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I'm still wondering why space is 3-dimensional.
This may seem pedantic, but a lot of assumptions brake down when you look at tiny or high energy things. So, it's really important to mark down all your assumptions.
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How can a dimension be under a size? The four regular dimensions (3d and time) can go infinitely in any direction.
Well, how can you go on forever without falling off the edge of the Earth? The surface of the Earth two-dimensional, and approximately flat... but there's small positive curvature, so you're continuously wrapping around to a different part of the space. The surface of the Earth can be meaningfully understood as a two-dimensional surface that possesses finite dimension. A three-dimensional space can be close to flat b…
Of course, if we a assume a multiverse with universes having regularly distributed, positive curvatures, then, the size of the universe would grow asymptotically as the curvature approached flat, so, statistically, life is more more likely to arise on the flatter universes.
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Here is a fun attempt to answer that: http://arxiv.org/abs/gr-qc/9702052
Anthropic arguments such as this are good for examining reasons why spacetime with a different number of dimensions might not support interesting universes, but they fail to ask answer the question why we have a spacetime with 3 dimensions. Some non-string theory attempts at formulating quantum gravity have started without an assumption of space-time and attempted to make it an emergent property, and given 3-dimensio…
A better question is: does a universe in which there is nothing (and never has been) still contain space? (Though a better question, I wrecked it by introducing "never", which presupposes that the universe has time---even though it contains nothing, and therefore no events take place.)
The question creates a bias because when we imagine matter being removed from the universe, we firstly imagine the removal as an event unfolding in time. Secondly, we continue to imagine the locations where pieces of matter used to be, and those locations continue to be separated by the abstract space which we continue to imagine.
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Does anyone have a good way of explaining to a layman how a dimension can be small?
Consider the outside of a straw. The surface is a curved two-dimensional space which is bounded in one direction only by the length of the straw, but is quite small in the other (the circumference of the straw). If the straw is very long and very thin then it may appear to be essentially 1-dimensional, but the surface is still two dimensional.
Spinning objects are made of particles that are all actually going in straight lines but forces against each other are causing them to change direction, cummulatively appearing to be spinning, like an extremely coherent eddie current or vortex. Their movement is in relation to each other, and there is no need for an objective space in which to spin.
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Well, how can you go on forever without falling off the edge of the Earth? The surface of the Earth two-dimensional, and approximately flat... but there's small positive curvature, so you're continuously wrapping around to a different part of the space. The surface of the Earth can be meaningfully understood as a two-dimensional surface that possesses finite dimension. A three-dimensional space can be close to flat b…
My understanding is that we have conducted experiments to measure the curvature of the universe, and come up with answers that are withing the experimental error of being flat. Without any theoretical reason why the universe should be flat, it is still possible that the universe is curved, but to slightly for us to detect, however, but the simplest interpretation is to say that the universe is flat. Of course, if we…
That would probably be more easily measured though. I don't know.
Spinning motion is an illusion and doesn't exist as a fundamental form of movement, similar to how lack of gravity in orbit is an illusion, in that you are continuously falling downward but missing the earth. Spinning objects are made of particles that are all actually going in straight lines but forces against each other are causing them to change direction, cummulatively appearing to be spinning, like an extremely…
What you describe are particules going in straight lines, but over what space/grid are they going on a straight lines? If they are going over straight lines on something then your description is one of an objective space.
If pulling forces are still exerted on its edges in proportion to said "spinning", then there exist a static field in space for which the object is in static alignment when the pulling force are at minima.
Interestingly the same observation could be made of two objects in orbit or the electrons orbiting individual atoms in the object, with the static alignment being observed when the acceleration between the objects is at a maxima i.e. they are falling into one another.
The question "would space still exist if matter disappeared" is posed with an ontological bias which influences the answer. A better question is: does a universe in which there is nothing (and never has been) still contain space? (Though a better question, I wrecked it by introducing "never", which presupposes that the universe has time---even though it contains nothing, and therefore no events take place.) The quest…
Given our current state of understanding, there really isn't a need to insist that one question is wrong and some other question is better, seeing as we are currently equally incapable of answering any of them.