UY1: Einstein’s Postulates of Special Relativity & Inertia Frames

Einstein’s First Postulate states that the laws of Physics are the same in every inertial frame of reference.

Inertial Frames

An inertial frame of reference is a frame of reference where Newton’s first law applies in its simplest form:

An object in motion stays in motion, and an object at rest stays at rest unless an external force acts on it.

In an inertial frame,

  • There are no “ficticious” forces. All forces are real.
  • The laws of Physics are simplest in this frame as there is no need to deal with ficticious forces.

Therefore, inertial frames may be moving but they are not accelerating.

So… Are you in an inertial frame right now?

Arguments for “no”:

  • You know that you are on a rotating Earth.
  • Therefore, you experience an acceleration that comes from the Earth’s rotation (Coriolis forces).
  • Therefore, you are not in an inertial frame right now.

Arguments for “yes”:

  • You do not notice any additional force beyond gravity (The Coriolis force is not very noticeable).
  • Therefore, you are in an inertial frame.

It should be obvious to you that we are not in an inertial frame. Although we are not in an inertial frame, there may be cases where the inertial frame is a good approximation.

  • Knowing when an approximation is reasonable will come in useful when simplifying a problem.
  • Suitable approximations can greatly simplify a problem with minimal loss of precision.

Consider a train moving along a straight track at constant speed.

  • In the ideal case of a perfectly straight track, the reference frame of the train is an inertial frame.
    • A person in the train does not feel any additional forces.
  • In a real system where the train shakes as it moves, the reference frame of the train experiences accelerations from side to side.
    • A person in the train will feel additional forces in the side to side direction although nothing seems to be acting on the observer.

Einstein’s Second Postulate states that the speed of light in a vacuum $c$ is the same in all inertial frames of reference and is independent of the motion of the source.

There is a weird effect that comes out from this postulate. Imagine a spaceship moving at a certain speed relative to an observer on Earth. The spaceship shines a light beam, which moves at a speed c relative to the spaceship. Einstein’s Second Postulate forces the speed of the light beam to be at speed c, relative to the observer on Earth. This is in contrary to “common sense” – which will assume the light beam to travel a a speed higher than c (speed of spaceship + speed of light), relative to the observer on Earth.

However, from numerous experimental tests, this universality of the speed of light has been thoroughly proven.

All observers will see the light beam moves at the same speed, $c$.

One of the experiment done is the Michaelson-Morley experiment. The Michaelson-Morley experiment was an effort to measure the speed of light in different directions. The experiment proved the Einstein’s second postulate and means that it is impossible for an inertial observer to travel at the speed of light in vacuum.



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