved spacetime under general relativity

While depictions involving bends in elastic fabrics are common to illustrate gravity, they are circular representations that rely on gravity in the real world to depict gravity in the model. The river model instead shows how bends in spacetime convert speed through time into speed through space, producing acceleration.

Because some models of the universe do not incorporate time, it may be an emergent property born from our limited perception of the universe, rather than a fundamental property of reality.

The graviton may be the last missing piece of the Standard Model

While the electromagnetic, strong nuclear, and weak nuclear forces can be explained through interactions with particles, gravity is instead best modeled through spacetime curvature. Discovering a quantum particle of gravity would unite the two pillars of modern physics—quantum mechanics and general relativity—toward developing a theory of everything.

Understanding time dilation

The faster you go, the slower time ticks for you. And the stronger the gravitational field acting on you, the slower time ticks for you. These phenomena – collectively called time dilation – were first explained by Albert Einstein’s theories of general and special relativity. In this 11-minute video, beloved astrophysicist Neil deGrasse Tyson explains them to comedian Chuck Nice.

A Belgian Catholic priest was the first to come up with the idea for the Big Bang

In 1931, Georges Lemaître presented his radical idea that the universe came from a “primeval atom,” challenging the long-held belief that the universe had always existed. Einstein initially dismissed Lemaître’s work as having “abominable” physical insight, only to accept it later.

Antimatter was predicted to exist four years before it was observed, though the mathematics responsible for the prediction described it as matter with negative energy.

Understanding how and when time began requires a theory of quantum gravity

Rewinding the universe to the big bang compresses all matter, energy, space, and time into a single point, necessitating a model that combines general relativity with quantum mechanics. Although physicists understand time to have begun when the universe did, a clear understanding of the mechanisms involved remains unclear.

The Big Bang became physically plausible thanks to Stephen Hawking’s thesis

Stephen Hawking's PhD thesis mathematically showed that singularities—points of no volume and infinite density—are an expected feature of nature. It laid the theoretical groundwork for a model of the universe where everything originates from a single point.

Massive objects can significantly bend light to produce gravitational lensing

The theory of general relativity posits that mass and energy bend space and slow down the passage of time. One consequence is that massive objects, such as black holes, curve spacetime to such an extent that light from background sources can loop around them, producing multiple images or ring-like patterns.

How string theory explains gravity on the quantum scale, but may be untestable

Combining the general theory of relativity with quantum field theory creates nonsensical mathematical outcomes, such as probabilities of infinity. These are resolved by treating particles as vibrating strings rather than points of matter. However, probing the scale of these strings to validate the theory requires technology equivalent to a particle accelerator the size of the solar system.

The underlying fabric of the universe—spacetime—changes shape in the presence of mass and energy, which affects measurements of space and time.

Worried that Nazi Germany could weaponize nuclear fission first, Albert Einstein wrote a 1939 letter warning President Roosevelt about the possibility of atomic bombs—a decision he later regretted.

Creating 'Interstellar's' black hole blended visual effects with real physics models

Theoretical cosmologist Kip Thorne was consulted and collaborated with the film's visual effects team to develop new rendering software, integrate general relativity, and generate ultra-high-resolution visuals. The results were so accurate, they were published in scientific journals.

Georges Lemaître, a Belgian Catholic priest who proposed the Big Bang theory in 1931, became president of the Pontifical Academy of Sciences in 1960.

By measuring them in hot-air balloons during a partial solar eclipse and at night, Victor Hess discovered cosmic rays and concluded they came from beyond the solar system.

Despite his disability, Stephen Hawking reshaped our understanding of black holes

His theoretical work—especially on black holes emitting radiation, now known as Hawking radiation—challenged long-held ideas. He also brought complex physics to the public through bestselling books like "A Brief History of Time."

View a gallery of Einstein rings

As light from a distant galaxy spreads in all directions, rays that pass around a massive object, such as another galaxy, may be bent around it. If the massive object is positioned between the distant galaxy and our telescopes, we may observe this deflected light forming a ring around it.

A look at the giants of quantum mechanics

German physicist Max Planck publishes his groundbreaking study of the effect of radiation on a “blackbody” substance, and the quantum theory of modern physics

LIGO made the first detection of gravitational waves

On February 11, 2016, scientists at the Laser Interferometer Gravitational-Wave Observatory announced the confirmed detection of ripples in spacetime, which were produced from the collision of two black holes 36 and 29 times the mass of the sun. The detection confirmed that gravitational waves travel at the speed of light, as predicted by Albert Einstein in 1915.

The interaction of quantum fields with black hole curvatures makes Hawking radiation

The classic explanation of Hawking radiation depicts virtual photons emitted from a black hole's event horizon. A more accurate explanation involves null geodesics, Bogoliubov transformations, and scattered quantum field nodes to explain the emission of thermal radiation.

Gravity Probe B verified that rotating objects drag spacetime

The experiment involved attaching four freely floating gyroscopes to a telescope aimed at a distant star for a year. The observed angular shift of the gyroscopes as a result of Earth's rotation pulling on spacetime was approximately 0.0000012 degrees from the amount predicted by general relativity.