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.

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).

Time may be an emergent, rather than a fundamental, property of the universe

Some theories of everything—mathematical models that try to explain all aspects of the universe, including quantum phenomena and gravity—do not incorporate time. If a time-neglecting version of such a theory were ever validated, it might suggest that time is a feature that emerges from our limited perception of the universe.

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.

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.

Discoveries in electromagnetism became the catalyst for overturning Isaac Newton

To maintain the consistency of experimental results involving electricity, magnetism, and light, time and space had to cease being absolute and could change in value to keep the speed of light constant. This cosmic speed limit forced Einstein to revise the existing model of gravity.

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.

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.

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.

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.

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.

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.

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.

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.

The Planck time is the smallest unit of time that could ever be theoretically measured

Equal to about 5.39 × 10⁻⁴³ seconds, the unit is derived from calculating how long it would take light to travel the Planck length—the smallest theoretically measurable length. Quantum physics allows events to occur on smaller timescales, making them undetectable and their order to lose meaning.

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.

Four video explainers on quantum fundamentals

Ready to level up your working knowledge of quantum mechanics? Check out these four TED-Ed Lessons written by Chad Orzel, associate professor in the Department of Physics and Astronomy at Union College

'Imagination is more important than knowledge. For knowledge is limited, whereas imagination embraces the entire world.'

- Albert Einstein

The extreme precision of atomic clocks highlights gravitational time dilation

Scientists at the National Institute of Standards and Technology have constructed clocks made out of stacked strontium atoms, which show differences in the passage of time across just a millimeter of height consistent with predictions from general relativity, where atoms closer to Earth's center tick off time more slowly.

Explaining the many-worlds interpretation

A mind-bending, jargon-free account of the popular interpretation of quantum mechanics, helping to explain how something can be in two states at once.

Explore our favorite visualization of the immense scale of space, from an astronaut to the size of the observable universe

Against his wishes, Albert Einstein's brain was removed before his cremation, and the pathologist responsible stored it for decades in mason jars within a beer cooler.

See the most iconic photos from four decades of LIFE magazine

Clever Hans was a 1900s horse that was believed to be able to solve math equations, tell time, and read and comprehend German, until a psychology student discovered how he got his answers.

While atoms are normally made of protons, neutrons, and electrons, exotic ones have been built with antimatter—alternate versions of normal matter that live for fractions of a second and are about a billion times as rare.

Chaos theory—informally known as the butterfly effect—is the reason why weather forecasts are presented with probabilities rather than certainties.

Existentialist writer Jean-Paul Sartre coined the famous phrase 'Hell is—other people' in his play 'No Exit'

Researchers believe the brain consolidates memories, processes emotions, and plans for the future during dream states

Explore fun facts from the USPS, including unique post office buildings, a stamp that traveled past Pluto, and more.

In 1945, Surrealist artist Salvador Dalí and legendary animator Walt Disney began collaborating on a short film that was not completed until 2003, years after both men had died.

The Mona Lisa's celebrity status and repeated restorations have obscured what made the painting so revolutionary for its time

While the sun's gravity keeps the planets in orbit, their gravity also pulls on the sun, causing it and everything else in the solar system to orbit around a mutual balance point called the barycenter—the true center of the solar system.

How Amazon operates a 'flywheel' business model, a self-reinforcing cycle that drives continuous growth

American dance legend Martha Graham, sometimes called 'the Picasso of dance,' refused to perform at the 1936 Olympics in Berlin and conceived the piece 'Chronicle' in response to the experience.

As of 2025, the most cited papers in science include a review of graphene, methods to improve image recognition, streamlining electron density calculations, and optimizing protein studies.

Learn how your body is, scientifically, like a firework with its own slow, controlled burn.

Watch a 1934 short film starring jazz legend Cab Calloway, a major figure in the Harlem Renaissance's music scene

English mathematician Ada Lovelace wrote the first computer algorithm a century before computers existed and hypothesized that computing devices would one day be able to compose music—foreseeing the generative AI systems of today.

Apeirophobia is an overwhelming fear of living forever, perhaps stemming from the brain's inability to conceptualize an infinite life.

Warren Buffett's former professor Benjamin Graham is known as the 'father of value investing,' a strategy in which investors seek to buy stocks trading below their intrinsic worth.

Massive 3D printers have been used to build homes by stacking layers of 'concrete toothpaste,' a fire-resistant material that effectively insulates against outside noise.

Exploring the Larry Bird punch that almost changed March Madness

A 2019 Facebook event called on attendees to "Storm Area 51, They Can't Stop All of Us," resulting in countless memes, the creation of a music festival, and eventually the arrests of those who did try to approach the area.