The Elegant Universe - Brian Greene [146]
A Moment of Truth
We all met at the Institute Saturday morning as planned. It was a bright sunny morning, and the atmosphere was jokingly relaxed. I, for one, half expected that Aspinwall would not show up; once he did, I spent 15 minutes extolling the import of this first weekend he had come into the office. He assured me it wouldn't happen again.
We all huddled around Morrison's computer in the office he and I shared. Aspinwall told Morrison how to bring his program up on the screen and showed us the precise form for the required input. Morrison appropriately formatted the results we had generated the previous night, and we were set to go.
The particular calculation we were performing amounts, roughly speaking, to determining the mass of a certain particle species—a specific vibrational pattern of a string—when moving through a universe whose Calabi-Yau component we had spent all fall identifying. We hoped, in line with the strategy discussed earlier, that this mass would agree identically with a similar calculation done on the Calabi-Yau shape emerging from the space-tearing flop transition. The latter was the relatively easy calculation, and we had completed it weeks before; the answer turned out to be 3, in the particular units we were using. Since we were now doing the purported mirror calculation numerically on a computer, we expected to get something extremely close to but not exactly 3, something like 3.000001 or 2.999999, with the tiny difference arising from rounding errors.
Morrison sat at the computer with his finger hovering over the enter button. With the tension mounting he said, "Here goes," and set the calculation in motion. In a couple of seconds the computer returned its answer: 8.999999. My heart sank. Could it be that space-tearing flop transitions shatter the mirror relation, likely indicating that they cannot actually occur? Almost immediately, though, we all realized that something funny must be going on. If there was a real mismatch in the physics following from the two shapes, it was extremely unlikely that the computer calculation should yield an answer so close to a whole number. If our ideas were wrong, there was no reason in the world to expect anything but a random collection of digits. We had gotten a wrong answer, but one that suggested, perhaps, that we had just made some simple arithmetic error. Aspinwall and I went to the blackboard, and in a moment we found our mistake: we had dropped a factor of 3 in the "simpler" calculation we had done weeks before; the true result was 9. The computer answer was therefore just what we wanted.
Of course, the after-the-fact agreement was only marginally convincing. When you know the answer you want, it is often all too easy to figure out a way of getting it. We needed to do another example. Having already written all of the necessary computer code, this was not hard to do. We calculated another particle mass on the upper Calabi-Yau shape, being careful this time to make no errors. We found the answer: 12. Once again, we huddled around the computer and set it on its way. Seconds later it returned 11.999999. Agreement. We had shown that the supposed mirror is the mirror, and hence space-tearing flop transitions are part of the physics of string theory.
At this I jumped out of my chair and ran an unrestrained victory lap around the office. Morrison beamed from behind the computer. Aspinwall's reaction, though, was rather different. "That's great, but I knew it would work," he calmly said. "And where's my beer?"
Witten's Approach
That Monday, we triumphantly