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Time dilation


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#1
RBT

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So as we all learned in chapter 17, time passes sower in the Abyss than it does on the surface. Or what is the same, time on the surface passes faster than in the Abyss.

 

Let's assume that 2 weeks in the 5th layer equate to 3 months on the surface. (ch 17)
 
14 / 90 = 0.1555...
Let's invert that so it's easier to understand.
90 / 14 = 6.4
 
So time passes 6.4 times faster on the surface than it does in the 5th layer. Now let's assume that the time dillation is linear with the depth and take the depth of the 5th layer into consideration.
The mid point of layer 5 is 12500 meters deep, so we'll use that for our calculations. We'll work with kilometers.
 
(90 / 14) / 12.5 = 0.514
 
And that would be the slope of our function.
 
time flow on the surface (X) = 0.514 * X
Where X are km
 
At a depth of 0 km, the time on the surface would go 0 times as fast as the time at km 0, which is also the surface. Hurr.
At a depth of 12.5 km, time on the surface would be going 6.4 times faster, which we already knew.
At a depth of 14.25 km (the middle point of the 6th layer), time on the surface would go 7.3 times faster.
At a depth of 16 km (somewhere in the 7th layer), time would go 8.2 times faster.
At a depth of 20 km, the deepest point that shows on the map from chapter 7, time on the surface would go 10.28 times faster.
 
So if we assume that the bottom is at 20 km, more or less, Ozen's guess that the 10 years Riko has spent on the surface would be only 1 year for Lyza is correct. (ch 17)
 
Remember that this is based on two very wild assumptions:
1. the flow of time between the 5th layer and the surface
2. the fact that the time dilation is linear with the depth

Edited by RBT, 18 July 2017 - 10:28 PM.


#2
BottomlessBag

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So looking at the numbers here, at the highest possible depth for the 4th layer (7km) time passes at 3.598 faster on the surface.

 

Nanachi's camp is located below that limit for for arguments sake lets assume she is at this same depth. While it does vary from person to person Riko remains at Nanachi's house for at least a week which is long enough for scar tissue to develop after her second surgery. They might have said how long she actually was down there but I'm not sure. At the current figures 25.186 days have passed on the surface during that one week for Riko & Crew.

 

The reason I'm curious about how much time they were down on the 4th layer is because of the extra story dealing with the birthday sickness. Jirou did fact honor his word to let Riko go if she got to the second layer, he's back on the surface and then the events of Extra 2 happen and I have been wondering how much time passed between that first day for Riko, and when he goes to see Ozen.


Edited by BottomlessBag, 20 July 2017 - 02:39 AM.


#3
Aereus

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I'm not sure how much the whole time dilation thing is supposed to be relevant anymore. An interview with the author mentioned that was originally supposed to be the nature of the curse, but after discussions with his editor, the idea transformed into what we have now: progressively worse physical/mental ailments. With that being the case, I dunno if we're still in for an "Inception" scenario where Lyza only had say, a year go by while Riko grew up over 10+ years.

 

I'm also left wondering why Lyza would choose to go on the Last Dive knowing how much she loved and risked to bring Riko to the surface. Hopefully that is revealed in time.



#4
smol potato

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Would people stop aging with this curse since Riko looks just about the same even though she made it all the way to the 6th layer...? Or maybe she just got there pretty quickly...



#5
gothicshark

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I've been thinking about this a ton after I read chapter 42. 

 

I've been wonder what the time line has been here. 

 

possible spoilers:

 

Lets consider how long she has traveled on each layer. 

 

Orth - 2nd layer less than a day.

2nd layer approximately 2 weeks (maybe more)

3rd layer at least 2 days. 

4th layer between 1-3 months. (6 months at least if in the modern word.)

4th layer travel to 5th 2 days

5th layer 3 - 4 days

6th layer 2 days (by chapter 42)

 

If we use the math above

 

1st layer  = (.85km * 0.514) =  1/2 day 

2nd layer  = 14(2.9km * 0.514) = 20 days 

3rd layer = 2(5km *0.514 ) = 5 days

4th layer = 90(7km *0.514) = 324 days

4th to 5th layer = 2(10k * 0.514) = 10 days

5th layer = 3(12km * 0.514) = 18 days

6th layer = 2(15.5km * 0.514) = 16 days

 

Riko time = 4 months or 114 days

Orth time passed since Riko left = 1 year 1 month or 393 days

 

I wonder what the time passage really is. Also what if she spent more than 90 days recovering? 


Edited by gothicshark, 13 October 2017 - 07:06 AM.