The Speed of Light: A very odd constant

Advertisement
One of the most remarkable things about light is its speed. At about 300,000 kilometres per second (186,300 miles per second) it's the fastest thing there is. Nothing, no matter how hard it tries, can go any faster. The speed of light is certainly very impressive, but it has another quality that is even more remarkable. In free space (i.e. a vacuum) its speed is constant. At first this doesn't seem all that odd, but, as we shall see, it's actually one of the strangest things in the universe. Before we can appreciate the significance of the speed of light being constant we need to learn a little more about light itself.

The Electromagnetic Spectrum

The word "light" has a more complex meaning in physics than it does in everyday life. The light we see by is referred to as "visible light" and is a small part of the electromagnetic spectrum. Radio waves, X-rays and microwaves are all part of the same electromagnetic spectrum. The difference between visible light and all the other forms of electromagnetic radiation is in the magnitude of the wavelength of the light. Light can be thought of as travelling in waves, the distance between any two crests of the wave being the wavelength:
Each different colour that we can see has its own particular wavelength. For example, red light has a has a longer wavelength than blue light. White light, similar to the light we get from the Sun or a light bulb, is a mixture of all the different colours we can see. If we take a look at a section of the electromagnetic spectrum we can see that the visible light our eyes are sensitive to forms only a small part of the total "kinds" of light we can makes use of:
The wavelength of any wave is related to its frequency (that is, if the wave is moving, the number of crests that pass a stationary point in a second) and its speed. These three quantities are related by the equation:
An explanation of this equation plus worked examples is available here. We now have the tools we need to examine some of the more interesting properties of light waves.

The Doppler Effect

Water waves, sound waves and light waves all share a number of properties, including what is known as the Doppler Effect. This says that when a wave is approaching us the length of each individual wave is compressed and when the wave is moving away from us the length of each individual wave is stretched out. For sound waves this manifests itself as a rise in pitch (i.e. frequency) for an approaching wave and a decrease in pitch for a receding wave. This is why we hear the siren of a police car change pitch as it passes us:
As we have noted, the speed, frequency and wavelength of a wave are all mathematically related. If we know any two of the three parameters we can calculate the third. For example, the speed of the wave is calculated from a rearrangement of the equation we saw in the previous section:
In fact, it is this equation and the Doppler effect that are behind the "speed trap guns" used by police forces. "Light" entering the gun has its frequency measured against a set value. The difference in the two frequencies is fed into a modified form of the above equation and a speed is calculated. While water and sound waves don't have constant speeds we've said that light does. So how can the police speed gun detect our speed? We know that the speed of the light stays the same so it must be the wavelength and therefore the frequency that changes. This manifests itself as a change in the colour of the light. The change is far too small to be seen with the naked eye, but quite easy to detect using electronic equipment, such as a speed trap gun. As a light wave approaches us its frequency is "shifted" towards the blue part of the spectrum. That is, if the light was white to begin with it will now have its wavelength compressed in such a way that it begins appear blue. Likewise, if the light is moving away from us it will appear red because its wavelength is stretched and its frequency is correspondingly lower than before. It's only when the light source is stationary that we can see what colour it really is.
The wavelength of each colour of light is different
We can use the Doppler effect of moving light sources to establish something quite extraordinary about the speed of light, and the universe.

An impossible Result?

