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.

What have you done with your

life so far?

ALICE detector – A Large Ion Collider Experiment

Atlas detector, LHCPhoto 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

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Inertial Reference Frames

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The Galilean Velocity Transformations

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The Constancy of the Speed of Light

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The Relativity of Simultaneity

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The Events in Ryan’s Frame

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The Events in Peggy’s Frame (??)

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The Actual Sequence of Events in Peggy’s Frame

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Figure 37.5b

Figure 37.5c

Figure 37.5d

Figure 37.6a

Figure 37.6b

Figure 37.10

Figure 37.12

Simultaneity is ToastEverything 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 t0 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

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The Twin Paradox

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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

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Lorentz Velocity Transformations

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Relativistic Momentum

where

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Relativistic Energy

The total energy is made up of two contributions:

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Conservation of Energy in Relativity

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