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I'm writing a novel centered around this concept. Imagine that an ancient alien race created a 'slice of Earth' (meaning an area between two meridians) and isolated it from the rest of the planet. The two border meridians are 'united with boundary conditions,' with continuity. So, a person sees them as if they are 'attached,' which, in reality, they are not, as there is the 'removed slice' in between. Essentially, the slice is completely isolated. What could be the evidence to look for someone investigating such a hypothesis?

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    $\begingroup$ What happens when you step over the boundary? Flora/fauna and landscape features suddenly jumping a few hundred miles might be a bit obvious, but what sort of answer are you looking for? $\endgroup$ Commented Jan 16 at 15:37
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    $\begingroup$ The answer to this question is entirely dependent upon how the boundary of this "slice" functions. Once you describe how it functions, the answer to this question will be any ways in which this "slice" would function differently from a world without it. $\endgroup$
    – sphennings
    Commented Jan 16 at 16:20
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    $\begingroup$ "What could be the evidence to look for?" Longitude is discontinuous? As I go west, and measure my longitude daily, it suddenly jumps 30°? As I move my head over the boundary the stars jump 30° forward and backward? $\endgroup$
    – AlexP
    Commented Jan 16 at 16:41
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    $\begingroup$ Not just the stars but the sun would jump to a different position as you cross the border - that would be pretty hard to miss. $\endgroup$
    – N. Virgo
    Commented Jan 17 at 11:31
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    $\begingroup$ Your question is very vague and impossible to answer. What do you mean with "isolated"? Is the slice moved to a completely different region in space, or are there just physical walls at the meridians that block crossing them? What does "united with boundary conditions" even mean? Do people from one side see the slice that was removed? Do they see the slice that was isolated? I have so many questions. $\endgroup$ Commented Jan 17 at 12:35

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Since you say "welded with continuity", I expect that the "magic" at work here qualifies as Enhanced Space, or Bigger on the Inside. Here you have "welded" a part of Earth into what looks like a space-time pocket, such as in an object containing more space than its outer dimensions allow. Therefore, the effects on the outside would be as follows:

  • When transferring the line, the sky would change, aka instantly shift the amount of degrees hidden; but there are kinds of spacetime pockets that also stretch observable spacetime metrics, so this might even not happen - you decide;
  • In case aliens were dumb, there would be a discontinuity in the landscape in form of a mountain or hill cut by the meridian, leaving exposed completely flat surface with residual layers, like in geology lessons;
  • In case they were actually smart enough to also cover the terrain discontinuity somehow, there will be harsh winds east/westward in places where a discontinuity like above would happen if aliens would be dumb, due to effective height difference being mitigated by the spacetime boundary;
  • The same should happen with ocean currents directed to the flatland, as water pressure on the side where it's ocean would push the water to the side where there's no ocean (elevated). Say if the east boundary has land elevation below sea level and the west one is above, the western side would be flooded;
  • Since both the above points add energy to the system by causing "free" elevation to matter, there should be excess heat developing at some points alng the boundary where the material anchors of whatever superstructure supporting the spacetime pocket are located, due to need to maintain the pocket closed and constant drain caused by exterior events;

Maybe more, but either the "dumb" or "smart" evidence should definitely happen, and in case of the slice being big, the sky shift upon travelling across the welded boundary would be noticeable. If the slice would be small, say 0.5 degrees or smaller, detecting this would be harder but still be doable.

On the inside - I expect it'll be eternal darkness, as the sunlight would have to also evade that part of Earth, or it would have to be redirected elsewhere thus making that part of Earth be seen from somewhere, space or surface.

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What you describe violates physics as we know it, but violating physics as we know it can generate interesting game or story settings. Assume that all visible/reachable parts of Earth really are an almost-sphere.

  • There would be a "dateline" with all sorts of strange effects when one crosses it. Even if a wanderer does not notice any difference on the ground, the local time would change suddenly. So would the visible stars.

    • In a sufficiently low-tech setting, shroud the border in perpetual fog and clouds. Or make it very high mountains with a few passes in deep shadows.
    • Alternatively, make the terrain flat, without orientation markers and with no means to mark the ground. Snowy plains or deserts with wind-swept dunes. How can you tell if the sun moved in the sky or if you lost your direction?
  • Some routes would inexplicably be shorter than they should be.

