We present a numerical approximation scheme for the Tomita-Takesaki modular
    operator of local subalgebras in linear quantum fields, working at one-particle
    level. This is applied to the local subspaces for double cones in the vacuum
    sector of a massive scalar free field in (1 + 1)- and (3 + 1)-dimensional
    Minkowski spacetime, using a discretization of time-0 data in position space.
    In the case of a wedge region, one component of the modular generator is
    well-known to be a mass-independent multiplication operator; our results
    strongly suggest that for the double cone, the corresponding component is still
    at least close to a multiplication operator, but that it is dependent on mass
    and angular momentum.



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