Einstein and the fourth dimension

Imagining a fourth dimension

Famous astronomer Carl Sagan attempts to describe what it's like to think about the fourth dimension using the famous Flatland example from author Edwin Abbott in this classic video.

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.

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.

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).

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...

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.

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.

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.

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

Time disappears when encompassing all quantum configurations across the universe

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.

According to the physics of black holes, our 4D reality may be a hologram—a projection of information coded on a 2D surface on the edge of the universe.

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.

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.

One model of the universe expresses all constants using only time

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.

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.

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.

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.

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.

The wave nature of matter can produce phenomena like negative time and retrocausality

Within quantum mechanics, matter simultaneously exists as both fixed particles and extended waves, allowing it to emerge across barriers—just as sound travels through walls—before it fully enters the obstacle. The resulting measurements can show that particles spent negative time within a barrier, with the future occurring before the past.

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.

According to the special theory of relativity, because the passage of time depends on how quickly objects move through space, people will not agree on the order of events they observe if they are moving at different speeds.

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."

The universe expands by stretching space itself, not into anything beyond it

Thanks to Einstein’s relativity and Hubble’s observations, scientists understand that space stretches, like rising bread dough between raisins, with no "outside" to expand into. Some theories suggest our universe might be just one "bubble" in a vast multiverse, possibly floating on a higher-dimensional surface called a brane.

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.

What Stephen Hawking said about time travel

When renowned theoretical physicist Stephen Hawking did not rule out the possibility of time travel in his posthumous book Brief Answers to the Big Questions, many hopefuls got excited. But, unfortunately for them, Hawking believed that yet-to-be discovered laws of physics will prove time travel impossible. This piece outlines some practicalities about the speed of light and wormholes that lend way to Hawking’s prediction.

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

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.

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.

The Planck time, equal to 5.39 × 10⁻⁴³ seconds or less than a millionth of a trillionth of a trillionth of a trillionth of a second, is the smallest unit of time that could ever be theoretically measured.

Quantum field theory, which has made predictions accurate to 12 decimal places, explained

Instead of being made of indivisible particles, all visible matter in the universe is built from underlying quantum fields—smooth, invisible entities that behave like waves and extend throughout space and time. The theory suggests these fields are fundamental, and particles are disturbances that move through them.

What is space-time?

Space-time is a complex subject, but this Livescience article makes an effort to disentangle the topic. Somewhat akin to a sheet of rubber that can be warped and bent in parts, space-time is a bit more involved that that. However, the analogy makes this and other aspects of the concept simpler to grasp.

The ideas of Einstein and Freud combined in 'The Persistence of Memory'

The Persistence of Memory was painted on a canvas roughly the size of a sheet of paper, depicting a desolate landscape with melting clocks, ants, and a distorted figure. The piece incorporates Freud and Einstein's ideas, resulting in a haunting composition symbolizing time's fluidity and Dalí's personal anxieties.

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.

Mathematician David Hilbert developed general relativity equations before Einstein

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.

Within quantum physics, the order of events across time may not follow causality

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 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.

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.

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.

In the 'block universe' model, the past, present, and future exist simultaneously

According to special relativity, observers do not experience the same events in the same order, but all perspectives are valid. This means what is considered one person's as yet unexperienced future may have already taken place in someone else's past.

Is time travel really possible?

The laws of physics, as currently understood, don’t categorically reject the possibility of time travel. But, scientists are skeptical, especially when it comes to traveling to the past. Hopping between past, present and future would require the world to have some wacky yet-to-be-discovered physical properties like negative mass, negative energy, and infinite density. Time travel also introduces philosophical questions about free will, causality, and chronology.

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.

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.

Photons do not experience distance or the passage of time.

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.

Time seems to stop for objects at the event horizon of black holes

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.

The Standard Model reveals an underlying organization to the universe

Using the framework of quantum field theory, it structures all known particles into 12 matter particles, alongside five particles that carry three of the four fundamental forces. Although remarkably precise and predictive, it cannot yet explain gravity, dark matter, or dark energy.

Within topology, time can be modeled as restarting after reaching its 'edge'

A manifold is any space that appears flat when zoomed in close enough, even if it is globally curved. Some of these structures can be curved to connect back on themselves, much like bending a line into a circle. This property can be mathematically established in a four-dimensional manifold by allowing time to loop back on itself.

Tachyons are theoretical particles that travel through space faster than light

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.

Wormholes, though unstable, would offer a theoretical shortcut through spacetime

These hypothetical distortions in the fabric of spacetime may connect vast distances across or even between universes. While science fiction often portrays them as traversable tunnels, the energy and matter required to keep a wormhole open defy current physical understanding.

Zooming out from Earth to the edge of space

For perspective on the universe's absolute massiveness, watch this four-minute video. Beginning at a facility in Germany, the "camera" pulls back revealing the surrounding countryside, Germany itself, Europe, the Earth, and so on. At one point stars form galaxies and galaxies, at a distance, become as seemingly "small" as the individual stars.