Category: Uncategorized

FIELD LANGUAGE. “Thus, with the rise of classical field theory, culminating in general relativity, the field gradually became endowed with properties previously thought peculiar to matter. Thus the electromagnetic field was discovered to possess mechanical properties like momentum and angular momentum, and (after the advent of special relativity) mass-energy. The ‘action-at-a-distance’ of Newtonian gravity readily admits a translation into the language of fields; and, of course, the theory of general relativity was couched in such language from the outset.” https://lnkd.in/dMm_YkR View in LinkedIn

THE EMERGENCE OF TIME. “The problem of time vs. the emergence of time. Perhaps the most obvious difference is that the problem of time is mostly about time rather than space; while as we said in Section 1, we intend ‘the emergence of time’ to also cover the emergence of spacetime, and so space. At a technical level, the tendency not to dwell on a ‘problem of space’ stems from the fact that, as noted above, in constrained quantization, the momen- tum constraint —which, from a spacetime perspective, shuffles spacetime points within a given 3-dimensional spacelike slice—is much easier to deal with, conceptually and technically, than the Hamiltonian constraint, which is related, at least classically, to diffeomorphisms that map points from one spacelike slice to another.” https://lnkd.in/dMm_YkR View in LinkedIn

MATTER AS A FIELD. “Some of the most distinctive characteristics of matter, at least as idealized by the mechanical philosophy of the seventeenth century—such as impenetrability and continuity— turn out to be only apparent; and others, such as massiveness, turn out to be shared with invisible fields that extend in ‘empty space’ arbitrarily far from their sources. Further, matter itself has come to be treated as a field, and this involves being represented mathematically by an assignment of a mathematical object—at its simplest: an item like a real number, or a vector, or a matrix—to each point of space or spacetime.” https://lnkd.in/dMm_YkR View in LinkedIn

PREQUANTUM TIME. “Rather, one has to confront the extremely difficult problem of solving a collection of very non-linear, coupled (elliptic) partial-differential equations. So far, this has proved intractable. This, then, is the first form of the problem of time: the problem of finding a time ‘before quantisation’.” https://lnkd.in/dMm_YkR View in LinkedIn

GRAVITY IS THE PROBLEM. “Many of the conceptual issues surrounding the emergence of time, or the problem of time, are much the same, whether or not one considers matter. For example, as Kuchar (this volume) says, “matter is not the heart of the problem [of time in geometrodynamics]; it is gravity”. https://lnkd.in/dMm_YkR View in LinkedIn

TANGLED KNOT. “What then is the problem of time? As emphasized by Kuchar it is really a cluster of problems that arise principally from the disparate ways in which time is treated in quantum theory and in general relativity.” https://lnkd.in/dMm_YkR View in LinkedIn

THE THIRD LEG. “We barely mentioned something that everyday thought takes to be much more unproblematically real than space and time: namely, matter! Why matter comes to play second fiddle to space and time.” https://lnkd.in/dMm_YkR View in LinkedIn

THE PROBLEM OF TIME. “The canonical quantisation of general relativity leads to a quantum state-vector which is a functional of 3-geometries; (this subject is known as ‘quantum geometrodynamics’). But there are immense mathematical and conceptual difficulties about this quantisation. Prominent among the conceptual difficulties is what is what is perhaps the best-known philosophical topic arising from quantum gravity: the so-called ‘problem of time’.” https://lnkd.in/dMm_YkR View in LinkedIn

OTHERNESS. “The Copenhagen interpretation is one that requires, not an observer, but a ‘classical background’ external to the system. And, arguably, one obvious candidate for such a background is the continuous spacetime manifold of our usual quantum theories (both quantum mechanics and quantum field theories). But we admit to giving this sort of interpretation little credence.” https://lnkd.in/dMm_YkR View in LinkedIn

THE OBSERVER REQUIREMENT. “The endeavour of quantum gravity is closely related to quantum cosmology, i.e., the attempt to have a quantum theory of the whole universe. And in quantum cosmology, the traditional Copenhagen interpretation, with its requirement of an observer external to the system, is obviously inapplicable.” https://lnkd.in/dMm_YkR View in LinkedIn