Assuming that the manifold is curved does not exclude the possibility of it being flat the latter is just a particular case of the former. Mind you that this is a very coordinate-dependent statement, to boot: if your curved spacetime is of the form "time + flat space" in one set of coordinates, in another set of coordinates, the spatial part may very well be curved, and the other way around. A flat space is just an example of a curved space, that is, flat space-times are contained in GR inasmuch this theory describes curved space-times.
one uses to define and to compute path integrals on flat spaces are briefly explained in. I suppose "curved space" would be an adequate description, though I can think of very few situation where you would want to explicitly emphasize the spacial curvature. 2.2 Hamiltonian Formalism and Curved-Space Ambiguities. I can't speak for the entire physics community out there, but I am under the impression that "curved spacetime" would be the commonly used expression.Įdit: Oh dear, I think I finally understood your question correctly. $$ds^2 = \frac,$$ such that for every $t$ fixed, we get a flat spacial slice, but the total space is most definitely curved. Also one loses the visual connection to the concept of curved space time. If a group of ants spend their entire lives on the essentially 2- dimensional surface of a trampoline, and. A simple analogy might help us to understand this notoriously hard-to-visualize concept. For example, flat space can be joined with a time coordinate to form a hyperbolic From the flat lightcone model we must deduce this fact. In fact, it turns out that gravity is nothing more than curved space, or, more specifically, the curvature or warpage of four- dimensional space-time. So when we debate whether space may be flat, we mean flat on cosmological scales. It can be curved though, depending on how you join the two to form a spacetime. Scientists believe, however, that our space is smoothly curved - more like a ball than a wad of paper - and thus the effects are only noticeable on cosmological scales. Space in the vicinity of a gravitating body cannot be perfectly flat, although typically space curvature is so small that it is not directly measurable.
This is how rockets get their thrust, how we're able to jump, and how cars move down the road. If space has no curvature (i.e, it is flat), there is exactly enough mass to. For humans, who move in three relatively flat dimensions, Newton's third law dictates that each force has an equal and opposite one. If space itself is curved, there are three general possibilities for the. Curved surfaces are ubiquitous in physics, biology, engineering, and mathematics but are defined by features that defy intuitions derived from flat space. The obvious example being Minkowski space, of course. Curved space is a fundamental part of modern physics, and is essential to understanding general relativity. Well, for starters, time + flat space, as you put it, isn't necessarily curved.
0 kommentar(er)
