# Einstein's Postulates of Special Relativity

This is part of the HSC Physics course under the topic Light and Special Relativity.

### HSC Physics Syllabus

• analyse and evaluate the evidence confirming or denying Einstein’s two postulates:
– the speed of light in a vacuum is an absolute constant
– all inertial frames of reference are equivalent (ACSPH131)

### Inertial and Non-inertial Frame of Reference

A frame of reference is the perspective from which the motion of objects is observed and/or measured.
• During projectile motion: the path of a projectile and its velocities are determined relative to its starting or launch point.
• During the operation of motors and generators, the rotational motion of the armature is observed with reference to its pivot or axle.

An inertial frame of reference is a reference frame that has a constant velocity. This includes a velocity of 0 m/s.

• Example: A camera fixed to the ground is stationary and thus will capture a video from an inertial frame of reference.
• Note: Whilst the Earth orbits the Sun and thus experiences centripetal acceleration, we still consider it as an inertial frame of reference since this acceleration is negligible.

A non-inertial frame of reference is a reference frame is one that accelerates and thus does not have a constant velocity. This acceleration may constitute only directional changes and the speed of a non-inertial frame of reference can thus be constant.

• Example: A camera falling down will capture a video from a non-inertial frame of reference since the camera itself is experiencing gravitational acceleration.

In Special Relativity, it is important to consider both the motion of the observer and the object being observed. If both travel at a constant velocity, then both are in an inertial frame of reference. Only then is Special Relativity said to 'apply'. If either one are in a non-inertial frame of reference, then the effects of Special Relativity are still observed, but occur alongside the effects of General Relativity. General Relativity is not required for the HSC course.

### First Postulate – The Principle of Relativity

The first postulate of special relativity states that the laws of physics and electromagnetism are the same in any inertial frame of reference.

This implies that the experiments performed in stationary and moving inertial frames yield the same results. As such, it is impossible to experimentally determine if an inertial reference frame is stationary or moving without observing it from an external reference frame.

Suppose two passengers are standing in two train carriages observing the falling motion of a ball under the influence of gravity. The first passenger (left) is standing in a stationary train while the second passenger (right) is standing in a train that is moving at constant velocity.

Both passengers are in inertial frames of reference and the laws of Newtonian physics apply in the same way for them. Both people will observe the ball falling in a vertical path. If the train carriages are windowless, the two passengers will have no way of knowing whether their train is stationary or moving at constant velocity.

### Second Postulate – The Principle of the Constancy of Light's Speed

The second postulate of special relativity states that the speed of light in a vacuum is constant at c = 3 x 108 m/s in all inertial frames of reference.

The second postulate is an extension of the first postulate. In the electromagnetism theory proposed by Maxwell, the velocity of electromagnetic waves is given by

$$c=\frac{1}{\sqrt{\mu_0\epsilon_0}}$$

This equation relates the speed of light to magnetic and electric constants which by law should not vary with an observer's frame of reference. In other words, the equation implies that the speed of light should be constant regardless of the relative velocity between the source of light and the observer who is measuring its velocity.

This postulate has several implications, primarily it contradicts Newtonian relative motion. If you were travelling at 0.5c in the same direction alongside a beam of light, Newtonian mechanics says you would observe the speed of the light beam to be 0.5c. However, according to Special Relativity, you would still be observing the speed of light to be at c! This leads to many effects that will be discussed in future sections.

When a stationary person measures the speed of light emitted on a train at rest, the speed is simply c. However, when the speed of light is still c even when the train is moving relative to the person.

### Thought Experiment to Understand Special Relativity

Imagine a train travelling at the speed of light. A person on this train looks into the mirror placed at the front of the carriage.

Will this person see a reflection of themselves in the mirror?

Newtonian Physics – no reflection is seen

A reflection is seen by the person when a light ray travels from the person to the mirror and returns to the person's eyes.

When Newtonian relativity is applied to this thought experiment, the mirror is moving at the speed of light, which means the relativity velocity between light from the person and the mirror is zero. This implies the light will never reach the mirror and hence the person will not see a reflection.

However, this outcome contradicts the first postulate of special relativity which implies that a person in an inertial frame of reference, such as this one, will not be able to identify whether the frame of reference is stationary or moving at constant speed.

If the person cannot see their reflection in the mirror, it informs them that the train must not be stationary as a reflection would be see if this was the case.

Special Relativity – a reflection is seen

The contradiction derived from Newtonian relativity in this thought experiment supports the constancy of light's speed. The second postulate of special relativity states that light's speed is constant in a vacuum for all inertial frames of referenece.

This means, from the perspective of the person and mirror on the moving train, light's relative velocity is still c, as opposed to zero. When light's velocity relative to the mirror is no longer zero, it will reach the mirror and be reflected to return to the person's eyes.

Therefore, the person will see a reflection of themselves in the mirror.

Previous section: The Photoelectric Effect and Quantum Model of Light

Next section: Evidence for Einstein's Postulates