Back to Special Relativity

##### Contents

- 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

##### Hermann **Minkowski**

**Minkowski’s Postulates**

**Line Elements**

**Line Elements**

View Line Elements

**Spacetime Diagram **

**Spacetime Diagram**View Spacetime Diagrams

**Intervals**

**Intervals**View Intervals

**Worldlines and Proper Time**

**Worldlines and Proper Time**View Worldlines and Proper Time

**Spacetime Diagrams for Reference Frames in Motion**

**Spacetime Diagrams for Reference Frames in Motion**View Spacetime Diagrams for Reference Frames in Motion

**Invariance of Spacetime Interval and Invariant Unit Hyperbola**

**Invariance of Spacetime Interval and Invariant Unit Hyperbola**View Invariance of Spacetime Interval and Invariant Unit Hyperbola

**Space, Time, and Spacetime**

**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.

- Space
- 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

- Δs
^{2}is the spacetime interval between two events- Δs
^{2}= –c^{2}Δt^{2}+ Δd^{2}- c is the speed of light

- Δs
- Spacetime is absolute and Δs
^{2}is the same for everyone.- Δs
^{2}= –3.6 x 10^{17}meters in the first person’s reference frame - Δs
^{2}= –3.6 x 10^{17}meters in the second person’s reference frame

- Δs

- Spacetime is a four-dimensional continuum of events
- Laws of Relativistic Physics are stated in terms of spacetime.

- A person measures the distance and elapsed time between two flashes of light and gets: