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I have an idea for a city surrounded by a giant time dilation field which causes time to run much faster inside it (think something like the Hyperbolic Time Chamber/Room of Spirit and Time). There's a river running through this city that connects it to the ocean.

Exactly what would happen to this river once this field is established? How would the altered flow of time on either side of the field affect the flow of water? Would the river appear to dry up inside the field due to the increased flow of time relative to the normal rate at which the river deposits water outside the field, or would the river continue to flow as normal?

I'm honestly having a bit of trouble parsing the logical implications of such a field, so I was hoping someone here could help me out.

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    $\begingroup$ Possible duplicate of Stopping time, by speeding it up inside a bubble - it's not about a river, but it covers logical implications of such a bubble in general and you can adapt some information into your question. $\endgroup$ – Mołot May 15 '17 at 16:12
  • $\begingroup$ Each post should only have one question. Could you remove the extra bonus questio? $\endgroup$ – sphennings May 15 '17 at 16:15
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    $\begingroup$ @Mołot The scale this question asks for seems sufficiently different that I wouldn't consider them duplicates, related to be sure. The other question focuses on how an individual interacts whereas this is on a geography level, I think having answers to both can be beneficial for this and other future users. $\endgroup$ – James May 15 '17 at 16:44
  • $\begingroup$ @James this question includes "what would a person experience" at the moment. $\endgroup$ – Mołot May 15 '17 at 16:59
  • $\begingroup$ @Mołot Yes but that is the "bonus" question, which should probably be removed both to keep the question focused AND because that is already answered in the potential duplicate mentioned. $\endgroup$ – James May 15 '17 at 18:27
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Rivers are measured in flow rate, the volume that passes a given cross section in a given period. This makes it easy for us because your town boundary is a cross section.

Let's go with cubic metres per second ($m^3/s$) for the flow rate and an arbitrary value of a factor of 10 on the time dilation.

Generally the flow rate of a river is fairly constant. It's increased by tributaries and other incoming water, but isolating the river from tributaries and other sources for the sake of this model, fundamentally what goes in at the top is what comes out at the bottom. We'll also define your river cross section as remaining constant all the way through the zone of interest* (the river equivalent of a spherical cow in a vacuum).

Entering the town changes the flow rate of the river because it changes the meaning of the second. However the effective volume of water flowing through the system doesn't change.

Say you're getting $1m^3/s$** approaching the boundary, within the boundary that becomes $1m^3/10s$ or $0.1m^3/s$, $1/10$ of the initial flow rate. Given that the river will most likely remain in its same basin, it has the same physical constraints, your reasonably fast flowing river outside the boundary will become a lazy river within the town then return to being a fast flowing river outside it again.


*This doesn't affect the flow rate, just the flow speed, but it makes it easier to visualise.

**In river terms, barely a trickle, but easy to calculate.

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  • $\begingroup$ As an addition, the sudden slow of flow rate means that less water "enters" the cross section of river in the town relative to what's flowing in. You will have a decrease in river volume/surface height as well as speed. Where the river flows into the town, you'll have a mini waterfall as the river falls to its new height, and where the river exits out back to the regular world, you'll have a jet stream as the same volume of water is pushed out of a smaller area, kind of like a straw. $\endgroup$ – Visfarix May 16 '17 at 19:02
  • $\begingroup$ @Visfarix nope, cross sectional area remains the same. Time is what changes $\endgroup$ – Separatrix May 16 '17 at 20:49
  • $\begingroup$ Then what does the river look like to people outside of the time dilation field? Does it appear to flow at the same rate as the river does outside of the field? Slower? Faster? Why? $\endgroup$ – Visfarix May 17 '17 at 14:17
  • $\begingroup$ @Visfarix, to someone outside, the river inside may look exactly the same as the river outside. There's a set of turbulence calculations that I'm far from qualified to run, especially when tied to a time compression field. What effect does it have on gravity and the perception thereof for example. $\endgroup$ – Separatrix May 17 '17 at 14:31
  • $\begingroup$ Should there be a force correct system in place, so all forces act as you would normally feel them, then the river would appear to be a calmer version of itself as outside. As though merely running at a 1/10 of its speed. $\endgroup$ – Separatrix May 17 '17 at 14:41
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Minor Misconception: Natural time dilation fields (from a black hole) aren't boolean (as in one side is slow the other fast) it's better to think of it as a gradient.

