Mirja said:
How (if) you would allow that as a GM, how would you resolve a player for doing this?
If not, why?
I generally wouldn't allow it.
Reason 1:
It'd change the universe.
I know this is a real boring objection. But it really would. Because your player has singlehandedly moved Jump Drive technology from TL16 to TL17 or TL17 to TL18 or whatever. Most players don't really think of what TL is, but this is exactly what TL describes: Evolutionary improvements to existing technology with the occasional revolutionary development thrown in.
If some scientist developed a drive of the kind your player wants to develop, in game terms it'd only mean a small difference in performance. In the game's "reality" it'd be a huge change. The scientist would literally be a celebrity for developing such a thing alone. Beyond that, she'd be famous within the jump drive manufacturer's societies. Big companies would offer nearly unthinkable amounts of money to buy her concepts off of her. The Emperor would invite her and shower her with titles. Within decades, pretty much every ship in the universe will have switched over to the new drive design.
Obviously, if you want you can take the more dark approach and have agents or whatever trying to kill/capture her to keep the secret to themselves, but I really doubt it. A design change like what the player would be some evolutionary development; while it's boring, megacorps and the Imperium are more likely to simply wave a bunch of money in her face instead of doing something more violent; these groups have tons of money, and if someone can be bought everyone is happy.
Mirja said:
has convinced the oother players to have an extra stateroom as her workshop.
Reason 2:
The lone scientist, working alone, in some basement workshop is pretty much a myth.
Complex technological development is something that requires millions, billions, or even more of (insert currency here) poured into R&D over years to develop, due to the complexity of devices. A Jump Drive is an extremely complex and expensive device. It'll require a lot more than a simple spare stateroom to do development.
My assumption is that the desire to make Jump Drives better in some way is shared by hundreds of other organizations, pretty much all of them vastly more wealthy than your player. These groups keep up on and fund research being done at universities and similar places and they're all pushing at the TL barrier to push TL to the next one. Once a discovery is made, it will require years (or given the slow pace of technological advancement in the Imperium, decades) before it becomes something usable. During this time, the original development might change, be refined, so many times it hardly even resembles the original concept.
Reason 3:
It's Unfair to the Other Players.
Things like money, power, and recognition are the reasons why players typically adventure. Making such a momentous discovery would fulfill all of them and make her the most important member of your adventuring group by far, creating an Out-Of-Character power imbalance. She might continue to adventure, but now the other players would be her lackeys/friends on her private yacht; getting audiences with nobles will be ridiculously easy, she just needs to drop her name and get invited to parties. Basically, her celebrity and power will have replaced slews of skills of other players.
Why is it that just one of your players is able to make some momentous discovery while everyone else cannot? Just because she asked while nobody else did? Why is it that she can do this with this out-of-character expectation of success at some point while other tasks in the game are uncertain? What would you do if I rolled up a character who had about 100k credits due to mustering out and simply said, "By the way, I invest this in the stock market. I know my ship won't come in immediately, but eventually it'll pay out and my character will reap a reward of hundreds of millions of credits. I'd like to have a stateroom so I can have a computer to keep track of all my financial transactions."
Okay, to stop being a killjoy:
Now as a GM I like to work with players and not flat-out tell them "no." I've given you the reasons why you shouldn't do it. Now I can give you some reasons how you could integrate something like this into your game:
1) Inform your player that success is not certain and unlikely.
2) If you enjoy letting your players be extraordinary individuals, you should let everyone be extraordinary in some way, not just one player.
3) If you're okay with #2, then perhaps your player has come up with some idea, some inspiration from somewhere. It doesn't matter where. For whatever reason, instead of simply patenting the idea or selling it (again, for the aforementioned millions), she's decided to develop it on her own. The concept likely to not actually be new; it's probably that the approach has been tried before, but there's some sort of problem with it and nobody has ever gotten it to work right (or perhaps, nobody has ever made it safe enough for sane people to use), despite repeated tries and lots of money fruitlessly invested in it in the past. As a result, most places have given up on it; your player simply has some approach that she thinks will work; obviously nobody is going to help your player develop some technology that's considered a dead-end.
4) At some point she'll leave the adventuring party because her discovery moves to a point where she is going to have to get a bigger lab, more money, more everything to move her idea forward. Her time with the group would be simply enough take her idea and perhaps struggle to research it sufficiently so she can prove to some megacorporate lab or university science department that her approach has merit and is worth pouring money into. Until then, she's going to need to have the highest TL components to tinker with; she can't go mess with the ship's Jump Drive. She'd need to find TL15 or TL16 components to work on because that's the state of the art and she's singlehandedly trying to push things past that.