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The Light Cone: Conclusion

Relativity is a theory of Spacetime

Our understanding of Spacetime

• ---

  Aristotle's spacetime: (300 BC-1600s)

  • Modeled by a "rigid cube sliced into horizontal 3-planes"
  • "Absolute Time" is represented by the preferred horizontal planes
  • "Absolute Space" is represented by the preferred vertical worldlines, associated with Aristotle's Prime Mover in "Absolute Rest"
  • however, this is not compatible with the physics of "Galileo's Principle of Relativity"

• ---

  Galileo's spacetime: (1600s-1905)

  • Modeled by a "stack of planes which can be slanted ("deck of cards")"
  • "Absolute Time" is still represented by the preferred horizontal planes
  • Galileo's Principle of Relativity

    No mechanical experiment can distinguish a state of absolute rest from uniform straight-line motion.

    abolishes "Absolute space" and "Absolute Rest".
  • Any (non-horizontal) straight worldline can "transform the spacetime diagram" ("bevel the deck") so as to regard himself as "being at rest".
  • however, this is not compatible with the physics of Maxwell's "The Speed of Light is a constant"

• ---

  Einstein's Spacetime: (1905-present)

  • Modeled by a "Light Cone sitting at each event."
  • "Absolute Speed of Light" is represented by the Light Cones
  • Einstein's Principle of Relativity

    No physical experiment (whether mechanical or electromagnetic or optical or whatever) can distinguish a state of absolute rest from uniform straight-line motion.

    or,

    All of the laws of physics are the SAME for every inertial observer.

    In particular, the speed of light is the same constant, independent of the motion of the source.

    abolishes "Absolute Space" and "Absolute Time".
  • Any straight worldline within the Light Cone can "transform the spacetime diagram" ("slide along hyperbolas") so as to regard himself as "being at rest".
  • As a result, it is seen that "Simultaneity is Relative".
  • That the worldlines must be within the Light Cone represents the physical observation that "No object's speed can exceed the speed of light".
  • SPECIAL RELATIVITY:
    • A uniform arrangement of Light Cones.
    • Spacetime is FLAT. Gravity is negligible.
    • Light travels in straight paths.
  • GENERAL RELATIVITY:
    • A non-uniform arrangement of Light Cones.
    • Spacetime is CURVED. Gravity is important.
    • Light travels in a curved path.
    • Example: THE BLACK HOLE
      The Light Cones are arranged so that there is region of spacetime where all Light Cones tip over and point inward. The boundary of this region is called the Event Horizon. Once past this boundary, no object can ever escape (since the Light Cones are so tipped-over).

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