A huge spaceship, or Interstitial Transposition Vehicle, is on its maiden voyage to the planet Eternity. One hour into the journey, with two thirds of the distance complete, Sugar McCauley checks on the passengers in her care. There are seventy nine in the executive lounge and more than seven hundred more in the main body of the craft. They were all lottery winners, including the crew. The only one who isn't is the 160 year old billionaire, Joseph Sterns Cluxton. He designed the engines that are driving them to their destination.

Lizzie Fisk approaches Sugar. She slips into the alcove beside her friend. She complains about her passengers: a pair of twins with a virtual device that rendered her naked while she was serving them, children who are too young for the voyage and Cluxton himself (who keeps touching her bottom).

Using their lash-boards to blink up their passengers' orders, they realise that Cluxton's champagne hasn't arrived. Sugar heads back to the galley to collect the order. She remarks that the journey is unspectacular; the only sign that they are travelling at all is the pink glow around the windows. Lizzie laughs and tells her that the glow is lights in the window frame to simulate movement.

In the galley Sugar can hear the murmur of the engines and then someone says her name. She turns around but there is nobody else there. Six artificials are preparing food. Another girl, serving in the main salon, runs out of the provision store, panicking. She claims that something in there knew her name, and that she could "see inside it". Sugar remembers her training, where it was mentioned that there may be some unusual effects due to the transposition. She wonders whether to call a doctor but decides that Cluxton's champagne takes priority.

She calls a follow-me robot to her and slaves it to her bio-signal. She loads the champagne onto the follow-me and is taking out the champagne flutes when she drops them in surprise. A small sphere, looking like molten glass, is hovering in the air in front of her, and then it grows as if it was squeezing out of another dimension. It glows red as blood and organs form within it. She turns and bolts into the corridor. A distance voice cries out behind her. She runs into a man she does not recognise and tells him there is something in the store-room. He tells her he is the Doctor and asks what she saw in the store. He points his sonic screwdriver at her. He wonders whether her lashboard is sending images into her eyes. Then he tells her to hold tight.

A bang, a jolt and a flash of light follow. There is the sound of metal tearing and for a moment the floor ids the ceiling. She asks the Doctor what happened but he can only suggest that the ship hit something. Sugar is puzzled that the Doctor doesn't know he is on an Interstitial Transposition Vehicle or that he is making the longest journey possible from one end of the human empire to the other. She demands to see his boarding card so he flashes his psychic paper at him but she sees it as blank. Before they can go on he points out that the engines are laboring badly. He suggests they check on the rest of the ship and strides off. Sugar and her follow-me chase after him. In the galley the artificials have stopped working, the wall log has gone onto standby and, worse, all of the passengers have vanished.

The Doctor promises her that he will find them all. He heads off to the main salon which is similarly empty. There is another, distant sound, like voices crying out from far away. The Doctor can't hear it but doesn't doubt that Sugar can. He asks her if there is a human crew flying the ship. Alarmed, Sugar leads him to where the crew are meant to be. She thinks they are going to crash but he tells her that is impossible. Their true danger is that they will travel forever and never arrive.

The Doctor gets into the flight deck with his screwdriver. There are six seats among the multitude of screens and controls. They are all empty. The Doctor sits down and surveys the controls. He adjusts some settings but can make no sense of what he is looking at. A notice to decelerate the engines appears on the screen but the Doctor says the controls are locked. He asks if the engines are accessible but Sugar says they are locked. The Doctor calls up a hologram of the engines and works his way through them. He tells Sugar to press a button near her. She does so and says nothing happened. The Doctor agrees, saying that was his intention. He shows her a visual display of the ship's flight: they are stationary with the engine running but the ship paused in quantum space.

The Doctor says this will give him time to access the engines. They make their way back through the salons where they are astonished to see a movement among the seats. They creep towards it. Sugar hears someone call her name but there is nobody nearby. Suddenly, a small yapping dog leaps out at them. Sugar catches hold of it and tells him it is one of three dogs that were travelling with the Dowager Collette. The Doctor wonders if it was there all along or if it has vanished and reappeared.

A voice asks him what he meant by 'vanished'. A man in a grey suit is standing behind him. He says there was a bump and everyone vanished except for the Doctor and Sugar. The Doctor introduces himself and the other man gives his name as Reston. Reston asks where the other passengers are. Sugar sees Cluxton's official biographer, a mousy man called Lars Bortnik, sprawling beside a seat. She goes over to tend to him. Bortnik asks where Cluxton has gone. He says there was a flash and someone called his name, then he found himself on the floor. The Doctor surmises that these people have come back. A sobbing woman begins to ask for Adam, her husband, from a seat further away. The Doctor asks Reston to look after her while he takes Sugar to the main salon. He tells her that these people have been away and come back.

In the main salon there are more than twenty people milling about. They bombard the Doctor with questions. Among them is Millie, the girl who said he had seen something in the store room earlier. Sugar introduces the Doctor to them and he goes round asking their names. He deflects their questions and calms them down. He suggests Millie and Sugar take the passengers to the executive salon while he goes to look at the engines.

