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We've made an important discovery. With the power of unobtainium and handwavium, a highly advanced species that lives in higher dimensional space has provided us a room on Earth that has its own passage of time. It's a gift to humanity, so an international agreement has been made to ensure that it's used properly.

The doorway can't be moved and it can't be destroyed.

Here are the rules and magical properties the advanced species has laid out:

  • When you enter the room, that room exists only for you and whoever enters the room with you before the door is shut. Once it's shut, if someone enters the room again, they get a copy of the room that exists only for them, and so forth.
  • Time continues normally within the room, but when you exit, it's as if you were only in the room for a brief moment. You continue to age within, so if you're in the room for 20 years, to outside observers you just aged 20 years within moments.
  • When you exit, the advanced species has ensured your safety from collision with other people who are exiting by placing your own unique exit door in a safe place (like your home).
  • The room contains a library of every book on Earth. When a new book is published (and has a record of it like ISBN or entry on Arxiv et al.), the library instantly has a copy. When you enter, it instantly has the latest copy of the internet, as well. So you can access every website and every subdirectory, but it won't get updated until you exit and come back.
  • Materials in the room stay in the room. You never run out of food or water, but the only things you can take out are things that you brought with you.
  • You can't communicate with the outside until you're back outside.
  • Physics holds within the room. You can hurt yourself and die in the room (and if no one came in with you, you can never be retrieved) and you can destroy things in the room, but if you leave and come back, everything is back to normal.

Edit - I've added some additional properties to answer some questions.

  • The exit door cannot be entered. You must take the trip to enter again.
  • The room is powered so you can bring in your own computer (and yes, supercomputer components) or robot. Retrieval of the robot would have to involve the robot having enough intelligence to exit on its own since you can't communicate with it from the outside.
  • You can write things down on a notebook and leave with the notebook you brought and the writing will be maintained as long as you use a writing tool that you brought with you.

Dimensions and Amenities

  • The library is sequestered in a long rectangular space (that always grows) with advanced moving parts that bring books of topics or titles you want close to you when you look for them. No one's ever been to the end to measure its size.
  • The main room is 10000 square feet and has a bed, a desk, and a wall mounted computer that runs the highest graphical/computer power available in the Nvidia/AMD market. The creators would rather you bring your own supercomputer. It's a fresh install of HandwaviumOS that can run any file or program. The internet is local and cannot connect to the outside world.
  • The kitchen is 500 square feet and contains a refrigerator which contains any food you tell it to contain. The creators have a lot of resources off-dimension.

What effect would this have on society? How would it influence science and technology and affect the future growth of our civilisation or problems that we face today?

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    $\begingroup$ I would finally be able to meet all my project deadlines. $\endgroup$ – Henry Taylor Dec 16 '15 at 17:54
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    $\begingroup$ Well everyone could use their own room as their house. If it belongs to them they wouldn't need to build housing elsewhere. $\endgroup$ – Sunspear25 Dec 16 '15 at 18:03
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    $\begingroup$ The unlimited food and water would solve world hunger, destroy most of our motivations for war and dissolve at least some of our reasons for working at all. Congratulations. You've taken survival off of humanity's list of prime motivators. How we act in its absence will teach us all much about ourselves. Who are we, when we are free to be anything we want to be. $\endgroup$ – Henry Taylor Dec 16 '15 at 18:23
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    $\begingroup$ @Wingman4l7 Time inside is faster than time outside, so your question should be phrased as "(1 year in the room = 1 minute on the outside)" $\endgroup$ – Draco18s Dec 16 '15 at 19:19
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    $\begingroup$ @CortAmmon Hm, that is a fair observation. However, because the energy's origin is the room, it shouldn't be able to leave the room. Your battery should die out the moment you leave. If you can come up with a workaround for that, I'll leave the exposure open and see what comes of it. $\endgroup$ – The Anathema Dec 16 '15 at 19:43
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The passage of time itself is the unlimited commodity on offer; how can you apply that to existing industries? To me, this is more interesting to consider what you can accomplish with the effect of time on objects and processes, rather than people. I see several different economic opportunities:

