"The theory that explains how speed, mass, time, and space are all interrelated, published by Albert Einstein in 1905."

Table of contents: 

1. Galileo's Dictum.

2. The Central Truth.

3. Einstein attacks Space + Time.

4. The Third Branch.

5. Convince Me.

Nicolaus Copernicus was a mathematician and astronomer who was the first to propose the heliocentric model - the idea that the earth and other planets orbit the sun and the moon orbits the earth.

This was controversial and revolutionary, astronomers at the time (16th century) believed the sun, moon and other planets orbited the earth. This was after all the most logical explanation as it neatly explained the movement of the night sky. However, as the principle of relativity explains, objects in motion perceive themselves as stationary and all other objects as moving around them.

Unfortunately, during his life Copernicus's heliocentric model was rejected because people at the time thought that an object as huge as the earth could not be in motion. They argued (wrongly) that if the earth was in motion then surely some test could be performed to prove the nature of it's motion. When Copernicus failed to justify how the earth could be moving, the heliocentric model was discarded.

However, close to a century later, a physicist, astronomer and engineer from Pisa, Italy came to the aid of Copernicus's failed theory. His name: Galileo Galilei.

Throughout Galileo's life he argued against the astronomers of the day, saying that the earth revolved around the sun. His counter-argument to the reasoning that crushed the heliocentric model was as follows:

Imagine yourself standing on a moving conveyer belt that is traveling at a constant speed relative to the stationary objects around it. If you take a tennis ball and throw it directly upwards and then catch it again the ball returns to your hands in the same way as it would if you were standing still - what I mean by this, is you don't have to reach behind to catch it, both you and the ball have travelled with the conveyer belt. 

Galileo reasoned that the earth played the part of the conveyer belt and any action performed on the Earth was therefore affected by the Earth's motion. From this, he produced his dictum:

Scientists at the time were confused by light because it traveled so ludicrously fast that it appeared to defy the very laws of physics.

To show these strange effects, consider a tennis ball. If it is thrown at 10 m/s in a given direction by someone stood perfectly still, the stationary person measures the velocity of the tennis ball to be 10 m/s relative to them.

Now imagine a second person running at 6 m/s in the same direction as the tennis ball. As the tennis ball passes the second person, they measure the speed of the tennis ball to be 4 m/s relative to them. This was not a new concept, but one that predated Einstein's relativity and was well known in the scientific community at the time.

The behaviour of the tennis ball is not the same as the behaviour of light in this scenario. Imagine an identical experiment is repeated but this time rather than throw a tennis ball, person 1 switches on a torch and directs the beam in the direction that person 2 is running in, in such a way that the beam passes person 2.

Person 1 measures the speed of the beam of light as 690 million mph (poetic license is employed here) relative to their (stationary) motion. When experiments of this nature were first performed, it was predicted that person 2 would measure the speed of the beam of light as 690 million-6 mph, in the same way that they measured the tennis ball as moving slower relative to them.

The truth revealed shocked the scientific community – regardless of how quickly person 2 runs, they will measure the beam of light traveling past them at the same speed = 690 million mph.

Einstein summarised this in his central truth but it wasn't until much later that the phenomena was explained.

Time DesynchronisationThought Experiment.

A set of three hikers are moving through the woods in a straight line, one after another. For undetermined reasons, they have decided to maintain a set distance in-between the 3 walkers (d) which must remain constant and equal.

To ensure this, all the walkers follow a strictly straight path and all 3 move at the same speed.

Imagine yourself as stationary (relativeto the moving people), watching the line of walkers pass through the woods in front of you – moving from the left to the right across your field of vision. A physicist would say 'your reference frame is perpendicular to the observed object's direction of motion.'

In order to maintain this set distance between the walkers, the middle hiker communicates with the leading and trailing hiker by means of radio waves, which travel at the speed of light. Let's imagine the hikers want to listen to a piece of music at the exact same time as each other – this means they must all press play in synch. The middle walker communicates this by radio to the other two by sending the message '3,2,1 play.'

Relative to each other, the 3 walkers measure each other as stationary because all 3 are moving at identical speeds in the same direction (remember Galileo's dictum). This means that as the walker's measure it the distance in-between the middle walker and leading walker is the same as the distance between the middle walker and trailing walker. In other words, the walker's proper spacing is measured as constant and equal, as seen above in line 2.

The radio wave is traveling at the speed of light which is always a constant (remember Einstein's central truth), so as the hiker's measure it, the '3,2,1 play' message reaches them at the exact same time. They therefore all hit play together and enjoy the song in perfect unison – the three songs are synchronised.

