Special Relativity

go back

• Newton: there is absolute time and space
• Ole Römer (danish)
• Hugygens - calculated ‘c’ based on the positions of Jupiter’s moons
• 1887 Michetson Morley Interferometer
• Fitzgerald - Lorentz

Einstein’s 2 postulates

1. The speed of light is constant (in a vacuum)
2. The laws of physics are equivalent in inertial reference form
3. Implications: objects contract in their length in their direction of motion
   1. For objects passing each other at speeds approaching “c”
      1. Each sees the other’s length to be contracted (gets shorter)
      2. Each time is dilated (seconds get longer)

Cherenkov radiation

Length Contraction

• The length of an object passing you (at speed approaching c) will be measured by you to be contracted in its length

• Only applies to dimension in the direction of travel

• The same observation is made of you by the object passing you i.e. motion is relative

• Everyone in all different inertial reference frames observes the length of everyone/everything in motion relative to them to be shorter

• Nobody sees anybody else’s lengths getting longer

• Only noticeable for objects where relative motion approaches c

• Proper length ($L_0$) is the length as measured by an observer in their own reference frame

• Relativistic length is the measurement made of a quantity in the observerd reference frame

• NB: Every reference frame has its own proper length/time/momentum etc, and measurements made of any other inertial reference frame will be relativistic length/time etc

Derivation of Lorentz formula

Relativistic addition of velocities

• Classical: simple addition
  • A person walking at 5 m/s toward the front of a ship moving forward at 10 m/sis moving at 5+10 = 15 m/s wrt a stationary observer
• Relativistic speeds
  • A spaceship travelling at 0.8c fires a missile at 0.3c
  • If classical mechanics applied, the missile would be travelling at 0.8c + 0.3c = 1.1c, which is impossible

$u=\frac{v+u^{\prime }}{\left(\frac{1+v{u}^{\prime }}{c^2}\right)}=\frac{0.8c+0.3c}{1+\frac{0.8c\times 0.3c}{c^2}}=0.887c$

Relativistic Momentum and Energy

“chemistry’s not even a subject” “just go c c c c in the multiple choice like you always do”

????? sad