Picard refuses to let Riker in on the discussion with Apgar or discuss the situation with him, telling him it is "not appropriate". The is an excellent move on his part - Picard has to serve as Riker's judge to an extent, so it's correct that he not have improper discussions about the issue with him. However, he asks Geordi to create the holodeck program that they use to decide the case. Geordi isn't accused of the crime, but he was a witness to much of what happened on the station; how is it that a witness with sympathies for the accused is allowed to be such a major part of the investigation? Indeed, you have to ask... how hard would it really be for Geordi to have reprogrammed the simulation to stage the whole end sequence 'proving' Riker's innocence?
Krieger waves are named for scientific consultant David Krieger; he overcame the problem of having the holodeck responsible for damaging the ship by coming up with the idea that the converter was not harmful in and of itself, but only in conjunction with the generator on the planet below. Krieger also suggested a line explaining that the waves suppress the strong nuclear force, making any matter exposed to the fissionable, but this was cut from the episode.
The away team, composed of Riker and Geordi, has been delivering a consignment of dicosilium to a research facility and making a routine assessment of the work of Dr. Nel Apgar. Apgar has been working to create Krieger waves, a technology that could be an important new power source.
Geordi returns to the ship, saying that Riker stayed behind for a moment to talk to Apgar. The engineer seems a little discomfited, though he is hesitant to say why. Riker begins to beam over from the research station - but as he does the station explodes. O'Brien is barely able to complete the beam out, but Riker materializes safely.
A thorough check of the transporter reveals no problems with it, certainly nothing that could have caused the disaster. Data reports that the explosion was consistent with an overload in the station's reactor core, but Riker and Geerodi say they can shed no light on why this would happen.
Chief Investigator Krag of Tanugan security beams aboard; on meeting Riker he tells him that he is here to take him into custody on murder charges. Riker is stunned, but Picard takes Krag to his ready room to talk - telling Riker that it would not be appropriate for him to be present. Krag tells Picard that two witnesses have come forward to testify that Riker made threats to Apgar. He points out that on Tanuga, people are presumed guilty when accused, and must prove their innocence - and since Riker was within their space, their laws apply. Picard notes that Starfleet regulations allow him the decision as to whether or not to allow the extradition of an officer, and that he will only do so if sufficient evidence is provided.
The two discuss the possibilities of investigating the crime on the Enterprise; Krag is suspicious of Picard's motives and doubtful that all the information can really be evaluated fully on the ship, but Picard suggests a solution - they can recreate the station on the holodeck, and use it to recreate the sequence of events in great detail. Krag agrees to go along with this, making all of his information available.
Picard assigns Geordi and Wesley to create the simulation, stating that his decision as to whether to extradite Riker will depend on this. It takes eighteen hours to complete the process, which is estimated to be 91.3% accurate. The interested parties gather on the holodeck to examine the testimony. First, Riker runs a recreation of events as he recalls them - throughout his version, Riker's hologram remains calm and composed, being nothing but reasonable to all concerned. In contrast Apgar is impatient, even somewhat desperate. Apgar's wife, Manua, is also present on the station, and is clearly very attracted to Riker, whilst being dismissive and disparaging of her husband. Krag questions Riker's recollection that it was Manua's idea for him and Geordi to stay on the station overnight, which Riker confirms. As the simulation continues Manua gets Riker alone and makes a pass at him, which he resists although she is quite insistent about it. Apgar walks in on this scene and reacts with fury, taking a swing at Riker which he dodges easily. Despite Riker's claim of total innocence, Apgar angrily states that he will file a formal complaint with Starfleet. The following day, Apgar questions whether his complaint will make Riker give a poor report to the project, and idea Riker dismisses. He wants Manua to come and explain the misunderstanding, but she and Apgar's assistant have gone down to the planet. Riker leaves for the Enterprise shortly afterwards.
Krag asks Riker if he fired a phaser as he beamed out, which Riker denies. However, the station's ground computers monitored a focused energy pulse just as the transporter engaged; analysis of the trajectory of the beam shows that it came from Riker's position. Krag shows a simulation of the beam out, in which Riker fires his phaser into the station's Krieger system just as the transporter beamed him out, destroying it in an overload.
Geordi, Data, and Wesley all check the results, and find that they do indeed appear to show what Krag claimed. None of them can understand it, but there is a clear sign of an energy pulse, and that pulse was not something that any of the station's equipment could have created. As they talk, Worf notes a radiation burst on Deck 39, of an unidentified type. The burst melts a section of wall, baffling Geordi and Wesley as they know of no radiation that could do that.
Back on the holodeck, Krag shows a recreation based on Manua's testimony. She accuses Riker of the murder before it begins; in her simulation Apgar is anxious about the upcoming visit whilst she is nothing but loving and supportive. Riker is the one interested in her rather than the reverse, which she finds uncomfortable. Riker more or less ignores her husband, dismissive of most of what he has to say about the project in favour of leering at Manua. Once alone he makes a pass so strong that he all but attacks her, forcing himself on her against her spoken objection and even physical resistance.
Watching this, the real Riker strongly objects. He denies this as a recreation of what actually happened, asking Manua why she would lie like this. After he has calmed down the simulation resumes; Apgar walks in on Riker's attempted rape and throws a punch as before, but this time Riker does not dodge but rather blocks the punch and retaliate with two blows of his own, leaving Apgar on the floor. When Apgar threatens to file his complaint Riker states in a threatening tone that this would be a big mistake.
After the session is over Riker asks Troi why Manua would lie like that, only to have her confirm that Manua wasn't deliberately lying; she honestly believed that this is what happened. Troi says that although she knows Riker could never behave the way they saw, this is what Manua thinks really happened, from her own point of view.
