# Special & General Relativity Questions and Answers

## Do electrons interact with past and future representations of themselves?

A good question. In the classical world which obeys Newtonian physics and Einstein's relativity, all macroscopic matter is precluded from coming into contact with its own past. Nature seems to go to great lengths to avoid creating 'time loops' or other violations of causality that can occur if time travel were permitted. Some theoreticians believe that time travel into the past may be possible, but this would only occur under very rare situations that involve exotic phenomena such as cosmic strings or certain kinds of black holes. BUT, in the quantum world, things are far less well defined.

According to Heisenberg's Uncertainty Principle, there is a built-in uncertainty in how well any experiment can tie-down with arbitrarily high precision, the exact place and speed ( position and momentum) of a particle, or its precise energy and time. This means that to specify the energy of a particle with complete accuracy, you must tolerate loosing a specific knowledge of at what moment it had that energy. The relationship between the uncertainty in momentum, Dm, and position, Dx, is reciprocal: Dm = h/Dx. Now special relativity states that no particle may travel faster than the speed of light, but in fact in the quantum world, particle speeds are allowed to exceed the speed of light because of the uncertainty in actually measuring how fast a particle is moving at a given place. So long as this violation lasts only a very short while, a particle can move from one place to another by moving slightly less than the speed of light, or slightly faster than the speed of light. In the later case, the particle's light cone becomes a fuzzy concept unlike the situation in special relativity. If a particle can move outside its light cone, however briefly, it can interact with past versions of itself over a limited range of times also dictated by Heisenberg's Uncertainty Principle.

I am not an expert in such matters, but so far as I have read in the technical literature, this is the only kind of time travel sanctioned by the known laws of physics. It is not something that can ever be detected experimentally.