Simultaneity in Special Relativity

One of the commonly touted consequences of special relativity is the twin paradox. This is an interesting story: a pair of twins is separated when one of them takes part in an interstellar mission of exploration. Traveling near to the speed of light, he arrives at his destination, spends a few years in exploration, then heads back to earth. When he arrives back, thanks to the miracle of time-dilation, he is only five years older, while his twin has aged thirty!

The experimental evidence to support this claim is based upon observations of track lengths for unstable particles generated at accelerator facilities. The clearest evidence comes from the muon, which decays slowly enough that it can be brought to rest. Measured lifetimes agree well with the relativistic predictions.

But the question remains, what would a rider on the muon observe?

There is an interesting philosophical note in quantum mechanics. Quantum field theory associates particles and antiparticles with the formalism of creation and annihilation operators. Early in the development of relativistic quantum mechanics, however, it was noted that the Dirac equation, which governs the physics of elementary fermions, predicted the existence of negative energy states. Two interpretations for those states were advanced: they were anti-particles, or they represent time-reversed propagation.

In some sense, a particle moving near to the speed of light has a predetermined future. It has a very large momentum, and changing its destiny requires a catastrophic event. In some sense, its past, present and future are intertwined.

Let's go back to relativistic time dilation with this idea in mind.