Special Relativity
Special relativity is a field of physics that describes the relationship between space and time. Developed by the notorious Albert Einstein, special relativity has revolutionized our understanding of the universe. Unlike Newtonian physics, which treats space and time as separate entities, special relativity unifies them into a single framework: space-time. One of the most counterintuitive consequences of special relativity is that time does not flow at the same rate for all observers. A person travelling at a speed close to the speed of light will experience time much more slowly than someone stationary. This phenomenon is formally known as time dilation and has been experimentally confirmed. From this, one can imagine that special relativity plays a crucial role in any science fiction which involves space travel.
Despite the deep implications of special relativity, its consequences are often misunderstood and simplified in mainstream media. However, popular movies such as Interstellar and Star Trek attempt to incorporate the implications of special relativity into their narratives. We will explore how some movies portray these effects with remarkable scientific accuracy, while others take creative freedom for storytelling purposes.
In this analysis, we will explore how the consequences of special relativity are portrayed in movies, and compare these portrayals to actual physics. We will also discuss how scientific discoveries and theories shape - and are shaped by science fiction.
Key Sections
In this section, we provide all the necessary background information to understand the concepts of Special Relativity and it's consequences.
In this section, we evaluate Interstellar and Star Trek's portrayal of Special Relativity and concepts such as time dilation.
In this section, we critically compare the portrayals of the two movies.
Background
Theory
A world line through a light cone in 2D space; a time dimension has also been added.
Image sourced from wiktionary.
Special Relativity, developed by Albert Einstein in 1905, is based on two fundamental postulates. The first states that the laws of physics are the same in all inertial reference frames, meaning no observer in uniform motion experiences any difference in physical laws. There is no absolute frame of reference—only relative motion between observers. The second postulate asserts that the speed of light in a vacuum is constant for all observers, regardless of their motion. This constancy contradicts our everyday experience of motion and forces us to abandon the notion of absolute space and time, leading to the interconnected framework known as space-time.
One of the most significant consequences of Special Relativity is time dilation, where moving clocks tick more slowly relative to stationary observers. This occurs because the speed of light must remain constant for all observers, which requires time itself to adjust. The amount of time dilation experienced depends on the Lorentz factor, which is determined by the object's velocity relative to the speed of light. The faster the object moves, the greater the time dilation equation. See our time dilation tool. In extreme cases, as an object approaches the speed of light, its passage of time almost stops relative to a stationary observer. This phenomenon is illustrated by the twin paradox, where one twin travelling at near-light speeds ages much slower than their Earth-bound sibling.
Another core prediction of Special Relativity is length contraction, where moving objects appear compressed along their direction of motion from the perspective of a stationary observer. This effect is also governed by the Lorentz factor. See our length contraction tool. The faster an object moves, the shorter it appears. However, this contraction is not physical but a difference in spatial measurements made by observers in different inertial frames. For instance, a spaceship travelling close to the speed of light would appear significantly shorter to an external observer, although the crew inside would notice no change.
Special Relativity also implies that no object with mass can reach or exceed the speed of light. As an object's velocity approaches light speed, its relativistic mass increases, requiring exponentially more energy to accelerate further. This is described by the relativistic energy equation, which shows that infinite energy is needed to reach light speed. This speed limit explains why faster-than-light travel remains purely speculative and why particles in accelerators like the Large Hadron Collider (LHC) can only approach but never attain light speed. See our relativistic energy tool.
Another critical aspect of Special Relativity is the relativistic Doppler effect, where the frequency of light changes due to the relative motion between the source and the observer. When an object moves toward an observer, its light waves are compressed (blueshifted), making the light appear bluer. Conversely, when it moves away, the light waves are stretched (redshifted), appearing redder. This effect is given by the relativistic Doppler shift equation and is crucial in astronomy, where redshift is used to measure the universe's expansion.
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Special Relativity is elegantly visualized through Minkowski diagrams, which illustrate how space and time are interconnected. A Minkowski diagram shows space on the horizontal axis and time on the vertical axis, with the light always travelling at 45 degrees, reflecting its constant speed. Moving observers have tilted time axes, representing time dilation, and their space axes are contracted, illustrating length contraction. These diagrams also show the relativity of simultaneity—events that appear simultaneous in one reference frame may not be simultaneous in another. This visualization reinforces the idea that space and time are not separate entities but interconnected dimensions of space-time. See our Minkowski diagram tool.
History
The development of Special Relativity was driven by the need to resolve inconsistencies between classical mechanics and electromagnetism in the late 19th and early 20th centuries. At the time, light was understood as a wave requiring a medium for propagation, leading to the hypothesis of the luminiferous aether—an invisible substance thought to permeate all space. Scientists believed that the speed of light would vary depending on the Earth's motion through this aether, just as the speed of sound depends on wind direction.
