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Alltimegreat1
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I'm having trouble understanding the terms "flat geometry of the universe" and "baseline curvature of the universe." How can a 3D universe be flat?
Flat is not the same thing as Euclidean.jfizzix said:3D space can be flat (i.e., Euclidean) in the sense that parallel lines never meet and keep the same distance from each other.
For nearly all intents and purposes, it is.Orodruin said:Flat is not the same thing as Euclidean.
Definitely not. For the application to cosmology, yes, but flattness and being a Euclidean space are different mathematical concepts.Chalnoth said:For nearly all intents and purposes, it is.
Perhaps, but that distinction is quite subtle.Orodruin said:Definitely not. For the application to cosmology, yes, but flattness and being a Euclidean space are different mathematical concepts.
This is not true either. Flatness is a local concept although it is perfectly possible to have completely flat spaces which do not wrap back on themselves and are not Euclidean. In particular, spaces with non-zero torsion come to mind.Chalnoth said:Perhaps, but that distinction is quite subtle.
Euclidean space and flat space have all of the same measurable properties, except for the possibility that a flat space can potentially wrap back on itself.
Alberto87 said:how can a flat space wrap back on itself?
Ah ok, but it only wraps back in one direction, the second direction cannot, am I right?Orodruin said:A cylinder is the most usual example of such a space. It is flat, but has a cyclic direction.
Note that we are talking about intrinsic curvature here, which is a property of the space itself, not of its embedding into a higher-dimensional space. Extrinsic curvature is something different.
It can wrap around in all directions. A torus is an example - whether it is flat or not depends on the metric you put on it.Alberto87 said:Ah ok, but it only wraps back in one direction, the second direction cannot, am I right?
It´s not possible for a flat space to be finite and unlimited, isn´t it?
Is the torus a flat space time?
Alberto87 said:Ah ok, but it only wraps back in one direction, the second direction cannot, am I right?
It´s not possible for a flat space to be finite and unlimited, isn´t it?
Is the torus a flat space time?
The geometry of the universe refers to the overall shape and structure of the universe. It is a fundamental concept in cosmology and is used to describe the curvature of space.
The three possible geometries of the universe are flat, open, and closed. In a flat universe, the overall curvature of space is zero. In an open universe, space has a negative curvature and expands forever. In a closed universe, space has a positive curvature and eventually collapses back on itself.
Scientists determine the geometry of the universe through various observations and measurements, such as the cosmic microwave background radiation, the distribution of galaxies, and the rate of expansion of the universe. These data can be used to calculate the overall curvature of space.
The geometry of the universe has important implications for the fate and behavior of the universe. It can help us understand the overall structure and evolution of the universe, as well as the nature of dark energy and dark matter. It also plays a crucial role in theories of the origin of the universe, such as the Big Bang theory.
No, the geometry of the universe is not constant. It can change over time due to the influence of dark energy and the expansion of the universe. In fact, the geometry of the universe has likely changed significantly since the Big Bang and may continue to change in the future.