The argument went something like this. What this book says (that time travel is possible) can't be true, because the past and the future don't exist. There's only the present. You can't travel to somewhere that doesn't exist. He was half right. We only experience one present ourselves, but it doesn't stop there being other versions of 'now' - that's the whole point of special relativity: we have to consider relative positions in spacetime, not just relative positions in space.
A simplistic counter to my critic's argument might be that we can see all sorts of other 'now's by looking up at the stars. We see the nearest star as it was something over four years ago, while telescopes let us peer billions of years into the past. But that wouldn't do the job. He could argue reasonably that we aren't seeing their 'now' but a record of their past, set in the aspic of the time it takes light to reach us. If there were inhabitants of a planet by one of those distant stars, they wouldn't be waiting for that light to get here - their 'now' would be moving on. Sort of.
So let's take a real, practical example of a device that has a different 'now' to us on the Earth that we can think about more realistically - a GPS satellite. When I talk about time travel to an audience I say how relatively (snigger) easy it is to travel forwards in time, but backwards is a whole different ballgame. What I really should say is that to travel usefully backwards is ridiculously difficult and quite possibly impractical. Because GPS satellites do travel backwards in time. (Before you get all excited about using one to win the lottery, this kind of backwards time travel wouldn't make that or time paradoxes possible.) And we know this, because the GPS system has to be corrected for it - if it weren't, your sat nav would go wrong by several kilometres a day.
There are two relativity effects on the satellite, which is essentially a very accurate clock, blasting out the time. Special relativity says that time on the satellite will run slow as seen from the Earth, because it is moving. General relativity, meanwhile, tells us that time will run quicker on the satellite than on Earth, because it is in a weaker gravitational field, and gravity slows time down. As it happens, general relativity wins and time on the satellites gets ahead of the Earth by about 0.000038 seconds a day.
Wait long enough, and time on the satellite would eventually be, say, a year ahead of time on Earth. Here's the part where my critic was right. Allowing for communications delay, both the Earth and the satellite would think there was only one 'now'. But the Earth would say that 'now' was 2014 (in some different numbering system, as it would be take many thousands of years for the satellite to get this far ahead) and the satellite would say it was 2015. And both would be right. If the satellite now came down to Earth, it would be travelling a year into the past. If you changed the scenario a bit, made the satellite big enough to have a city on and made the differential 100 years, the people of that city could have produced exciting new technologies in the time between 2014 and 2114. Whole new generations would be born. They would be visitors from the future when the they came down to Earth.
Wouldn't a satellite dweller know the next 100 years of Earth lottery results? No - because all she sees looking down is Earth in the past - those lotteries haven't happened yet. And what happened to the time paradoxes? To make them happen, you would have to travel from the Earth's 2114 to the Earth's 2014. But that hasn't happened. Imagine someone on the satellite was the grandson of someone on Earth, born in 2080 on the satellite. If they try the grandfather paradox and kill their grandfather back on Earth (who could be younger than they are), nothing would happen to the grandson. Because even though 2014 is 66 years before they were born, they had come from a different speed of time stream. There is no paradox.
So in a sense there is only one 'now'. But by moving to somewhere where time has run slower or quicker we can make that 'now' the future or the past. Mind boggling, it's true, but a lot more fun than the critic's insistence on a single present that is uniform across the universe.
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