  • "instantaneous" aging of any food products whose value increases over time (wine, other liquors, cheese)
  • speeding drug development by running human medical trials inside the room
  • running any sort of lengthy computer processing (climate modelling, protein folding, cracking encryption)
  • decontamination of radioactive waste via "accelerated" radioactive decay; retrieval unnecessary! (idea courtesy of lbotinelly's comment)
  • other useful implementations of the process of decomposition
  • propagating slow-growing plants (automated care system would be required)

There would be a boom in the market for robotic automation and "rovers" to allow you to place objects into the room and retrieve them after a preset interval of time; there's no reason to keep humans in the loop! This would stimulate interesting advances in fault tolerant hardware & software. Easy retrieval but no communication is a flip-flop of the situation faced by our current planetary robotic probes. Power generation could also be a hurdle -- would you need to run everything off RTGs, or could you have rovers self-dock (a la a Roomba charger) with an existing power outlet provided in the room?

If a human presence was required for "babysitting" certain objects, an online marketplace to schedule room shifts might spring up, so a long period could be completed in more manageable increments of time.

Use of the room could be punitive in nature, as it basically amounts to solitary confinement. It could be used for incarceration or prison work-release programs. This would have serious ethical considerations, of course. This raises another question: can the door be barred from the outside?

The big question: Is time passing faster in this room in relation to the outside world in an absolute sense -- is there a concrete function representing the ratio of time passed (1 year in the room = 1 minute on the outside)? Or does it only pass faster on the inside to a human observer?

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    $\begingroup$ xkcd.com/821 lower left corner. $\endgroup$ – Draco18s Dec 16 '15 at 18:48
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    $\begingroup$ Unfortunately, to have a 25 year brandy, someone has to wait in the room with it for 25 years. It's going to cost a lot to have someone give up a significant portion of their life for some nice booze. $\endgroup$ – Samuel Dec 16 '15 at 18:49
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    $\begingroup$ @Samuel: I think we might be surprised who'd be willing to do that. Talk about an insidious prison work-release program! Maybe it could be done in 1-year shifts. Besides, you can't put the bottle of brandy on a wheeled robot with a timer for it to drive back out through the door in 25 years? :D $\endgroup$ – Wingman4l7 Dec 16 '15 at 18:54
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    $\begingroup$ Your first topic made me think of another - near-instant decontamination of radioactive waste material, if robotic automation is allowed. Heck, just get rid of it - close the door forever, no need to retrieve it. $\endgroup$ – OnoSendai Dec 16 '15 at 18:56
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    $\begingroup$ @Wingman4l7 That's correct, given the limitations. You'd have to use the room to research more humane and superior incarceration. : ) $\endgroup$ – The Anathema Dec 16 '15 at 19:26
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This room has a second amazing benefit that's sort of hidden because it was presented more or less as a side effect in the original description:

When you exit, the advanced species has ensured your safety from collision with other people who are exiting by placing your own unique exit door in a safe place (like your home).

This sounds to me like instant, free teleportation. Of course, the starting point is fixed, which is not optimal, but that's massively outweighed by the fact that exit portals could be placed in all kinds of places that are difficult or dangerous to get to.

Workers trapped underground in a mine accident? Send a rescue party into the room with food, medical supplies and tools and ask the advanced species to locate the exit in the mine. Doing research and need to set up camp in the middle of the jungle or desert? Make the first half of your trip through the room. This could even work for the moon, Mars or further, once we develop the technology to retrieve people from those places, and assuming the door is large enough to bring vehicles through. (Or, if the exit is movable while the room is occupied—the original wording doesn't address this—people could go in, throw robots/sensors out the door, then wait for the advanced species to move the exit back to Earth before walking out themselves.)

The other answers already cover a lot of ground with the primary (time) aspect of the room. I do want to add one thing: when I read the question, one of the first things I thought of was "wow, people would be able to finish school/get their PhDs a lot faster by studying in the room" (relative to the passage of time for the rest of us here on Earth). Yes, there would be a huge lack of human interaction in those school experiences, but people have been attending school via correspondence courses and online programs for a long time. It's not too hard to imagine intelligent, highly motivated (probably mostly introverted) people popping into the room, coming back out for exams, repeating for a few "semesters" and going from secondary education to thesis defense in just a few weeks or months.

