The principle of locality

It is not often that we think of events as isolated incidents separated by a vast divide in both physical and virtual distance. In our day to day existence with near instantaneous methods of communication and a pervasively global information network, significant events are easily taken note of. But when the distance separating the event from the recipient exceeds our Earthly bounds, an interesting phenomenon occurs. Even on the scale of the solar system, light from the Sun takes approximately 8 minutes to reach our sunny skies here on Earth. If the Sun happened to go supernova, we would have no acknowledgment of the fact until some 8 minutes after the event actually occurred. While not completely revolutionary, this concept has deeper ramifications if the distances are again increased to a Universal scale.

While we are accustomed to thinking of light as travelling at a fixed speed limit, it is not often that one thinks of gravity as a force that requires time to cross intergalactic distances. But indeed it does. Gravity waves propagate at the speed of light; slight perturbations on the surfaces of incredibly massive objects (eg neutron stars or binary star systems) act as the catalyst for these disturbances. Unimpeded by objects, gravity waves are able to pass through the Universe without effect. They act to warp the nature of spacetime, contracting and expanding distances between objects as the wave passes through that particular locality.

Here on Earth, information is similarly transferred quickly along the Internet and other communication pathways at an average of close to the speed of light. Delays only arise when traffic is heavy (pathways severed, technical problems, increased use). As the distances involved are relatively small in comparison to the speed of the transfer, communication between two points is practically instantaneous. But what if we slow down the speed of travel? Imagine the event occurs in an isolated region of desert. The message can only be transmitted via a physical carrier, thus mimicking the vast distances involved in an interstellar environment. Observer B waiting to receive the message thus has no knowledge of what has happened until that message arrives.

Revisiting the scenario of the Sun exploding, it seems strange that mammoth events in the Universe could occur without our immediate knowledge. It is strangely reminiscent of the Chinese proverb; does a falling tree make a sound if no one is around to listen? Cosmic events are particularly relevant in this respect, as they most certainly do have immense ramifications (‘making a noise’). If the Universe suddenly collapsed at the periphery (unlikely but considered for the purposes of this exercise), our tiny speck of a planet would not know about it until (possibly) many, many millions of years. It is even possible that parts of the distant Universe have already ‘ceased to exist’; the fabric of time and space from the epicentre of this great event expanding like a tidal wave of doom. What does this mean for a concept of Universal time? Surely it must not be dependent upon physical reality, for if it did, surely such a catastrophic event would signal the cessation of time across the entire cosmos. Rather, it would be a gradual process that rushes forth and eliminates regions of both space and time sequentially. The final remaining island of ‘reality’ would thus act as a steadily diminishing safe haven for the remaining inhabitants of the cosmos. Such an event would certainly make an interesting science-fiction story!

Einstein became intimately aware of this universal fact of locality, making it a central tenet in his grand Theory of Relativity. He even offered comments regarding this ‘principle of locality’ (which became a recognised physical law);

“The following idea characterises the relative independence of objects far apart in space (A and B): external influence on A has no direct influence on B; this is known as the Principle of Local Action, which is used consistently only in field theory.”

A horribly simplified description of relativity states that what I experience is not necessarily the same as what you will experience. Depending on how fast you are travelling and in what direction relative to myself (taking into account the speed and direction at which I am travelling), our experience of time and space will differ; quite markedly if we approach the speed of light. Even the flow of time is unaffected, as observers aboard objects travelling at high velocities experience a slowing notion of chronicity compared to their colleagues. It would be intriguing to experience this phenomenon first hand in order to determine if the flow is psychologically detectable. Perhaps it would be experienced as an exaggerated and inverted version of the overly clichéd ‘time flies when you’re having fun’.

Locality in Einstein’s sense is more about the immediate space surrounding objects rather than causes and their effects (although the two are undoubtedly interrelated). Planetary bodies, for instance, are thought to affect their immediate surroundings (locality) by warping the fabric of space. While the metaphor here is mainly for the benefit of visualisation rather than describing actual physical processes, orbiting bodies are described as locked into a perpetual spin, similar to the way in which a ball bearing revolves around a funnel. Reimagining Einstein’s notion of relativity and locality as causality (and the transmission of information between two points), the speed of light and gravity form the main policing forces in managing events in the Universe. Information can only travel some 300,000 km/s between points, and the presence of gravity can modify how that information is received (large masses can warp transmissions as in gravitational lensing and also influence how physical structures interact).

Quantum theory adds to the fray by further complicating matters of locality. Quantum entanglement, a phenomenon whereby an effect at Point A instantaneously influences Point B, seems to circumnavigate the principle of locality. Two points in space dance to the same tune, irrespective of the distances involved. Another quantum phenomenon that exists independently of local space is collapsing wave functions. While it is currently impossible to affirm whether this ‘wave’ actually exists and also what it means for the nature of reality (eg many worlds vs Copenhagen interpretation), if it is taken as a part of our reality then the act of collapse is surely a non-local phenomenon. There is no detectable delay in producing observable action. A kicked football does not pause while the wave function calculates probabilities and decides upon an appropriate trajectory. Likewise, individual photons seem just ‘know’ where to go; instantly forming the familiar refraction pattern behind a double-slit grating. The Universe at large simply arranges its particles in anticipation of these future events instantaneously, temptingly inviting notions of omniscience on its behalf.

Fortunately, our old-fashioned notions of cause and effect are preserved by quantum uncertainties. To commit the atrocious act of personifying the inanimate, it is as though Nature, through the laws of physics, protects our fragile Universe and our conceptions of it by limiting the amount of useful information we can extract from such a system. The Uncertainty Principle acts as the ubiquitous protectorate of information transfer, preventing instantaneous transfer between two points in space. This ‘safety barrier’ prevents us from extracting useful observations regarding entangled particles without the presence of a traditional message system (need to send the extracted measurements taken at Point A to Point B at light speed in order to make sense of the entangled particle). When we observe particles at a quantum level (spin, charge etc) this disturbs the quantum system irrevocably. Therefore the mere act of observing prevents us from using this system as a means of instantaneous communication.

Causality is still a feature of the Universe that needs in-depth explanation. At a higher level is the tireless battle between determinism and uncertainty (free-will). If every event is predetermined based on the collisions of atoms at the instant of the Big Bang, causality (and locality) is a moot point. Good news for reductionists whom hope to uncover a fundamental ‘theory of everything’ with equations to predict any outcome. If, on the other hand, the future really is uncertain, we certainly have a long way to go before an adequate explanation of how causality operates is proposed. Whichever camp one claims allegiance, local events are still isolated events whose effects travel at a fixed speed. One wonders what the more frustrating result of this is; not having knowledge about an important albeit distant event or realising that whatever happens is inevitable. The Universe may already have ended; but should we really care?