Minkowski Spacetime Relativity

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Contents
Hermann Minkowski
Minkowski’s Postulates
Line Elements

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Spacetime Diagram

View Spacetime Diagrams

Intervals

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Worldlines and Proper Time

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Spacetime Diagrams for Reference Frames in Motion

View Spacetime Diagrams for Reference Frames in Motion

Invariance of Spacetime Interval and Invariant Unit Hyperbola

View Invariance of Spacetime Interval and Invariant Unit Hyperbola

Space, Time, and Spacetime
  • In 1908 Hermann Minkowski developed the concept of spacetime to reformulate Einstein’s Special Relativity in geometric terms.
  • The beginning of Minkowski’s lecture on the topic:
    • “Gentlemen! The views of space and time which I want to present to you arose from the domain of experimental physics, and therein lies their strength. Their tendency is radical. From now onwards space by itself and time by itself will recede completely to become mere shadows and only a type of union of the two will still stand independently on its own.”
  • Before Special Relativity (1905) and Minkowski’s Spacetime (1908)
    • Space
      • Space is a three-dimension continuum of points
      • Δd is the distance between two points
      • Space is absolute and Δd is the same for everyone.
    • Time
      • Time is a one-dimensional continuum of instants
      • Δt is the interval between two instants
      • Time is absolute and Δt is the same for everyone.
    • Laws of Newtonian Physics are stated in terms of space and time.
  • After Special Relativity and Minkowski’s Spacetime (1908)
    • A person measures the distance and elapsed time between two flashes of light and gets:
      • Δd = 800,000,000 meters
      • Δt = 3 ⅓ seconds
    • A second person measures the distance and elapsed time between the same two flashes and gets:
      • Δd = 0 meters
      • Δt = 2 seconds
    • The measurements of both people are correct.
    • Space is not absolute and Δd is not the same for everyone.
      • Δd = 800,000,000 meters in the first person’s reference frame
      • Δd = 0 meters in the second person’s reference frame
    • Time is not absolute and Δt is the not same for everyone.
      • Δt = 3 ⅓ seconds in the first person’s reference frame
      • Δt = 2 seconds in the second person’s reference frame
    • Spacetime
      • Spacetime is a four-dimensional continuum of events
        • An event is a point at an instant
      • Δs2 is the spacetime interval between two events
        • Δs2 = –c2Δt2 + Δd2
          • c is the speed of light
      • Spacetime is absolute and Δs2 is the same for everyone.
        • Δs2 = –3.6 x 1017 meters in the first person’s reference frame
        • Δs2 = –3.6 x 1017 meters in the second person’s reference frame
    • Laws of Relativistic Physics are stated in terms of spacetime.