The context for such research is general relativity, in which the continuum of space and time can be distorted by gravity. Or, more accurately, in which gravity is caused by such distortions,
'curved spacetime'. In place of a time machine, the physicists look for a 'closed timelike curve'.
Such a curve corresponds to an object that travels into the future and ends up in its own past, and so becomes trapped in a closed 'time loop'.
The best known way to generate a closed timelike curve is to use a wormhole. A wormhole is a short-cut through space, obtained by fusing a Black Hole to its time-reversal, a White Hole. Just as Black Holes suck in anything that comes near them, White Holes spit things out. A wormhole sucks things in at its black end and spits them out at its white end. Of itself, a wormhole is more a matter-transmitter than a time machine, but it becomes a time machine when allied to the famous Twin Paradox. In relativity, time slows down for objects moving at very high speeds. So if one member of a pair of twins heads out to a distant star at very high speed, and then returns, she will have aged less than the other twin who stayed at home. Suppose that the travelling twin takes with her the white end of a wormhole, while her sister keeps the black end. Then when the travelling twin returns, the white end is younger than the black end: the exit from the wormhole lies in the past of the entrance. So anything that is sucked into the black end is spat out in its own past. Because the white end is now right next to the black one -the twin has come back home the object can hop across to the Black Hole and go round and round this closed loop in spacetime, tracing a closed timelike curve.
There are practical problems in making such a gadget, the main one(!) being that the wormhole will collapse too quickly for an object to pass through it, unless it is held open by threading
'exotic matter' with negative energy through it. Nonetheless, none of this is forbidden by the current laws of physics. So what of the paradoxes? It turns out that the laws of physics forbid genuine paradoxes, although they permit many apparent paradoxes. A useful technique for understanding the difference is known as a Feynman diagram, which is a picture of the motion of an object (usually a particle) in space and time.
For example, here is an apparent time travel paradox. A man is imprisoned in a concrete cell, locked from the outside, with no food, no water and no possibility of escape. As he sits in a corner in despair, waiting for death, the door opens. The person who has opened it is ... himself.
He has returned in a time machine from the future. But how (the paradox) did he get to the future in the first place? Well, a kind person opened the door and set him free ...
There seems to be something very odd about the causality in the story, but the corresponding Feynman diagram shows that it violates none of the laws of physics. First, the man follows a space-time path that puts him inside the cell and then removes him from it through opened door.
This time-line continues into his future until he encounters a time machine. Then the time-line reverses direction, heading into the past, until he encounters a locked cell. He opens it, and his time-line reverses again, propelling him into his own future. So the man follows a single zig-zag path through time, and at every step the laws of physics hold good. Provided his time machine violates no physical law, of course.
If you try to 'explain' the grandfather paradox by this method, it doesn't work. The time-line leading from grandfather to killer is severed when the killer returns; there is no consistent scenario, even in a Feynman diagram. So some stories of time travel are consistent with the laws of physics, and have their own kind of causal logic, albeit twisted; but other equally plausible stories are inconsistent with the laws of physics. You can rescue the Grandfather Paradox by assuming that changing the past in a logically inconsistent way switches you into a different alternate universe -say a quantum-mechanical parallel world. But then it wasn't your grandfather that you killed, but the grandfather of an alternate you. So this 'resolution' of the Grandfather Paradox is a cheat.
Faced with all this, the way that the wizards handle the complications of time travel seems quite reasonable!
ALL THE GLOBE'S A THEATRE
The elves did not spend a lot of time in serious thought. They could control people who could do the thinking for them. They didn't play music, they did not paint, they never carved stone or wood. Control was the talent, and it was the only one they had ever needed.
Nevertheless, there were ones who had survived for many thousands of years, and while they had no great intelligence they had accumulated that mass of observations, experience, cynicism and memory that can pass for wisdom among people who don't know any better. One of the wisest things they did was not read.
They had found some clerks to read the play.
They listened.
Then, when it was over, the Queen said: 'And the wizards have been showing great interest in this man?'
'Yes, your majesty,' said one of the old ones.
The Queen frowned. 'This ... play is ... good. It treats us ... kindly. We are firm but fair with mortals. We offer rewards to those who deal well with us. Our beauty is satisfactorily referred to.
Our ... issues with our husband are treated more romantically than I would like, but, nev ertheless ... it is positive, it enhances us, it places us yet more firmly in the human world. One of the wizards was actually carrying this.'
One of the senior elves cleared its throat. 'Our grip is loosening, your majesty. Humanity is becoming more, shall we say, questioning?'
The Queen shot it a glance. But it was older than many Queens, and did not step back.
'You think it will do us harm? Is it a plot against us?'
The senior elves looked at one another. The main reason that they thought it was a plot was that they were predisposed to see plots. In the court of Faerie, an inability to see it coming meant that it took you by the throat.
'We think it may be,' one said at last.
'How? In what way?'
'We know the wizards have been seen in the company of the author,' said the elf.
'Then perhaps they are endeavouring to stop him writing the play, have you thought of that?'
snapped the Queen. 'Can you see any way in which those words harm us?'
'We are agreed that we cannot ... nevertheless, we have a sense that in some way—'
'It is so simple! At last we are done some real honour and the wizards will try to stop it! Are you so stupid that you cannot see that?'
Her long dress swirled as she turned on her heel. 'It will happen,' she said. 'I will see to it!'
The senior elves filed out, not looking at her face. They knew those moods.
On the stairs one said to the others: 'Purely out of interest ... can any of us put a girdle around the Earth in three minutes?'
"That would be a very big girdle,' said an elf.
'And would you wish to be called Peaseblossom?'
The eyes of the old elf were grey, flecked with silver. They had seen horrible things under many suns, and in most cases had enjoyed them. Humans were a valuable crop, the elf conceded. There had never been a species like it for depth of awe, terror and superstition. No other species could create such monsters in its heads. But sometimes, it considered, they were not worth the effort.
'I think not,' it said.
'Well, now, Will - do you mind if I call you Will? Oh, Dean, fetch Will another pint of this really unpleasant ale, will you? Now ... where was I ... oh yes, I really enjoyed that play of yours.