“A Bloch sphere is a concept in quantum mechanics,” Jacob said. “It’s a geometrical representation of the uncertain state of a particle—say an electron—that’s spinning both up and down at the same time.”
“How can something spin up?” Sheppard asked.
“It’s the right-hand rule,” Jacob said. “Take your right hand and curl it in the direction of the spin.” He held out his hand in a loose, thumbs-up gesture. “The direction your thumb is pointing is the direction of the spin vector.”
“Only his is backward, from my perspective, because to me, that’s his left hand,” I said. I held out my right hand and curved the fingers the same way, causing my thumb to point down instead. “See? We represent both states at the same time.”
“Which of you is the real one?” Terry asked.
“Neither,” I said.
“At least not yet,” Jacob added.
I eyed him warily and caught him returning the look. It was oddly thrilling for another person to understand me so quickly and so completely. The problem was, it wasn’t another person. It was me, and when all this was over, only one version of me could survive. Was this what had happened to Brian? Had he killed himself to make sure his version was the one that lived?
“That doesn’t make sense,” Jacob said, as if guessing my thoughts. “The two versions are the endpoints of a probability waveform—the real Jacob exists in all possible states between the two of us, with a certain probability. The wave will eventually collapse to be you, or me, or some average value in between. So if Up-Brian killed Down-Brian, that wouldn’t make Up-Brian the final version. It would just raise the probability that the final version would be dead.”
“Though Brian might not have realized that,” I said.
Sheppard held his head in his hands. “What are you two talking about?”
“Okay, look. Every little bit of matter or energy in the universe, whether it’s a beam of light or a comet or a bacon cheeseburger, is made of tiny particles,” I said.
“They’re not really particles,” Jacob said. “They can diffract and interfere with each other, so really they’re waves. They have a certain wavelength, usually quite small, that governs how they behave.”
“Don’t interrupt,” I said. “It’s no good thinking of them as waves, as if they were ripples on a pond. They can be counted. You can have just one. They have some odd wavelike properties, but they’re clearly particles.”
Jacob was ignoring Sheppard now. “How can you call them particles? They’re not Newtonian; they have no classic idea of position or velocity. The ‘particle’ concept is just a crutch for an inadequate imagination.” He turned back to Sheppard. “What we call matter and energy are just simple wave functions. The difficulty some people have in accepting that is purely psychological.”
“Waves of what?” I asked.
“What?” Jacob said.
“A wave is the fluctuation of a medium. These waves you’re talking about—what is doing the waving?”
“The quantum-mechanical substrate.”
I threw up my hands. “And what is that? It’s just a word you made up to fill the void in your reasoning.”
“They’re waves,” Jacob said.
“Particles.”
“Waves!”
Sheppard stepped between us and waved his hands. “Stop it,” he said. “This is insane. What does this all mean? What are you going to do?”
I took a deep breath. Maybe coming here hadn’t been such a good idea. “When does the trial start?” I asked.
“Hard to say. The NJSC is a big political sore spot, so the media are running away with this one, poking at the possibility of a politically motivated killing. That will put a rush on the trial procedure, but it will still be months probably.”
“That gives us plenty of time to work, then,” Jacob said.
“The most important thing is to make sure that the final Jacob Kelley…” I said.
“…whoever he is…” Jacob added.
“…is found innocent of all charges.”
CHAPTER 20
After Officer Morales’s testimony, the jury was given an hour and a half to walk the streets and find lunch, or, if they were brave, to eat in the courthouse cafeteria. Lunch for me was a roast beef sandwich and a Coke in a tiny meeting room under the baleful stare of an armed guard. I made it last as long as I could, but a sandwich can only stretch so far. When it was done, I had nothing to do but sit and stare at the walls and miss Elena and the kids.
After lunch, the trial shifted to a new phase. It was the defense’s turn to start calling witnesses. Terry stood and regarded the courtroom like a king surveying his new domain, holding on to his lapels. So far, Haviland had been calling the shots, and he had just been doing damage control. Now it was his turn. The physical evidence against me was going to be difficult to overcome, but we had a few tricks up our sleeves. One big surprise in particular, but that wouldn’t come out until my testimony at the very end.
Jean was marvelous on the stand. She had dressed up for the occasion, in a classy black pantsuit and high heels. I had never seen her in anything but jeans and a sweatshirt before. She and Terry knocked questions and answers back and forth like professional tennis players, leaving the jury swiveling their heads back and forth in comic time between the two. She was funny, informal, and best of all, comprehensible. Terry was the perfect foil, pretending ignorance while tossing up the perfect leading questions.
“Dr. Massey, we all learned about atoms in school,” he said. “We’re all made up of them. But tell the jury—just how small are they?”
She smiled. “A piece of tissue paper is about one hundred thousand atoms thick.”
Terry pretended astonishment. “Really? But our case is dealing with things even smaller than that—subatomic particles, correct? So how big is, say, a proton, compared to an atom?”
“About a hundred thousand times smaller.”
Astonishment again. “So tissue paper is a hundred thousand atoms thick, but a proton is a hundred thousand times smaller than that? What about an electron?”
“An electron has no size at all.”
“How can something have no size? Doesn’t that mean it’s not there at all?”
“It has mass,” she said. “And spin, believe it or not, and of course a negative electric charge. But no, it’s a point particle, with no actual size to it at all.”
“Are there any other particles?”
“Sure. Neutrons, muons, pions, taus, neutrinos, quarks, photons…”
“Photons? Aren’t those light?”
They went on in that vein, driving the jury through a crash course in basic particle physics. Terry had gotten his nephew to convert some of Jean’s illustrations into graphics displays, which he showed the jury on the courtroom’s ancient plasma screen.
“So if atoms are made of protons, which are so tiny, and electrons, which have no size at all, an atom is mostly just empty space, isn’t it? So if I’m just made up of empty space, why don’t I just fall right through this table when I lean against it?” He leaned against the table to prove his point.
“It’s because of the electron field surrounding the atom,” she said. “They prevent the other atoms from passing through.”
She went on to describe the double slit experiment, which shows how subatomic particles aren’t really particles, but aren’t really not-particles, either. Haviland objected frequently to the relevance of the testimony, but Judge Roswell allowed it, citing the groundbreaking nature of the case and the complexity of the science involved. After several coin and tennis ball illustrations to establish the concepts of superposition and entanglement, they finally got to the crux of the matter.