By appealing to differential geometry, it is known that surfaces possesses certain properties (like curvature) independent of any embedding. For example, take the 2D surface of a sphere embedded in 3D space. We can readily visualize this manifold as the surface of a ball. Interestingly, the curvature of a sphere of radius r (K = 1/r^2) is independent of this embedding (i.e. does not depend on the nature of the higher-dimensional space). In fact, the embedding is not even necessary -- the curvature is intrinsic to the surface! (The 3D embedding space for the case of the ball helps us visualize this curvature, but it's there even in 2D space). Cosmological models are based on the differential manifolds of general relativity, and so there is no embedding in cosmology either. This means that cosmological models don't consider anything outside the universe -- the spacetime manifold representing the universe is the whole of the physical reality described by the theory.Rosen said:I was inquiring as to what models may have described such an area, and wondering if the uncertainty principle applied there. Great forum by the way. Thank you.
bapowell said:In fact, the embedding is not even necessary -- the curvature is intrinsic to the surface!.
Right. In particular, that you can make this determination by measuring the surface itself, irrespective of the space the Earth happens to be floating in.94JZA80 said:is this statement evidenced by the fact that the sum of the interior angles of the triangle formed by the Prime Meridian, the 90° line of longitude, and the equator = 270° (as opposed to 180° on a truly flat surface)?
TIA,
Eric
The Dimensionless Void Pre Big Bang theory proposes that the universe existed in a state of absolute nothingness before the Big Bang, with no dimensions or physical laws. This concept challenges the traditional belief that the universe began with a singularity and suggests that the Big Bang was a phase transition from this void state to the universe we know today.
The theory suggests that the void state was unstable and underwent a quantum fluctuation, resulting in the creation of the universe. This fluctuation caused the dimensions and physical laws to emerge, leading to the Big Bang event. It also proposes that the universe goes through cycles of expansion and contraction, with each cycle starting and ending in the void state.
One of the main pieces of evidence for this theory is the cosmic microwave background radiation, which is believed to be leftover radiation from the Big Bang. However, the theory also explains the observed homogeneity and flatness of the universe, as the void state would have been a completely uniform and flat state. Additionally, the theory is consistent with the laws of thermodynamics and quantum mechanics.
The traditional view of the Big Bang suggests that the universe began with a singularity, a point of infinite density and temperature. However, the Dimensionless Void Pre Big Bang theory proposes that the universe had no physical properties or dimensions before the Big Bang, challenging the idea of a singularity. It also suggests that the universe has existed in some form for an infinite amount of time, rather than having a specific beginning.
If this theory is proven to be true, it would revolutionize our understanding of the origin and evolution of the universe. It would also have significant implications for our understanding of space, time, and the laws of physics. Additionally, it could potentially lead to new insights into the nature of the void state and the mechanisms behind the Big Bang event.