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The world is an infinite plane with an Earth-like surface. It has an atmosphere, but it has finite height

Because of this, and how fields work, this should give us the same gravity all the way up, which has implications for light; all light that leaves the atmosphere will eventually turn around and hit the ground, as no matter how high it travels up, it will still be under the same gravity, and so it must eventually be turned around and fall back to the ground. And due to the atmosphere's finite height, it stands a decent chance of reaching the ground again

This raises the question of what that would actually look like. Specifically, what images would these falling beams form when seen by the human eye?

Ichthys King
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5 Answers5

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Frame challenge: Atmospheric collapse

You have an infinite plane with infinite matter, initially evenly distributed with an initial density of an earth-like atmosphere, or about 2-3 x 10^25 particles per m^3.

That matter has mass, and that mass has gravitational pull. Molecular clouds with a density of a mere 3*10^8 particles/m^3 are considered stellar nurseries, and we're exceeding that by seventeen orders of magnitude.

Daniel B
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    Day by day people would notice fires burning brighter and faster. And their voices getting lower and lower. – Willk Jan 31 '22 at 02:04
  • How could there be a 'boundary' to the atmosphere, if gravity were constant? No matter how 'high' up, the gravitational pull on an atmospheric particle would be the same, so the atmosphere would stretch forever, and the atmosphere itself, having mass, would 'pull' everything towards it, like the inside of a sphere. There would be no gravitational pull. – Justin Thyme the Second Jan 31 '22 at 14:04
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    The atmosphere has a finite height, and, more importantly, has a gravitational pull on itself. – Daniel B Jan 31 '22 at 16:32
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    And the atmosphere is not, and cannot be, perfectly uniform to start. (If nothing else, thermal fluctuations are enough). – TLW Feb 01 '22 at 01:53
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    This. Also, don't forget why all celestial bodies are spherical: It's because gravity is powerful enough the differential forces non-spheres experiences are strong enough to collapse them to spheres. This flat 2D planar "Earth-like surface" will find local pockets of high density. Planets slowly form around them. This is in addition to Daniel B's stars slowly forming from the atmosphere. TL;DR when a system is not in equilibrium, it tends to be forced towards equilibrium. And infinite energy means this happens really fast (geologically speaking). – Ton Day Feb 01 '22 at 04:25
  • But a slab of infinite atmosphere pulls itself equally in all directions, it should be a "there's no gravitational pull from a hollow planet if you are inside of that planet" type of deal. On the other hand, there are inequalities in thickness, caused by the geography of the infinite plane. – Darth Biomech Feb 01 '22 at 13:38
  • @TLW If it were a perfectly flat infinite plane why would there be thermal variations? There would be no rotation, no seasons, no temperature fluctuations. – Justin Thyme the Second Feb 01 '22 at 16:35
  • @Ton Day Since there is no end to the plane, and thus no edges, the 'pull' would be uniform throughout. There could be no 'unbalanced edge effect'. – Justin Thyme the Second Feb 01 '22 at 16:38
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    @JustinThymetheSecond - I think you have several fundamental misunderstandings here. Too many to answer fully in a single comment. Some pointers: a) gas molecules have a distribution of velocities, even if the gas is at a single temperature, b) gas is made up of atoms, and as such cannot be perfectly uniform in the first place c) it's a positive feedback loop, d) dirt is nonuniform at these scales. – TLW Feb 02 '22 at 02:35
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    You might also look up the Jeans instability (and star formation in general). It's not quite the classic case because this starts in 2.5d, but the same issues apply. – TLW Feb 02 '22 at 02:38
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    @DarthBiomech - as an aside: the pull anywhere inside a hollow spherically-symmetric sphere is zero. The pull inside a hollow cylindrical-symmetric hoop is non-zero, except at the exact center of the hoop. I wish this was always taught at the same time as the Shell theorem... – TLW Feb 02 '22 at 02:42
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    @DarthBiomech - it's an unstable equilibrium. It will collapse once a perturbation occurs - and, it being a gas with nonzero temperature, will have perturbations. – TLW Feb 02 '22 at 02:44
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Rainbow skies, happy times

The world described would seem to be a dark world, since any Sun would have fallen to the ground far, far away. It would seem to be a doomed world, with all heat energy going up and coming back, like the heat death of the universe brought to a human scale, with tribes huddled around geologic deposits. But that's not the way I want to go, so...

  • The sky is a vast and lovely aurora. Whatever bizarre physics or gods made this world, they left behind a little gas far, far above the world. It falls without limit and lands as powerful cosmic rays. These particles strike the atmosphere and light up the planet.

  • We can calculate how far light goes before it has to come back. Every kilogram of light has a potential energy of 9.8 m/(s^2) times however many meters high, times 1 kg. Every kilogram of light has (3E8 m/s)^2 of total energy. So by the time it gets to about 1E16 m (1 trillion kilometers) high, the light is redshifted to nothing and has to either fall back down or disappear. (comparing black holes, this distance might be halved for reasons I don't understand but might have to do with both the light and the spacetime being pulled by gravity) We know light bends in gravity, so unless it goes perfectly up, I'm betting it falls back down. This adds a steady "Earthshine" glow to the background.

