Any ideas how an advanced alien race could speed up time in a specific region of space?
I'm working on a storyline in which an alien race uses a time bubble to accelerate time so the construction of a structure can conclude quickly, as seen by outside observers. (The bubble is faster on the inside!)
I'd like this to be reasonable in plausible science fiction, not just a trope, to the extent possible.
Quite simply, you cannot make this scientifically plausible, as no existing scientific theories support the manipulation of time.
I would advice you to just technobabble it, as increased entropy or spacetime distortion fields or whatever, and do not go into details of how it works.
Some things to be aware of though is that while we cannot speculate about how it would be done we can discuss consequences.
Power: You would most likely need generators inside the bubble, power coming in from outside is going to start dropping in frequency as the time dilation kicks in.
Light: Light from inside will look blue to observers on the outside. Light from outside will look redder and redder to people inside and eventually go dark if you speed up time enough. This is something people never consider in "time stop" scenarios. People moving through frozen time would need to keep moving or run out of air and would be able to see nothing outside of their "bubble". They would also need to carry a light source of some sort just to illuminate the area around them and that would only extend to the edge of the bubble. Everything else would be absolutely black, perfect absorption, as the light would leave the area around you and from your perspective stop.
Heat: I'm not sure on this one, it's possible that you would overheat due to heat not escaping but equally possible that you would freeze due to heat not coming in.
Air: Now this is interesting. Since air inside is moving faster it will tend to accumulate at the boundary. Effectively you become a high pressure area. It's possible your air will all leave the inside of the accelerated zone (or at least atmospheric pressure will drop). Again this one I'm not sure on, you could argue that the opposite will happen or nothing at all. Working out which would involve expertise I don't have.
Oxygen: This one is clear though, even if the pressure stays even (but see previous point, I think it would most likely drop) you are going to consume the oxygen inside and only have a limited supply coming in from outside.
Now all these consequences are going to start off mild and become more and more serious the more you ramp up the time dilation.
There's no way to achieve this in the known laws of physics.
However given that near a mass the time "goes slower". I guess if you could create a negative mass, near it time should "go faster". So if you assume there's a way to create a large negative mass, then you could do that near that mass.
OK, so how do you create negative mass? Well, you create negative energy, because thanks to $E=mc^2$ you then get negative mass.
But how do you create negative energy? Well, you simply postulate a field that has negative energy. Such a negative energy field doesn't exist in the real word (and probably would cause major problems), but unless you're writing hard-SF I think it's an acceptable deviation from reality.
So your aliens create a bubble of strong phlebotinum field which has negative energy, and due to that negative energy time goes much faster. Note that you'll have strong anti-gravitation; that is, you'll need to invest a lot of energy to get into that bubble. Probably it would be best to first bring all the materials into the space volume, and then activate the field bubble.
If you don't prevent it, things in that bubble will fall outwards. You might have a sphere where you can walk on the inside due to that outwards force (the sphere would be stabilized by the outwards force the same way as a balloon is; of course it would have to be strong enough to support all the structures built on it).
In real science, there is no such thing and nothing that looks like a way in for something like that. Everything has a world line that moves along at a constant velocity in spacetime. If not moving in space and applying all its motion in the time direction, time passes fastest. Contrast, if moving at the speed of light in space, there is zero movement through time and it experiences none.
Gravity bends spacetime and has similar effects. In a galactic void time is fastest, and strong gravity makes it run slow. But our minor gravity here doesn't have much effect, so going into space would only speed up time by a tiny amount. There are other questions specifically on that, here on WB.
This time and space thing is on the level of space and time, without regard to any atoms or quantum mechanical stuff. It's rock-bottom basic features.
So, it's not real. That has not stopped science fiction from postulating it. Star Trek has temporal anomalies that make fruit rot instantly and Picard's fingernails grow out. The original series had something in the water, and this was right out of H.G. Wells from 1901!
You can have a chamber where time runs faster inside, and if well-written need not be explained as hard SF would. Just realize that it's not "hard" SF.
