# Measuring Distances in Astronomy with GeometryPage 2

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## Special Theory of Relativity (STR)

Speed of light (in vacuum): c = 300,000 km/s

Constancy of the speed

of light: Michelson &

Morley experiment

No signal or object can travel faster than c

[The ultimate speed limit!]

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Basic Principles

The speed of light is the same to all observers

The laws of physics are the same to all observers

Observable Consequences

Simultaneity is a relative concept

Length contraction: moving rulers appear to be short

Time dilation: moving clocks appear to run slow

The apparent mass (inertia) of an object increases as its speed increases (impossible to accelerate it up to c)

Equivalence of mass and energy: E = mc2

Special Theory of Relativity (STR)

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Special relativistic effects are important when the SPEED of an object is CLOSE TO THE SPEED OF LIGHT: v ≈ c

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Simultaneity and time are relative, not absolute

Marion Jones sees A flash before B

Marion Jones sees A and B flash simultaneously

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Measuring the length of a moving object: Length Contraction

The apparent (i.e., measured) length of a moving object is shorter than the “true” length (measured when the object is at rest)

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Measuring time on a moving clock: Time Dilation

A moving clock runs slower than its counterpart at rest

Stationary Clock

Moving Clock

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A Thought Experiment: Length Contraction and an Apparent Paradox The Garage Attendant’s Perspective

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Solution: The driver and garage attendant do not agree on the question of whether the two doors were closed simultaneously

A Thought Experiment: Length Contraction and an Apparent Paradox The Driver’s Perspective

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The scientist in the laboratory witnesses time dilation,

while the Uranium atoms “witness” length contraction

A Real Laboratory Experiment: Direct Verification of Time Dilation and Length Contraction as Predicted by the Special Theory of Relativity

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