Synopsis:
 Laws of nature must be uniform
 Laws must be the same in all frames of reference that are "inertial"
 The speed of light is the same in all directions
 Lorentz transformations
 The length of an object and the duration of an event are relative to the observer
 All quantities must have four dimensions, a time component and a space component (e.g., energymomentum)
 Equivalence of mass and energy (E=mc2)
 Space and time are not absolute
 "Now" is a meaningless concept
 The past determines the future
 Nothing can travel faster than light
 Time does not flow (no more than space does), it is just a dimension
 Space and time are different dimensions of the same spacetime continuum
 Each observer has a different perspective on the events in the spacetime continuum (e.g., length or duration)
 Past and future are segments of spacetime continuum
 Each observer's history is constrained by a cone of light within the spacetime continuum
 Each observer's history is a "world line", the spatiotemporal path that the observer is actually traveling through spacetime
 "Proper" time is the spacetime distance between two points on a world line (the time experienced by the observer as she travels along its world line)
 Relativity for systems accelerated with respect to one another
 Principle of Equivalence: Forces produced by gravity are in every way equivalent to forces produced by acceleration
 It is no possible to distinguish between gravitational and accelerational forces by experiment (e.g, an acceleration of 9.8 m/sec2 in outer space is "equivalent" to gravitational force on the Earth)
 All forces (gravitational or not) are due to acceleration
 Newton's hypothesis that every object attracts every other object is unnecessary
 Masses curve spacetime.
 Spacetime's curvature determines the motion of masses.
 Einstein's law of gravity: Every object, which is not subject to external forces, moves along a geodesic of spacetime (the shortest route between two points on a warped surface), its "world line"
 Spacetime "is" the gravitational field
 When an object appears (in 3D space) to be "at rest" but under the effect of gravitational attraction, it is actually being "accelerated" (attracted) towards the center of the earth along its worldline (in 4D spacetime) which happens to be curved by the spacetime curvature caused by the Earth's mass
 It is spacetime that is curved, not the geodesic.
 Gravitation is not a force
 Physics = Geometry of spacetime
 Gravitation = spacetime curvature
 Relativity theory is ultimately about the nature of gravitation
 Relativity explains gravitation in terms of curved spacetime, i.e. Geometry
 "Gravitational force" becomes an effect of the geometry of spacetime
 The curvature of spacetime is measured by a "curvature tensor" (Riemann's geometry)
 Each point is described by ten numbers (metric tensor)
 Euclid's geometry is one of the infinite possible metric tensors (zero curvature)
 Other geometries describe spaces that are not flat, but have warps
 What causes the "warps" is energymass
 Clocks slow down in a gravitational field
 Light is deflected in a gravitational field
 Cosmological constant to counterbalance the effect of gravity
