Life in a universe with 2 time dimensions

Greg Egan's novel Dichronauts is now available on Amazon - and soon it will show up elsewhere. It's about life in a universe with 2 dimensions of space and and 2 dimensions of time!

I urge you to read the excerpt on his website and also check out the pages where he explains the physics! For example, the dark cone. Ordinary physics has a light cone: the directions in spacetime along with light can move. Egan's universe has a cone of directions in which light can't move... but other things can. Paraphrasing from him:

No light source can emit a beam in any of these directions, and no one would be able to see anything by looking in a direction that lies within the dark cone.

We are used to thinking of any restriction so powerful that even light must obey it as applying to all material objects as well: for example, when we hear that light can’t escape from a black hole, it follows that no ordinary object, travelling even more slowly, could hope to escape either. But in the case of the dark cone, nothing could be further from the truth!.

So, the dark cone contains no light, but material objects are free to move in these directions. And since sound waves are nothing but vibrations in material objects, sound is also free to move in the dark cone.

When I was in grad school I took a course with the mathematical physicist Victor Guillemin, which touched on the beautiful things that happen in a universe with 2 space and 2 time dimensions. Since I was interested in real-world physics I thought this was a bit weird.

Only later did I learn enough math to realize that the split real form of spacetime, with almost the same number of space and time dimensions, is mathematically the nicest in many ways: you can see the geometry coming from the O(n) Dynkin diagram most clearly in this case.

If you don't know what the hell "O(n) Dynkin diagram" means, well, now you see why I didn't understand it back then!

And if you're wondering why I said almost the same number of space and time dimensions, well, if you've got an even number of dimensions you can split them equally into space and time, like 2 = 1 + 1 or 4 = 2 + 2. And the cool part here is that then there's fundamentally there's no difference between which dimensions are space and which are time! (If I understand correctly, Egan creates one by choosing a state of the universe that breaks this symmetry. I haven't read the book yet.)

But what if you have an odd number of dimensions? Then you split these dimensions into space and time as equally as you can, like 3 = 2 + 1 or 5 = 3 + 2 or 7 = 4 + 3. That's what gives you the 'split real form', which is mathematically the nicest choice.

"Mathematically the nicest" does not mean the nicest for the physics we know and love - not in this case! Most physicists are appalled by the idea of 2 or more time dimensions. If you study theories like that they call you a dirty two-timing rat.

But Egan goes ahead and sees what it might be like.

My new novel Dichronauts is officially published in the US on July 11, but copies are already in stock at Amazon, and it might already be available from your favourite bookshop.

You can read an excerpt by following the link below, and supplementary material about the universe of the novel by following the links from that page.
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