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In the , we have learned how to describe motion; we now want to explain it. In newtonian mechanics, we do this by defining quantities such as momentum, energy, force and so on. To what extent can we do this in the context of relativity, with our new 4-vector tools?
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.
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.