Henry Baker <hbaker1@pipeline.com> wrote:

We can't tell "from inside" whether we're in a left-handed universe or a right-handed universe. Thus, there's no way "from inside" to distinguish +t from -t.

Yes, there's entropy, which is the usual way to tell a normal movie from a time-reversed movie, but all the usual mechanical laws are time-symmetric.

In the -t direction entropy is lower and there are events which we remember. In the +t direction entropy is higher and we have free will. (You can choose today what to have for breakfast tomorrow. You can't choose today what to have had for breakfast yesterday.) It's exactly the same in the Orthogonal universe -- until the events of the third book.

"Keith F. Lynch" <kfl@KeithLynch.net> wrote:

...

(Disclaimer: That's special relativity. In general relativity, reverse causality appears to be possible under extreme conditions.)

With GR, gravitational waves from coalescing black holes seem to distinguish +t from -t;

Certainly. That's an instance of entropy increasing. In fact the first announced LIGO observation of gravitational waves was the most rapid entropy increase ever observed -- tne energy equivalent of 200 solar masses radiated per second, albeit only for a few milliseconds. (It's ironic that one of the LIGOs is at Hanford. Once that town was known for studying the most dangerous known radiation. Now they're studying the least dangerous known radiation. I estimate it would take at least 10^30 watts of gravitational waves hitting you to kill you.) But I was thinking of subtler applications of GR. Tipler's rotating cylinder. Stabilized wormholes. Flying through the center of a donut-shaped black hole.

it might be possible to focus gravitational waves onto a black hole to get it to split in two, but that might be asking a little too much from our current technology.

To focus gravitational waves all you need is a gravitational lens. Observing continuous smooth point-source gravitational waves through a massive object would be a useful way to probe the mass distribution inside the object. If everything is reversible in principle, why can't black holes be turned into stars? You wouldn't even need to focus any gravitational waves, since a radially symmetric collapse doesn't generate any. At least in Egan's universe they don't have any black holes or event horizons to worry about. Note that if you want to play around with an event horizon (in our universe) you don't need a black hole. SImply accelerate, and there will be an event horizon behind you. Its distance in light years is roughly equal to the reciprocal of your acceleration in Gs. Although you can never travel faster than light, light from behind that event horizon can never reach you (as long as you continue with the same acceleration). In your frame, time is going backwards there.

Perhaps I should read these books; I'm having a hard time (!) understanding how one could consider one of the space coordinates as a time coordinate.

The characters have a hard time with it too. Time doesn't *seem* like a spacial dimension to them any more than to us. They finally just have to accept that that's how the universe is. Under ordinary conditions time behaves exactly like in our universe. Their version of Newton's laws are identical to ours.

As you point out, how do you set up a differential equation in "quaternion space" such that a wave can propagate in the other space coordinates?

Answered in the books and on Egan's website. Hint: In their universe the speed of light varies with wavelength, and can be anything from zero to infinite. Also, light has three polarizations, each at right angles to the other two. In addition to the two polarizations we all know and love, there are longitudinal waves, in which the fields are in the direction of motion.