Why can’t anything travel faster than light?

Roger Rassool looks at how we first began trying to measure the speed of light, and why it is finite.

We now know there is a cosmic speed limit, but until the 1600s it was assumed light moved instantaneously. – ALFRED PASIEKA/SCIENCE PHOTO LIBRARY

We all know the number one traffic rule of the universe – nothing can travel faster than the speed of light. And that happens to be 299,792.458 kilometres per second. But why is it so?

Before the 1600s most people assumed light moved instantaneously. Galileo was among the first to think that light travelled at a finite speed.

In 1638 he tried to measure it. He and an assistant perched themselves on distant mountaintops with covered lanterns. The idea was that as soon as Galileo’s assistant saw the flash, he uncovered his lantern. Galileo would then time how long it took to see the return flash. The experiment failed dismally! To succeed, Galileo would have had to register a time difference of microseconds. He had no such time keeping device and his reaction time would be way slower than that.

Undaunted, Galileo concluded that light’s movement, “if not instantaneous, is extraordinarily rapid”.

But not long after, in 1676, we got a fair estimate of light’s speed from a young Danish astronomer by the name of Ole Römer. One of the ways sailors at sea checked their clocks was to observe the eclipse of Jupiter by its moon Io. The time for Io to make one complete circuit around Jupiter had been measured at 1.769 days. However there was a minor problem.

Römer observed that the time between eclipses varied slightly depending on the time of year. At times when the Earth was moving away from Jupiter, the time between Io’s eclipses gradually increased; as it moved closer the time decreased. The cumulative effect meant the predicted times could be in error by more than 10 minutes.

Römer realised his observations could be explained by the varying distance between Jupiter and Io, and Earth. The different times for Io’s orbit reflected the different distances light had to travel. It also allowed Römer to estimate the speed of light as 214,000 km/s. Not bad!

The first experimental measurement of the speed of light came 150 years later with Hippolye Fizeau. He came up with an ingenious advance on Galileo’s method. In his experiment, a beam of light was projected onto a rapidly rotating cog-wheel. The teeth of the rotating cog chop the light up into very short pulses. These pulses travelled about 8 kilometres to where Fizeau had positioned a carefully aligned mirror. On the return trip, the reflected light pulse could only reach Fizeau by passing back through one of the gaps in the cog-wheel.

What happened? At slow speeds, the light pulse always got back to Fizeau through the same gap in the cog’s teeth. But as Fizeau turned the wheel faster, at a certain speed the pulse was blocked by the following tooth. Knowing the rotational speed, Fizaeau thus could calculate how long it took for light to travel 16 kilometres – and so how fast the light must be travelling. His remarkable result of 315,000 km/s was within about 5% of our most recent measurements using lasers.

The faster something travels, the more massive it gets, and the more time slows – until you finally reach the speed of light, at which point time stops altogether.

OK. We know that light travels at a finite speed. But why is it finite?

This question gave Albert Einstein pause for thought. If light has a finite speed, what if you strapped a torch to the front of a moving rocket? Wouldn’t the light coming from this torch be travelling faster than the speed of light? Einstein puzzled over this issue with several “Gedankens” (thought experiments) and came up with a crazy solution: the motion of an object must somehow make time slow down. Time was no longer constant and so relativity was born.

Many experiments have carefully tested Einstein’s predictions.

In 1964, Bill Bertozzi at MIT accelerated electrons to a range of speeds. He then measured their kinetic energy and found that as their speeds approached the speed of light, the electrons became heavier and heavier – until the point they became so heavy it was impossible to make them go any faster. The maximum speed he could get the electrons to travel before they became too heavy to accelerate further? The speed of light.

In another crucial test, physicists Joseph Hafele and Richard E. Keating flew synchronised, super-accurate caesium atomic clocks on various trips around the world on commercial airliners. After the journeys, all the moving clocks disagreed with each other and the reference clock back in the lab. Time ran slower for the moving clocks just as Einstein predicted. So the faster something travels, the more massive it gets, and the more time slows – until you finally reach the speed of light, at which point time stops altogether. And if time stops, well then, so does speed. And so nothing can travel faster than the speed of light.

By the way, the next time you use your smart phone be aware that the GPS satellites orbiting Earth have to take the slowing of time (time dilation) into account. Disable these relativistic corrections and the modern world would be lost forever.

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Roger Rassool is a particle physicist at the University of Melbourne. His outreach programs have switched on a new generation to the wonders of physics.
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