Special Relativity Fundamentals

Study Notes

Lorentz Transformation

A mathematical formula describing how space and time coordinates are affected by relative motion
Developed by Hendrik Lorentz in 1904
Describes how observers in different inertial reference frames measure the same event
Key equations:
- Time dilation: t' = γ(t - vx/c^2)
- Length contraction: x' = γ(x - vt)
- Velocity addition: u' = (u + v) / (1 + uv/c^2)
Where:
- γ is the Lorentz factor (1 / sqrt(1 - v^2/c^2))
- v is the relative velocity between the two frames
- c is the speed of light
- t and x are time and position in one frame
- t' and x' are time and position in the other frame

Michelson-Morley Experiment

Conducted in 1887 by Albert Michelson and Edward Morley
Tested the hypothesis that light travels at a constant speed in all directions
Experiment design:
- Split a light beam into two perpendicular beams
- Sent each beam to a mirror and reflected back to a detector
- Compared the time it took for each beam to complete a round trip
Results:
- No significant difference in the speed of light in different directions
- Challenged the concept of a fixed, absolute ether
- Led to the development of special relativity by Albert Einstein

Mass-Energy Equivalence

Concept proposed by Albert Einstein in 1905
States that mass (m) and energy (E) are interchangeable
Equation: E = mc^2
Where:
- m is the rest mass of an object
- c is the speed of light
- E is the total energy of the object
Implications:
- A small amount of mass can be converted into a large amount of energy
- A large amount of energy can be converted into a small amount of mass
- Has far-reaching implications in nuclear physics and beyond

Description

Test your understanding of special relativity principles, including Lorentz transformation, Michelson-Morley experiment, and mass-energy equivalence. Learn how these concepts led to a fundamental shift in our understanding of space and time.