Chapter 36 The Special Theory of Relativity (Special Relativity Principle)

Introduction Our goals –Better appreciate some underlying assumptions of CM –Get new understanding and insight into physical reality –Appreciate some practical applications and impacts on thinking of SR –Better appreciate science as a process in contrast to a body of knowledge

Introduction (cont’d) Our plan –Look at the Historical/Intellectual context –Identify the assumptions of Special Relativity –Draw our first conclusions Time dilation Length contraction –Look deeper: The relativity of simultaneity –Introduce space-time diagrams (part 1)

Introduction (cont’d) Our plan (cont’d) –Introduce proper space and time intervals –Introduce the Lorentz transformation Contrast with Galilean transformation –Introduce relativistic Energy and Momentum The question of “relativistic mass” An expanded understanding of mass –Use of the Lorentz transformation –Continue with other topics depending on interest and time

Historical/Intellectual Context Knowing (constructed knowledge) –Choice of theoretical framework The clash of CM, E&M –Galilean Relativity Absolute space  relative space, absolute time Absolute time and space intervals A pattern of absolute to relative quantities –The absolute velocity of EM –Specific difficulties seen at the time Light in box, catching up with light, etc. No ether medium for light waves

Assumptions of SR The Relativity Principle The Constancy of the Speed of Light in a vacuum (Hence the need to reformulate physics) A different approach than what we have seen so far –Not a new dynamics –Adherence of a symmetry principle

Our first conclusions Time dilation –Proof –Evidence (planes, satellites, muons) Length contraction –Proof (built on time dilation) –Evidence (muons, space travel plans) Explanations depend on space or time –Hence the connection between space and time (also electricity and magnetism)

Deeper: Relativity of Simultaneity Cup and Arrow thought experiment/demo Classic train/embankment example (1917) –Both perspectives presented and compared – YA&feature=relatedhttp:// YA&feature=related Quantitative result (next time) Space-time diagrams (part 1) –The “experiment” from the embankment –Comment on the relation of frames

The Lorentz Transformation What the Galilean and Lorentz transformations describe Mathematically, the Galilean and Lorentz transformations

Use of the Lorentz Transformation Results –The addition of velocities –Time dilation –Length contraction –Lack of simultaneity (problem 31)

Completing Mechanics Relativistic momentum –“relativistic mass”??? –further meaning of mass Relativistic kinetic energy & total energy –mass-energy relation –photon mass Space-time geometry –Metric relation to unify space-time Further topics, time permitting –make your suggestions

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