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Spoilers for TNG episodes "Elementary Dear Data" and "Ship in a Bottle".

In "Elementary Dear Data", LaForge accidentally creates a sentient computer program based on the villain Moriarty from Arthur Conan Doyle's "Sherlock Holmes" books, when he asks the holodeck to create a Shelock Holmes scenario with an adversary that is capable of defeating Data. After the Moriarty program convinces the crew that it is indeed sentient, it tries in many ways to leave the holodeck, and Picard explains that the technology for that doesn't exist and he promises to provide Moriarty with such technology as soon as it becomes available. The sequel episode revolves around the same quest, with the Moriarty program still trying to find a way out of the holodeck and into the real world. In both episodes, Picard seemed sincere in his promises to Moriarty that he would help if he could, but the technology simply doesn't allow it.

But then if such a technical feat is impossible, why is the Doctor on Voyager able to pull it off so easily? Can't the technology that allows him to appear anywhere in the ship be easily applicable to the Moriarty program as well ? Or was Picard lying, and he never had the intention of helping him?

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The EMH is confined to Sick Bay and its attendant holo-emitters in precisely the same way that Moriarty is confined to the holodeck. Later on, the crew of the Voyager gain access to technology from the 29th century in the form of a mobile emitter but this is a unique technology, one well in advance of what they would normally have access to (by more than 500 years) and not something they seem immediately capable of replicating.

CHAKOTAY: They removed a lot. Five tricorders, three phaser rifles, a couple of photon torpedo casings, two antimatter injectors, a month's supply of emergency rations.

PARIS: No great loss there.

DOCTOR: Excuse me. You're forgetting the most important thing of all. My mobile emitter. Without it I'm stuck in Sickbay. I can't go anywhere.

VOY: Concerning Flight

Theoretically one could kit out a larger and larger area with holo-emitters until you had the illusion of freedom, but a hologram is always confined to those areas where their matrix can be supported.

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    In the Voyager episode "Message in a Bottle", Voyager's EMH was transmitted to the USS Prometheus, whose own EMH was not confined to Sickbay due to ship-wide holo-emitters. Picard would have had access to that technology, so the Federation could have given Moriarty a small ship of his own that was similarly equipped, at least. Similar to what Picard did at the end of the TNG episode "Ship in a bottle" but for real. Moriarty would still have been confined to a holomatrix system, but at least he would have had freedom to explore the universe. – Remy Lebeau Aug 24 '17 at 2:42
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    @RemyLebeau - Confined to flying places and just looking out of the window? What would he have done as soon as he needed to fix the wipers or fill up the tank? – Valorum Aug 24 '17 at 7:03
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    @RemyLebeau - I smell a spinoff! – Valorum Aug 24 '17 at 7:32
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    When Picard said he would help Moriarty out I doubt he meant by giving him an entire starship, In fact since that technology did exist at the time he clearly had discounted it. – mattumotu Aug 24 '17 at 8:56
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    @RemyLebeau "Picard would have had access to that technology". Nope, 'fraid not. The USS Prometheus was an experimental prototype. Ship-wide holo-emitters were one of the technologies being tested on that ship, it was not an available option for every starship. – DisturbedNeo Aug 24 '17 at 10:40

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