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Quantum field theory and relativity share the need for point particles (besides we have learned how to deal with extended objects with more or less success). Heisenberg uncertainty principle introduces a limit into the simultaneous measurement onto a point particle and generalizations can be found for p-branes in the literature. However, is it really unavoidable that point-like particles will loose their sense in a quantum theory of space-time, if this space-time is only effective, what are the pointless geometry we are seeking? Even string theory, as we understand it, makes use of the conformal fields, but can we avoid points (and space-time or fields at the end!)? If so, why are they so precise? Do we really have a way to probe if REAL point particles are meaningful or only a deep and useful model of reality?

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  • $\begingroup$ The point particle is just an approximation; we know that they cannot be point particles other wise, for example, they would become mini black holes and evaporate practically instantly through a burst of thermal energy. As long as the length scales are kept far from the Planck length, a QFT can have some power left, even though the energy scales at which the Standard model starts becoming doubtful are well below the Planckian. It is only natural, thus, to consider extended objects. Whether these are string or p-branes or even something else, no one can be certain, not yet anyway. $\endgroup$ – Panos C. May 6 '18 at 1:51
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"In quantum mechanics, the concept of a point particle is complicated by the Heisenberg uncertainty principle, because even an elementary particle, with no internal structure, occupies a nonzero volume." Wikipedia

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