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To test this, the Michelson-Morley experiment (1887) was conducted. Using an interferometer to compare the speed of light in different directions, the experiment expected to detect changes caused by Earth’s movement through the aether. However, the results were null—no variation in light speed was observed, contradicting the aether theory and challenging the existing framework of classical physics. This paradox could not be explained by Newtonian mechanics, which assumed absolute space and time.
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Einstein’s ideas were initially met with scepticism but gained acceptance through experimental confirmation. In 1909, Walter Kaufmann and later Max von Laue confirmed relativistic mass increase using particle deflection experiments. In 1919, Arthur Eddington’s observations of starlight bending around the Sun during a solar eclipse provided empirical evidence supporting Einstein’s theories. Further confirmation came from the Hafele-Keating experiment (1971), which demonstrated time dilation by flying atomic clocks around the world and comparing them to stationary ones.
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Einstein's original paper on Special Relativity can be viewed here: Albert Einstein, 1905, "On the Electrodynamics of Moving Bodies".
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In 1905, Albert Einstein resolved this paradox by introducing Special Relativity. He proposed two revolutionary postulates: the laws of physics are identical in all inertial reference frames, and the speed of light is constant for all observers, regardless of their relative motion. By accepting the constancy of light speed, Einstein eliminated the need for the aether and fundamentally changed the way space and time were understood. His theory showed that space and time are interconnected dimensions of a single entity called space-time, leading to counterintuitive but experimentally verified consequences, such as time dilation and length contraction.
Special Relativity revolutionized physics, disproving the notion of absolute space and time while establishing the Lorentz transformations as the mathematical framework for space-time. It also laid the foundation for General Relativity, where gravity is understood as the curvature of space-time. Today, Special Relativity is fundamental to modern physics, influencing everything from particle accelerators to GPS technology, and continues to shape our understanding of the universe.
A stock image depicting Einstein's famous equation.​​
Mathematical Appendix
Interstellar
Christopher Nolan’s Interstellar is one of a handful of movies that makes a serious attempt to incorporate real physics into the storytelling. With professional guidance and consultation from physicist Kip Thorne, the movie accurately portrays the concept of time dilation, an idea central to special relativity. The film demonstrates the two contexts where time dilation occurs, being gravitational time dilation, and velocity-based time dilation.
Time Dilation on Miller’s Planet: Gravitational Time Dilation
One of the most striking moments in Interstellar occurs when Cooper visits Miller’s Planet, which orbits in the proximity of a supermassive black hole, called Gargantua. It is stated in the film that one hour on the planet is equal to seven years on Earth, which is not being influenced to the same degree gravitationally. This gravitational time dilation effect happens because gravity, according to Einstein’s General Relativity, is not just a force, but a direct consequence of the curvature of space-time. A black hole, which is an object with unimaginable mass, warps space-time so severely that time moves much more slowly for observers in its proximity, compared to a region with weaker gravity.
To understand this, it is helpful to visualize space-time as a stretchable fabric. If an object was placed on such a fabric, you can imagine a distortion of the fabric due to the object's presence. A mass such as the Earth, creates only a shallow dent in the fabric, compared to an object such as a black hole which creates a deep well. Since this fabric is composed of space and time, a general distortion of the fabric translates to a distortion in both space and time. This is why, when Cooper returns from Miller’s planet, years have passed for those on the Endurance, but only a few hours for Cooper. See our interactive tool here
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Velocity-Based Time Dilation
While Interstellar mainly focuses on gravitational time dilation, it also hints at velocity-based time dilation, which is a direct consequence of special relativity. The equations of special relativity tell us that the faster an object moves, the slower time flows compared to a stationary observer, with this time dilation effect becoming extreme at speeds close to the seed of light.
In the movie, the crew travels immense distances through space, including a trip through a wormhole. While not explicitly shown, the ship travels at relativistic speeds, therefore indicating that the crew experiences time slower than those on Earth. This effect of time dilation is governed by what’s known as the Lorenz factor, which determines how much time slows down, given the speed you are travelling. We will explore this more rigorously in a later section.
Time dilation and Red Shift:
A pivotal moment of the movie is when Cooper falls into Gargantua, heading straight for the event horizon, which is the boundary of the black hole that nothing can escape, not even light. As Cooper approaches the black hole, time dilation becomes extreme from the perspective of a stationary observer watching. The stationary observer would see Cooper appear to slow down more and more, never actually seeing Cooper cross the event horizon. This happens because time dilation at the event horizon approaches infinity, meaning the external observer would never see Cooper fall in completely. However, from Cooper’s perspective, which is what we see in the film, he crosses the event horizon in a finite amount of time.
