On the surface, the story behind the movie Planet of the Apes is simple: three astronauts travel into space at near the speed of light, and end up crash-landing back on planet Earth. They soon come to realize that during their trip, they aged more slowly than the people on Earth. The astronauts have effectively traveled into Earth's future - a dystopian future, in which the planet is ruled by apes.
The Planet of the Apes scenario is a dramatized version of the so-called “Twin Paradox.” The Twin Paradox is a well-known problem posed to students of physics and relativity. Imagine two twins decide to join NASA. One twin is sent on a mission into space, while the other stays home. The traveling twin goes 10 light years (~60 trillion miles) away, turns around, and comes back. Upon his arrival, the traveling twin is several years younger than the twin that stayed on Earth. How did this happen?
To understand what's going on, you first need to understand Einstein's Theory of Special Relativity. This theory is based on two immutable facts. First, that the laws of nature are the same everywhere. While your measurements of the world around you might differ from someone else's, the laws of physics are still affecting you in the same way. Second, that the speed of light is a constant, and nothing can exceed it.
The idea that the measurements you take of the world can differ from someone else's is known as relativity. We encounter relativity on a daily basis. If you were sitting on a train traveling at 50 MPH, you wouldn't feel like you were actually moving. But someone standing on the station platform would measure your speed to be 50 MPH. Through the window, the person on the platform appears to be traveling away from you at 50 MPH, even though they are not really moving.That's because you are moving relative to one another.
While riding on the train which is moving at 50 MPH, you throw a ball forwards through the train at 10 MPH. The speed of the ball, as measured by a person standing on the station platform, would be 60 MPH (50 MPH + 10 MPH). Now imagine that you turn on a flashlight while sitting on the train. How fast is the light moving? You might be tempted to say that the speed of the light would be the speed of light plus the speed of the train, but this isn't the case; remember, nothing can travel faster than the speed of light, and the speed of light itself cannot change (according to Einstein). So how is the speed of light affected by motion? It isn't; space and time itself are altered instead.
The speed of light is defined as the distance light travels divided by the time it takes to travel that distance. In the case of the flashlight on the train, the light is traveling a longer distance than it would if the train weren't moving. In order to keep the ratio between distance and time the same (which is necessary to not change the speed of light), the denominator (time) must also be bigger. In other words, time itself is stretched to account for the movement of the train. To the observer on the platform, it seems like the seconds are ticking by more slowly for the person on the train. This effect is called time dilation. When you move faster through space, you necessarily move slower through time.
But there's something else at work here, too. For the person on the train, they don't notice that anything is wrong. They turn on the flashlight, and see the light move at its normal speed. Remember: they don't feel like they are moving. But they experience another consequence of relativity: length contraction. That is, distances outside the train are squished, according to the traveler on the train. So the light from the flashlight doesn't really travel a greater distance just because the train is moving, and, once again, the speed of light is measured to be constant.
How does this apply to the Twin Paradox?
According to the twin that stays on Earth, the astronaut is moving so fast that their internal clock appears to run slowly (i.e. he ages slowly). But the astronaut will see the same thing if he looks back at the twin on Earth. According to the traveling twin, the twin on Earth appears to be moving away at a high speed, and thus the Earth-bound twin's internal clock appears to run slowly. Yet, when the astronaut returns home, both twins agree that the astronaut is younger. How can that be? That's the paradox.
If an astronaut travels to a distant star 10 light years away, and travels at half the speed of light, two things will happen. First, his internal clock will appear to tick more slowly according to the person back on Earth (i.e. he'll appear to age more slowly). Second, he will measure the distance between Earth and the star to be shorter than it really is. It's this second observation that resolves the Twin Paradox. We've already seen why the Earth-bound twin will think the astronaut is younger when he returns home. Moving clocks run slow, so the traveling twin aged more slowly during his journey. But what about the astronaut? As he travels to the star, he doesn't measure the distance to that star as 10 light years. He thinks it's only 8.6 light years away. That is due to the length contraction he is experiencing as a result of his speed. Traveling at half the speed of light, the total round trip takes him 34 years. But before he left, he measured the distance to the star while he was standing still, and knows it was 10 light years away. Traveling at half the speed of light, it should have taken him 20 years to get there, and 20 years to get back. So it makes sense to him that the Earth-bound twin has aged 40 years.
Can we actually do this? Could we send an astronaut so far into space, traveling so fast, that he comes back to glimpse the future of Earth? The answer is: probably not. The problem is not necessarily in getting the astronaut to travel at very high speeds, although that is a challenge (the fastest spacecraft in production could reach speeds of 0.0067% of the speed of light ). The real problem is in accelerating up to that speed. To avoid long-term injury to astronauts, NASA controllers try to keep the acceleration of their spacecraft under 3 G's (3 times the strength of Earth's gravity).  At that acceleration, it would take about two (very uncomfortable) months to accelerate to half the speed of light. That G-forces would feel like the big drop on a roller coaster...but it would last for two months. You would be pinned to your seat by the force of acceleration, unable to move. Your heart would be pumping furiously to push blood through your circulatory system. The human body can only withstand 3 G's for an hour before sustaining serious injury leading to death.  A more reasonable acceleration would be 1 G (the strength of Earth's gravity), but that means it would take almost 6 months to get up to speed!
In Planet of the Apes, the astronauts leave Earth in 1972 and return in 3978, more than 2000 years in the future, having aged only 1.5 years. This implies that they were traveling at 99.99997% the speed of light. To accelerate up to that speed, even at 3 G's, would have taken them almost 4 months. Of course, the G's would kill them long before they get home.
So, while “time travel” (by way of time dilation and length contraction) is a real effect, significant time travel appears to be impossible for humans to achieve.
Laura Haney (@LauraVican)
Co-founder and COO, Signal to Noise Magazine
PhD, Physics and Astronomy
 Scharf, Caleb A. The Fastest Spacecraft Ever?Scientific American Blog Network. Scientific American, 25 Feb. 2013.
 Tyson, Peter. All About G Forces. PBS, 01 Nov. 2007.
 Cavelos, Jeanne. The Science of Star Wars. New York: St. Martin's Griffin, 2000.