Study Guide

Special Relativity In the Real World

  • Pop Culture

    Time Dilation in Planet of the Apes

    Most people think of Planet of the Apes as a movie. It was actually first published as a book, and presents a much better story than any of the movie versions. Sorry, Hollywood, that's just the way it is.

    Planet of the Apes is a remarkable French novel written by Pierre Boulle and published in 1963. It tells the story of a space expedition launched in 2500 from Earth to the distant star system of Belgeteuse. The expedition is conducted by a few humans, including a man called Ulysse and his genius professor friend, the inventor of a spaceship that can travel near the speed of light.

    In his novel, Pierre Boulle writes that the effects of time dilation allow the passengers to complete their trip in 2 years as opposed to 350 years. We know how they do it!

    Proper time here is Δto= 2 years and relativistic time is Δt = 350 years. Using our equation Δt = γΔto, we can solve for γ and figure out the spaceship's speed.

    Since ,we find γ = 175. Then β = 0.9999837 using

    That's much better than what The Albertian can do.

    Back to the story. The spaceship reaches an Earth-like planet where a troubling role reversal has occurred over time. Apes are now the masters while humans are their slaves. The main character, Ulysse, is captured with other humans and stuck in a lab for scientific research purposes. Amongst a hoard of animalistic human beings screaming about in a cage, he blends right in.

    So what does Ulysse do to convey the message he's far superior than his kind? He relies on math. He draws the Pythagorean theorem on a piece of paper and shows it to a flabbergasted female ape, surprised that a mere human animal has powers of higher thinking.

  • Philosophy

    We've been talking your ear off about how cool the speed of light is the ultimate limit, which can never be broken. Let's revisit this issue from a non-mathematical point of view.

    Approaching the speed of light forces time to slow down, and this is how we can travel to the future.

    If a twin decides to go space-gallivanting and takes off in The Albertian, he might become younger than his twin. The math tells us that after traveling at a speed of 0.5c for 5 years, 7.5 years will have passed on Earth, where his now, younger twin remained. The Earth twin will be 2.5 years older than the astronaut-twin.

    It's more complicated to calculate an exact time dilation effect with general relativity, but the idea is the same. If the Earth twin decides to get even and takes a turn in space around a black hole for a while and then returns to Earth, he'll be the youngest twin once again. Cosmetic companies promoting eternal youth just might be joining forces with modern physics in the next century.

    We experience this kind of time dilation every day while driving, jogging or biking, but since we are moving at speeds much less than c, time dilation doesn't occur at a noticeable level.

    Having this upper limit on velocity implies no information can be relayed faster than c. It takes eight minutes for a sunray to reach Earth. If the Sun exploded, we wouldn't know until eight minutes had passed. When we look up at stars at night, we see them as they were thousands and even millions of years ago. Entire star systems could've died and been reborn and we wouldn't even know. We'd just blissfully gaze up at the stars and try to impress our date for the night by pointing out all these neat facts.

    There are other ramifications to the speed limit, too.

    If we ever detected a signal coming from an advanced alien civilization, chances are the civilization would already be long gone by the time their greeting ever reached us. Even traveling at the speed of light, cosmic distances are just too great. It could be bad luck. Or it could be that perhaps we simply aren't meant to communicate with other intelligent life forms. Earth seems to have enough problems already dealing with its own species.

    Or maybe we are meant to break the barrier of light speed, in spite of the fact that, according to special relativity, we'd need an infinite amount of force or energy to accelerate an infinite mass. Other ways have been suggested, such as equipping spaceships with warp drives and cutting through the fabric of space-time by building wormholes.

    Since information travels at the speed of light, going faster than c would allow us to get our hands on that information before it reached us. We could in theory change the course of things and set up a new future. In other words, we could travel into the past.

    This would imply the possibility of paradoxes. Let's say both twins go back in time. Their great-great grandfather, Lord Thomas Cobb, invites them out on a hunt around his palace grounds. They accidentally shoot him while trying to kill a animal on the endangered species list in their own time. Doesn't the death of Lord Thomas Cobb imply they were never born?

    Perhaps there's a reason we can't go faster than the speed of light. It guarantees a continuous flow of time where causality can never be broken.

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