It's About Time*

Continuing with the study of relativity the next concept we come to is that of time. Einstein stated that compared time intervals were not the same in all reference frames but depended on the relative speed of the reference frames. Einstein called this effect time dilation (sometimes the term time dilatation is used). Students find time dilation a difficult concept for at least two reasons:

1. Time is an abstract concept in itself.  What is time? What does time dilation mean?
2. Many time dilation questions in textbooks are poorly worded and this causes confusion.

What is time?

When a ball rolls along a track in the science laboratory its distance from the starting point changes as its travel time increases. To generalise this we can say that time is a number that increases as events happen in a reference frame. Time can be thought of as nature’s arrow. As time increases events happen in their natural order.

What does time dilation mean?

Imagine that a rocket is moving at 90% of the speed of light relative to the Earth. The crew of the rocket do an experiment. At the end of the experiment they look at their on-board clock and note that the experiment lasted for a time interval of 1 hour. Mission control on the Earth watched the crew do the experiment and according to their clock the experiment lasted for 2.3 hours. To generalise this we can say that time dilation means that the time interval measured by a clock in a stationary reference frame is greater than the time interval measured by a clock in a rapidly moving reference frame.

What causes time dilation?

The reason why time is “dilated” is that when a ray of light is made in a moving reference frame (such as when a ray of light travels from the floor of a high speed train to its roof in a device called a light clock) the light travels a greater distance when seen from a stationary reference frame than when seen by someone in the train. An observer on the ground sees the light travel in a diagonal path, a person on the train sees the light move in a straight line. As the speed of light is constant in all reference frames, the travel time as seen from the stationary reference frame is greater than the travel time observed from the moving reference frame. A very good simulation of this, with some commentary by John Archibald Wheeler, one of the greatest researchers in relativity, is available here.

What is a practical application of time dilation?

Global Positioning System (GPS) satellites require precise timekeeping in order to produce accurate positions of objects on the Earth. Due to the satellites high speed (though still very small compared to the speed of light), Earth based clocks will show dilated time compared to a clock on the satellite. Einstein’s time dilation equations must be used to take into account the high speed of the satellite.

Has time dilation been verified in laboratory experiments?

Yes. Experimenters have used a device known as the Experimental Storage Ring to accelerate lithium ions to one third of the speed of light. The frequency of the radiation emitted by electron transitions in the high speed ions were measured and compared with the frequencies emitted by ions at rest. As the frequencies can be used to calculate time periods, the stationary ions and rapidly moving ions were used as clocks to test for time dilation. The results supported Einstein’s theory to a very high accuracy. See Nature News, 19 September 2014 for details.

Here are some common misconceptions students have about time dilation.

1. “Moving clocks run slower”. This is a common catch phrase but is misleading. Nothing happens to the mechanical properties of the clock when it moves at a high speed to make it run slower. What this phrase means is that the time interval measured by a clock at rest in a moving reference frame is less than the time interval measured on a clock at rest in a stationary reference frame. A person on the Earth ages more rapidly than another person travelling away at a high speed in a rocket.
2. “Time dilation is only an apparent effect and is not real”. This is false. Time dilation actually happens to small particles moving at speeds approaching the speed of light in experiments. Subatomic particles called muons are created 15km above the ground when cosmic rays from space strike air molecules in the atmosphere. The muons move towards the ground at a speed of 0.999c. At this speed a clock on the ground records a time interval 22 times that of a clock moving with the high speed muons.
3. “All of the muons created in the upper atmosphere reach the ground”. This is not technically correct. Experiments show that approximately one third of the muons reach the ground. Muons decay after an average lifetime of 2.2 microseconds in their own reference frame. For a muon to travel 15km to the ground at a speed of 0.999c the travel time is 50 microseconds. Due to time dilation a clock on the ground measures the average lifetime of a muon as 48 (22x2.2) microseconds. This means that a large number of the muons decay before they reach the ground but a smaller number survive as we are dealing with average values. The arrival of muons at the ground is experimental proof of time dilation. Nearly 200 muons arrive on each square metre of the Earth every second!
4. “Length contraction and time dilation are not related”. This is not true. Space and time are linked into a geometry known as spacetime. In the muon example, from the muons perspective the distance that it has to travel to reach the ground is contracted to 670 metres. Its high speed allows it to travel this distance and survive to reach the ground. From an observer on the grounds perspective, the travel time is dilated to 48 microseconds. This increased travel time allows the muon to survive and reach the ground.
5. “A spaceship travelling at the speed of light undergoes time dilation”. This is incorrect. No material object can travel at the speed of light. Remember that time dilation is a relative concept. There would be no time dilation between two spaceships moving at the same speed. The student should say “A clock on the Earth shows time dilation relative to a clock on a spaceship moving at a speed approaching the speed of light” or “Time on a clock on Earth is dilated compared to time on a clock on a spaceship moving at a speed approaching the speed of light”.
6. “Time is the fourth dimension”. Strictly speaking, this is not correct. The fourth dimension is ict where i is the square root of -1, c is the speed of light in a vacuum and t is time. Do not be thrown off by this. Think of i as being a number like 2 or -3 and multiply it by ct.

*And for those who like trivia, this was the name of the 1960s TV show about two astronauts who travel faster than the speed of light and go back in time. And no, you cannot travel faster than the speed of light and no you cannot go back in time but you can go forward in time (in theory at least!).