Experience of time is one of the primordial human experiences which is deeply tied to human consciousness. But despite this intimate relation of time with human conscious experience, time has proved to be very elusive. Particularly in physics, though there is already some understanding of time, there are still so many paradoxes that plague this understanding. In this paper we take rather a different route to question of time. We first attempt to come up with a theoretical understanding of time perception. Quite interestingly we find that quantum theory provides an algebraic formulation within which we can understand some essential aspects of time perception by human mind. We then ask whether a similar formalism can furnish the understanding of time as well and find connections of our formulation of time with similar works by other researchers. Our underlying approach to question of time has been inspired by R. W. Hamilton who considers algebra as science of pure time. Hence our work has an extensive algebraic flavor. Our work also incorporates another approach based on Kauffman's iterant algebra which relates time to underlying recursions and oscillations. We believe that our work will initiate more investigations in this direction.
Experience of time is one of the primordial human experiences which is deeply tied to human consciousness. But despite this intimate relation of time with human conscious experience, time has proved to be very elusive. Particularly in physics, though there is already some understanding of time, there are still so many paradoxes that plague this understanding. In this paper we take rather a different route to question of time. We first attempt to come up with a theoretical understanding of time perception. Quite interestingly we find that quantum theory provides an algebraic formulation within which we can understand some essential aspects of time perception by human mind. We then ask whether a similar formalism can furnish the understanding of time as well and find connections of our formulation of time with similar works by other researchers. Our underlying approach to question of time has been inspired by R. W. Hamilton who considers algebra as science of pure time. Hence our work has an extensive algebraic flavor. Our work also incorporates another approach based on Kauffman's iterant algebra which relates time to underlying recursions and oscillations. We believe that our work will initiate more investigations in this direction.
However, the observations encompassed by classical physics excludes the observer from the physical reality, yet the deep-down understandung of nature --{\it the quantum theory}-- can not avoid the intrusion of observer into the measurement process. Indeed, the quantum physics experiments have knocked the door of a new paradigm: in which science of consciousness is an important axiom. In the present work, it is argued --by taking into account of the views of learned scientists and philosophers-- that modern science is incomplete and lacking something in the basic understanding of nature \cite{r}. Classical physics has failed to explain the dynamics of the microscopic particles, eventhough modern scientific researches are based upon the prejudice posed by classical physics: keeping the outer physical universe as a separate entity, that is something quite independent of the observer --human mind. One should not forget that human-being is a part of nature and human mind is an essential component of our observations. Basically, it is the observer --the consciousness-- which makes perception possible. The working of human mind must be included in our scientific theories. In fact, human free will is an illusion and nothing in the entire universe (with life) lies outside the domain of science and determinism.
In this review we present the problem of time in quantum physics, including a short history of the problem and the known objections about considering time as a quantum observable. The need to deal with time as an observable is elaborated through some unresolved problems. The lack of a consistent theory of time is currently hindering the formulation of a full-fledged theory of quantum gravity. It is argued that the proposal set forth by several authors of considering an intrinsic measurement of quantum time, besides having the conventional external time, is compelling. Recently several suggestions have been put forward to revive the proposal of Page and Wootters (1983), elaborating and resolving some of the main ambiguities of the original proposal and opening new scope for understanding its content. The approach followed in these new contributions exposes the need to go beyond the limitations enforced by the conventional approach of quantum physics. The attitude of covariant loop quantum gravity, in which it is called to completely ignore time, is also discussed. This review could be a step forward in an endeavour to reform our outlook of the unification of the theory of relativity and quantum physics by furnishing the conceptual ground needed for this goal. Intentionally, some technical details are avoided since we aim to present the approaches to resolve the problem in a simple way with the clearest possible outlook. These can be looked up in the original references provided.
Is mind quantum-like? Is consciousness quantum physical? Does consciousness have a role to play in the emergence of the classical world from the underlying quantum universe? Or is this dichotomy between classical and quantum an illusion? How can world philosophies enrich our views on these matters and interact with the best scientific theories? These are some questions that motivated us to conceive the current book. We also felt an urgent need to discuss the central philosophical questions haunting the emerging frameworks of quantum cognition and quantum-like framework (QLF). We have observed that there are very good technical or mathematical works being done in the emerging fields of quantum cognition and QLF, but there is still a great need for exploring the underlying and open philosophical questions they demand. Quantum cognition developed as a frontier research programme in understanding various cognitive phenomena that are hard or impossible to describe based on classical cognitive science paradigm. Classical cognitive science draws philosophically and mathematically from classical physics and classical probability theory. For example, cognitive realism thinking is deeply motivated by the scientific realism of classical physics. However, as we explore, there are numerous empirical findings which demonstrate clearly that human mind and cognitive processes exhibit features that are more quantum-like. Central to these features are indeterminacy, context dependence, and complementarity of cognitive phenomena, for example, perception, information retrieval, and even qualia. Many good works in the previous decade have demonstrated the efficacy of quantum-like mathematical modelling in such cases. However, given that efficacy, we cannot simply conclude that mind is quantum. Rather there are features that go beyond what is allowed in standard quantum formalism.
The question of time in quantum mechanics has been a topic of intense discussion since its inception.Dating back to the works of the founders of the subject, the notion of time and how it fit in the theory was already a point with a lack of a formal explanation, especially in aspects such as the uncertainty principle and canonical commutation relations.A theorem by Pauli set in stone that any attempt at trying to understand time with the formalism in use at the time for quantum mechanics was impossible.Through studies on the logical basis of the subject and establishing different sets of axioms, more modern works were able to relax sufficiently the impositions on the concept of observables so that time could then be understood as a 'generalized' observable.Not only that, but it was shown that the correct way to interpret eventual time measurements was through the formalism of Positive Operator Valued Measures.Latest works then were focused in the direction of constructing either direct measures and time operators, or, in the case that was followed throughout this work, to establish a procedure to construct measures.This work was then an in-depth study of the work done by Brunetti and Fredenhagen, with the intent to do the first steps in generalizing their ideas by establishing their method to be covariant with respect to Poincaré transformations.
Quantum theory has been proved as an outstanding mystery in modern science. The predictions of science have turned out to be probabilistic. The principle of determinism has failed. For systems like weather, earthquakes, rolling dices etc... and of course human behavior it has proved impossible, for science, to describe a state of the system accurately for a long time into the future. Moreover, modern cosmology has to rely on philosophical assumptions. It is argued -- by taking into account of the views of learned scientists and philosophers -- that modern science can never explain everything and it is a hard fact to discover the ``Theory Of Everything''. On the other hand, modern scientific technology have damaged our environment and posed serious threats for the future development of science. All these facts and results put a big question-mark (?) on the grass-root level working of science. In fact, all scientific researches are based upon ordinary sense perception, which keeps the outer physical universe as a separate entity, that is something quite independent of the observer. Basically, it is the observer -- the knower -- which makes perception possible. Astonishingly, the knower -- human mind -- is not included in our scientific theories. One should not forget human-being (human mind) is a part of nature and an essential component of our observations, so it's inclusion in scientific theories is must in order to recover modern science from the drastic state of trauma.