In sickbay, Crusher is working on a patient when Worf calls from the bridge urgently, calling on them to evacuate sickbay - another radiation burst is coming in their location. As they hurry out parts of the wall begin to turn grey and melt. Afterwards Geordi and Wesley examine the spot, confirming that it is the same effect as before. They are worried - there is still no sign of what is causing this, and if it happened to the warp core or antimatter pods the ship would be in big trouble. Data observes that the events happened five hours, twenty minutes and three seconds apart - and the space station exploded at four times that interval the previous day. The timing is almost exact, with only a 0.0014 second variance that is unexplained. It seems that the destruction of the station may be linked to whatever is happening to the ship in some way. Picard tells them that if they have not found some way to protect the ship by the time of the next burst, they will leave orbit of the planet.
Back on the holodeck Dr. Apgar's assistant, Tayna, is next up. She recounts what Apgar told her about the incident between himself and Riker - hearsay, but admissible in Tanugan law. This time Apgar walks in on them and it is Riker who throws the punch, which Apgar dodges before knocking Riker off his feet. When Apgar says he will file a complaint Riker is openly threatening, calling Apgar "a dead man!" The simulation moves on to show Apgar urging his wife and Tayna to leave. Everybody seems fearful of what Riker may do but Apgar is determined to remain behind, saying he will take care of it. As the simulation ends Tayna states that she just knows Riker is a killer. Krag states that he has established a method, motive and opportunity for Riker to be the killer, more than enough to secure an extradition.
In his ready room with Troi, Picard is forced to reluctantly agree - he believes in Riker's innocence, but as things stand he really has no choice but to hand Riker over, despite that leading to an almost certain conviction. Data calls Picard to the bridge at that moment, and reports that he has found a possible link between the radiation and the station's destruction; there is a field generator on the planet which Apgar used in his work, and it emits an energy pulse automatically each time it recharges. It was apparently left on, and has been discharging the pulses into space. However, they are still at a loss to explain how this could damage the ship, as the energy pulses from the generator are completely harmless. As he thinks about it Picard suddenly realises the answer, along with the cause of the explosion and who killed Dr. Apgar.
They meet once again on the holodeck for a presentation by Picard. He shows elements from the previous scenarios - Manua's testimony reveals that Apgar was worried about setbacks in his work, and upset that it might be cancelled. Picard suggests that Apgar had in fact already produced Krieger waves, citing as proof the damage to the Enterprise - the harmful radiation has been identified as Krieger waves. A baffled Krag says that this can't be - even if Picard is right, with the station destroyed there is no longer anything to create the waves. However, the simulation of the lab itself contains the Krieger apparatus; although a simulation, this is still functional. As the generator on the surface sends an energy pulse out, the converter is producing Krieger wave bursts that are damaging the ship. The holodeck safties didn't work as the computer only knows that the converter is harmless in and of itself.
Krag asks what motivation Apgar had to lie about his progress, and Picard points out that in the simulation Apgar promised Manua that his work would yield great rewards, not once but twice. However, Apgar would not have made anything much off his work for Starfleet. He could, however, have made a great deal of money with Krieger wave weapons sold to the Ferengi or Romulans. The order for extra dicosilium fits with the theory, as one use for it would be to make a larger, more powerful converter capable of weapon level effects. This explains his concern about the away team coming early - he must have suspected that Starfleet was suspicious of him. Whatever the truth about the incident with Riker and Manua, this could only have added to Apgar's dislike and distrust of Riker. He also points out Tayna's testimony, in which Apgar states that he will "take care" of Riker himself. As Tayna leaves the simulation shows Apgar sitting at some controls. She confirms that these are the controls for the generator on the planet below.
Krag points out that the energy pulse that destroyed the reactor came from Commander Riker's position. In response Geordi suggests that Apgar intended to kill Riker by firing a Krieger wave at him during transport, in hopes that it would appear to be a transporter accident. However, the beam reflected off the transporter beam back into the reactor. This is why there is a slight time discrepancy - it is just exactly the time required for the beam to bounce back off Riker.
Krag is highly doubtful about all this but Picard tells him they have arranged a little demonstration; the ship has taken the exact orbit the station had previously with respect to the generator, and a new simulation will be run in which Riker simply beams out. The simulation proceeds - and just as the holographic Riker begins to beam out the generator on the planet below discharges, producing a beam that does indeed reflect off the transporter effect. An instant later the holographic station explodes, leaving everybody sitting on an empty holodeck.
Finally convinced, Krag drops his extradition request and offers Riker his apologies. The Tanguans leave, and the ship departs the planet.
Also, Manua's wife really doesn't work as a character. She comes over as flat and uninteresting, about one third badly written and about two thirds badly acted.
My main complaint is in the mystery aspect. Yes, it's really cleverly constructed. But the whole point of a mystery is that you're supposed to present the audience with what they need to find the answer, but do so in such a way that they miss it. The whole art of a mystery is in making the audience go "oh, but of course, I should have worked that out!" when they find out the answer at the end. Here, though, the audience knows next to nothing about Krieger waves or the physics of what's going on because it's all made up science. This isn't to say that it's implausible, or that the answer doesn't work - it does, it's just that the audience can't possibly go "Oh, of course, it's the Krieger waves!" because we have no idea what they are or what they could do. As a result, this episode is like watching a person solve a problem in a field you know nothing about - you only know it's a hard problem that they were smart to solve because they say so as they explain it to you along the way, you have no context of your own to judge it by.
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