The Postulates Of Special Relativity

The Postulates Of Special Relativity

Special Relativity is a theory proposed by Albert Einstein.

It is used to model motion of objects moving at a constant velocity (inertial reference frames) and where the effects of gravity are negligible. This is why it is called special relativity as it only works in these specific cases.
Later on Einstein managed to develop the theory of general relativity which can be used for accelerating reference frames and where gravity is acting.

Einstein takes two statements and assumes them to be true despite there seeming to be an inconsistency. They came from Galilean relativity and Lorenz Maxwell's equations on electromagnetic waves (light is a type of electromagnetic wave) . By holding both postulates to be true; Einstein changed the ideas on how the universe worked and found many new ideas such as E=mc^2, time dilation and length contraction (will be discussed later).

The First Postulate

The first assumption (postulate) that was made is that the laws of physics, when stationary, are the same as when moving at a constant velocity.

If you are standing still and throw a ball upwards what would happen? The ball would travel vertically up then down.
If you did the same thing while on a cruising airplane: the same thing would happen. The ball would travel vertically up then down.
If the plane had no windows and there was no turbulence; you would not be able to tell the plane was travelling at a constant velocity and you might think the plane is actually stationary!
You would feel no forces acting on you since Newton's 2nd law of motion states that F=ma.

Force = mass x acceleration.
Since acceleration is 0
Force = mass x 0
Any number x 0 = 0 and so
Force = 0

Galileo Galilei did this experiment on a ship in the hull and saw that the ball fell straight down and that he could not tell whether the ship was stationary or moving at a constant velocity.


If we go back to the plane and look out the window we would see clouds going past the plane. From out point of view we feel no forces and so could think that we are stationary and that the clouds are the ones moving past us.
If we however saw things from the clouds point of view, they would say that we are the ones moving and that they are not moving. The clouds would also claim that you did not drop the ball straight down. They would see the ball fall but also move at the same velocity as the plane. They would see the ball take a downward curving path. This means that you would measure the balls horizontal speed to be 0 but the cloud would measure it to be the same speed as the plane. This shows that there is no true value for an objects velocity but that they depend on the point of view (frame of reference).

You can continue to see this if you consider that the earth is spinning. If you were standing still you would say you are moving at 0 m/s (meters per second) but from the point of view/frame of reference of the moon; you move at 1600km/hr since the Earth is spinning. This again changes when you look from the Sun's frame of reference. The Earth orbits the Sun at 30km/s and so from the Sun's frame of reference you actually move at 30km/s. This can continue and you can see velocities change as the frame of reference changes.

If this idea is hard to understand, this video linked below shows these kind of examples of how different perspectives lead to different thoughts on how an object moves.

https://www.youtube.com/watch?v=bJMYoj4hHqU

After understanding this you may believe that if you throw a ball at 50 miles per hour out of a car travelling at 50 miles per hour, an observer by the road (stationary) would measure it to be travelling at 100 miles per hour. This is correct. The person in the car would measure it to be travelling at 50 miles per hour. This is also correct due to how frames of reference change measurements for velocity.

We now know that the laws of physics in any inertial (moving at a constant velocity) frame of reference are the same.

The Second Postulate

If we change this however and say the car is travelling at half of the speed of light and we shine a light out of the car. How fast is the light travelling? ( We will from now on refer to the speed of light in a vacuum (3 x 10⁸ meters per second) as c.) Your initial thought might be that the person in the car measures light to be travelling at c and the person on the road measures light to be travelling at 0.5c + c (1.5c). According Galilean relativity (what we just looked at) this is correct. We can see that speeds are additive (you can add them up). 

This example further supports this.
For an ball moving at speed u' in frame of reference (e.g a car) moving at a speed v. The speed of the ball if looking from the road would be v + u'. We will call this u.

We however are always told that c is the fastest speed anything in the universe can travel at. Which one is correct then? Surprisingly both observers measure the light to be travelling at c. There were many experiments before 1905 supporting this and showing the speed of light to be invariant. This brings us to the second assumption which must be made. All observers measure light at the same speed (c), no matter the frame of reference. This contradicts the Galilean relativity that u' + v = u and our intuition. This is because strange things occur when travelling at the speed of light.

This is the apparent contradiction between the postulates and by assuming them both to be true; the theory of special relativity is derived and completely changes the way we now think about space and time.

Thanks for reading and I encourage you to leave comments about your thoughts on the topic, things I haven't covered in this post, how you think I can improve my posts, what you liked about this topic etc..

If you enjoyed this post or any of my others, follow this blog.

Be sure to also share this around with your friends and family.