Time is fundamental to humans. It structures their lives, their plans, and their thoughts. It has always fascinated people. In particular, the beginning of time and the origin of the universe have been the setting for many ancient mythologies. The one that springs immediately to mind is that of the Ancient Greeks. In their creation mythology, Chronos was the personification of time, being involved in the creation of the universe (Chronos should not be confused with the Titan Cronus, who was the father of the gods in Greek mythology). Where Chronos came from seems to be an obvious question without any answer.
In modern times, interest in time has if anything become an obsession. We are bombarded frequently with speculative films and stories involving time travel, alternative universes, and such like. This is not surprising given our interest in science and science fiction. What helps legitimize such speculation is the fact that GR, Einstein’s theory of space and time, a greatly respectable and good theory of large-scale gravitation, does not exclude the exotic possibility of spacetimes containing closed timelike curves, or CTCs as they are generally referred to. A timelike curve is a path in spacetime that a physical observer could follow without violating any of the known laws of classical physics. If such a curve were closed, then an observer could in principle travel along such a curve to return to their past, that is, travel in time.
We have two aims in this book. First, we want to describe and review various facets of the time concept, particularly focusing on those encountered in various mathematical physical theories about the universe. Second, and more importantly, we want to advance a particular view of time: that all concepts in physics are contextual. It is our assertion that time should not be discussed as an absolute thing or in isolation but only in terms of processes of observation.
Although it seems unscientific, we cannot escape the thought that the concept of time is intimately involved in how humans think. Various observations lead us to this view. For instance, animals do not seem at all concerned about the remote past and their interest in the long-term future is generally instinctive and centred on survival strategies: many animals gather and store food during summer in preparation for the coming winter. Certainly, dogs can remember where they buried a bone and can plan strategies to get around obstacles, but they do not hold services of remembrance or enrol onto three-year university degrees. They are very much creatures of the present, the enigmatic ‘moment of the now’. Humans, on the other hand, often seem overly preoccupied about the very distant past, such as what really happened on the day Julius Caesar was assassinated. This is undoubtedly directly connected with memory, the transmission in time of quasi persistent patterns in complex molecular structures in our brains. We should not make the mistake of thinking that these patterns are necessarily faithful three-dimensional model images of what we observe visually. As with the compact discs that are used to play back music and films, information can be stored in many ways and it is the decoding and interpretation of it that matters.
In addition to using memory to review the past, humans have the ability to make extraordinarily complex plans for the future. Indeed, anyone who does not make plans for their next meal, their careers, or their retirement, is unusual. Plans can be thought of as maps of proposed, possible, or potential futures. As far as we know, no matter how many alternative plans for tomorrow we make, only one of them at most can ever materialize as reality. However, some quantum theorists disagree. We shall discuss that point later on in this book.
Human interest in the past or future is often taken to extremes and turned into entertainment in the form of historically based films and novels depicting events that are known never to have happened and, in the case of science fiction, stories about possible futures based on fictitious laws of physics.
We can be sure that animals other than humans make plans: we have only to witness a pride of lions organizing an attack on a herd of gazelle to see sophisticated planning in operation. We may dismiss such planning as merely instinctive, but we should not forget that we humans are animals too, albeit with more complex mental faculties. We may believe that we have free will, but neurological evidence suggests that humans are much more under the control of their subconscious processes than they ever imagine or care to admit [Halligan & Oakley, 2000].
The development of religion and science required an awareness of time. Both systems of thought are attempts to understand humanity’s place in the physical universe, although each system is based on very different standards of logic and evidence. It is difficult to believe that any organism lacking some concept of the past would develop either religion or science. As far as we know, non-human animals do not have religious beliefs or interest in science.
The conventional dictionary meaning of the word paradigm defines it as an example or model, particularly in semantics. In recent usage it has come to mean something deeper and specific, particularly as far as science is concerned. In this book, we shall use this word in this latter sense. It will denote a relatively complete and distinct mental attitude or perspective held by a theorist with associated belief structures concerning some aspect of the universe. When a person thinks according to a specific paradigm, their thoughts and beliefs tend to be channelled into certain directions whilst other directions are excluded because they appear inconsistent with that given paradigm. For example, a person who believes in any particular religion adopts the paradigm provided by that religion and explicitly rejects other religions. Many events and phenomena encountered by that person are then interpreted according to those beliefs. A paradigm is essentially a mechanism for the interpretation of phenomena.
Different paradigms may be mutually inconsistent. For example, the flat Earth paradigm is inconsistent with the spherical Earth paradigm. Sometimes apparently exclusive paradigms are tolerated by individuals despite apparent inconsistencies. This may occur because of personal history, or for convenience.
Science too has its paradigms. For example, scientists may choose to believe in classical mechanics or in quantum mechanics, but they would find it difficult to believe in both simultaneously, although that is not impossible to contemplate. The study of time in particular encounters numerous different and exclusive paradigms, and so it will be necessary for the reader to be ready to switch mental frames of reference whenever necessary.
It is generally accepted that the role of experimental science is to provide objective data, information about the universe that is independent of any observer’s belief structures. This is the basis of the scientific motto of the Royal Society of London: ‘nullius in verba’, which translates as ‘take no one’s word for it’. This motto encapsulates a core principle in science. But there is a subtlety here that impinges on all discussions of time and which we should keep in mind: any discussion of any observed process, such as an object falling under gravity, requires us to state who or what is observing it, how they are observing it, and how they are interpreting what they observe. To think otherwise, to believe that things can happen without observers looking at them, is to think classically and metaphysically. The physicist Wheeler went so far as to state the participatory principle, which asserts that the only statements that mean anything are our observations. This principle is of critical importance to us in this book: it is our belief that the time concept can be discussed meaningfully only in terms of observers. Essentially, we will emphasize that time is a process and not a ‘thing’.
-  What happens along a CTC when quantum mechanics is involved is still the subject ofinvestigation.