# Einstein’s Special Relativity

I’m sure most of you have heard of Albert Einstein and more importantly his contributions to the world of physics including the theory of relativity and the principle of mass-energy equivalence i.e. E = mc².

His theory of relativity can be broken down into:

• Special Relativity - speed of light and laws of physics are constant for everyone
• General Relativity - matter distorts space-time

So what did Einstein mean by special relativity? He believed that motion could be interpreted between different inertial frames of references. An inertial frame of references is basically a ‘snapshot’ in time and space in which Newton’s law of inertia holds i.e. any body remains in the same state of motion unless an outside force acts on it.

The two main postulates (fancy word for ‘assumptions’) of special relativity are:

1. All the laws of physics are the same in all inertial reference frames
2. The speed of light stays the same regardless of the motion of the source/observer

Firstly, let’s look at an example that helps us visualise the first postulate a bit better.

Imagine a person is standing at a bus stop and they are in a specific inertial reference frame. If they place their bag on the ground beside them and they exert no force on the bag, it will naturally remain stationary (Newton’s First Law) relative to them.

Now, if a bus drives past the bus stop at a constant speed, all the passengers are in another inertial reference frame. If one of the passengers places their bag on the bus floor, their bag is stationary relative to them.

Although the two different observers will disagree about the net velocity of the bag on the bus, they won’t disagree about the laws of physics, such as the conservation of momentum or the bag’s kinetic energy.

There are three different concepts that are covered by the second postulate:

a) The Relativity of Velocity

If a woman is standing on a bus, which is moving at 15 m/s, and she throws a ball at 5 m/s, logic dictates that the speed that would be calculated by an observer on the side of the road would be 15 + 5 = 20 m/s, but that is incorrect. Let’s take another example. If a spaceship is travelling at a speed of 3/5c towards the Earth and the spaceship emits a beam of light at the speed of c, then the speed of the light beam measured by someone on Earth would logically be 3/5c + c = 8/5c. This is clearly impossible as there is nothing faster than the speed of light (c). This is where a bit of maths comes in: you can use the relativistic formula to calculate the ‘addition of velocities’ correctly.

So if we apply the formula above, we get a final answer as c, which proves that speed of light, stays the same regardless of the motion of the source or observer.

b) The Relativity of Time

Let’s say that a man hiccups twice on a space ship that is travelling at 2/3c. Although the physics laws stay the same and the speed of light is uniform, the time measured between the two hiccups by me would be different to the time measured by the man on the spaceship. Seems weird, right? Well, time is relative. You can use the relativistic factor (also known as the Lorentz factor) to calculate the relative time measured.

When you look at the formula above, you will realise that the denominator of the fraction is never greater than 1 and so therefore, γ is always greater than or equal to 1. If suppose the time the man measured was T₁, the time measured by me would be T₂ and this is equal to γ * T₁. This means the time calculated by the observer will always be longer than the time measured by the actual passenger. In a different scenario, let’s say someone went on a space ship (speed of 0.99c) for 2 years. Since the value of the speed is so large, the value of γ is almost 50 and so the people on Earth would believe the person travelled for 50 * 2 = 100 years! This is known as time dilation.

c) The Relativity of Distance

Hate to break it to you but length is also relative. If we imagine a spaceship is hurtling through space at 9/10c and the passengers measure the length of the spaceship as 150m, we on Earth would disagree. Using the relativistic factor formula again (above), if the length of the space ship is L₁ from the passenger’s perspective, the length we would measure would be L₂ which is equal to L₁/γ. Since γ is always greater than 1, the length we would measure would be shorter than the length measured by the passenger. This is known as length contraction.

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