5. Relativistic mechanics and E = ...

This is a text+animation version of the video chapter from Einsteinlight.

So it is necessary to apply relativistic corrections when observing motion in other frames.

When we apply a force to accelerate an object, the work we do becomes its kinetic energy. But observers who disagree on length and time must also disagree on acceleration and work, so relativity gives different results: in Einstein's physics, momentum and kinetic energy increase rapidly as the speed approaches that of light, as this animation shows.

This animation is discussed in detail in this link.

When we calculate kinetic energy, mc² appears as a term associated with a mass that has no relative motion. Einstein's insight was that this term is its proper energy: an energy associated purely with its mass, independent of its motion, and that thus mass and energy might be exchanged or transformed.

This proper energy, mc², is the energy equivalent of mass m.

This explains why nuclear power and nuclear weapons need so little fuel. The speed of light c is large, so the conversion of a tiny mass produces great quantities of energy.

But this equation is also essential for our understanding the strong forces in the nucleus, without which there would be no chemistry.

Relativity is needed in engineering, too, such as this electron source used to treat cancer patients and in satellite navigation systems.

Relativity has revolutionised our thinking about time and space. It is weird and counter-intuitive, but if you want to get the right answer when speeds or energies are high, you simply must use it. Scientists and engineers do, every day.

Go to the text+animation version or video version of chapter 6 from Einsteinlight.