Minkowski Spacetime Relativity

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Hermann Minkowski

Minkowski’s Postulates

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
    - View Reference Frames
- 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.

Hermann Minkowski

Minkowski’s Postulates

Line Elements

Spacetime Diagram

Intervals

Worldlines and Proper Time

Spacetime Diagrams for Reference Frames in Motion

Invariance of Spacetime Interval and Invariant Unit Hyperbola

Space, Time, and Spacetime

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