In quantum electrodynamics (QED), Feynman diagrams involving a virtual electron-positron pair influence the photon propagator. While the SEP may be consistently imposed in classical physics, somewhat surprisingly it is violated in quantum theory (see Further information). In the conventional theory, however, this is supplemented by a further simplifying assumption, known as the strong equivalence principle (SEP), which requires that dynamical laws are the same in each of these local inertial frames. This principle leads directly to the description of gravity by a curved space-time that is locally flat. Einstein’s theory of gravity is based on the weak equivalence principle, which states that at each point in space-time there exists a local inertial frame – in other words a freely falling observer does not feel a gravitational force. This is the loophole that may allow the possibility of superluminal propagation in general relativity. Crucially, a causal paradox requires both of these conditions to be met. In special relativity, such a return path is guaranteed by the existence of global inertial frames. A genuine causal paradox requires a signal to be sent from the emitter to a point in its own past light-cone – a time-reversed return path must also be possible.
However, by itself this is not sufficient to establish the familiar causal paradoxes associated with time travel. In other words, viewed in a certain class of inertial frames, a superluminal signal travels backwards in time (figure 1). In special relativity, the problem arises because while all observers agree about the time ordering of events linked by a subluminal signal, for a superluminal signal different observers disagree on whether the signal was received after or before it was emitted. To understand these new developments, we first need to question the origin of the received wisdom that superluminal motion necessarily leads to unacceptable causal paradoxes. Quantum effects such as vacuum polarization in gravitational fields appear to permit “superluminal” photon propagation and give a fascinating new perspective on our understanding of time and causality in the microworld. Difficulties with causality only arise if a return signal B´ to C is possible, where C is in the past light-cone of A. A superluminal signal A to B that is forward in time in one inertial frame may be backward in time A to B´ in another inertial frame related to the first by a Lorentz transformation. Graham Shore describes recent research that sheds new light on these old questions. Is it possible to travel faster than light? Can we travel back in time, or send signals into the past? These questions have intrigued physicists since the discovery of special relativity nearly a century ago highlighted the fundamental nature of the speed of light and revolutionized our concept of time.