In the mid-1800s the physicist James Clerk Maxwell discovered the theoretical basis behind electromagnetism. His work was so good that it's still used today in the design of electric motors and a thousand other items that we take for granted. Your computer probably has at least one electric motor driving the hard disk drive and maybe another for a CD or DVD drive. Even in his day Maxwell's equations on electromagnetism were seen as very far reaching and of practical use in any number of applications. There was, however, a problem. Every time Maxwell rearranged his equations to make the speed of light the subject and plugged in the numbers he got a very strange result. The speed of light always came out the same, regardless of the speed of the light source. This result seemed absurd! It's common sense that anything cast from a moving body will have a speed that's calculated from both the moving body and the object. For example, the speed of a bullet is often said to be twice the speed of sound, that is, around 1500 mph. This is only true if the gun that fired the bullet is stationary. If we put the gun on an aeroplane flying at 500 mph it's obvious that the initial speed of a bullet as it leaves the gun is now 1500 mph + 500 mph = 2000 mph relative to a stationary observer:
What Maxwell's equations seemed to be showing was that light didn't behave like this, at least in theory. Instead the equations stated that the speed of light was the same no matter what the speed of the source. In other words it wasn't possible to add or subtract the speed of the object carrying the light source:
This result was so strange that it was seen as an embarrassment in an otherwise sound and well tested theory. No one accepted its conclusions at face value and it was thought only a matter of time before a better theory was found which showed light to behave the way everyone expected it to. For the sake of completeness I will include the equation, as derived by Maxwell, that is now accepted as the correct theoretical basis for calculating the speed of light:
While a full explanation of this equation is outside the scope of these pages a few words are perhaps instructive. We have said that light is part of the electromagnetic spectrum. The permittivity of free space is otherwise known as the electric constant and is derived from the force of electricity felt by two electrically charged particles in a vacuum. The permeability of free space is known as the magnetic constant and is derived from the magnetic force felt on an object in a magnetic field. Light is a combination of both of these constants; it is both electric and magnetic, hence light is electromagnetic.

Another impossible Result?

Towards the end of the 19th Century it was fondly thought that the work of the world's physicists was almost complete. There were only a few odds and ends to tie up and that would be the end of the matter. One of these odds and ends was the rather annoying prediction in Maxwell's equations that the speed of light was constant, and many people set out to show that this was the nonsense it seemed to be. No one really believed that the speed of light could possibly be constant and it was just a matter of finding some experimental evidence to show that light behaved the way everyone expected it to. In 1887 two particularly ingenious experimental physicists conducted an experiment to measure the speed of light changing as a consequence of the Earth travelling around the Sun. This experiment would use the Doppler effect as its basis. The physicists were the Americans Albert Michelson and Edward Morley, and they are now, sadly, almost always remembered for all the wrong reasons. Around this time it was thought, and widely accepted, that space was filled with a transparent substance called the "ether". It was this, it was thought, that allowed light waves to get from place to place, just as air allows sound to travel (note that sound can't travel in a vacuum). The arguments for the ether were so strong that we still refer to it today. For example, we talk of radio waves travelling through the ether, and it wasn't such a long time ago that many computers were connected to networks by the Ethernet. Using a series of mirrors and an instrument for measuring the wavelength of light (called an interferometer) the two scientists carried out what is now referred to as the Michelson-Morley Experiment. They expected, as did everyone else, that they would find that the Earth's rotation around the Sun would show up as a colour shift in the (stationary) ether due to the speed of light being added to the Earth's speed in the direction of orbit, and subtracted in the direction that the Earth was moving away from.
What they found however just didn't seem to make sense. Their results showed that there was no difference in the speed of light in either direction. Not only that, but they couldn't actually detect the ether at all! Everyone, including Michelson and Morley, put this down to experimental error. The equipment was improved and the experiment tried again. Still the results came out the same; the speed of light seemed to be constant! In fact, the experiment was carried out a number of times, each time with improved equipment and every time the results came out the same. With hindsight it's easy to criticise the whole scientific community for not seeing what was staring them in the face. This would be quite unfair, however. They were being asked to believe something that challenged not only all of the very successful scientific doctrine of the previous 200 years, but also common sense itself. However, there is no evidence that the universe is constructed in such a way that it always has to make sense to mere humans beings! Just occasionally though, there are human beings who look at the universe a little differently.

