RELATIVITY 
Summarized by MP00e

Theory

Special theory of relativity
- Postulates of the special theory of relativity (by Einstein in 1905):
1) The laws of physics have the same form in all inertial reference frames
2) Light propagates through empty space with a definite speed c independent of
the speed of the source or observer
- Experimental support: Michelson-Morley experiment with an inferometer: the
speed of the earth in relation to the “ether” is zero
- Special theory of relativity holds true within inertial (nonaccelerating) reference
frames
- Velocity of light, 3*108 m/s is the “speed limit” of the universe
- All inertial reference frames are equal
- Clocks moving relative to an observer are measured by that observer to run
more slowly (as compared to clocks at rest)
- The length of an object is measured to be shorter when it is moving relative to
the observer than when it is at rest; the moving objects are shortened in the
direction of the motion
- The correspondence principle: the two theories (StoR & GtoR) must correspond
where their realms of validity overlap
- Two events can not be said to be simultaneous (depends on the observer)

General theory of relativity
- GToR deals with accelerating rfs
- Gravitational mass = inertial mass
- An observer can not deduct by measurement whether he is in accelerating
motion or inside a gravitational field
- Large bodies of mass bend the four-dimensional space time 
- If a star is massive enough a black hole can be born (even light can’t escape)
- Light always travels along the shortest distance or geodesic
- Also light is bent in gravitational field
- Gravitational redshift: the frequency of monochromatic light decreases as it
leaves a heavenly body -> clocks run slower near a massive body of mass

Formulae

- # = sqr[1-(v²/c²)]

- The Lorenz transformation: x’ = x - vt/#; t’= (t-vx/c²)/#
- Length contraction: L = Lo# (-> Muon decay in atmosphere)
- Time dilation: T = To/# (-> Muon decay in atmosphere)
- Relativistic mass: m = mo/#
- Relativistic momentum: p = mov/#
- Gravitational time dilation: T = To / sqr[1-(2GM/Rc²)]
- -”- near the surface of the earth: T = To / sqr[1-(2gR/c²)]

- Energy-mass relationship: e = mc²
- Rest mass energy of a particle = E = moc²
- KE of a high-speed particle = KE = mc²-moc² = [(1/#) -1]moc²
- Relativistic energy of a particle = E = mc² = sqr(p²c²+moc²c4)

Relativistic addition of velocities
- A = rest observer, B = moving observer ->, C = projectile fired by B ->
- u’ = v of projectile as seen by B, u = v of projectile as seen by A
- u = v+u’/[1+(vu’/c²)]
- u’ = u-v/[1-(uv/c²)]