    • Put varied and hard-to-travel terrain on the "outer" side of the meridians to make sure that no caravan route is faster than it should be.
    • Sabotage attempts to survey the area through impenetrable forests, nasty swamps, etc.
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  • $\begingroup$ how would anyone know how long a route "should" be unless they already mapped the whole planet with satellites? $\endgroup$ Commented Jan 17 at 19:56
  • $\begingroup$ Most of Earth was reliably mapped way before satellites were invented. Surveying with 19th (or 18th, or most of 20th) century equipment is a lot of work, but accurate more than enough to notice that some routes are a few meters shorter than they should be. $\endgroup$
    – Pere
    Commented Jan 17 at 22:43
  • $\begingroup$ @Pere, go to the South Pole. Send four teams north at 90 degree angles to each other and make camps one kilometer from the pole. Start at one camp and travel west. You should go through three other camps before you come to your starting point, and the one trip which crossed the magic meridians would be shorter than the others. Hence my suggestions above how to obscure this fact. $\endgroup$
    – o.m.
    Commented Jan 18 at 5:25
  • $\begingroup$ @o.m. My comment was an aswer to the question in previous comment "how would anyone know how long a route "should" be unless they already mapped the whole planet with satellites?" $\endgroup$
    – Pere
    Commented Jan 19 at 10:30
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Map makers would find something odd

Already in acient egypt the circumference of earth was calculated to a high accuracy (-2.4% to + 0.8%).
These calculations grew more and more precise with ever more modern mathematics and equipment. However when the map makers started to make more precise maps of the whole world after the age of discovery, there seemed to be a disparity. The observed world seemed to always be a bit smaller then the calculated world. Given, early world maps were everything else than precise, but together with astronomy the coordinates of any point could actually be calculated pretty accurately.

The latest point in time where the map makers would have had a very serious dispute with the mathematicians would be the time where satelite images were used to cartograph the earth, probably earlier. When calculating the circumference with any mathematic approach, the result would always be bigger than that of any actual measurement. And the the difference would always be in the same ballpark leading to the conclusion that both seem to be correct and there is something "missing".

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  • $\begingroup$ +1 for pointing out that the circumference of our wonderfully spherical world was reasonably well known a long honking time ago, so it's only a matter of time between the first ocean-crossing ships and the first satellite when the existence of the slice is definitively known. $\endgroup$
    – JBH
    Commented Jan 17 at 19:02
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This depends on how the isolation trick works.

Harry Potter $\times$ Galactic Hitchhiker Style

In the world of Harry Potter there is a spell that hides a building by distracting people away from it. To the affected people, the spells makes it seems as though the buildings adjacent to the enchanted one are joined. People simply walk by, oblivious to the presence of the building. In this, Rowling took a page from Douglas Adams's SEP Field:

The Somebody Else's Problem field... relies on people's natural predisposition not to see anything they don't want to, weren't expecting, or can't explain. If Effrafax had painted the mountain pink and erected a cheap and simple Somebody Else’s Problem field on it, then people would have walked past the mountain, round it, even over it, and simply never have noticed that the thing was there.

This brings a couple issues here. Rowling's wizards used this trick to hide a 2 story house. Adams's aliens used this trick to hide a (possibly truck-sized) spaceship in a

For you: for every 1 degree of meridian you hide, we are talking about roughly 111km (69 miles) at the equator. This means someone in Brazil or Africa might traverse that distance and not notice that they've done so. That would take a LOT of distraction to happen without someone noticing. Maybe stick to seconds of degrees or less to make it believable.

Regardless of that: the distraction factor is implicit to both tricks I described above. In both cases, people are only able to even figure it out if first they have reason to believe that they are being played. In Harry Potter's case, people knew there was a house they couldn't see there, so they purposely put guards on the adjacent buildings to try and catch someone entering the hidden one. In Adams's work, the SEP field is defeated by catching it by surprise and/or with the corner of the eye.

In other words: people would naturally ignore the apparent discontinuity in flora, perfectly cut terrain and buildings etc. Until the moment someone points it out and everybody stops to have a second look. Then either the effect is dispelled, or people actually see that something is wrong but whatever technomagic the aliens have keeps people from being able to mentally process the isolated area.

Literally removing it

The Earth is a planet, which by the IAU's definition means a body orbiting a star blah-blah-blah but specifically one whose own gravity keeps it in a spheroidal shape. If you remove a relevant portion of a planet, it either ceases being a planet (such as the body that broke into what we current call the Asteroid Belt) or, more likely in this case, whatever remains collapses back into a spheroid again.

This will send shock waves through the globe, destroying whole cities worldwide. The fastest shock waves travel the surface of the crust at speeds of up to 8km/s, so they could cover the entire surface of the Earth in like 40-something minutes.

Those closest to the removed section will notice the missing parts immediately, but they won't live enough seconds to consciously understand what happened. The survivors elsewhere will know something happened. But probably only archeologists and scientists from thousands of year later will be able to figure out what happened.

