Dimensional Analysis Of The Time Corridors

We refer to Poul Anderson, The Corridors Of Time.

Does the temporal dimension within a time corridor correspond to one of the three spatial dimensions outside the corridor or is it a fifth dimension and purely temporal in nature? Argument (i) assumes the latter whereas (ii) is applicable either way and also repeats a point made earlier but I think that this is legitimate in the interests of clarity.

(i) Hypothesis: the familiar four-dimensional continuum endures along a fifth dimension that is not a fourth spatial dimension but a second temporal dimension. A human being, with his three perceived spatial dimensions and one experienced temporal dimension, inhabits a four dimensional cross-section of the five dimensional totality. Because the fifth dimension is temporal, not spatial, any two four dimensional cross-sections are not "above" or "below" but "before" or "after" each other. A time corridor extends along the first temporal dimension and endures, or ages, along the second temporal dimension. Thus, anyone who enters a corridor, spends some time within it, then re-emerges from it, emerges not into his original cross-section/continuum but into a later continuum that is identical with the original except for any changes that he makes, the first such change being his arrival. It would follow from this that, whenever someone travels along a corridor, he leaves behind him a continuum from which he has disappeared and to which he never returns. Clearly, this is not the metaphysic assumed by Anderson. His time travelers always return to the continuum from which they had departed and are unable to alter it. If this is case, then what more complicated metaphysic would account for Anderson's scenario?

(ii) A time corridor extends along the familiar temporal dimension. Therefore, a spatial distance within the corridor corresponds to a temporal interval outside the corridor. Therefore, people entering the corridor from different times outside the corridor should arrive in the corridor with only a spatial distance, not a temporal interval, between them within the corridor. Therefore, they should all meet every time they use the corridor.