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2: Foundations

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    • 2.1: Causality
      Our intuitive belief in cause-and-effect mechanisms is not sup- ported in any clear cut way by the laws of physics as currently understood. For example, we feel that the past affects the future but not the other way around, but this feeling doesn’t seem to translate into physical law. For example, Newton’s laws are invariant under time reversal, as are Maxwell’s equations.  In fact, the weak nuclear force is the only part of the standard model that violates time-reversal symmetry.
    • 2.2: Flatness
      Euclidean geometry is only an approximate description of the earth’s surface, for example, and this is why flat maps always entail distortions of the actual shapes. The distortions might be negligible on a map of Connecticut, but severe for a map of the whole world. That is, the globe is only locally Euclidean. On a spherical surface, the appropriate object to play the role of a “line” is a great circle. The lines of longitude are examples of great circles.
    • 2.3: Additional Postulates
      We make the following additional assumptions.
    • 2.4: Other Axiomatizations
      Einstein used a different axiomatization in his 1905 paper on special relativity.
    • 2.5: Lemma - Spacetime area is invariant
      The area in the x−t plane is invariant, i.e., it does not change between frames of reference.
    • 2.E: Foundations (Exercises)

    Thumbnail: Einstein cross: four images of the same astronomical object, produced by a gravitational lens. Image used wtih permission (Public Domain; NASA and ESA).

    This page titled 2: Foundations is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Benjamin Crowell via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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