Enter Albert Einstein

In 1905 Albert Einstein was working as a patent clerk in Switzerland. He always claimed he new nothing of the Michelson  and Morley experiments and this is quite possibly true; Einstein's physics were usually carried out without reference to experimental results. Instead he relied on his own intuition and mathematical experimentation. His isolation from the physics community was probably a bonus in that he was allowed to think freely without being swayed by contemporary ideas or doctrine. Einstein started by asking the almost child-like question "what would it be like to ride on a light beam?" The answer to this simple question eventually led him to deduce his theory of relativity. In order for his ideas and equations to make any sense he had to do something no one had dared to do before – he had to accept the constancy of the speed of light at face value. Once this is done the constancy of the speed of light is one of only two postulates needed for the whole of special relativity:
Postulate I: The principle of relativity: The laws of physics are the same in same in all inertial frames. Postulate II: The principle of the constancy of the speed of light: The speed of light (in a vacuum) has the same constant value c in all inertial frames.
The whole of special relativity; time dilation, the twin paradox, moving clocks running slowly, space-time and even E = mc2  all stem from just these two postulates. Once the speed of light is accepted as a constant, as it had already been seen to be both in theory and experiment, everything slots into place. That the speed of light is constant has been checked over and over again using ever more sophisticated equipment. Probably the most startling demonstration of the second postulate being correct is the detonation of an atomic bomb. Whatever one thinks of the merits of such devices it's undeniable that they work. The basic principle behind an atomic bomb is that matter is converted into energy via the famous equation E = mc2. This equation is derived directly from the second postulate. There are few more convincing ways in which a "theory" can be demonstrated to be correct.
Albert Einstein (1879 – 1955)
Bullet speed = 1500 mph
Jet speed = 500 mph Bullet speed = 1500 mph Total bullet speed = 2000 mph
Copyright © http://www.emc2-explained.info
Jet speed = zero mph Light speed = 186,300 miles/sec Jet speed = 1500 mph Light speed still  = 186,300 miles/sec Copyright  http://www.emc2-explained.info
Addition of normal speeds
The speed of light remains constant
Wavelength
Copyright © http://www.emc2-explained.info
The wavelength of a wave
Compressed sound wave Stretched sound wave Direction of car The Doppler effect: As the police car approaches the sound waves are compressed and the pitch rises. As it recedes the sound waves are stretched and the pitch decreases. Copyright  http://www.emc2-explained.info
Copyright © http://www.emc2-explained.info
Speed of Earth plus light speed? Speed of Earth minus light speed? Earth in orbit around the Sun Copyright  http://www.emc2-explained.info
Advertisement  

The Speed of Light: A very odd constant

One of the most remarkable things about light is its speed. At about 300,000 kilometres per second (186,300 miles per second)  it's the fastest thing there is. Nothing, no matter how hard it tries, can go any faster. The speed of light is certainly very impressive, but it has another quality that is even more remarkable. In free space (i.e. a vacuum) its speed is constant. At first this doesn't seem all that odd, but, as we shall see, it's actually one of the strangest things in the universe. Before we can appreciate the significance of the speed of light being constant we need to learn a little more about light itself.

The Electromagnetic Spectrum

The word "light" has a more complex meaning in physics than it does in everyday life. The light we see by is referred to as "visible light" and is a small part of the electromagnetic spectrum. Radio waves, X-rays and microwaves are all part of the same electromagnetic spectrum. The difference between visible light and all the other forms of electromagnetic radiation is in the magnitude of the wavelength of the light. Light can be thought of as travelling in waves, the distance between any two crests of the wave being the wavelength:
Each different colour that we can see has its own particular wavelength. For example, red light has a has a longer wavelength than blue light. White light, similar to the light we get from the Sun or a light bulb, is a mixture of all the different colours we can see. If we take a look at a section of the electromagnetic spectrum we can see that the visible light our eyes are sensitive to forms only a small part of the total "kinds" of light we can makes use of:
The wavelength of any wave is related to its frequency (that is, if the wave is moving, the number of crests that pass a stationary point in a second) and its speed. These three quantities are related by the equation:
An explanation of this equation plus worked examples is available here. We now have the tools we need to examine some of the more interesting properties of light waves.

