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Looking for the name of a SciFi novel set in Scotland. Scientists working at home develop a way of sending messages back in time using quantum mechanics. Messages can only be received by the machine they design - thus setting a "earliest date" boundary for messages into the past.

One of the scientists has a love interest with a female scientist working at a research facility, supercollider I think.

They team sends a message back in time several times, thus resetting the time line, and there's a brief focus on stray cat and a scrap of paper litter. The paper is nudged different directions, presumably by random quanta, for each reset. The paper and the cat, somehow precipitates, or prevents, the encounter of the two love interest scientists.

The crisis comes when the time scientist team figures out that something dangerous to the planet is happening, either from the other scientist's work (possibly stray mini singularities), or an ecological event, and they send messages back in time to prevent the events. There is focus about their efforts to persuade, first themselves, and then politicians, of the validity and importance of the messages.

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This is Thrice Upon a Time by James P. Hogan

In December 2009, Murdoch Ross and his friend Lee Francis Walker visit Murdoch's grandfather, Sir Charles Ross, in his castle in Storbannon, Scotland. Sir Charles is a Nobel Prize winner for his work in particle physics — more specifically the isolation of free quarks.

In this novel, when a nucleon decays into three quarks, the first two quarks appear immediately and the third quark appears on the order of a few millionths of an "yoctosecond" later. A widely accepted theory is that the original decay produces two quarks and also a third unknown particle, dubbed the "quason". This is subsequently transformed into a third quark.

Sir Charles offers a different and radical explanation: all three of the quarks are created at once, but the first two are "propagated back in time". Charles dubs the energy which had allowed the propagation through time as "tau waves". Although his theory is seemingly valid and consistent, the physicists of his time refuse to accept it because of its implications — namely the failure of some of the physical laws of conservation. Sir Charles then retreats to his family's castle in Scotland to continue his research in private. There, he succeeds in building a time machine capable of sending messages to the future and the past.

After Murdoch and Lee have gotten over their initial amazement, they decide to experiment with the machine. Murdoch tries to fool the machine into creating a causality paradox, by deliberately receiving a message from the future, and not sending the message back at the due time. Suddenly, the entire system turns bizarre, and they are flooded with messages from all over the ten-minute range of the machine. Then they abruptly turn off the machine and leave.

While outside, Murdoch and Lee talk about the implications of the machine's existence and how the space-time continuum could allow for time travel without introducing a paradox. They formulate theories similar to the many-worlds interpretation, finally deciding that none of the theories they discuss fit their previous observations.

The next day, Ted Cartland, a friend of Charles and a former Royal Air Force officer, arrives to examine the machine he had helped build. They repeat the experiment, and Ted is bewildered as well. Ted, however, has a trick up his sleeve. He writes a computer program to do what Murdoch had done the day before, to remove the human element from the experiment.

The machine picks up an unexpected message, telling the experimenters that a glass jar had been broken. True enough, Lee was on the verge of accidentally pushing a jar off a shelf. However, they are unable to contact their future selves with the broken jar, since they apparently no longer exist. Sir Charles decides that upon sending the message back, the copies of themselves in the future had changed their past and thus had been erased from existence. The altered timeline, with its unbroken jar, overwrote the old one rather like recording over an old TV program on a videotape. Thus causality had been preserved. The fear of being erased chills them, and so they quickly disable the machine again.

As time goes by, they establish an experimental protocol, and they set up automated tests to gain more information about the physics behind the machine. The machine is upgraded to allow for more data throughput and a time range of about 24 hours. Murdoch also meets a young woman named Anne Patterson when she trips over Sir Charles's kitten while she was out shopping in Kingussie.

They immediately fall in love. It turns out later that she is a physician at the site of the new fusion reactor in Burghead. Elizabeth Muir, another close friend of Sir Charles, works there as well, and he invites her to his castle to investigate the peculiar machine.

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