Alone, he wanders aft. The engines are making a warbling noise. The service area is gloomy. The hatch to the engine takes a long time for the screwdriver to penetrate. Beyond the hatch is a vast chamber, three decks deep. Two huge engines are encased in ovoid shells. There are no monitors or diagnostics; he has no way to inspect the engines. Dormant artificial humanoids stand near the walls. The Doctor approaches one and removes its face plate. He examines the interior. Sugar comes down from the catwalk above. She says she has reassured the passengers and checked the flight deck but none of the crew has returned. She asks the Doctor to explain what is going on.

The Doctor says the engines have altered reality due to a misfiring: some people have been shuffled into an alternative dimension. He says the engines are sealed and no humans are allowed in the engine rooms to prevent spying. He needs to access the engines and decycle them. This might bring back all of the missing people. The Doctor stares into her eyes and explodes into a victory dance. He says the answer is her lashboard. He will use her eyes to interface with the robot. He aims his screwdriver at her eyes, and then pokes the screwdriver in to the artificial. This causes the artificial to begin a simple diagnostic check. He tells her to use her lashboard to see what the artificial can see. He is just about to give her an instruction when Reston arrives, holding a pistol and tells them to stop what they are doing.

Reston says that the Doctor is not the onboard ship's doctor, nor is he supposed to be on the ship. Reston says he is the transit marshal and is taking charge of the situation. The Doctor tells him that he has a trans-dimensional vehicle of his own. When Reston refuses to believe him he tells him that he is a Time Lord and everyone on the ship is in danger. Reston demands that the Doctor stop saying his name but the Doctor says it must be an audio distortion. Reston starts to panic and the Doctor hears a noise nearby. The apparition from the store room begins to reappear. Reston shoots at it but the body begins to solidify even more rapidly. The noise is getting louder, voices calling and screaming. The apparition reaches out and touches Reston who begins to turn transparent before melting away. The Doctor grabs Sugar's hand and tells her to run.

Reston's gun hits the deck and fires a bullet into the bulkhead. The entity chases the Doctor and sugar down the compartment. The sound of its footsteps tells the Doctor that it is solid now. He takes the stewardess behind the motionless artificial while it prowls around searching for them. The girl is terrified until the creature has gone. The Doctor thinks it has faded back to where it came from. Sugar tells him that she and Milly saw the entity in the store room. He wonders whether the creature is dangerous or if Reston's disappearance was an accident.

They make their way to the faceless artificial. The Doctor resets Sugar's lashboard so that she can see the artificial's diagnostic controls. With another burst of sonic energy he projects what she can see into the air in front of him. He instructs her to blink on certain menus and controls until the engine noise changes, then he shuts down her lashboard. He has decycled the engines so that the ship can land safely when flown from the flight deck. They run back to the salon where the Doctor tells the passengers they are about to land.

On the flight deck he sits in the pilot's seat and selects a flight plan to take them into Eternity. A message tells them they have only fifteen seconds until arrival. It counts down to zero but there is no sense that they have stopped moving. Sugar asks how the Doctor knows they have arrived. He switches off the pink glow at the windows and she is satisfied until she declares herself disappointed by the lack of drama in their flight, meaning that there was no sense of actually moving. The Doctor says that there seemed to be more than enough drama for him.

The hatch opens and the pair of them step out into daylight. The Time Lord glances across the Eternity terminal and says that the drama hasn't ended yet.

The terminal is an imposing structure built of chrome, glass and steel. Ships are dry docked. Towers reach into the sky. Sugar has long dreamed of seeing this awesome place. What she hadn't expected was the emptiness. There is nobody there to meet them. Stands have been erected, a red carpet laid out, but not a soul is in sight.

The Doctor steps out onto the landing platform and looks at the giant grey ship he has arrived on: six hundred metres long. The vehicle is parked in a reception cradle. The Doctor hurries down to the red carpet. Sugar follows, asking where everyone is. She wails that the welcoming crowds are nowhere to be seen. The Doctor heads for the terminal, shouting that he needs to find an answer. In the distance they hear voices calling. The Doctor wonders how the problem can be in Eternity if the problem was caused by the ship's engines.

They notice that Millie and some other passengers are disembarking. The Doctor hurries back to get everyone into the terminal building. Lars Bortnik looks at the sky. He points out that the arrival was meant to be at sunset, but in the 45 minutes since their arrival the sky has not changed, the sun has not set.

In the terminal they find an urn of hot coffee: most mysterious. Bortnik wonders where Reston has gone but the Doctor changes the subject. Instead he turns his attention to the ship. He also adds that eight billion people have disappeared from the colony. Sugar tells him she can still hear the noises. It scares her like a noise she once heard in her auntie's chimney, caused by a trapped seagull that had been sucked into the heating system. The Doctor thanks her for giving him a brilliant idea. She reminds him that he never told Reston why he was there. The Doctor tells her that he arrived on the ship by accident.

He goes on to talk about the transposition technology. He says that it is years ahead of its time, and will change the whole of human history, except he has never heard of it. He has never heard of Cluxton either. Sugar realises that the Doctor is from the future.

