Young pulsars and the pulsar wind nebulae (PWNe) or supernova remnants (SNRs) that surround them are some of the most dynamic and high-powered environments in our Universe. With the rise of more sensitive observations, the number of pulsar-SNR and PWN associations (hereafter, SNR/PWN) has increased, yet we do not understand to which extent this environment influences the pulsars impulsive radio signals. We studied the dispersive contribution of SNRs and PWNe on Galactic pulsars, and considered their relevance to fast radio bursts (FRBs) such as FRB 121102. We investigated the dispersion measure (DM) contribution of SNRs and PWNe by comparing the measured DMs of Galactic pulsars in a SNR/PWN to the DM expected only from the intervening interstellar electrons, using the NE2001 model. We find that a two-$sigma$ DM contribution of SNRs and PWNe to the pulsar signal exists, amounting to $21.1 pm 10.6$ pc cm$^{-3}$. The control sample of pulsars unassociated with a SNR/PWN shows no excess. We model the SNR and PWN electron densities for each young pulsar in our sample and show that these indeed predict an excess of this magnitude. By extrapolating to the kind of fast-spinning, high magnetic field, young pulsars that may power FRBs, we show their SNR and PWN are capable of significantly contributing to the observed DM.
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