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dioib
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How do we know that the (effective) dimensionality of "space" is three in a typical physical theory?
tom.stoer said:a) because we see it
b) because we can measure it, e.g. via the Coulomb law which shows a behaviour like U(r) ~ r-(D-2)
c) because there are a huge number of physical predictions depending on the dimensionality (besides the Coulomb law there are the gravitational potential, diffusion processes, ...)
yes i have the same confusiondioib said:Thank you for breaking it down into parts:
a') Because we can't see/perceive "further/higher".
b',c') Taking (a'), how can I make sure it will not affect (b,c)?
The dimension of space refers to the number of coordinates needed to specify the position of a point in space. In our everyday experience, we live in a three-dimensional world with length, width, and height. This means that we need three coordinates (x, y, z) to pinpoint the location of an object in space.
We know that the dimension of space is 3 through various mathematical and scientific experiments. For example, Euclidean geometry, which is based on three dimensions, has been used for centuries to describe and measure objects in our world. Additionally, modern physics theories such as relativity and quantum mechanics also rely on the assumption of three dimensions of space.
While we cannot definitively say that the dimension of space cannot change, there is currently no scientific evidence to suggest that it can. Our current understanding and mathematical models of the universe rely on three dimensions of space, and any changes to this would require a significant shift in our understanding of physics.
Visualizing higher dimensions of space is a challenging task as it goes beyond our everyday experience. However, mathematicians and scientists have developed various techniques, such as projections and animations, to help us conceptualize higher dimensions. These techniques use analogies and simplifications to represent higher dimensions in a way that is easier for us to understand.
While there is currently no direct evidence for the existence of higher dimensions of space, some theories in physics, such as string theory, suggest the possibility of additional dimensions. However, these theories are still highly speculative and have not yet been proven. Further research and experiments are needed to determine if higher dimensions of space exist and how they may affect our understanding of the universe.