## Chapter Objectives and Summaries

### CHAPTER 30 Special Relativity

LEARNING OBJECTIVES
Knowledge of subject matter
• The meaning of the following terms: velocity of light, special relativity, general relativity, Galilean transformations, inertial system, non-inertial system, space contractions, relativistic dynamics, rest energy, four dimensional space, time dilation, relativistic time, dilated time, proper time, rest mass, proper length, rest length, relativistic length, parallel track, anti-parallel track.
• The velocity of light measurements.
• The Michelson-Morely experiment.
• Newton's assumptions of absolute time, space and motion.
• Galilean transformations.
• The origins of the relativity theory.
• Difference between Special Theory and General Theory of Relativity.
• Explain the historical development of theories of relativity.
• The meaning of the symbols t, to, l, lo.

SCIENTIFIC PROCESSES

• Analyse physical situations.
• Distinguish between fact and fiction with regard to the special theory of relativity.

COMPLEX REASONING PROCESSES

• Solve novel and/or complex problems using relativity formulae:
• t = to./SQroot(1 – v2/c2) ; L= Lo.SQroot(1 – v2/c2)
m = mo./SQroot(1 – v2/c2) ; Ek = mc2 – moc2
• Predict and be able to interpret the consequences of high speed travel
• Critically analyse the significance of Einstein's energy - mass equation on human kind

### CHAPTER 30 SUMMARY

• A reference frame that moves with constant velocity with respect to an inertial frame is itself also an inertial frame. All inertial reference frames are equivalent for the description of mechanical phenomena. No one inertial reference frame is any better than another.
• The Michelson-Morley Experiment showed that there is no 'ether' or absolute frame of reference.
• The two postulates of the Special Theory are:
The laws of physics have the same form in all inertial reference frames.
Light propagates through empty space with a definite speed c independent of the speed of the source or observer.
• Two events in a reference frame are simultaneous if light signals from the events reach an observer halfway between the events at the same time.
• Two events which are simultaneous to one observer are not necessarily simultaneous to a second observer moving with respect to the first.
• Moving clocks are measured to run slowly: t = to/(1 - v²/c²)½; where to is proper time and t is dilated or relativistic time. Dilated time is longer than proper time.
• A light-year (ly) is the distance travelled by light in one year.
• Moving objects contract: L = Lo (1 - v²/c²)½ where Lo is the proper length or the rest length and L is the relativistic length.
• Summary of relationships for space travel: v = L/to = Lo/t
• You can travel into the future - but only someone else's future. You can travel into the past - but only someone else's past.
• Addition of velocities: vAB = (vA - vB)/(1 + vAvB/c²)
• Mass-increase formula: m = mo/(1 -v²/c²)½ where mospeed in the universe.
• The kinetic energy of a particle is given by EK = mc² - mo
• The total relativistic energy (Etot) of an object equals mc² ; total energy equals the rest energy Eo plus the kinetic energy: Etot = Eo + EK = moc² + EK