It’s all Relativity

March, 1905: Twenty six year old Albert Einstein demonstrates the particle nature of light by explaining the photoelectric effect. He won the Nobel Prize for that in 1921.

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ALICE detector – A Large Ion Collider Experiment

Atlas detector, LHC Photo and detector courtesy of CERN The Higgs boson, dark matter, and a few extra dimensions

Einstein’s First Postulate: The laws of physics are the same in every inertial frame of reference.

Einstein’s Second Postulate: The speed of light in a vacuum is the same in all inertial frames of reference, and is independent of the source.

June, 1905, Einstein proposes the special theory of relativity. Measurements of distance and time are not absolute, but depend on the motion of the observer. Isaac Newton’s laws were only part of the story.

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Two Standard Reference Frames Slide 27-14

Inertial Reference Frames Slide 27-15

The Galilean Velocity Transformations Slide 27-16

The Constancy of the Speed of Light Slide 27-19

The Relativity of Simultaneity Slide 27-26

The Events in Ryan’s Frame Slide 27-27

The Events in Peggy’s Frame (??) Slide 27-28

The Actual Sequence of Events in Peggy’s Frame Slide 27-29

Figure 37.5b

Figure 37.5c

Figure 37.5d

Figure 37.6a

Figure 37.6b

Figure 37.10

Figure 37.12

Simultaneity is Toast Everything is Relative  The different times of flight aren’t just an artifact  They mean that time is not a fixed, rigid, linear system  Time dilation is the first result  Solve the eqns for t 0 in terms of t, eliminating d and you find that time depends on the frame of the observer  2 d/c ≠ 2 l/c

The Lorentz Transformations  Gamma, the core equation of relativity. This relation crops up so many times that it has its own name.  Time and space both vary with gamma.  They are no longer linear or independent, but are interwoven and termed “spacetime.”

Figure 37.8

Time Dilation Time in a reference frame that is moving in relation to the observer passes more slowly. The difference is small at low velocities, and become infinite as the speed of light is approached. Newton’s linear model of space and time collapses at what are called “relativistic velocities. ”

This is “special relativity” relating to motion. General relativity is more general

Time Dilation and Proper Time Slide 27-32

The Twin Paradox Slide 27-33

Length Contraction Length of object in frame in which it’s at rest Length of object in a frame in which it’s moving at β = v/c Slide 27-34

Lorentz Velocity Transformations Slide 27-35

Relativistic Momentum where Slide 27-36

Relativistic Energy The total energy is made up of two contributions: Slide 27-37

Conservation of Energy in Relativity Slide 27-38