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"I know it's been quite some time since you traded in the hard sciences for the softer variety."
With unknown intentions, Stahngun requested Bill's help in demonstrating the machine, to the chagrin of the guests. Bill hesitated at first, but eventually decided that he would assist him. The experiment went ahead, but failed; the time machine exploded with Bill inside, taking Stahngun with it.
Future Luke explained to Layton and Luke at the Gilded Seven Casino that, in the accident, while Bill had perished, Stahngun had survived. Layton had helped him hide from the uproar over the prime minister's death, and took interest in Stahngun's research. Layton began consorting with criminals, and eventually took over the London underworld with his masterful interllect, bringing in enough funds from all kinds of shady businesses for Stahngun to finish his time machine. It now resided in the clock shop; a wormhole between the ten year gap, being incomplete.
Future Luke had grown apart from Layton in the last ten years, never finding out why he was so entranced by Stahngun's time machine research.
When Layton and Luke spoke to Chelmey about the accident, he said that, even though forensic examination had been carried out on the site, there was no trace of the missing people's remains. He then explained that after looking through public records, there was no evidence of a Dr. Alain Stahngun ever existing.