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neginf
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Is it known if space:
1. is "grainy" or smooth ?,
2. has singular points ?,
3. is like R^3 ?
1. is "grainy" or smooth ?,
2. has singular points ?,
3. is like R^3 ?
For all intents and purposes, space-time is very smooth. On the smallest scales, we don't know; its possible that space-time is riddled with vacuum fluctuations just like quantum fields. We might need a quantum theory of gravity to find out.neginf said:1. is "grainy" or smooth ?
General relativity (GR) says that space-time does have singular points, but most people believe that's just a sign of GR's incompleteness---and once we have a good quantum theory of gravity, those singularities will be smoothed out.neginf said:2. has singular points ?
I'm not sure what you mean here. If you mean, is space euclidean---then the answer is 'asymptotically yes', but locally no---thats why we need general relativity.neginf said:3. is like R^3 ?
neginf said:Could physical space have a different topology than the usual R^3 ?
aimilvping said:the physical space i think is amazing, you know its exist but sometimes it is so abstract!
How does this interplay with measurements of flatness? The universe is flat to some high percentage, so does that place limits on the curvature of such a torus (i.e. analogous to the toroidal radius of a 2-torus)? Then, if such limits were placed, would that provide limits on the size of the universe?Nabeshin said:Yes, the simplest of them being a 3-torus.
zhermes said:How does this interplay with measurements of flatness? The universe is flat to some high percentage, so does that place limits on the curvature of such a torus (i.e. analogous to the toroidal radius of a 2-torus)? Then, if such limits were placed, would that provide limits on the size of the universe?
Nabeshin said:The 3-Torus is actually spatially flat everywhere, so the measurements of flatness only support such a theory. One idea of how to place limits are whether or not we see radiation running along the compactified dimensions of the torus, i.e. multiple images of the same objects. This of course gives you only an lower limit to the 'radius' of the torus, but I don't know of any actual experimental bounds on this from CMB data, for example.
Physical space refers to the three-dimensional extent in which objects and events occur and have relative position and direction. It is commonly described as the area and volume occupied by matter and energy.
The three properties of physical space are length, width, and height. These dimensions define the size and shape of an object or space and are essential for measuring and describing its physical properties.
Physical space is the tangible and measurable extent in which objects exist, while abstract space refers to the conceptual or mental understanding of space. Physical space has specific physical properties, while abstract space is a construct of the mind.
Yes, physical space can be altered or changed through various processes such as movement, deformation, or transformation. For example, the arrangement of objects in a room can alter the physical space, and natural forces such as erosion can change the physical properties of landforms.
Scientists study physical space through various fields of study, such as physics, astronomy, and geology. They use a combination of theories, experiments, and observations to understand the properties and behavior of physical space and the objects within it.