The Doppler Effect

Water waves, sound waves and light waves all share a number of properties, including what is known as the Doppler Effect. This says that when a wave is approaching us the length of each individual wave is compressed and when the wave is moving away from us the length of each individual wave is stretched out. For sound waves this manifests itself as a rise in pitch (i.e. frequency) for an approaching wave and a decrease in pitch for a receding wave. This is why we hear the siren of a police car change pitch as it passes us:
As we have noted, the speed, frequency and wavelength of a wave are all mathematically related. If we know any two of the three parameters we can calculate the third. For example, the speed of the wave is calculated from a rearrangement of the equation we saw in the previous section:
In fact, it is this equation and the Doppler effect that are behind the "speed trap guns" used by police forces. "Light" entering the gun has its frequency measured against a set value. The difference in the two frequencies is fed into a modified form of the above equation and a speed is calculated. While water and sound waves don't have constant speeds we've said that light does. So how can the police speed gun detect our speed? We know that the speed of the light stays the same so it must be the wavelength and therefore the frequency that changes. This manifests itself as a change in the colour of the light. The change is far too small to be seen with the naked eye, but quite easy to detect using electronic equipment, such as a speed trap gun. As a light wave approaches us its frequency is "shifted" towards the blue part of the spectrum. That is, if the light was white to begin with it will now have its wavelength compressed in such a way that it begins appear blue. Likewise, if the light is moving away from us it will appear red because its wavelength is stretched and its frequency is correspondingly lower than before. It's only when the light source is stationary that we can see what colour it really is.
The wavelength of each colour of light is different
We can use the Doppler effect of moving light sources to establish something quite extraordinary about the speed of light, and the universe.

An impossible Result?

In the mid-1800s the physicist James Clerk Maxwell discovered the theoretical basis behind electromagnetism. His work was so good that it's still used today in the design of electric motors and a thousand other items that we take for granted. Your computer probably has at least one electric motor driving the hard disk drive and maybe another for a CD or DVD drive. Even in his day Maxwell's equations on electromagnetism were seen as very far reaching and of practical use in any number of applications. There was, however, a problem. Every time Maxwell rearranged his equations to make the speed of light the subject and plugged in the numbers he got a very strange result. The speed of light always came out the same, regardless of the speed of the light source. This result seemed absurd! It's common sense that anything cast from a moving body will have a speed that's calculated from both the moving body and the object. For example, the speed of a bullet is often said to be twice the speed of sound, that is, around 1500 mph. This is only true if the gun that fired the bullet is stationary. If we put the gun on an aeroplane flying at 500 mph it's obvious that the initial speed of a bullet as it leaves the gun is now 1500 mph + 500 mph = 2000 mph relative to a stationary observer:
What Maxwell's equations seemed to be showing was that light didn't behave like this, at least in theory. Instead the equations stated that the speed of light was the same no matter what the speed of the source. In other words it wasn't possible to add or subtract the speed of the object carrying the light source:
This result was so strange that it was seen as an embarrassment in an otherwise sound and well tested theory. No one accepted its conclusions at face value and it was thought only a matter of time before a better theory was found which showed light to behave the way everyone expected it to. For the sake of completeness I will include the equation, as derived by Maxwell, that is now accepted as the correct theoretical basis for calculating the speed of light:
While a full explanation of this equation is outside the scope of these pages a few words are perhaps instructive. We have said that light is part of the electromagnetic spectrum. The permittivity of free space is otherwise known as the electric constant and is derived from the force of electricity felt by two electrically charged particles in a vacuum. The permeability of free space is known as the magnetic constant and is derived from the magnetic force felt on an object in a magnetic field. Light is a combination of both of these constants; it is both electric and magnetic, hence light is electromagnetic.

Another impossible Result?