If you want techobabble, maybe the chamber works by surrounding the occupied bubble of normal space with a different false vacuum state where different rules apply. Maybe they pop out into hyperspace, something you want for FTL anyway.
Now, here's an idea that can accomplish the same result. With any form of FTL travel you also have time travel. Sit in the box for a year, then jump it back to a week after you started.
With a wormhole, it's clear: events (coordinates in space-time) are separated by a week in normal space, but spur of spacetime connects two mouths. Rather than make it shorter to cross through the wormhole, which is the point of using it for travel, you make it longer. This can easily be explained and diagrammed, and is a natural side effect of the drive technology.
Or just use Narnia. Same thing really.
Commenting on @tim-b 's answer.
Temperature: Since temperature is related to the speed of motion/vibration of atoms, the materials inside will appear "hot" to an outsider. Interestingly, an object's temperature is proportional to the square of the (root-mean-square) speed of the atoms, while Wien's displacement law states that the peak in the black-body radiation spectrum is proportional to the speed, unsquared. It should therefore be possible to distinguish a hot and a time-sped object from afar.
What about the speed of light?
One caveat on light: for a photon, wavelength * frequency = speed of light. If the speed of light is always observed as a constant, but the frequency of anything inside the bubble speeds up, the observed wavelength will reduce, giving a blueshift as you state. But then you can have scenarios where something inside the bubble is observed as moving faster than the speed of light to an outside observer. This breaks relativity. If the speed of light is allowed to increase within the bubble, frequency and lightspeed will increase in lockstep, giving no blueshift.
Then people start hacking the system
Regardless of how you solve the speed of light problem, you would be able to transmit a signal into the sphere and have it exit the other side having travelled faster than the outside speed of light. This violates locality and opens the door to both faster-than-light travel and sending messages to the past.
This is looking more and more like a explanation for why this alien race went extinct. I'm calling for a ban on all time-bubble research!
The questioner wants plausible science fiction and there is plausible science to back it up. Let's not forget the time-bubble is constructed by an advanced alien race.
@celtschck suggested negative mass and negative energy, and quite correctly too. We may cast aside any objections about how to obtain negative matter and negative energy for the purposes of plausible science fiction and simply grant that our aliens are sufficiently advanced.
Robert L Forward described a negative matter time machine thus: "Suppose we had a negative matter which is very dense. Time would run faster near or in the negative mass and we could make a hollow sphere of dense negative mass to speed up time." (in Robert L Forward, "Far Out Physics", Analog, August 1975, pages 161 and 163).
This doesn't speed up time in an unlimited way,the speed-up factor is only square of two faster. This is roughly only forty percent faster. Forward proves this from basic gravitation equations which look like they're adapted from equations about the mass of black holes (my guess!). Forward's article isn't detailed like a scientific paper, alas.
Assuming special relativity is preserved inside a Forward-style dense negative-mass hollow sphere, then if time is faster lengths will be dilated so any measurements of lightspeed remain invariant as required by special relativity. Essentially as time is 'speeded-up' lengths inside the negative matter time machine will increase.
Like @Ruok2bu I had considered the possibility of a parallel universe where time is faster relative to that of our own universe. Yes, @JDLugosz, like Narnia.
Also various forms of time travel could be used to create an illusory version of speed-up time not just interesting arrangements of wormholes. A long space trip in a Godelian rotating universe would achieve in a similar result. The pity is rotating universes are always hard to find.
There is another way of creating speeded-up time. It involves special relativity and travelling at superluminal velocities. R T Jones published in the American Journal of Physics the possibility that travel faster than light results in time passing at the rate of the distance traversed. Basically for every light year a spacecraft travels one year passes shiptime.
So a FTL spacecraft only has to choose a suitable superluminal velocity to ensure enough speed-up time can pass. Since this is plausible science fiction, we can assume there is a chronology protection principle in this fictional universe to take care of any causality problems, Namely, there won't be any to worry about. This isn't exactly the time-bubble the OP wanted, but it is one way to speed up time.
