In notes 3, Einstein worked his magic conceptual spanner around the issues of distance and time in a moving frame of reference when observed from a stationary frame. This can be treated mathematically such that the same event observed in different frames of reference moving with constant velocity relative to one another can be represented by co-ordinates in one frame in terms of co-ordinates in the other, by means of the Lorentz Transformations (the derivation of which are included in an appendix of the book).

Consideration of the transformations on measuring rods and clocks lead to the following:

-a measuring rod is shorter when moving than at rest, when observed from a stationary frame of reference, and the quicker it is moving, the shorter it is. (In a frame of reference moving with the rod, though, the rod isn’t moving and hence isn’t shortened),

-for a clock moving relative to a frame of reference, time runs more slowly when observed from the stationary frame of reference. The faster it moves, the more slowly time runs. For an observer in the same frame of reference as the clock, though, time is not slowed.

So, time runs more slowly, and distances are shorter in a moving object (a train, or a space ship), when observed from a stationary frame of reference (on the embankment, or in the space port). But, in the train and space ship both time and distance are unchanged.

A consideration of the equations, as the velocity of the object approaches the speed of light, shows that the velocity of the object can approach the speed of light, but cannot reach it. The speed of light is a non-obtainable upper speed limit.

-considering a moving mass, relative to a stationary frame of reference, absorbing energy; the equations of (special) relativity demonstrate that conservation of mass, and conservation of energy are effectively the same thing, and e=mc^2 (when observed from a frame of reference moving with the mass) – the rest (inertial) mass.

All of these arise once the constancy of the speed of light (regardless of the frame of reference of an observer) is accepted. Time, space and mass, are dependent on the context of the observer. Gulp.

# Gravitation (notes 4)

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