Class 12 > Unit # 24: Relativity > Special Theory Of Relativity & Lorentz Transformation

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Special Theory Of Relativity & Lorentz Transformation - Class 12 Physics - Unit 24 Relativity

Video Lecture: Special Theory Of Relativity & Lorentz Transformation

Watch the complete physics lecture exploring the breakdown of absolute quantities, the two postulates of special relativity, the constancy of light speed, and Lorentz transformations:

Introduction to Relativity & Postulates

Classically, quantities such as length and time were considered absolute, meaning they yield identical measurement values regardless of the observer. The Special Theory of Relativity changes this perspective by showing that these quantities are relative to the observer.

1. First Postulate: Principle of Relativity

The laws of physics are identical in all inertial frames of reference. Whether an observer is in a state of rest or moving with a uniform (constant) velocity with no acceleration, physical laws remain completely unchanged.

2. Second Postulate: Principle of Light Constancy

The speed of light in a vacuum ($c$) is the same for all observers, regardless of the motion of the light source or the observer.

• Exact Value of $c$: $299,792,458 \text{ m/s}$ (typically rounded to $3 \times 10^8 \text{ m/s}$).
• Unlike ordinary objects (where velocities add up relative to a moving vehicle), light speed never changes or adds up with the source's velocity.

Experimental Context: Michelson-Morley Experiment

The Michelson-Morley experiment utilized a setup consisting of mirrors and a beam splitter (a partially silvered glass plate splitting light beams into perpendicular paths) to measure variations in the speed of light due to changing mediums or directions. Despite altering positions, sources, and directions, the measured speed of light remained constant at $299,792,458 \text{ m/s}$, verifying the invariance of light speed.

Lorentz Transformation

Because classical Galilean transformations fail when applied to velocities close to the speed of light, Hendrik Lorentz introduced corrected transformation equations.

1. The Lorentz Factor ($\gamma$)

$\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$

This factor is essential when dealing with objects traveling close to the speed of light.

2. Transformation Equations for Space and Time

• X-Axis Coordinate: $x' = \gamma (x - vt)$
• Y-Axis Coordinate: $y' = y$ (remains unaffected)
• Z-Axis Coordinate: $z' = z$ (remains unaffected)
• Time Transformation: $t' = \gamma \left(t - \frac{vx}{c^2}\right)$

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