Faster than a speeding bullet or how to measure the speed of a beam of light.

Do you remember how fast we are travelling? I did tell you back at the start of this journey.

“Well that was a while ago Albert, but as we’re travelling on a beam of light we must be going at the speed of light.”

If I told you we’d covered 18,382,965,104,070,000 miles in just over three thousand years could you work it out from that?

“I guess that means we must be going very fast.”

186,000 miles every second. Light moves so fast that it seems to arrive without any delay at all. Light could get from London to New York in just two hundredths of a second. That's faster than a human blink.

“So what’s our speed in miles per hour, I can’t really imagine a speed in miles per second.”

Oh, let’s see. Almost 671 million miles per hour.

“Wow, how could you measure something going that fast?”

It’s difficult but not impossible. How would you do it?

“I don’t suppose we have a speedometer with us do we? Would a stop watch work?”

Not a bad idea. You can measure the speed of anything if you can record how far it goes in a second. That idea works fine for checking the speed of people running or even cars but as light goes 186,000 miles in a second it gets a bit difficult. Can you think why?

“Because I couldn’t see that far? I’d have to be able to see the start and the finish line to see when the light beam started and finished.”

Of course you can see that far. The moon is further away than that. The furthest object in the sky you can see, the Andromeda galaxy, is 2.5 million light years away. The real problem is that the light coming from the starting line would take exactly the amount of time to reach you as the beam of light you were trying to measure. So by the time you saw it leaving it would have arrived at your position and appear to arrive with no delay at all.

“That’s weird.”

But true. Imagine a bullet being shot at you and travelling faster than sound. You would be hit by the bullet and dead even before you the sound of the gun being fired reached you.

“Kind of unfair, but I can picture that.”

So if the bullet was travelling at exactly the same speed of sound you would hear the bullet at the same moment it hit you. It would seem to have arrived without delay. It would be the same if the gun was two feet away. The sound and the bullet would always arrive at the same time.

“I could look for the flash from the gun. That would arrive faster and use that to measure the speed of the bullet.”

True but for measuring light you would need something much faster than light.

“How about radio signals?”

No, radio waves travel at the speed of light because they are part of the same electromagnetic spectrum as light. That is the one of the starting points of my theory of relativity, nothing travels faster than light.

“So just by knowing that nothing travels faster than light, I can understand a little bit of your theory of relativity?”

Not just a little bit, a very important part of relativity. Thinking about the speed of light and when things seem to happen is the heart of special relativity. I told you earlier that one of my scientific heroes, Galileo, was the first person to start thinking about relativity almost four hundred years ago. Galileo was also the first person to challenge the ancient Greek ideas about how light travelled by measuring the speed of light. It was clear to the ancient Greeks that light and sound don't travel at the same speed. The delay between lightning and thunder when a storm isn't overhead showed that light travels much faster than sound but they thought it just arrived without any delay.

“How did Galileo do it. I thought you just explained that you couldn’t measure the speed of light?”

Not at all. I was trying to show that it is difficult but not impossible. Galileo managed to solve the problem we were talking about by being at the starting line and finishing line at the same time.

“How can you be in two places at the same time?”

It happens all the time in a lap race. The start and finish are usually at the same place aren’t they?

“Yes, but light travels in straight lines”

Usually yes, but you can reflect it back or get someone to send another light beam back, like a relay race. That’s what Galileo tried. He sent an assistant to a hill a mile or so away and positioned himself on another hill so there was nothing blocking their view of each other. Galileo had sorted out lamps for himself and his helper and the plan was for Galileo to switch his lamp on and start a clock. As soon as the assistant saw the first lamp light go on, he would turn his lamp on. By measuring how long it took before the light from the second lamp to get back, Galileo hoped to work out how fast light was travelling. Unfortunately even a remarkable man like Galileo couldn't spot the 5 millionths of a second delay while the light travelled from one hill to another a mile away.

"So he just needed a better clock."

Well a better clock would have helped but that kind of accuracy was centuries away, but a much bigger distance for the light to travel would help. With a little thought a Danish astronomer by the name of Ole Rømer had a go at measuring the speed of light in 1676 and came up with a speed of 133,000 miles per second.