I say weeks or months instead of minutes or hours because the school thing makes the assumption that the human authorities have opened up use of the room to pretty much anyone, instead of just VIPs. In that case, a lot of people would probably want to take advantage of the opportunity, and there would be a fairly long line to get in. Some sort of bureaucracy would develop over room entry/usage rules ("Now serving number G39, we're ready to let the person with ticket G39 into the room..."). A small town would likely develop around the location of the entrance to the room, or if it was already in a populated area, a door visitor sub-economy would spring up, in the form of extra hotels, restaurants, co-working spaces, that sort of thing—the Breezewood of superhuman travel, basically.

On a societal level, we'd be forced to adapt our laws to account for time travel. A simple, trivial example: if you go into the room on your 15th birthday and live there for what feels to you like 10 years, are you 15 or 25 when you come out? Can you legally drink? Vote?

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Wingman4l7 already listed some good things you could do with that room. However as with everything else, it would also be used for evil purposes. And also for those, there are ample possibilities:

  • The perfect murder: You enter the room together with the victim, kill the victim there, and leave the room. Nobody will ever find the corpse. If someone saw you enter the room, just claim the victim wanted to stay a bit longer, and you have no idea what happened; maybe the victim just decided to stay for the rest of his/her life. Nobody will be able to prove otherwise.
  • Similarly, if you want something to disappear forever (say some papers proving illegal business), you may take it into the room and leave it there. Since everyone gets a fresh room, whatever you leave there will be lost forever.
  • If you have to flee from the police, staying the rest of your life in that room, unreachable by the police, may be preferable to staying the rest of your life in prison. Especially since you can leave the room at any time should you ever change your mind.
  • Also, if you flee from the police, even if you immediately leave the room after entering it, the fact that the exit door may be anywhere can be helpful to hide your traces: You'll effectively have instantly moved to another point of the planet unknown to the police.
  • Forgers may value the near-instant ageing of materials. With enough people working for them, they could get that effect without the individual people ageing too much, by just passing the materials through the room several times, where each time someone else accompanies it, and each individual stay is not too long (say half a year). Given the library, the person can use the time inside to learn more about the stuff to forge.
  • The availability of the complete internet, coupled with nothing having an effect on the outside until you leave, is also perfect for black hat hackers trying to break into web sites. They have all the time of the world to look for vulnerabilities and, if they find them, copy out data, without anyone else noticing or being able to respond with counter measures, as the hacking will not be visible from the outside.
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  • $\begingroup$ I was hoping that someone would say some of these. In my imagination I wanted a sense of vetting for people who entered or even intervention from the creators if it were used for evil, but ultimately I decided against it in the question because I didn't want to restrict the future. How we used the room would say a lot about us (to ourselves and the creators). $\endgroup$ – The Anathema Dec 16 '15 at 22:23
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With infinite computing time, cryptography would be meaningless. Which means, no government or individual could keep any secrets, and anyone's money could be stolen at a moment's notice. If a crypto arms-race developed, hardware durability would be very important - your machines are still ageing in there.

Scientific advancement would improve rapidly, and as mentioned in another answer, robotics would become important.

The problem is, we aren't taking everything out of those rooms, and we're putting a lot of computers in. Humanity would rapidly run out of materials to make any kind of robots, computers, or even basic electronics.

Either we would utterly wipe out our planet, or we would develop the technology to turn energy into matter, and make a room that generates infinite amounts of energy and pipes it out the exit door to replenish our rapidly shrinking planet.

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  • $\begingroup$ Since you cannot re-enter to get the results, a human must accompany the calculation and bring the results out. And that means the available time is not infinite, as each cycle is limited by the human lifetime, and the supply of humans is finite (and the supply of humans willing to stay most of their life alone in a library is probably rather small). $\endgroup$ – celtschk Dec 16 '15 at 23:44
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    $\begingroup$ Advanced types of encryption (AES-128, 256, etc) still take too long. Even if I say that the room is outside the impact of the universe's heat death, the atoms that compose the robot or computer doing the algorithm will not live that long. Good durability becomes irrelevant when protons themselves don't persist enough, and I imagine encryption will still become stronger because of people using the room to boost that technology, as well. $\endgroup$ – The Anathema Dec 17 '15 at 22:19

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