However, this is not the version of events you measure. Because you perceive the walkers to be moving(remember the crews perceive each other to be at rest), you measure the '3,2,1 play' signal as taking longer to reach the leader than the trailer. This is because the message has to catch up to the leader whereas the trailer walks into it.

This means that from your perspective the trailer hits play before the leader and so the three songs are not played at the same time – they are desynchronised. In other words, the walker's coordinate spacing is not equal and constant. However, from the crew's perspective they all listen simultaneously as seen above in line 3.

So who is right?

The pre-relativity concept of time described it as a universal constant that was measurably the same in all parts of the universe. However, as seen in the previous thought experiment, if the speed of light is to remain a constant then different parts of spaceexperiencedifferent timeso the idea of universal consistency was shattered.

Einstein concluded that in order to keep the speed of light absolute rather than relative, time itself had to become relative rather than absolute.

The desynchronisation of time (think of the desynchronised songs played by the walkers) became a core pillar of special relativity and allowed Einstein to continue his series of thought experiments.

Length ContractionThought Experiment.

We return to our outing of walkers from the first thought experiment. Your reference frame remains unchanged and the 3 still wish to maintain equal and constant spacing between the trailing and leading people. However, in this scenario rather than co-ordinate a sing-a-long, they wish to walk faster. In order to achieve this without violating the rules of spacing, all three will have to accelerate at the exact same time - if any of the hikers accelerate too late or too early the space between them will have changed.

The middle hiker broadcasts the signal '3,2,1 speed up' (by means of radio waves and so the message travels at the speed of light). In exactly the same way as the earlier signal, the walkers perceive the message to arrive simultaneously. And so all 3 start walking faster at the same time. The proper space between them remains constant and the walkers remain happy. This is seen in line 1 above.

Once again this is not the series of events that you, the independent observer, see! Just the same as in the first scenario, you perceive the trailing walker as receiving the message before the leading walker and therefore accelerating first. This means that for some amount of time( the longer the distance between the first and third walker the longer the time) the trailer is traveling fasterthan the other 2 hikers. We can see this in the second line above.

The middle walker also travels faster relative to the leader for some amount of time – the leader is the last to accelerate. The practical application of this is that you perceive the space between the walkers shrinking - their coordinate spacing has shrunk (observe line 3). But as they perceive it, the spacing between them remains constant and equal.

Once again we ask: who is right?

The way Einstein explained the shrinking of the space between the ships is to realise that the people themselves are made of atoms, with a certain space between each atom. In this way, the moving atoms are like miniature hikers and so just as you measure the distance between hikers being reduced, you also measure the distance between the atomsinside the hikersbeing reduced(in the world of thought experiments we have very sensitive measuring equipment!).

The space between the atoms is shrinking at the same rate as the space between walkers is shrinking – space itself has shrunk! IT IS SO ABSOLUTELY VITAL TO NOTE THAT THE SPACE ONLY SHRINKS IN THE DIRECTION OF MOTION OF THE OBJECT: THE WALKERS HAVE GOT SKINNIER BUT REMAIN THE SAME HEIGHT.

It can be hard to wrap your head around this concept; the idea of shrinking space is perhaps harder to understand than that of changing time because as humans our perception of space is much more concrete than that of time. By this I mean that because time is already an abstract concept, when I tell you that motion through time has changed I'm making an abstract thing more abstract. If I start messing around with space, which is much more solidly understandable, it seems stranger.

Time DilationThought Experiment.

By combining the ideas of time desynchronisation and length contraction, another change to the idea of time can be made through a third thought experiment:

Imagine two identical cars pass each other on opposite sides of the road and you want to find out their relative speed past each other. There are two ways to find out:

Way 1: riding in the nose of your car measure how long it takes for you to pass from the nose to the tail of the other car. This is seen in line 1 above.

Way 2: measure how long it takes the nose of the passing car to go from the nose to the tail of your car (this method requires two people in your car.) This is seen in line 2 above.

At first glance, these methods should produce the same result but once relativistic logic is applied we find that the time measured by way 1 is shorter than the one way 2 measures.

This is because of length contraction. As you observe the passing car in method 1, you measure its length to be shorter because the ship has contracted space (in the direction of its motion). This is only true because you're reference frame is perpendicular to the car's motion.

However, in method 2 the length of the passing car is irrelevant and so it appears to you that method 1 gives a shorter length of time (and so a faster relative speed) than method 2.

