Stephen said, "Yes, but perhaps an insightful trick."
"We don't have a truly deep understanding of time," I replied, "so replacing real time with imaginary time doesn't mean much to us."
"Imaginary time is a new dimension, at right angles to ordinary, real time," Stephen explained. "Along this axis, if the universe satisfies the 'no boundary' condition, we can do our calculations. This condition says that the universe has no singularities or boundaries in the imaginary direction of time. With the 'no boundary' condition, there will be no beginning or end to imaginary time, just as there is no beginning or end to a path on the surface of the Earth."
"If the path goes all the way around the Earth," I said. "But of course, we don't know that in imaginary time there won't be a boundary."
"My intuition says there will be no blocking in that special coordinate, so our calculations make sense."
"Sense is just the problem, isn't it? Imaginary time is just a mathematical convenience." I shrugged in exasperation at the span between cool mathematical spaces and the immediacy of the raw world; this is a common tension in doing physics. "It's unrelated to how we feel time. The seconds sliding by. Birth and death."
"True. Our minds work in real time, which begins at the Big Bang and will end, if there is a Big Crunch -- which seems unlikely, now, from the latest data showing accelerating expansion. Consciousness would come to an end at a singularity."
"Not a great consolation," I said.
He grinned. "No, but I like the 'no boundary' condition. It seems to imply that the universe will be in a state of high order at one end of real time but will be disordered at the other end of time, so that disorder increases in one direction of time. We define this to be the direction of increasing time. When we record something in our memory, the disorder of the universe will increase. This explains why we remember events only in what we call the past, and not in the future."
"Remember what you predicted in 1980 about final theories like this?" I chided him.
"I suggested we might find a complete unified theory by the end of the century." Stephen made the transponder laugh dryly. "OK, I was wrong. At that time, the best candidate seemed to be N=8 supergravity. Now it appears that this theory may be an approximation to a more fundamental theory, of superstrings. I was a bit optimistic to hope that we would have solved the problem by the end of the century. But I still think there's a 50-50 chance that we will find a complete unified theory in the next 20 years."
"I've always suspected that the structure never ends as we look to smaller and smaller scales -- and neither will the theories," I offered.
"It is possible that there is no ultimate theory of physics at all. Instead, we will keep on discovering new layers of structure. But it seems that physics gets simpler, and more unified, the smaller the scale on which we look. There is an ultimate length scale, the Planck length, below which space-time may just not be defined. So I think there will be a limit to the number of layers of structure, and there will be some ultimate theory, which we will discover if we are smart enough."
"Does it seem likely that we are smart enough?" I asked.
Another grin. "You will have to get your faith elsewhere."
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