The Time Machine And The Corridors

Is time a fourth dimension?

If so, do we move along it, either mentally or physically, or might we begin to do so?

I have discussed these questions on the Logic of Time Travel blog and in Time Travel And Poul Anderson.

Wells' Time Traveler wrongly claims that he accelerates along the temporal direction. On the contrary, he experiences time dilation because his bodily processes and thoughts happen more slowly than everything else. He should neither experience a sensation of headlong motion nor become invisible and intangible to everyone else. By contrast, Anderson's Wardens and Rangers do walk or drive along corridors that have been rotated onto the temporal axis.

However - has the Time Machine rotated so that the temporal dimension has become one of its spatial dimensions, then generated around itself a long invisible corridor along which it accelerates, this corridor somehow accounting for the Machine's invisibility and intangibility, just as Anderson's corridor travelers are concealed from external observers?