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Published online by Cambridge University Press: 05 June 2012
This concludes Part III of this book. I hope you have been able to grasp the basic logic of where the equation E = mc2 comes from. To summarize the important points:
In Einstein's relativistic dynamics, the state of motion of an object is represented by an arrow called the energy–momentum vector. The vector's time-component (vertical component) is the energy, and the space-component (horizontal component) is the momentum, and they represent what might be called the “tenacity of the motion” or the “tendency of the motion to continue as is” in their respective directions in spacetime.
The energy–momentum vector depends on the frame from which the observation is being made. However, the area of the diamond with the energy–momentum vector as one of its sides and the diagonals at 45° from the horizontal is invariant and equal to (mc)2 where m is the object's mass.
Changes in the motions of objects are represented by changes in their energy–momentum vectors. In a system of interacting objects, the energy–momentum vector of each individual object will change via interactions, but the total energy–momentum vector of the system will be conserved.
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