Can someone please explain to me the current theories of Time? I have an idea I want to put forward to you all, but need to get a little groundwork in first. Based purely on what I learned in school, time is currently veiwed as linear, if so, how is this even possible? Much appreciated, thanks.
The modern concept of linear time is probably the most popular one. It is practically being used in the formulation of a physical theory. But theories of relativity (special and general) both combined time with space to form spacetime. And in string theories, spacetime's dimension were increased only for the space part while the time dimension remains linear. If time is linear, the logical thing is for it to have two directions. But according to the theory of thermodynamics, only one arrow of time is found, this is the direction of increasing entropy. The other arrows of time are implied in: electromagnetic radiation always emanates outward from a source never inward; the cosmological expansion of space (spacetime?); and, in psychology, we remember the past but not the future.
Time as a linear measurement? Intresting. I assume this is correct but (unless I am wrong) time must not only have direction but velocity. By that I mean it must travel in the direction of 3-D shapes and it must have its own factors. Although we have put a measurement on time it is still independed to everthing else (I mean to say it works wih space independently). Might be the greatest load of rubbish you have every heard but here it is anyway. The Bob (2004 ©)
Time has a velocity component only in spacetime. While spacetime is the fabric of the cosmos; it is the background to everything else: space (stand alone), matter, and energy.
Therefore this means that time could be independent, like space can be, and so we have put a measurement on it and really it could change and we would be none the wiser. The Bob (2004 ©)
Spacetime is independent of time iff spacetime is static. But spacetime is dynamic then the metric of spacetime will depend on the local motion of space and time.
What I am asking is is it possible for Time to 'fold' like space? If so is it not, therefore, independent to everythin (in realtion to space)? The Bob (2004 ©)
Up to planck length, and then it is unobservable? If such dimensions are compacted how would we ever know? Time would become immediate and so would the actions of "spooky" at any distance? We look ever deeper for the "interactive phases" that might represent solutions about that space? Everyone is saying no "hidden variables," yet we had not discerned relevance to Glast in geometrical considerations, so to all intensive purposes, this was hidden
In spacetime, this folding is called the curvature of spacetime. But spacetime can still be curved while it can remain static. But in general relativity this is a tautology because of the existence of matter: matter dictates spacetime how to curve and the curvature of spacetime dictates matter how to move. This does not say anything if you want to find the origin of matter.
A theory can still be logical even though not observable. If I put myself in the shoe of a zero dimensional spacetime point, and ask myself who are my nearest neighbors and how many are there? The logical answer is six. This answer is based on the assumption that the topology of an infinitesimal sphere is equivalent to that of an infinitesimal cube as the length of edge of the cube approaches zero.
To the detriment of strings and LQG there defintiely has to be some consistancy How did you arrive at that? It becomes a little more difficult then this in term of defining the coordinates references for sure, but then the move to topological consideration overtakes this issue when we continue to think of the Reinmann and the spherical considerations. How did you get there? Matter considerations can become very fluid and along side of this, gravitational considerations as well. So how well would we define such points without considering the space of considerations without understanding even in the gaussian world there was issues to contend with, that move along side of GR into the dynamical world of QM?
Therefore is it possible for time to pull away from space (if only for a small period of time) and change speed and then merge back in? The Bob (2004 ©)
Riemannian geometry is static. But if the geometry is dynamic, i.e. introducing a force into the geometry, then the sphere can never be a closed surface. There at the least should have one hole in the form of a point. But the projection of this point into the sphere is an infinitely extended plane and for the infinite points of spacetime there should exist infinite numbers of orthogonal planes and three of these planes intersect at the said point at (0,0,0). These planes also formed a lattice structure separated by a constant distance which experimental limit is the Planck length.
My research goal is to verify the genus of spacetime. At present, I don't think is that of a sphere. I am more incline to say that the topology of spacetime has genus equals 1 similar to that of a doubly twisted Moebius strip. A sphere, in reality, separate spacetime into an inside and an outside with no connection between points inside and outside except through points on the boundaring spherical closed surface. Once a point is picked on the surface, it is the same thing as creating a hole, literally speaking.
http://ccins.camosun.bc.ca/~jbritton/animcup.gif http://scholar.uwinnipeg.ca/courses/38/4500.6-001/cosmology/donut-coffeecup.gif Topology is the branch of mathematics concerned with the ramifications of continuity. Topologist emphasize the properties of shapes that remain unchanged no matter how much the shapes are bent twisted or otherwise manipulated. http://scholar.uwinnipeg.ca/courses/38/4500.6-001/cosmology/wormhole.jpg A wormhole is a genus 1 topological defect in space. http://scholar.uwinnipeg.ca/courses/38/4500.6-001/cosmology/Properties-of-Space.htm I think I should have better asked the question on deviation from discrete to continuity and how this would have been defined mathematically. In coordinate frames, as have been pointed out in various posts, none have really dealt with the issue of dimension other then within those confines. Continuity has to explain dimension, and leads from classical discriptions now faced with, higher recognition of four dimensions of space(cube to hypercube), within the issues of topology and recognition of curvature? The consistancy in geometrical expression has to be define through the different phases of that geometry(gravity has been defined up to this point) U(1) is a point, also a circle, it's length as a one dimensional string defined in the brane:) The energy determination of the circle in U(1)is describing a means by which such consistancy might have been recognized? Immediately one wrap of the string, more energy more wraps, hence the length of that string? This movement is defining not only the lenght but is determining its twists and turns. Does this make sense?
The topology of spacetime is continuous. But spacetime has two distinct topologies merged together. This combination form a discrete dynamic "shape" (I am not going to use the word topology again so that there is a separate concept between discrete and continuous). This shape is analogous to the Hopf ring or doubly twisted Moebius strip when one the two dimensions is shrunk to zero. The continuity of spacetime comes from its individual topology but the combination of these topologies creates a discrete shape for spacetime structure. This discrete shape is the square of energy and in vector notations: [itex] E^2 = \psi_E \times \phi_E \cdot \psi_B \times \phi_B [/itex] where the [itex] \psi_i [/itex] is the metric and [itex] \phi_i [/itex] is the force but for time independent structure, it is the linear momentum and then the shape becomes a double actions or two interlinked angular momenta (square of Planck constant).
sol2, Thanks for the beautiful pictures and the web links on topology and will visit them again and again.