This afternoon I was talking to my brother and somehow we began discussing the theoretical behavior of a perfectly flat, two dimensional object that exists in a three dimensional world.

Here's a few of the conclusions I came to:
-The surface of the object would be perfectly flat, therefore the object would experience no friction along its two sides. There might be friction along its edges, but this is negligable since nothing would ever meet the edge of the object head on.
-You could stack the objects face to face infinitely without taking up any amount of space.
-The objects, being perfectly thin, could move through anything their "edges" come into contact with. Dropping such an object into the ground would cause it to fly "through" the ground, straight to the Earth's core.

But what kind of behavior would you predict from a perfectly flat two dimensional object in three dimensional space?

While conceptually possible, 2D is very likely not a real physical phenomenom, so it is impossible to draw conclusions from such a concept. You can only speculate what it could behave like.

Perhaps it is best seen as how massless particles behave, while we are all familiar with mass particles. Yet somehow massless particles interact with us. Two dimensional objects are only able to interact in the way they have a surface, as you describe. Although I do not know the mathematical implications of such a particle design, it could be that it forcefully requires its width to pop up in a different form of space and energy than we know, that on that level is where interactions with, like, gravity, are physical.

But these speculations are entirely unfound and just made up. Without a little scientific backup for a 2D particle, I can't provide much more.

The real world in nono-scale is more like you building something from legobloxks or rubber balls.

You will never have a perfectly 2 dimensional object.

If it where perfectly 2 dimensional (thin), it would simply be transparent for everything, and thus not noticable.

The object in question is comprised of two dimensional particles like Joozey was talking about. The object doesn't have any depth to speak of, so it completely lacks mass. Nevertheless, while it lacks volume, it still has area, so the object could be thought of as a two dimensional plane in 3D space.

It must have a depth though, there's no possible way it could exist.
If it were possible it's volume would be (depth x area) which as you're saying would be (0 x area) therefore always resulting in 0.

Or what if a 3D object were to travel along the non existant axis of the 2D object, as the 3D object could not collide with the 2D object as it has no depth and would occupy the 2D objects space, therefore the 2D object would not be able to exist at where it is.

but quantum physics do what they want, and don't necessary follow silly laws like volume=depth*area. Events on quantum scale do not naturally roll into our macro scale due to quantum dilatation, but scientists are able to force events into our measurable realm. Who knows what else is possible when we are able to control that area better.

A century ago massless particles were an absurd idea too.

Perhaps it turns out gravity is a 2D plane into our 3D dimension. We experience its force but it's caused by nothing we can measure. The 2D object redeemer describes might translate a bit differently in the real world than the concept. It is probably not as straightforward as line->square->cube. Dimensions might work in a different way. It is just a simple way to illustrate how different dimensions are constructed. A 2D particle in the 3D world might thus translate as a quantum particle (2D) affecting macro particles (such as protons and neutrons, 3D).

maybe gravity is simpler than we think..

Anyhow: this 2D/3d discussion shows the differnce between
Math and Physics.

Its like the idea in Math, what will havppen if you close up
to an object, every step going half the distance from before.
Will it ever reach the object?
In physics this is nonesense, because there is a limit of
how small distances you can move something.
Below that its uncertain how it moved at all.

who knows the novel flatland?