I have often heard that there are more than 4 (3 space and 1 time) dimensions of spacetime. What are the theories that say so, and how many does each predict? Has any experimental evidence been conclusive? And how are these extra-dimensional theories to agree with our daily observations?
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We are not really sure.
Classical theories are based on 4 total: 3 for the observed spatial directions, and 1 for time. However, string theory introduces a whole collection of other possible numbers. Some commonly used ones include 10, 11, or 26. Those extra dimensions are supposed to be "compactified" to explain our inability to observe them.
Willie Wong
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