The Relativity of Time

Perhaps no other idea has ever shaken the foundations of science as powerfully as the relativity of time. Scientists took resolve for thousands of years in the idea that, no matter what other subjects and worldly concepts fell victim to relativism, the standard of absolute time always held steady. I once heard someone say, “Time is God’s way of keeping everything from happening at once.” A second is a second. A year is a year. These are things no one can change…right?

In 1905, a twenty-six year old Albert Einstein published a paper proposing time is not absolute, that the length of a second depends on the motion of the clock. This wasn’t some mechanical idea, as though the force of moving will affect the gears or springs within the clock in some way to alter the readout. No, Einstein argued that the physical laws governing the universe made the relativity of actual time itself inevitable. And, astonishing as it may seem, this has been experimentally verified.

To understand this concept, we will need to use our imagination to perform a thought experiment. Have you ever stood on the side of the road as cars whizzed by, perhaps waiting for a bus or to get your mail? Did you notice how the sound of the car’s engine got higher pitched as it approached you and lower pitched as it drove away? If you listen to a young child playing with a toy car, they usually mimic this noise as they pretend the car is whizzing by a break-neck speeds. This is called the Doppler Effect. The car is emitting sound waves that leave in all directions at a speed of about 340 meters per second (m/s). But if the car is speeding down the road at 70 miles per hour (or about 31 m/s), it’s traveling about 9% the speed of sound. That means that it’s constantly “catching up” with the sound waves it emits in the forward direction and “running away” from the sound waves it emits out the back in a noticeable way. This causes all the waves to get very close together (increase in frequency) in the direction of motion and spread out (decrease in frequency) in the opposite direction. Our ears hear an increase in frequency as an increase in pitch, so the car engine sounds higher as it moves toward you and lower as it goes away.

The frequency of the wave (number of peaks in a certain area) increases in the direction of motion.

I know what you’re thinking. What does that have to do with the relativity of time? As it turns out, lots. The relativity of time is not unlike the relativity of frequency. The only difference is speed. For us to hear a Doppler shift in sound waves, the object has to travel at some noticeable fraction of the speed of sound, which isn’t very fast; even a relatively slow object like a car traveling down the road gets us almost a tenth of the way, and we exceeded the speed of sound in 1947. To deal with the relativity of time, we need to move fast. Damn fast.

Imagine now a new scenario. There is a space rocket, and the pilot aboard has a perfectly reliable clock. On top of the rocket is an extraordinarily bright bulb which can be flashed on and off. Back on Earth, which we will call motionless, the pilot’s brother (who instead became a physicist) is using perfectly sensitive laboratory equipment, which includes another perfectly reliable clock, to record the flashes of light that come from the rocket. They decide to perform two experiments to test Einstein’s theory.

For the first experiment, the rocket sits motionless in space. The pilot on board releases a flash of light every six minutes until he has released a total of twenty flashes. When he adds up the time between all the flashes, he determines that he has been in space for two hours:

6 minutes × 20 flashes = 120 minutes = 2 hours

Although it takes a few moments for the light from the rocket to reach the brother on Earth, there is no relative motion between the two, so the laboratory equipment measures the exact same thing: twenty flashes in six-minute intervals. At the end of the experiment, the physicist agrees with the pilot that two hours have elapsed.

Now let’s do the experiment again, but this time the pilot will travel away from Earth at about half the speed of light during the first ten flashes, then back towards Earth at the same speed for the last ten flashes. He will make certain to keep everything else exactly the same, flashing once every six minutes. Just like before, his brother on Earth will measure the time between flashes to determine the time of his brother’s round trip.

The pilot takes off away from Earth, and here we see our first problem. Just like the car was travelling some significant fraction of the speed of sound, the rocket is travelling some significant fraction of the speed of light (this is much faster than sound, at about 300,000,000 m/s). So as the car was running away from the sound waves it was emitting in the opposite direction of motion, the rocket is running away from the light flashes it emits in the opposite direction of motion (i.e. towards his brother on Earth). Because of this, there seem to be bigger gaps between the flashes in that direction, meaning the frequency of flashes has gone down for the stationary brother on Earth. As a result, he measures the first ten flashes emitted by the rocket as twelve minutes apart instead of six minutes. About this time, the pilot turns the rocket around and heads back to Earth, emitting the other ten flashes. But, of course, this has the opposite effect, increasing the frequency of flashes as measured by the Earth brother to once every three minutes.

So the pilot finally gets back and compares information with his brother, who is worried about all these changes in frequency of flashes. But the physicist consoles himself and says, “So the frequency of flashes was halved on the way out and doubled on the way back. So what? I’m sure that will average out no different than if they had stayed consistently six minutes apart the entire time.” The pilot does his math first, but finds that it’s no different than when he was stationary in space:

6 minutes × 20 flashes = 120 minutes = 2 hours

The physicist does his math, adding his time for the outgoing trip and the return trip, and finds something extremely amazing:

(12 minutes × 10 flashes) + (3 minutes × 10 flashes) = (120 minutes) + (30 minutes)             = 150 minutes = 2.5 hours

“Great Caesar’s Ghost!” he exclaims. “My brother measured that he was gone for two hours, but my clock measured a full thirty minutes extra! The clock in motion, my brother’s clock, ran slower, as though a second was slightly longer for him than it was for me!” As far as the pilot is concerned, he traveled thirty minutes into the future. And the faster he had driven the rocket, the more he would have affected the frequency of flashes as observed on Earth, and the greater the discrepancy between their perceptions of time. This effect, which I’ve described using the Doppler effect, is called time dilation. The relationship between the two measurements of time is as follows:

You might wonder why we don’t notice time dilation all the time, but you must remember that it requires traveling some significant fraction of the speed of light. There are, however, lots of objects that travel fast enough to notice relativistic effects, namely subatomic particles and, to a lesser degree, satellites. But have fun with the math! Try plugging in different velocities to find out how fast you’d need to travel (and for how long) to see your best friend’s 80th birthday, or the turn of the next century…or millennium!

This kind of stuff is fun and, best of all, it’s real. There is no science fiction here. So run up to the next person you see, shake them by the shoulders, and tell them about the relativity of time. I’m sure they’ll either be excited to hear about it, or they’ll call the police.

*Note: This example is only one of several ways to visualize special relativity, but it’s as close as you can get to full understanding without delving too hard into math.