"...there must be an extra temporal dimension which unifies the various string theories. Again, an extra dimension of time would go a long way to explain non-locality and superposition - but it is vigorously resisted because it would also do injury to physical causality (time being a plane instead of a line)".
A-G, I was wondering if you could further explain how, exactly, physical causality is injured by the extra time dimension. How would adding an extra time dimension change anything that we currently percieve to be true?
Have you ever perceived a phenomenon or event in the actual present of the occurance? ... We are arranged to perceive that which has already happened, thus we are 'in the present' perceiving 'the immediate past' (or in the case of distant stars, the remote past).
Mathematics however is more open-minded as it were. F-theory which is also called "father" theory because it unifies other string theories (Cumrun Vafa, Harvard) suggests that there is an extra time dimension.
An extra time dimension would mean that what we perceive to be a timeline in our 4D worldview is actually a plane. There is no necessary cause/effect relationship, it could just as easily be effect/cause - or not related at all. Past, present and future would all co-exist on the plane. Arrows and directions are moot.
However, because there would be no actual arrow of time, entropy would be an illusion to observers traveling a worldline in a general direction.
OTOH, non-locality could make sense - splitting a photon and measuring the one at a certain space/time coordinate determining the other regardless of "distance" between. What would seem like a violation of the speed of light in non-locality would not be a violation if time is a plane and not a line.
Likewise, superposition could make sense - the cat would be both alive and dead since there is not a necessary cause/effect relationship as is required with a time line, an arrow of time.
IOW, the "arrow of time" would be the perception of an observer on a worldline - not what was actually physically happening. This is similar to the multi-world theory that all possibilities actual manifest in parallel universes. The "you" which did not read this post exists as does the "you" who did read this post - in parallel "universes" (or selections of coordinates) on different branches of your worldline as observer.