Time invariance seems to leave physicists in a bit of a quandary with some suggesting that time could move backwards in a different epoch or inside a spinning black hole etc., but it seems to me to be a simple consequence of Einstein's strong equivalence principle. If all physics is independent of a chosen coordinate system, then it has to hold for changes of the scale of the dimensions used, and therefore a simple change of scale factor for time (from +1 to -1) could not affect the underlying physics. I detail this a little bit more at http://blackholeinside.com/bhi/time-reversal.html
I would love to hear your views on this.

Dave Proffitt
http://blackholeinside.co.uk