Locality is defined in physics as the characteristic of the universe in which no effect, influence, or communication can propagate faster than the speed of light. This is the local universe assumption of Special Relativity. demonstrably and
Non-locality, on the other hand, allows instantaneous effects to act over arbitrarily long distances. A Cause happening at one point, can thus have an instantaneous Effect at the other end of the universe and at all points in between. Non-local effects may appear to be “random” to human intelligence in that the Cause is not observable even when the Effect is pretty much right in one's face. Such randomness, however, may appear to a higher intelligence to be a perfect example of Causality .
Non-local implies a connectedness to anything and everything in the universe. It may be the basis of Mach's Principle, the essential ingredient in Quantum Physics and its fundamental Pauli Exclusion Principle, the resolution of the EPR Paradox, and the wherewithal of Consciousness. Non-locality is a divestiture of physical limits and/or boundaries, and is in accordance with the open-endedness of true scientific inquiry the most logical, mathematically precise, and physically justified of the two locality possibilities.
One of the attributes of Connective Physics, for example --- as well as the physics contained in The Fifth Element -- was the extension of the speed of light limit to much higher speeds purely on the basis of radical changes in a given input. This is described in a degree of mathematical detail in Relativistic Variations on a Theme. Another challenge to the advocates of a speed limit to such things as interstellar exploration is contained in Relativistic Space Contraction -- a plausible alternative explanation of the so-called confirming experimental evidence supporting Special Relativity and its speed of light limitation.
The reluctance of some scientists to accept non-locality might be resolved by some fascinating experiments reported on by Douglas Adams. In these experiments it became obvious that there was one thing which could be shown to have
regularly exceeded the speed of light in going from point A to point B. This near-instantaneous transmission was Bad News, which was clearly moving faster than the speed of light. Adams goes on to note that a serious effort was made to utilize this Speed of Bad News Principle in a transportation or propulsion system. Unfortunately, it quickly became obvious that anyone or anything reaching their destination using the Bad News principle would not be welcome in any case (i.e. nobody welcomes bad news), and thus there was really no point in arriving earlier by that method.