“By all conventional measures,” Lizzie said steadily, “all of the things we’ve been talking about are impossible: psychometry, telepathy...” She shrugged. “If you believe that there are things we can neither explain nor understand scientifically, and manifestly there are, then this is only one other thing on the list.”

Arthur was silent again. His head was bent and there was a heavy frown on his brow. Lizzie could sense his emotions even though she wasn’t touching him: there was anger and conflict in him, but she knew it was because he was very close to believing her—and he did not want to acknowledge that. It was way too much, too soon. She could understand that. She surreptitiously gestured to the waitress to bring her another cake.

“Johnny could be in Scotland, or Peru, or...or on a beach in Bali,” Arthur said. “All of those are far more likely scenarios than that he’s somehow gone back in time.”

“I agree,” Lizzie said steadily, “and if Johnny pops up having spent a fortnight in Bali I’ll be delighted. But I don’t think he will.” She leaned forward. “You don’t really think he will either, do you, Arthur?”

Arthur scrubbed an exasperated hand through his hair. “It’s insane. Even if it were a physical possibility, why would he want to go back? Where would he go? What is he trying to achieve?”

“I think I know the answer to that,” Lizzie said. “I think Johnny believes that if he can change the past, he will be able to prevent Amelia’s death.”

“The past can’t be altered to change the present,” Arthur argued. “I’m not even going to start on the butterfly effect or parallel universes or all those theories—” He stopped. “Are you eating cake at a time like this?”

“I can’t help it,” Lizzie said, her mouth full of icing. “I have a sweet tooth and stress gives me a sugar craving.” She swallowed. “Arthur, the point is not what we believe but what Johnny believes. To stand any chance of finding him, we need to think like he did.”

Arthur swore. “You really believe this, don’t you?” His dark gaze fastened on her. “Shit.” He shook his head. “I can’t believe we’re even talking about this and at the same time I can—because of this.” He touched Johnny’s green notebook. “I think you said you didn’t ever get the chance to look through it properly?”

Lizzie shook her head. “After I’d tried to use it to connect to Johnny that first time, I was too exhausted and disturbed to touch it again,” she said.

“It makes for interesting reading,” Arthur said, “especially in view of your theory about Johnny. I thought at first that it was notes for a history project—Johnny’s studying history along with maths and design at school in Oxford. Then I realised it was much more than that.” He gave the book a little push towards Lizzie. “Take a look,” he said. “I don’t think it will hurt you now. It feels...it feels as though its power is spent somehow, if that makes sense.”