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We show that for all Euclidean dimensions d \~{}=dₖ-d₅, where Lₑ^ { \~{}} is the effective resistance between two points separated by a distance comparable with the correlation length, d₅ is the fractal dimension of the backbone, and dₖ is the fractal dimension of a random walk on the same backbone. We also find a relation between the backbone and the full percolation cluster, dₖ-d₅=dₖ-d₅. Thus the Alexander-Orbach conjecture (d₅{dₖ}=23 for d>~2) fails numerically for the backbone.
Stanley et al. (Sun,) studied this question.