The Twin Paradox:
How the Universe Slows Down Time
In the film Interstellar, a global crop blight is slowly rendering the Earth uninhabitable.
To save Earth’s population, a NASA pilot named Cooper must leave his young daughter and lead a team of researchers across the galaxy to find out which of three possible planets could become humanity’s new home. During the journey, Cooper makes a number of unexpected discoveries. For the audience, the most jarring revelation occurs when Cooper returns home to discover that his daughter has become an old woman while interstellar flight has caused him to remain a young man.
Is this fanciful speculation, or a plot device based on real science?
The Temporal Effects of Gravity and Velocity
We are already traveling into the future at a velocity of 1 second per second. Can we speed this up? Einstein’s relativity equations show us two ways to do this.
Both gravity and velocity slow the passage of time. These effects give us a way to travel into the future. To accomplish this, we can move away from our planet at high velocity or move to a location with a strong gravity field. Both will slow our body clocks as compared to those of the people left on Earth.
The Twin Paradox is a popular representation of how to age only incrementally. It utilizes the effect that velocity has on the passage of time, namely, to slow it down.
Let’s say that you have a twin sister and the year is 2020. You are both 40 years old. She stays on Earth while you take a trip in a rocket ship that accelerates you to 99.9992% of the velocity of light as you travel to a planet 250 light years (150,000,000,000,000 miles) away.
To make your trip comfortable, the ship accelerates at a modest 1g. This is the acceleration that gravity produces on the Earth’s surface and gives us our weight. You travel 250 light years to reach the planets and another 250 light years to travel home. In earth time, it takes you 6 years and 3 weeks for each leg of the journey.
Because you are travelling close to the speed of light, time has run very slowly in your rocket ship. Your on-board clock registers 12 years and 6 weeks for your round trip. When you land on earth, you discover that 1,000 years have passed since you left. Your sister who was 40 years old at that time has died, along with everyone you knew, whereas you are now only 52 years old.
The paradox arises because the earthbound twin can assume that she is traveling and that her sister in the spaceship is standing still. In this case the earthbound sister would be aging slowly, and her sister on the stationary spaceship would be aging quickly. But the situations differ because the twin in the spaceship has to turn around to return to Earth. The acceleration required for the ship to slow down and reverse course locks in the time dilation for that person.
The Effects of Extreme Gravity
Intense gravitational fields provide another way to travel to the future. The stronger the gravitational field, the slower time runs in its vicinity. Gravity on the surface of the earth is stronger than gravity at the altitude of a synchronous satellite.
If you had a twin living in the space station, 25,000 miles above the Earth, he or she would age faster than you do because time is running faster there.
Black holes are the remains of collapsed stars. Their gravitational fields are so strong that not even light can escape from their surface.
A black hole’s immense gravitational field can also cause you to age slower than if you were in the Earth’s weaker gravity. If from your vantage point near the black hole, you were able to observe a clock far out in space from the black hole, you would see the hours pass as though they were seconds.
Time is Relative
Time is a relative phenomenon; its effects cannot be observed unless someone moves at a velocity comparable to the speed of light or spends time on objects where space time is bent by gravity.
In the movie Interstellar, Cooper does not age as fast as the humans on earth because (a) he travels around a wormhole at the speed of light (2) he passes into the tesseract (cubic center) of a black hole where gravity is so dense that not even light can escape.
In both cases, the cells in Cooper’s body age in “slow motion” relative to his daughter back on earth. In terms of time, while Cooper spends 3 years in space, his daughter spends 60+ years on earth. Which means she lived/experienced 20 times more time than Cooper during his interstellar journey.
