Having described motion, we can now explain it. We introduce the conserved 4-momentum, and with it the ideas of energy-momentum, conserved mass, and scattering.

We introduce the maths required to describe motion. We define 4-vectors, and specifically the velocity and acceleration 4-vectors. We can also define the frequency 4-vector, and using it straightforwardly deduce the relativistic Doppler shift.

An introduction to the book, covering key ideas and concepts.

But in the dynamic space of the living Rocket, the double integral has a different meaning. To integrate here is to operate on a rate of change so that time falls away: change is stilled…. ‘Meters per second’ will integrate to ‘meters.’ The moving vehicle is frozen, in space, to become architecture, and timeless. It was never launched. It will never fall.

Understand the importance of events within Special Relativity, and the distinction between events and their coordinates in a particular frame; and appreciate why we have to define very carefully the process of measuring distances and times, and how we go about this.

In , we used the axioms ofto obtain the Lorentz transformation. That allowed us to describe events in two different frames in relative motion. That part was rather mathematical in style. Now we are going to return to the physics, and describe motion: velocity, acceleration, momentum, energy and mass.

We are now able to deduce the Lorentz transformation, relating two inertial frames. We examine three paradoxes, namely the famous twins paradox, the pole-in-the-barn paradox, and the so-called Bell's spaceships paradox. We also take another look at the relationship with electromagnetism.

We look at the immediate consequences of the two axioms, and discover, qualitatively and then quantitatively, the phenomena of length contraction and time dilation.

We survey relativity's contact with experiment and observation, briefly discussing the classical tests of SR and of GR, and including a discussion of the famous 1919 Dyson-Eddington observations of the bending of starlight during the solar eclipse. In the latter, we look at the historical and social pressures on the scientists involved, and what effect these have on the processes of theory choice.

A brief recap of some mathematical topics.

Inwe saw how observers could make measurements of lengths and times in frames which are in relative motion, and reasonably disagree about the results – the phenomena of length contraction and time dilation. In , we were able to put numbers to this and derive a quantitative relation, Eq. (), between the duration of a ‘tick’ of the light clock as measured in two frames. We want to do better than this, and find a way to relate the coordinates of any event, as measured in any pair of frames in relative motion. That relation – a transformation from one coordinate system to another – is the Lorentz transformation (LT). The derivation inhas a lot in common with the account given in .