###### By Don Lincoln**, **Fermilab

## The idea of time dilation—that moving clocks tick more slowly than stationary ones—is awfully hard for many people to accept. It simply runs totally against all of our experience. And there’s a reason for that. The reason is that the effects due to Einstein’s theory of relativity are imperceptible unless one is going incredibly fast.

### The Fastest Objects Ever Made

In order to understand time dilation, let’s think about some of the fastest things we might have encountered. Suppose we put a clock in a NASCAR race car, moving at about 200 miles per hour. What would be the difference in how a clock in the car ticks compared to one on the ground? It’s tiny—just five trillionths of a percent. How about a clock traveling with the fastest bullet ever manufactured, the .220 caliber swift? Those bullets zip along at the incredible speed of a little more than 3,000 miles per hour. As fast as that is, a clock traveling along with such a bullet will only tick a billionth of a percent slower than a stationary clock.

What about the fastest object ever made by mankind? That would be the Parker Solar Probe, which is a spacecraft tasked to pass extremely close to the Sun. It is traveling at the mind-boggling speed of 150,000 miles per hour; fast enough to circle the globe in about 10 minutes. How much slower is a clock on the probe compared to one on Earth? Well, that clock is ticking about 2.5 millionths of a percent slower. Basically, one would never notice.

The point all these examples underline is that time dilation and the effects due to relativity are negligible until we get to super-fast speeds. It’s not at all shocking that our common intuition doesn’t think that relativity is real.

### Difference in the Percentage of Time

This observation also begs the question, how fast would a clock have to be moving to experience a difference in the percentage of time of just 1%? The answer thus, would be, really fast. For instance, in order for two clocks—a stationary and a moving one—to tick with a difference of only 1%, we will have to be moving about fast enough to circle the entire Earth in a single second. And if we were hoping to have a moving clock tick half the speed that a stationary one does, the clock would have to be moving at about 85% the speed of light, or just over 160,000 miles per second. This is why nobody has good relativistic intuition!

And yet, there is a group of people who work with objects moving at speeds that require we take relativity and time dilation into account. That group includes particle physicists who need to use relativity properly or they won’t get the right answer when they compare a measurement to a calculation.

Now, clearly, this isn’t an observation that one can make on their own. So, how is it that particle physicists are so certain that moving and stationary clocks really do tick at different rates?

This article comes directly from content in the video seriesThe Evidence for Modern Physics: How We Know What We Know. Watch it now, on Wondrium.

### Pions

To study relativity and time dilation, we need much faster clocks. The atomic clocks that form the basis of the international global positioning system tick about 10 million times a second. In order to test relativity, we need a clock that ticks very quickly and is light enough to be able to get it up to very high speeds. A perfect example is an atom or some other subatomic particle. So, how can an atom or particle form a clock? The easiest way is to exploit the fact that some of these objects undergo decay. Some atoms undergo radioactive decay, sometimes with a very long lifetime, sometimes with very short ones. And subatomic particles do the same thing and so does the common subatomic particle called the pion.

Pions are made in great numbers in both particle accelerators and in cosmic ray collisions. Electrically charged pions, which are the kind that make neutrinos, have a half-life of about 18 billionths of a second or 1.8 times 10 to the minus eight seconds. So, if we know the lifetime of the pion and we know its speed, we can figure out how far it can travel before it decays. We do that by multiplying the velocity and time together.

### Studying Relativity and Time Dilation

Tests were conducted at Fermilab to study relativity and time dilation by making a beam of pions. In the test, the 18 nanosecond half-life of a pion is measured when it is nearly stationary, which can be done in very low energy collisions. But, of course, the pion is not usually stationary when we make a beam. It’s traveling near the speed of light and relativity says that clocks traveling near the speed of light tick more slowly.

What was observed was exactly what relativity predicts. In 17 feet, only about 1.5 percent of the pions were observed to have decayed, not the 50% that we would see if relativity didn’t exist. In fact, when the tunnel was built for pions to decay, it was 2,160 feet long, or nearly half a mile long. And that in itself is compelling evidence that relativity is right as if relativity wasn’t real, the pions would have decayed in a mere 17 feet.

### Einstein’s Equation

But that wasn’t clearly the case. As per the predictions of relativity, Einstein’s equation calculates E equals m c-squared, which says that an object at rest has a certain amount of energy. A moving object has even more energy. If an object like a subatomic particle has 10 times the energy it does when it isn’t moving, it will live 10 times longer. Thus, the pion should have had a half-life of 180 nanoseconds and travel 170 feet instead of 17 feet.

And, at Fermilab, it proved it correct, demonstrating relativistic time dilation. The bottom line is that the statement that moving clocks tick more slowly than stationary ones isn’t simply some incorrect prediction of relativity theory. We have real measurements and they agree exactly with the equations that Einstein invented over a century ago.

### Common Questions about Relativity and Time Dilation

**Q: What is the fastest object ever made by mankind?**

The fastest object ever made by mankind is the Parker Solar Probe, which travel at a speed of 150,000 miles per hour.

**Q: What do we need in order to test relativity?**

To test relativity, we need a clock that ticks very quickly and is light enough to be able to get it up to very high speeds.

**Q: What is the half-life of electrically charged pions?**

Electrically charged pions have a half-life of about 18 billionths of a second.