Introduction to Special Relativity

10 Pages

English

Undergraduate

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Foundations and Postulates

1. Classical Relativity and Inertial Frames

2. The Principle of Relativity

3. Constancy of the Speed of Light

4. Events, Coordinates, and Reference Frames

5. Einstein Synchronization of Clocks

Spacetime Transformations and Effects

6. Lorentz Transformations: Connecting Moving Frames

7. Relativity of Simultaneity: When “At the Same Time” Depends on Motion

8. Time Dilation: Moving Clocks and Proper Time

9. Length Contraction: Measuring a Moving Object

10. Velocity Addition and the Invariant Spacetime Interval

1. Classical Relativity and Inertial Frames

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Why does a train moving at constant speed feel different from one that accelerates?

Are Earth-based laboratories inertial frames?

Inertial frame:

Galilean transformation:

Relative velocity:

Inertial frame:

Galilean transformation:

Relative velocity:

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2. The Principle of Relativity

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Does the principle of relativity mean every observer measures identical quantities?

Can an accelerating observer use the principle of relativity?

Principle of relativity:

Preferred frame:

Lorentz transformation:

Principle of relativity:

Preferred frame:

Lorentz transformation:

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3. Constancy of the Speed of Light

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Does a moving light source make its light travel faster?

Why is light slower in glass or water?

Speed of light in vacuum:

Light cone:

Invariant:

Speed of light in vacuum:

Light cone:

Invariant:

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4. Events, Coordinates, and Reference Frames

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Do different observers refer to different physical events?

Why is the spacetime interval more useful than distance alone?

Event:

Reference frame:

Spacetime interval:

Spacelike separation:

Event:

Reference frame:

Spacetime interval:

Spacelike separation:

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5. Einstein Synchronization of Clocks

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Why cannot one clock alone define time everywhere in a frame?

Is disagreement about simultaneity merely due to the time light takes to reach an observer?

Einstein synchronization:

One-way light travel time:

Simultaneity:

Einstein synchronization:

One-way light travel time:

Simultaneity:

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6. Lorentz Transformations: Connecting Moving Frames

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Why do the Lorentz transformations contain both position and time?

What happens to the transformations when relative speed is zero?

Inertial frame:

Lorentz factor:

Speed of light:

Inertial frame:

Lorentz factor:

Speed of light:

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7. Relativity of Simultaneity: When “At the Same Time” Depends on Motion

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Can observers disagree about whether two events happened?

Does relativity of simultaneity permit changing the past?

Simultaneity:

Event:

Einstein synchronization:

Simultaneity:

Event:

Einstein synchronization:

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8. Time Dilation: Moving Clocks and Proper Time

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Does a moving person feel their own time slow down?

Is acceleration the direct cause of time dilation?

Proper time:

Time dilation:

Muon lifetime:

Proper time:

Time dilation:

Muon lifetime:

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9. Length Contraction: Measuring a Moving Object

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Does an astronaut see their own spacecraft become shorter?

Why is contraction not visible as an ordinary photograph-like squeeze?

Proper length:

Length contraction:

Simultaneous measurement:

Proper length:

Length contraction:

Simultaneous measurement:

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10. Velocity Addition and the Invariant Spacetime Interval

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Can two speeds less than light add to more than light?

Why is the spacetime interval more fundamental than distance alone?

Relativistic velocity addition:

Spacetime interval:

Timelike interval:

Spacelike interval:

Relativistic velocity addition:

Spacetime interval:

Timelike interval:

Spacelike interval:

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