Answer: Nothing (dependent on circumstance)

To visualize: imagine the river was flowing into an empty pit through your field. It would appear first gelatinous then getting increasingly more fluid like watching butter melt in the microwave. Now if there was an empty pit there, the water from the ocean would be flowing back into the pit in much the same way. This brings our focus to pressure. If pressure remains the same as it was going in then NOTHING changes. However if your city is drinking that water and not putting it back via sewage then the water level in the river would drop leading to water slowly flowing in (like melting butter) from entrance and exit.

As long as pressure remains the same the water coming in and leaving would remain the same. The pressure of the water leaving the bubble is still exerting the same force on the water behind it as it would had the time dilation not been there. Now the water inside the bubble would appear much like a placid lake than a river.

If it helps more you could think of it as a stick of butter with its center melted but both ends are still solid. The butter wrapper is the geological shape of the river, one end is the entrance, and the other end is the exit.

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Depending on the factor of time acceleration, the river becomes much smaller or potentially even dries up.

If you speed up the city by a factor of 10, then you'll have 10 times less water getting through to the inside of the field, because the river is essentially moving 10 times faster.

Your city can easily still get plenty of water provided the time shift isn't too severe - One tenth of a river is still a LOT of river.

Also, keep in mind the time dilation field affects the day/night cycle, too, making them that much longer, and decreasing the amount of light. Going with my previous 10x multiplier, days would last 10 times as long, and so would nights. And days would end up with 10 times less sunlight. If this is technologically-based stuff, you'd need a whole lot of street lights and ways to grow food. Plant life would probably be a little messed up.

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  • $\begingroup$ if anything, it's slower, not smaller river $\endgroup$ – Mołot May 15 '17 at 16:28
  • $\begingroup$ @Mołot if -- relative to outside the bubble -- time runs 10x as fast inside the bubble, then river water would flow 10x as fast, too. A really big backlog of water would be created just downstream of the bubble. $\endgroup$ – RonJohn May 15 '17 at 16:34
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    $\begingroup$ @RonJohn How so? If we will turn the bubble on, and bubble size will be relatively small, then we will get 1/10 of water at the entry point, and the exit point will work as a dam, keeping water level roughly unchanged. $\endgroup$ – Mołot May 15 '17 at 16:38
  • $\begingroup$ System-wide, the water level will be unchanged. What do your mean by "we will get 1/10 of water at the entry point"? (I say that the river would immediately run 10x faster. Thus, the river level inside the bubble would suddenly be much lower; that's not the same as getting 1/10th the water.) Regarding the dam: you're right, the water would pool up at the end -- and on the inside -- of the bubble. $\endgroup$ – RonJohn May 15 '17 at 16:51
  • $\begingroup$ Would the damming action occur if the river exit were 10x as wide? $\endgroup$ – RonJohn May 15 '17 at 16:56
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If the river outside the city was flowing at 5mph (which seems to be an average speed for a river), and you speed up time by a factor of ten, then the river inside the city will look like it is moving one-tenth as much water.

There are two ways for a river to move less water: (1) the water level could drop way down, so that the river is still moving water at 5mph but there's less water to be moved, or (2) the river could move much slower, so that it's moving water at 0.5mph but it's the same size river.

The water level probably doesn't drop, though, because the water level needs to be the same on both sides of the time bubble. So, unless the city specifically wants a fast river and they're doing something with pumps near the edge of the time bubble, you just get a 10x slower river.

In theory, if the time bubble accelerated time to move very very fast, you could get a situation where the river was evaporating faster than new water was flowing in. If this started happening, you would get weather weirdness -- there would be lots of rain from all the water vapor entering the atmosphere. But you probably aren't accelerating time that fast.

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Simple, as soon as the water enters the sped up time, the river falls into a trickle. There simply isn't enough water being fed into the river fast enough once it enters the city.

Interestingly, this has the opposite effect on the other side of the river. Water would be coming out so fast and in such a small stream that it would almost be like a super pressure washer that would likely allow the river to resume at an appropriate distance away from the city.

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  • $\begingroup$ Same volume, but faster flow rate. Tee hee. $\endgroup$ – Draco18s May 16 '17 at 17:00
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I would tend to agree with JustSnilloc's answer except it is more of a Newtonian response. What if you used the principle of quantum entanglement to justify the flow of the river as being unchanged. Admittedly this is more of a notional thing and not a purely scientific response, but it might go something like this:

The water inside the bubble "knows" there's water feeding it and accepting it outside the bubble so it just flows as normal. No change.

Not sure how to handle the removal of water inside the bubble, but I suppose from the inhabitant's point of view, it might be just the same as removing water outside the bubble.

So essentially the same answer as the first couple of guys to respond.

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