By now they have arrived back at the passenger lounge. The Doctor tells the others to stay where they are while he looks for the central controls. Bortnik says he can lead the Doctor straight to it. The Doctor and Sugar (n and her follow-me) accompany him. On the way Bortnik says it has only been three years from Cluxton's breakthrough idea to the ship. The Doctor says that is impossible. He must have envisaged the whole technology in one moment. Bortnik agrees, saying he has the original plans, scribbled in mere hours, in his notebook. The Doctor asks to see the notebook and Bortnik reluctantly agrees.

The Doctor is amazed that these ideas are Cluxton's original plans, with no corrections and revisions. Sugar wonders if they were copied from somewhere. Bortnik is outraged. The Doctor thinks that the idea that the plans were copied changes everything. Bortnik looks up, saying someone is calling. All of them hear voices, getting louder. The source seems to be ahead of them. They see a teenage boy, Lincoln Tang, who was with them on the ship, some three hundred metres in front of them. The boy waves to them. The Doctor yells to him but Lincoln's reply is inaudible. The Doctor runs towards the boy, leaping across a flat, leaf-shaped sculpture. As he does so his feet and shins feel cold but he dismisses it in his hurry. Lincoln says he is chasing the dog which has escaped. Suddenly he, too, seems to hear the voices. Sugar and Bortnik catch up as Lincoln asks if the Doctor called his name. Sugar says someone called her, too. Bortnik shrieks, pointing at a sphere of matter, appearing in the air. It becomes a humanoid shape. The dog approaches it but as the entity bends towards it the dog flees to Sugar who scoops it up and runs. The Doctor and Lincoln run but find themselves cut off by another materialising entity. The voices are calling all around them, intoning their names. A wind gets up and a third entity appears quickly beside Bortnik. It touches him and he becomes transparent, and then vanishes. The three entities turn towards the Doctor. They are in different stages of completion. One has the shape of claws, and a line of a mouth; broader than a shark's and full of teeth. The Doctor fires a modulated burst from his screwdriver. One of the entities vanishes and the other two become less complete.

In the offices of the terminal the remaining trio of travellers hides behind a terminal. Lincoln asks where Bortnik went but the Doctor does not elucidate. Instead he tells Sugar that these events are not an accident as he first thought. Now he realises it is an invasion from another dimension. All three of them realises that they are soaked from the knee down. The sculptures they ran across were fountains but they can't see the water because it is moving. Just like all the other people, it is on another wavelength. The Doctor surmises that everyone else is still there, they did not vanish. If anything, the ones who have disappeared are the Doctor and the people with him.

Sugar asks what he means. He tells her that they have been knocked sideways in reality. He looks at a computer and scrolls through data of the ship's flight plan and comparing it to details from Bortnik's notebook. He adds that the invading entities sent a blueprint to Cluxton so that he could build transposition engines to allow them into his reality. The Doctor says he is trying to find a way to jolt himself back to his own reality and also shut the door on the invaders. After twenty minutes he writes down a page of notes and declares he has mastered the theory. All he has to do is recycle the engines and get everyone back on board.

Making their way back down the corridors the Doctor says he cannot save Reston or Bortnik. Sugar says she can tell that something else is bothering him. He agrees, saying that when he shut the engines off he had already foiled the invasion but now he has to turn the engines back on.

When they reach the other passengers some of them refuse to re-board the ship until Lincoln explains what happened to Bortnik. Sugar takes over and orders everyone to get back aboard in no uncertain terms. As they move the voices return. A breeze picks up and screams echo around them. Their names are being called. The Doctor confides that this is how the entities lock onto people. When they reach the ship they see dozens of entities appearing around them. The Doctor tells Millie and Sugar to get the passengers back to their original seats.

He stops, dumbfounded. He tells Sugar that someone called his name. He says that he didn't think there was anyone left in the universe who knew what it was, except for him. He slams the door behind the last passenger and hurries to the flight deck. He flops into the command seat and enters his data. The engines start up as does the pink glow round the window. The engines cycle up. Before they reach the correct frequency his name is lisped and two entities grow around him out of the air. The Doctor dodges out of their grasp and runs back towards engineering. Sugar runs after him and hears her name being called. When he gets to engineering he listens to the noise and smiles. He tells her that they have arrived in their own reality. Before he can celebrate three fully formed entities block him off from the engines. He groans, saying that he only needs a quick blast of his screwdriver to complete his plan.

He gets Sugar to put his screwdriver into the follow-me's cradle and sets it trundling across the floor. The entities remain oblivious to its existence- they don't know its name. There is a crash, greater than the jolt that began the adventure. The engines make a terrible noise and shut down. The entities tremble and shatter like glass before vanishing from the reality forever.

In the executive salon Lizzie is delighted to see Sugar back. Cluxton looks apoplectic at Bortnik's disappearance. Sugar tells Lizzie that the ship is never going to fly again and goes to look for the Doctor. He tells her that he has sabotaged the engines so they will never work again. He leads her out onto the landing gantry. They gaze out onto Eternity terminal where crowds are cheering their arrival.