Additionally, this moment in the movie introduces gravitational redshift, which is another relativistic effect. The light that is reflected off Cooper that radiates back into space is stretched from the black hole's gravitational field. This stretching of the light shifts the wavelength towards the red side of the spectrum. Therefore, to an outside observer, Cooper would appear increasingly redder and dimmer, until he becomes invisible, meaning no more light is being reflected off Cooper. On the other hand, Cooper, looking from inside the black hole, would observe the light from the rest of the universe as blue shifted, due to light being compressed as opposed to stretched, ultimately making everything appear brighter.​​​​​​​​​​​​​​​​
Star Trek
While Interstellar takes a scientifically grounded approach to relativity, Star Trek explores space travel in a way that prioritizes storytelling. A key element of the Star Trek universe is the famous warp drive, which is a piece of hypothetical technology that allows for spacecraft to travel faster than the speed of light. However, this directly violates Special Relativity, which states that no object with mass can reach or exceed the speed of light without requiring infinite energy. So, how does Star Trek bypass the laws of physics and exceed this fundamental limitation?
Warp Drive & Faster-than-Light Travel
In Star Trek, the USS Enterprise and other federation ships can travel at speeds far greater than the speed of light by utilizing a warp drive. Unlike conventional propulsion mechanics which deals with objects moving through space, a warp drive moves space itself. The idea here is that, relative the the region of space that the warp drive moves, the spaceship is technically stationary. The term used for this is a “warp bubble”. This ultimately allows the ship to travel at vast speeds without violating special relativity since it is space that is moving, and not actually the ship.
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There is in fact a real analogue to the warp drive. The concept was originally inspired by real theoretical physics, more specifically, the Alcubierre drive, proposed by Miguel Alcubierre. His equations suggest that, in theory, space-time could be warped in a way that allows spacecraft to effectively move faster than light without breaking the speed barrier, imposed by Special Relativity. However, for such a device to work practically, it would require matter with negative energy density, which has not been proven to exist.
​Does “Warp Travel” Avoid Time Dilation?
One of the primary consequences of near-light speed travel is time dilation. If a spacecraft were moving with a conventional propulsion mechanism, time for the crew onboard would sow down drastically compared to stationary observers. This means that a journey that feels like a few days for the crew, would feel like years or even decades passing for people back on Earth. This is known as the twin paradox, a thought experiment that conveys the effects of time dilation from Special Relativity.
However, Star Trek largely ignores the effects of time dilation. Since the warp drive distorts space-time itself rather than relying on conventional speed, it is often assumed that time dilation does not occur conventionally in the space way. The ship and its occupants remain within a stationary warp bubble, meaning their passage of time is not significantly different from external observers. This is convenient in the context of the overarching narrative, allowing characters to travel and interact without significant differences in the passage of time.
Whether or not a warp drive actually bypasses the time dilation effect due to Special Relativity is still debated amongst physicists today. However, the physical application of such a device remains purely speculative and fictional.
Wormholes & Space-Time Shortcuts
Another concept frequently explored in Star Trek is the use of wormholes as a means to travel faster than light. A wormhole is a hypothetical tunnel-like structure that connects two distance points in space-time. If wormholes exist, they could serve as a shortcut through space, allowing near-instantaneous travel between points in space that are immensely separated.
While wormholes don’t violate the cosmic speed limit, no evidence of their existence has been found. Wormholes are mathematically possible and are compatible with Einstein’s field equations, it is hypothesized that “exotic matter” is needed to keep them stable, thus giving us the physical limitation of them being real.
We rate: "Interstellar"
We rate: "Star Trek"
How do they compare?
Interstellar certainly stands out as a film which is scientifically accurate, more specifically in its depiction of gravitational time dilation near a black hole. While the movie does take some creative liberties, such as Cooper surviving falling into the black hole, the film remains one of the best cinematic exhibitions of both gravitational time dilation and velocity-based time dilation. This overall, makes the movie Interstellar a perfect case study for how movies can introduce complex physics to a general audience.
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Unlike Interstellar, which operates within established scientific frameworks (Special & General Relativity), Star Trek takes a more speculative approach, ultimately pushing the laws of physics for the purpose of storytelling. The notion of a warp drive ultimately provides a creative way for space travel without “inconvenient” effects from time dilation. While inspired by genuine theoretical physics such as the Alcubierre drive, warp travel remains physically inapplicable due to the system’s requirement for a type of matter that is not confirmed to exist.