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    $\begingroup$ Technically, Grimmauld 12 wasn't hidden by a SEP, it was hidden by Enhanced Space instead; and with Enhanced Space such tricks as requested are doable with relative ease. (It's just that building an enhanced space the size of a part of a planet is pretty difficult) $\endgroup$
    – Vesper
    Commented Jan 16 at 19:24
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Geologist might find evidence

As you mention that this was done by a "ancient" alien race, I guess the cut was done long ago. Probably tens of thousands of years ago, maybe even more. Back when they did cut out the piece, the boundary was quite noticeable for a dozen to hundreds of years. The sudden jumps in height along the boundary would have given it away quite easily. However if humans were around at all, they were on tribal nomadic level and aside from wondering a bit about the unusual landscape they accepted it. Maybe they even feared the border and it was a taboo to go near.

Anyway in the tens of thousands of years since then, errosion and tectonic has smoothed out the boundary to a point were it is not different from anything else anymore.

However geologists digging in that area will find something odd. When going through the geological eras they would at first find a homogenous landscape. But the deeper they go, the more the two digging sites (that are just a few dozen meters apart) diverge extremly.
Trying to understand this divergance, the geologists dig a trench from one site to the other and find something really odd. The once clearly visible jump in height is still there, just buried deep in the paleozon (or some other geological era).
That will get them thinking...

At the same time another geological team sits in a computer lab halfway across the planet. They are running a computer simulation on the tectonic shifts on earth, backwards in time, to see how the continents might have looked in the past. When hitting a certian point in time they observe a very curious arrangement of the continental plates: the edges of some of the plates align in a perfect straight line from north pole to south pole.
At first they think there might be an error in their simulation but they are unable to find it.
A curious anomaly.

Later that year on a geologists convention one of the "simulation team" might hear a lecture of the "digging team" about their curious find. They get talking and run the simulation again. And yes, that digging area was exactly on that "straight line" area, back when the plates aligned.
Reason enough for more research

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Circumstantial possibilities

  1. Is there such a slice that has coastlines closely enough matched that someone trying to create a map wouldn't realize there's a continuity problem? (This one is dependent on whether you're asking from the perspective of someone inside the slice or outside the slice.) Coastlines aren't the only problem, but they're an obvious one. If you're outside the slice, then having half a mountain disappear would be a problem (what would that look like? From one side of the barrier you see mountain, at the barrier it's a perfect cliff?).

  2. Is the slice wide enough that we can ignore weather discontinuities?

  3. Does the slice contain enough internal hydrology to continue to support life despite solar warming?

  4. Is the slice thin enough that there won't be a daylight disparity looking into one barrier? (This one is dependent on whether you're asking from the perspective of someone inside the slice or outside the slice.)

  5. How far out into space do the barriers extend? Far enough to guarantee that sunrise/set and moonrise/set occur where they should and don't suddenly appear on the wrong side of the slice? (I'm not sure that the barriers can extend far enough to guarantee this, thus the discontinuities of sunrise/set and moonrise/set would be the earliest and easiest indicator of something being very, very wrong — or at least leading to some wonky scientific theories. Note that how this one transpires is incredibly dependent on which side of the slice the observer is on. Insiders might come up with horribly complex astrolabes. Outsiders will figure out very early on there's a problem.)

Serendipitous possibilities

  • A meteor is seen crossing the sky to land somewhere to one's left... but it actually impacts somewhere to one's right due to entering the atmosphere between the barriers and then passing through one barrier.

And others...

  • What happens at the poles would be.... interesting... If someone stood at one of the poles, would they explode or be shredded (remember that per your rules the only "real space" is the quickly-closing-to-infinitely-small space inside the slice.) Similarly someone outside the slice... they'd have the same problem. Sucks to be Robert Peary or Roald Amundsen. In fact, there comes a point approaching either pole when someone could throw a rock toward the barrier and hit themselves in the back of the head. There's nowhere on Earth today where that can happen.

  • Ocean currents inside the slice won't (or likely won't) exist unless the slice is quite large. See my question about whether or not life can even exist (no prevailing westerlies to move heat around). That slice might be a perpetual winter (the more I think about it, the more it is.)

  • significant wind might not exist inside the slice, either. (The more I think about it...)

  • Better hope the bees don't die inside that slice.... (I'm rambling a bit on this topic, I'll shift.)

  • Regarding sunrise/set, If the arc of the slice is less than about, what, 18% of the circumference of the Earth? then people will see no sun until it rises above the barriers and potentially might see two suns as it passes over one barrier, then two again as it passes over the other. Man, this would be one weird world (if you could survive the cold).

As I typed, I began to realize that some of my first questions are resolved or, worse, made worse by later observations.... I've not taken the time to fix them. Sorry.

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If I understand your “boundary condition correctly” than walking across this boundary should cause sun to apparently “jump” by 15 degrees (if the slice was one 24th of earth) if on equator. That seem like something that would be noticed fairly early.

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