Charge quantization, the topology and 3-dimensionality of the universe, and abolishing monopoles
نویسنده
چکیده
Why do all electrons have the same charge and why do all protons have exactly the opposite charge? Dirac provided a possible answer by proposing the existence of magnetic monopoles. We propose a simple possible topological explanation of why charge is quantized, involving a tiny permanent magnetic field trapped in the topology of the universe. The idea apparently works for every possible compact 3-manifold topology for the universe except for the 3sphere S and elliptic 3-geometry. This picture does not need to assume magnetic monopoles exist, and indeed looks incompatible with their existence. Which topologies for the universe are consistent (or not) with laws of physics? We present an argument that all orientable 3-manifolds should be consistent with a very wide class of possible laws of physics; but almost all n-manifolds for each n 6= 3 won’t be. This is perhaps a “reason the world is 3 dimensional.” Next we argue that if point monopoles exist, and Dirac’s wave equation of quantum mechanics in static (scalar and vector) potentials holds, then a contradiction arises. Hence monopoles cannot exist – or: they are not points; or: Dirac’s equation for quantum mechanics is not correct. Meanwhile non-point monopoles lead to other unpalatabilities or contradictions. Hence there are reasons to prefer our topological explanation of charge quantization to Dirac’s monopole
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