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## Main Question or Discussion Point

Hi.

Why did the founding fathers of QM know that the Hilbert space of a composite system is the tensor product of the component Hilbert spaces and not a direct product, where no entanglement would emerge? I mean today we can verify entanglement experimentally, but this became technologically possible far later than for example the EPR paper.

My knowledge about functional analysis is pretty limited, is there a mathematical reason to exclude the direct product?

Why did the founding fathers of QM know that the Hilbert space of a composite system is the tensor product of the component Hilbert spaces and not a direct product, where no entanglement would emerge? I mean today we can verify entanglement experimentally, but this became technologically possible far later than for example the EPR paper.

My knowledge about functional analysis is pretty limited, is there a mathematical reason to exclude the direct product?