"But he got the wrong answer?"

OK, so he got the wrong answer by 50,000 miles a second or so, but back then that was a pretty impressive achievement. But he did show that light took time to get places, it didn’t just arrive.

"Better than a million miles off I suppose. So how did he measure the speed of light?"

He used a clock but didn't need to measure millionths of a second because the light he was measuring wasn’t coming from a nearby hill but from the planet Jupiter which is 400 million miles away at its nearest point to Earth. Rømer carefully measured the time it took for Jupiter's moons to circuit the planet. He noticed that the times when the planet Jupiter's moons disappeared from view behind the planet, like an eclipse, seemed to be different at different times of the year. Since the Earth's moon is regular as clockwork this seemed odd. It only made sense if light from Jupiter's moons took some time to reach the Earth. At those times of year when the Earth was nearer to Jupiter, the light had a shorter distance to travel so the eclipses of Jupiter's moon seemed to happen earlier. Later on when Jupiter was getting further away, the light had further to go so it arrived later. It looked as though the moon had disappeared behind Jupiter later than it should have done.

“So how did scientists come up with the answer of 186,000 miles per second?”

A Frenchman called Leon Foucault used an updated version of Galileo's idea in 1862 but rather than use an Italian servant to open the shutter on a lamp, he used a rotating mirror.

"How does that help?"

If the light beam is reflected off a spinning mirror before being sent off to another mirror some distance away, then by the time the light gets reflected back to the spinning mirror it will have rotated a fraction.

“So?”

So the reflected light beam doesn’t get back to where it started but ends up a small distance away because by the time it gets back the rotated mirror….

“…rotated.”



Exactly so the light beam is reflected off at an angle. It's easy to measure the distance the light beam has moved with a ruler and how fast the mirror is spinning than it is to measure a few millionths of a second. So much easier that Foucault only needed to bounce light from a mirror sixty feet away. He got an answer pretty close to the actual figure but was finally beaten by an American in 1879. Albert Michelson improved on the Frenchman's machine by borrowing $2,000 from his father-in-law to built a bigger better version. This was no mean feat as $2,000 was a huge sum in those days and would be the same as almost a million dollars today. Michelson’s final answer was a speed of light of 186,355 miles per second which is impressively close to the figure accepted today of 186,282 miles per second or 299,792,458 metres per second.

“Impressive but does measuring the speed of light that accurately really help anyone?”

It was an important step for physics. A few years later in 1887 Albert Michelson also helped finally to bury the idea that light needed a strange substance called ether to carry it through space.

"Who's Ether?"

Ether, or aether, is a non-existent substance invented because no one could imagine waves without water.

"I don't follow."

Remember I explained that light can act like a wave.

"Like a sound wave or a wave on the ocean?"

Precisely, but what is left of an ocean wave if all the water is taken away?

"The fish?"

Very funny, the real answer is absolutely nothing. When you take away air and make a vacuum, sound waves disappear like ocean waves without water. A Mexican wave in a football stadium is carried by the spectators, with an empty stadium there is no conceivable way of having a Mexican wave. So if space is empty then how can light waves cross it? Some people were so attached to light being a wave that they said – ‘Simple, space isn't empty, it is full of ether and that's the stuff that carries light waves’.

Proving ether didn't exist rested on the simple idea that swimming in a river with the current is faster than swimming against the current. As the Earth rotates around the sun each year then it must be sweeping through the ether if it exists, effectively producing a flow of ether in the same way as wind whistles past a moving car even on a windless day. Light travelling in the same direction as the movement of the Earth will be travelling into this ‘headwind’ and so get slowed down. Light travelling sideways compared to the Earth won't face any extra resistance. In 1887 Michelson and Morley measured light travelling in these two directions and showed there is no difference in the speed of light. Discounting the remote possibility that all the ether in the universe was rotating around the sun in exact unison with their laboratory on Earth, this showed that light can't be travelling in anything like ether.

“So what difference did that make?”

With ether gone, the time was right for a complete rethink about how the universe works. That rethink was my theory of relativity. Now give your brain a rest for a while. Next time I’m going to throw some really strange ideas at you.