Towards the end of the 19th Century it was fondly thought that the work of the world's physicists was almost complete. There were only a few odds and ends to tie up and that would be the end of the matter. One of these odds and ends was the rather annoying prediction in Maxwell's equations that the speed of light was constant, and many people set out to show that this was the nonsense it seemed to be. No one really believed that the speed of light could possibly be constant and it was just a matter of finding some experimental evidence to show that light behaved the way everyone expected it to. In 1887 two particularly ingenious experimental physicists conducted an experiment to measure the speed of light changing as a consequence of the Earth travelling around the Sun. This experiment would use the Doppler effect as its basis. The physicists were the Americans Albert Michelson and Edward Morley, and they are now, sadly, almost always remembered for all the wrong reasons. Around this time it was thought, and widely accepted, that space was filled with a transparent substance called the "ether". It was this, it was thought, that allowed light waves to get from place to place, just as air allows sound to travel (note that sound can't travel in a vacuum). The arguments for the ether were so strong that we still refer to it today. For example, we talk of radio waves travelling through the ether, and it wasn’t such a long time ago that many computers were connected to networks by the Ethernet. Using a series of mirrors and an instrument for measuring the wavelength of light (called an interferometer) the two scientists carried out what is now referred to as the Michelson-Morley Experiment. They expected, as did everyone else, that they would find that the Earth's rotation around the Sun would show up as a colour shift in the (stationary) ether due to the speed of light being added to the Earth's speed in the direction of orbit, and subtracted in the direction that the Earth was moving away from.
What they found however just didn't seem to make sense. Their results showed that there was no difference in the speed of light in either direction. Not only that, but they couldn't actually detect the ether at all! Everyone, including Michelson and Morley, put this down to experimental error. The equipment was improved and the experiment tried again. Still the results came out the same; the speed of light seemed to be constant! In fact, the experiment was carried out a number of times, each time with improved equipment and every time the results came out the same. With hindsight it's easy to criticise the whole scientific community for not seeing what was staring them in the face. This would be quite unfair, however. They were being asked to believe something that challenged not only all of the very successful scientific doctrine of the previous 200 years, but also common sense itself. However, there is no evidence that the universe is constructed in such a way that it always has to make sense to mere humans beings! Just occasionally though, there are human beings who look at the universe a little differently.

Enter Albert Einstein

In 1905 Albert Einstein was working as a patent clerk in Switzerland. He always claimed he new nothing of the Michelson  and Morley experiments and this is quite possibly true; Einstein's physics were usually carried out without reference to experimental results. Instead he relied on his own intuition and mathematical experimentation. His isolation from the physics community was probably a bonus in that he was allowed to think freely without being swayed by contemporary ideas or doctrine. Einstein started by asking the almost child-like question "what would it be like to ride on a light beam?" The answer to this simple question eventually led him to deduce his theory of relativity. In order for his ideas and equations to make any sense he had to do something no one had dared to do before – he had to accept the constancy of the speed of light at face value. Once this is done the constancy of the speed of light is one of only two postulates needed for the whole of special relativity:
Postulate I: The principle of relativity: The laws of physics are the same in same in all inertial frames. Postulate II: The principle of the constancy of the speed of light: The speed of light (in a vacuum) has the same constant value c in all inertial frames.
The whole of special relativity; time dilation, the twin paradox, moving clocks running slowly, space-time and even E = mc2 all stem from just these two postulates. Once the speed of light is accepted as a constant, as it had already been seen to be both in theory and experiment, everything slots into place. That the speed of light is constant has been checked over and over again using ever more sophisticated equipment. Probably the most startling demonstration of the second postulate being correct is the detonation of an atomic bomb. Whatever one thinks of the merits of such devices it's undeniable that they work. The basic principle behind an atomic bomb is that matter is converted into energy via the famous equation E = mc2. This equation is derived directly from the second postulate. There are few more convincing ways in which a "theory" can be demonstrated to be correct.
Albert Einstein (1879 – 1955)
Bullet speed = 1500 mph Jet speed = 500 mph Bullet speed = 1500 mph Total bullet speed = 2000 mph Jet speed = zero mph Light speed = 186,300 miles/sec Jet speed = 1500 mph Light speed still  = 186,300 miles/sec
Addition of normal speeds
The speed of light remains constant
Wavelength
Copyright © http://www.emc2-explained.info
Compressed sound wave Stretched sound wave Direction of car The Doppler effect: As the police car approaches the sound waves are compressed and the pitch rises. As it recedes the sound waves are stretched and the pitch decreases.
Copyright © http://www.emc2-explained.info
Copyright  http://www.emc2-explained.info Speed of Earth plus light speed? Speed of Earth minus light speed? Earth in orbit around the Sun Copyright  http://www.emc2-explained.info