Galilean Relativity/ Galilean invariance

• the laws of motion are the same in all inertial frames of reference

Limitations of Newtonian Mechanics

• Handling of Constraints:

  • Constraints in systems can complicate the analysis and predictions.

• Galilean Invariance:

  • Galilean invariance (Newtonian relativity) is violated by electromagnetic phenomena.
  • This leads to the development of the Special Theory of Relativity.

• Stability of Atoms:

  • The stability of atoms cannot be explained by classical physics.
  • This limitation leads us to ultimate brainfuck , please clap for quantum mechanics.

Reasons & Postulates of Special Theory of Relativity

• Electromagnetic Phenomena:

  • The electromagnetic wave equation is not Galilean invariant.
  • Observations of the same phenomena differ in different inertial frames.

• Moving Coil and Magnet:

  • When a magnet is at rest, its magnetic field exerts forces on charges in a moving coil, generating current:
  $$\text{Force}=q(\overrightarrow{v}\times \overrightarrow{B})$$

• Moving Magnet and Coil:

  • When a coil is at rest and a magnet moves, the time-varying magnetic flux creates an electric field on charges, described by Faraday's Law of induction:
  $$\text{Motive EMF}=-\frac{d{\mathrm{\Phi }}_B}{dt}$$

• Speed of Light:

  • The speed of light is the same in all inertial frames, supported by experimental evidence.

Postulates of Special Theory of Relativity (Einstein, 1905)

1. Same Physical Laws:

   • The same physical laws apply in all inertial frames.

2. Constant Speed of Light:

   • The speed of light has the same value in all inertial frames.

• Good Resource to enjoy:
  https://youtube.com/playlist?list=PLoaVOjvkzQtyjhV55wZcdicAz5KexgKvm&si=KrO6LX8HW971CYmu

• SpaceTime Diagram

Symmetry of Observers:

Symmetry and Relative Velocity