  • But ... it'll keep accumulating energy until it roasts? Nope. I'm going to say that the planet, nay plane has a special trick to dump heat energy, because otherwise it isn't 'Earthlike' and that goes against the premise. My favorite is neutrino pair production - sending 3/2 kT of energy out on every single neutrino. Do that and you can have cooling spots somewhere that are keeping the planet at a steady temperature.

Putting this all together, the skies have brilliant rainbow aurorae stronger than Earth's, but this shares the light with a constant muddled background of Earthshine. The aurorae dominate where the currents of space are stronger, and the Earthshine can be tracked back in an arc to some far-distant horizon. If you look very closely, perhaps the outlines of continents can be made out in that background light, to the degree that they can be from a trillion kilometers away.

Mike Serfas
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  • Could there ever be such a thing as light traveling parallel to the surface? – Justin Thyme the Second Jan 31 '22 at 18:36
  • @JustinThymetheSecond light travelling parallel to the surface should fall, like any other object, and therefore curve to be no longer parallel. Additionally, the spacetime it is passing through should... not fall, but bend, by I think precisely the same amount. (Something like this comes up in the tests of light deflection by the Sun - Einstein predicted twice Newton's effect) – Mike Serfas Jan 31 '22 at 21:24
  • Which means there would be no such thing as light traveling parallel to the surface. It would always curve and always hit the ground. – Justin Thyme the Second Feb 01 '22 at 01:28
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(this answer assumes the thickness of the plane is about 1 Earth radius, that is about 12,000km, according to the link HDE 226868 provided in the comments, there will be 9.81g everywhere, on either side of the plane)

Paradise for a few weeks.. then it gets perforated, again and again

So how would the sky look, at first..

Depends on the atmosphere the gods arranged for your infinite flat world. Suppose the weather will be stable, suppose some Earthly gods were involved in the creation and you'll have oxygen, water, blue sky and sunshine.

A week after creation (see calculation below) the inhabitants would notice their plane starts to warm up.. End of paradise will come soon..

Every 96 days, your sun will impact and perforate the plane

There are no stable orbits around the plane. Everything will fall.. When would the sun arrive ?

enter image description here

This formula works, until light speed is reached. Fillin the values, suppose the sun 1 AE away from you, that is 149,597,870,700 meters. If you multiply that by 9.81 your sun won't reach light speed.

So invert the formula, enter s = 1AE = 149,597,870,700 meters in t square s / 0.5 g = 30,581,039,755, square root of that is 180,000 seconds, which is 48 days. Your sun will crash the plane and perforate it, proceeding its path through the plane and coming back again. After another 12 weeks, the sun will return and perforate your plane again, from the other side.

This can be prepared for, inhabitants could survive this: suppose your plane is infinite, the sun would arrive perpendicular, leave perpendicular and travel back through the same hole. Any place within 1AE of that point needs to be evacuated. Maybe it is advisable for the gods, to create a suitable hole in the plane, beforehand..

Blue shift

Your plane will now have a (local) "day night cycle" of 96 Earth days followed by a night of 96 Earth days, the sun oscillating through the plane.

Not only your sun, the whole sky accelerates toward you. This will cause the sky to be full of blue stars at night. Instead of red shift (expanding) your universe will show blue shift.

.. it goes into ultraviolet shift, your sky will get dark

When your plane has existed for a few months, the surrounding stars will start to approach with the speed of light. Remote stars and planets will reach your plane at light speed eventually, so you won't see them arriving. Their blue shift becomes an ultraviolet shift.

after that.. color oscillates, red-blue shifts alternate: purple skies ?

Disasters keep reoccurring, every few years the stars will return to your plane, perforating it.. and it will be quite difficult for the gods, to predict where these impacts will take place, to prepare holes for it. Suppose these gods are omnipotent, they could prepare holes in your plane for every star and black hole in your local galaxy..

The end..

After some 3 million years, the first neighbouring galaxies will start to collide.. and slowly, everything in the cosmos would come to rest on your plane. Oscillations would stop and every celestial object will come to rest in a hole, somewhere in your infinite plane. For black holes, these perforations will be giant. Light years of your plane will simply vanish. The inhabitants will have to move.. euuhm.. away from these perforations.

==========

NOTES about paths of light

I think locally emitted lights would not behave differently than light on earth, that is

Horizontal light rays travel horizontal until out of sight

Eventually, a horizontally directed light would reach the ground.. question is when and would that happen in sight ? I think not, with g=9.81 G the path of the light would not differ from Earth.

Vertical light rays travel very far away

There would not be any relevant effect. The light will travel against an infinite gravitational pullback and as Mike Serfas pointed out, the light will travel a trillion kilometers, until it comes to a standstill and fall back (?? I have to hand-waive this actually). But whatever happens, the distance is beyond any visible range, so the returning light will be so weak it can only be seen by Hubble.

