...Just as acceleration and gravity have underlying symmetries, here's an interesting example of where space and time may be linked in hidden ways ...and just how "essential" time may really be...

In Fabric of the Cosmos, Brian Greene says in a footnote (Chapter 12, #7,Page 527)

And here's another twist: (footnote # 6, Page 527)

Don't base anything on black holes. Inside the event horizon, time and space don't make any sort of sense. Just do what I do and hope they are a mistake and that one day someone will prove it. :-)

The black hole example is not necessary. There are other illustrations of the concept time = space. This is a view to which I whole-heartedly subscribe, and had arrived at indepednantly before encountering it in the popular literature.

Since Einstein's Special Relativity, time and space have been unified into space-time, and concepts of simultaneity mix one observer's space with another's time. Lorentz boost transformations are effectively imaginary rotations between space and time axes. All of that is well understood.

Gravity calls attention to the fact that time differs from space, in that the primary effect of a gravitational potential is to change the effective value of c, the conversion factor between space and time, as seen from a distance, and more generally the shape of space-time.

However, what happens to time and space inside black holes (in the frame of an outside observer) is something else on any scale, involving a combination of infinite quantities and hypothetical exchanged imaginary space and time axes. You may read many mystical things about black holes, but I don't think they prove anything except the limits of our understanding.

Time and space inside a black hole make almost as much "sense" as in special and general relativity. Relativity whispers about spacetime issues which black holes seem to scream.

A black hole example IS necessary, I think, although not necessarily the example I cited, because strange "goings on" occur on this side of the event horizon and at the event horizon as well. How can mass and light, viewed from a distance, and approaching the event horizon slow and whoaaaaaaa, come to a stop before getting there!!! Now that's crazy, if true!!! In addition it's a good example because we know quantum theory and relativity don't apply under black hole conditions; that alone makes theoretical phenomena fascinating...and shows we don't know as much as we might think....Black Holes may also offer critical insights to information theory and holographic representations of matter and forces.

These two insights, whether eventually confirmed or proven wrong ,are the kinds of perspective that makes reading different physicsts thinking worthwhile...

Interesting perspective...I always thought the reverse: that the variation in c between the two meant they ARE connected in subtle ways we don't fully understand...I was just reading some "frame dragging" material and Dr Kaku says, in Parallel Worlds, Stockum's infinite rotating cylinder where spinning the cylinder at near light speed would drag space-time along with it permitting travel to the (limited) past...And the fact that supposedly traveling faster than c moves one back in time also suggests a more intimate connection between space and time than we might understand...

Either way, it's enough to give one a "physics headache".