Now we reach the fun part.

Suppose another avid physicist is riding in the other car and they also want to measure the relative speeds of the two cars. Their plan of attack is identical to yours and they use both method 1 and method 2.

There is no special view of the universe, that is to say there is no reference frame which is any more/less reliable than another reference frame. This means that the other physicist measures method 1 to take less time than method 2 in the exact same way that you did.

It is important to note here that method 1 for them is method 2 for you (and vice versa) as the roles are reversed.

How can it be that they measure method 2to be faster but you measure method 1 to be faster?

There is only one way, as Einstein realised, to explain this and it means accepting another change in the way you view time. It must be that you measure the other physicist's clock to be slow, that is it ticks at a slower speed in comparison to your clock.

You perceive their clock to be slow so from your point of view, the propertime produced by your clock is faster than the coordinatetime you measure from their clock.

This effect of time is known as time dilation and it describes the phenomena that as a body travels through space, its speed through time is perceived by others to be slowed (the object themselves measures their proper time to be correct and all other times slowed in the same way both you and the other physicist believe they are correct).

An interesting note on time dilation is that time is slowed by the same factor that the moving object is shrunk by length contraction. The length by which the object is shrunk and the subsequent slowing down of time are in direct proportion to each other. This can be represented mathematically by a constant called the Lorentz factor, which we will have lots of fun with in the next chapter.

A good way to visualise space contraction (the fancy relativity term for shrinking space) is to imagine a drawing of the three walkers (as seen right in an exaggerated way) . When viewed from a perpendicular frame of reference, the hikers appear to have a constant width (x) and also appear to have some constant distance (xd) between them.

Now imagine the drawing is rotated so that you view it from side on. The new walker width (y) and the distance (yd) between them has also shrunk.

The rate of shrinking is proportional as seen in x/y = xd/xy. Therefore, space has shrunk!

A Thought Experiment with Cars and Crates.

The energy (work done) put into an object is calculated by:

Work done (E) = Force (F) x Distance (d)

Distance is how long an object moves at a given speed so:

E = F x Speed (s) x Time (t)

Remember the above formula carefully.

Picture a perfectly circular road with a car driving around it. If we assume the road to be frictionless (we are allowed to do this because we are currently experimenting in the mysterious world of thought experiments). We know from Newton's first law that the car would keep going around the track forever- assuming that the car already had some motion.

Returning to our particle accelerators, we can see that when an electron is accelerated up to 0.99c, its speed is essentially c and can hardly change at all so the car/crate formula can essentially be rewritten as:

E = m x c^2

Where c is the speed of light (in a vacuum). This equation is perhaps Einstein's most famous work and it was certainly revolutionary at the time because it allowed scientists to work out the weight of energy by rearranging the equation:

m = E / c^2

We have found our convenient way to measure the mass of energy: an electron travelling at (almost) the speed of light has this much mass added per unit of energy. Therefore, all types of energy follow this equation.

One easy pitfall to fall into is to think that an object's mass always increases if its speed increase. However, MASS ONLY INCREASES IF ENERGY IS PUT INTO THE SYSTEM NOT CONVERTED.

To prove this, think of a rocket accelerating as it lifts off from the ground. It may be assumed that it gains mass as it has now greater kinetic energy. However, there is no associated increase in mass because no energy is transferred into the system.

The associated mass-energy of the chemical potential energy in the fuel is the same as the kinetic energy the rocket has when moving (assuming no friction). Therefore, energy has only been converted within the system not added to the system and so it is logical no mass increase is seen.

Time Dilation Proof.

Herbert Ives was an anti-relativity physicist in the 1930s and 1940s. Ironically he performed an experiment that confirmed the effects of time dilation although he argued many different conclusions to the outcome.

An experiment to provide concrete evidence for special relativity was exceptionally hard to create because to look for time dilation or length contraction the object would have to be moving at relativistic speeds (a reasonable fraction of the speed of light) and the energy required for this is ludicrous.

Ives was cunning though, he used a strong electric field to accelerate hydrogen atoms in a glass vial. Modern day particle accelerators use a very similar concept but use strong magnetic fields rather than electric ones.

Modern day particle accelerators can get atoms to move at 99.9999999% the speed of the light. Almost 100 years earlier, Ives managed to get these ions moving at around 1100 miles per hour, around 0.000164% the speed of light. Although it sounds puny, the speed of Ives experiment was a scientific marvel at the time and allowed time dilation to be observed.