Goodies
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  • Suppose the sun rotates in a circle above the plane. Either in an orbit perpendicular to the planetary surface or parallel or some angle between. Or an infinite number of suns rotating in an infinite number of orbits above the plane. – Justin Thyme the Second Feb 01 '22 at 16:43
  • @JustinThymetheSecond an orbit perpendicular to the gravitional field ? There are no orbits near this plane.. the peculiar thing about it: gravity force will remain constant g=9.81 everywhere, to an infinite distance! this requires a thickness of Earth radius, and the complete universe will crash onto the plane within ca 14 billion years, ref science based answer here https://worldbuilding.stackexchange.com/a/12443/627 – Goodies Feb 01 '22 at 17:08
  • Nothing in the question precludes an infinite number of suns in parallel orbits one on top of reach other in a cylinder shape 'all the way up' instead of 'turtles all the way down'. Give each sun enough mass that it pulls the sun in the orbit in the 'cylinder' below it from 'falling down'. Make all the gravitational forces balance perfectly. If you are talking about infinity, go all the way. This is obviously a 'parallel universe' that has formed somewhat differently to ours. – Justin Thyme the Second Feb 01 '22 at 17:31
  • @JustinThymetheSecond anything will fall onto this plane, because the gravitational force of g=9.81 will exist irrespective of distance from this plane. On both sides. The plane has infinite mass. Check out Samuel's answer in my link. I have tried to put some consequences of that. The opener's gods have created a great attractor nothing can escape from. If your suns are ordered in a cylinder, they will all start to spiral down, toward the plane. g=9.81 will simply add a accelleration/velocity vector toward it. The complete universe will start moving toward this plane, after its creation. – Goodies Feb 01 '22 at 17:44
  • Exactly WHAT keeps 'this plane' in 'position'? The plane could be 'falling; just as fast as the suns are falling towards the plane. – Justin Thyme the Second Feb 01 '22 at 18:06
  • Nope, this plane won't go anywhere. It will stay where it is created, unless the gods provide it with an impuls, in some direction. In that case, the plane will move in that direction eternally, with constant speed. When the plane is created stationary by the gods, it will stay put under all circumstances. Even the largest impacts cannot move it.. because it has infinite weight. A sun, or a black hole could punch it and travel right through.. the plane itself won't leave its position. It can't be moved, because an infinite mass can't translate kinetic energy from a collision into impulse. – Goodies Feb 01 '22 at 18:37
  • In that case, the suns' orbits have been made immoveable. – Justin Thyme the Second Feb 02 '22 at 15:29
  • @JustinThymetheSecond stars have no infinite mass, the plane has. The sun will fall into the plane, it will not remain in any orbit, let alone go stationary. All stars will start moving toward the plane. They will keep (some) orbit around their galactic center as well, but eventually, this orbit will not remain.. even the galactic center itself (black hole) will fall onto the plane. I find that a fascinating idea. Nature does not handle "infinite size" well, but when the question was put here, I did not realize the consequences. After reading Samuel's answer in the other topic I put my answer. – Goodies Feb 02 '22 at 15:54
  • And there is no such thing as an infinite flat plane. Your point? – Justin Thyme the Second Feb 03 '22 at 05:05
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What is up there? Can the light hit it?

You discuss light leaving the atmosphere then turning around and hitting the ground. If it must turn around to hit the ground I take that the ground is the source of light. OK; glowy ground. That will make for a sweet anime.

/It has an atmosphere, but it has finite height/

It is not the atmosphere that has finite height but the plane or dimension itself because /all light that leaves the atmosphere will eventually turn around and hit the ground/. It is possible to leave the atmosphere. I take from this that the boundary of this plane is some distance above the glowy ground and the atmosphere.

The question I have is the nature and position of this boundary. If the boundary is so far away that light leaving the ground never hits it before turning around, it does not seem relevant to the question of light. If this boundary is close enough to the ground that light leaving the ground hits it before the light can turn around, then what it looks like depends on how the boundary works - whether it emits light, reflects light, absorbs light etc.

Willk
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  • If gravity is equal 'all the way up' why is there a boundary to the atmosphere? There is no 'escape velocity'. If you can jump off the ground, you can jump into space. – Justin Thyme the Second Jan 31 '22 at 18:33
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It Seems Like Your Describing An Infinite Mirror

All of the light gets turned around, eventually. Depending on the height of your atmosphere, and the size of the dust and other particulates in it, this light gets scattered to a varying degree - blue first, then other colors. It may be impossible to clearly see the ground reflected above them, but maybe some larger structures like mountains and forests can be dimly seen reflected in the sky.

But when the light comes back down, it is absorbed by the ground. Since the universe ends at the “sky”, it would seem that all new light comes from the ground. Maybe that’s your intent. Or, maybe this is a one-way mirror, and new light from beyond can enter the system. And some sort of heat balance takes the excess energy and dumps it on the other side of the Earth, or an effectively infinite (for the time frame of your story) heat sink in a cold core.

James McLellan
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