Oh gods can we get any more off-topic *wink* [was Re: [Python-ideas] Inconsistencies]

[Steve D'Aprano]

On Thu, 15 Sep 2016 04:02 pm, Random832 wrote:

> On Wed, Sep 14, 2016, at 23:12, Steve D'Aprano wrote:
>> Yes it does. Even an infinitely large flat plane has a horizon almost
>> identical to the actual horizon.
> 
> Your link actually doesn't support the latter claim, it goes into some
> detail on why it wouldn't if it were infinitely large due to
> gravitational effects on light.

No, the horizon would still be horizontal. It merely wouldn't *look*
horizontal, an optical illusion.

And even there, I have my doubts. In a universe where at least one
infinitely large flat planet existed, gravity would clearly have to be
significantly different from our universe's gravity, lest the universe be
destroyed.

In the scenario given by the article, the flat earth is acting as a
Newtonian black hole: light cannot escape the planet. In addition, anything
that came into range of the flat earth's gravity -- which would be
*everything* in the universe -- would experience a 1 gee force[1] towards
the earth, no matter how far away it was. There would be a steady rain of
meteors, comets and even stars onto the planet.

The planet would also be gravitationally unstable in the horizontal
direction. Consider a single atom somewhere in the flat plane. It is
gravitationally pulled by an infinite number of other atoms in one
direction, say to the left, balanced by an infinite number in the opposite
direction, to the right. But those infinite forces will only be in balance
if the body of the planet is utterly, perfectly, 100% uniform. Any tiny
variation in density will lead to an inbalance in one direction or another,
which will increase the variations in density and hence increasing the
preferential gravitational force.

For a normal planet, the gravitational forces are typically smaller than the
electromagnet repulsion of atoms to each other, and so there's a limit to
how densely packed the planet will be. But in an infinitely large planet,
the forces can increase without limit, leading to the planet either
collapsing into a relativistic black hole (it's already a Newtonian black
hole!) or being torn apart. Or both.

In any case, even if the earth is flat, it's not infinitely big. We know
that because some stars dip below the horizon. Unless there are convenient
tunnels for them to travel through...


Personally, I'm more fond of the Hollow Earth theory. The earth is a sphere,
but it's a hollow sphere, and we're on the inside...

:-)




[1] Yes I know gee is a unit of acceleration, not force. Someone else can do
the dimensional analysis, there's a limit to how much care I'm going to put
into counter-factual physics like infinitely large flat planets.


-- 
Steve
“Cheer up,” they said, “things could be worse.” So I cheered up, and sure
enough, things got worse.