Visualize how the order of events changes, according to special relativity, when the perspective is changed between observers who move relative to one another.

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.

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).

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.

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.

When objects emit or reflect light, it takes time for the light to reach an observer and be detected. During the travel time, the object may have changed, limiting detections to describing the conditions of the object when the light was first emitted or reflected, before it was detected.

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.

Although working independently of one another, the two exchanged correspondence in the lead up to November 1915, when Hilbert submitted their gravitational field equations five days before Einstein presented their work. An error in Hilbert's formulation and its nonpublication until March 1916 would leave credit for general relativity to Einstein.

The phenomenon, known as the Doppler effect, is the result of experiencing an increase in the frequency of observed waves when approaching a source and a decrease when moving away. Because this property corresponds to color, approaching objects appear bluer than normal—blueshift—and receding objects appear redder than usual—redshift.

Although time is considered a fixed, ordered mapping of events, where the past affects the future, quantum superposition breaks down causality, suggesting that future events can occur simultaneously with past ones. Within the quantum model, the notion of cause and effect is not a fundamental feature of our universe.

The equations of special relativity require these objects to possess imaginary mass, and they would travel faster the more energy is taken away from them. The existence of tachyons would necessitate an unknown form of matter and lead to paradoxes involving information that can hypothetically travel backward in time.

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."

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.

The Wheeler-DeWitt equation, a modified version of the Schödinger equation—the formula that describes the evolution of the quantum configuration of a system—describes the quantum state of space-time across the universe. The transformation causes the variable of time to disappear, suggesting it is not a fundamental, physical parameter of the cosmos.

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.

About seven base units, such as meters for length, have historically been used to describe everything in our physical reality. However, researchers have shown that, through relativistic space-time, clocks can serve as replacements for rulers, scales, and other instruments, allowing everything to be measured in terms of time.

As electromagnetic waves interact with particles in a transparent medium, particles vibrate and generate their own electromagnetic waves. The interference of the original and generated waves, which are slightly delayed, results in ensemble light with an effective slower speed but unchanged color.

At that location, the warping of space-time is so severe that the entirety of an object's space-time motion is solely through space, leaving it immobile in the time dimension. Faraway observers looking at the object would see it appear frozen before slowly dimming and reddening.

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.

Einstein's model of light as a wave and a massless particle of energy revolutionized physics, and scientists' application of the model led to groundbreaking technologies, including medical imaging and treatments, telecommunication signals, and probes of the quantum and cosmological realms.

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.

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.

In "Velocity Raptor," space and time warp as you make your way across a room of obstacles at "normal" speeds. Take advantage of these relativistic effects to solve puzzles involving clocks running at different rates and colors shifting as a result of your movement.