Is there a true one-dimensional object?

Question

I'm reviewing and expanding my knowledge of dimensions.

We live in three spatial dimensions but, apart from volume, we also have the concept of surface and curve. However, if you write a line on paper, it won't be a true two-dimensional object since you can assign a volume to the ink. Similarly, the paper itself has some non-zero width.

Therefore, it seems to me that we can't have a two-dimensional object in a three-dimensional environment. Maybe the best realization of this idea is to consider the image from a screen: we can see two-dimensional output on computer monitors; each pixel has length and width. However, is there a true one-dimensional object?

What I mean by "true" is something that can be observed in our 3D world, as opposed to a false example, such as a line on a piece of paper that becomes a 3D object when zoomed in.

Answer 1

As far as we know, there are no one-dimensional objects in the real world. A one dimensional object (an object that has length but no width or height) is a mathematical abstraction.

Having said that, there are objects in the real world (like long strings or wires) that are approximately one dimensional, because their length is very much greater than their other two dimensions. And it can be useful to use a one-dimensional model to describe and think about such objects. But do not confuse the model with reality.

Answer 2

While other answers have pointed out that there is no 1D or 2D “physical object” in the real world, you could make the argument that they do exist depending on what you mean by "object".

If you accept that points in space exist then there is no reason you couldn’t specify some set of points which define a plane or line segment. Sets of points like this can correspond to meaningful physical boundaries too. @Vincent Thacker has pointed out that a Kerr black hole has a 1-dimensional singularity; additionally, the black hole event horizon is arguably a 2d surface. The edge of a wavefront traveling through space is a 2d surface, and relatedly an observer's "light cone" is a 2d sphere expanding at the speed of light.

Answer 3

Ideal mathematical objects only exist in human imagination, not in the real world. It sometimes happens that a particular mathematical object is a useful (if imperfect) model for something in reality.

Answer 4

Actually, if you think about it, there isn't anything that's 3 dimensional either.

Any physical object is made of atoms. The frontier of such object is undefined (since atoms & electrons do move and interact with other non object atoms). Atoms are made of quarks and bosons and leptons and none of them have an actual position in space (you can estimate the most probable position by using a quantum wave function)

So you have to define a limit to your mental model.

If your limit is: the set of atoms for this object at a given time, then a 1D object does exist. You can make a single layer of atoms (think graphene) or a single chain of atoms.

In reality even the 3 dimensions are just a convenience representation of an overall infinite distance in 2 dimensions or less.

Take this thought experiment:

1. I'm using a spiral. It's a 1 dimensional object that's defined by its step p and the angle of rotation w. Every (2 pi + w) rotation, the point on the spiral is one step away from the point that was at w rotation.
2. Yet you can locate any point on the spiral by using a single dimension: the distance from the origin l. That's the distance an ant would have traveled from the origin to your point.
3. A spiral lives in a 2 dimensional plane where you normally need 2 coordinates to locate any point.
4. Now, choose any point A in this 2 dimensional plane and find the closest point on the spiral. Let's call the distance between this point and the spiral d
5. It's very easy to demonstrate that this distance d will be zero when the step p of the spiral decreases to zero.
6. There you have a mind blowing issue: the point A that's requiring 2 coordinates in 2 dimensional space can be found with a single coordinate l: the distance traveled on the spiral (that will reach an infinite distance when the step decreases to zero)

Since there is a minimal distance (the Planck's limit), where it's impossible to measure a difference in spatial position, it means that where d is zero, the step p isn't zero so l isn't infinite.

Thus the 2 dimensional coordinates can be expressed in a single dimensional coordinate that's not infinite but very very large.

Similarly, you can express any 3 dimensional position with a single coordinate: the distance traveled on a space filling curve with infinitesimal step => Everything is just 1 dimension anyway.

So the answer is yes, every object is a 1 dimensional object.

Answer 5

In reality there's no 1D objects, nor 2D objects, everything has width, height and depth. Even molecules, atoms and electrons (although many particles in some branches of physics are modeled as zero dimensional objects (dots), where their shapes can be considered irrelevant).

Pixel is like rectangle

No. Here's your zoomed-in pixel of LCD display:

Blue spheres are LCD crystal molecules which when controlled by electrodes current changes configuration and alignment and by that polarizes light in one or the other way.

Green-transparent blocks are electrodes which manages electric current.

Red-transparent blocks are orthogonaly polarizing filters.

So LCD display smallest controllable element "pixel" is like everybody else in this world,- a 3D patch.

Answer 6

It really depends on what you mean by "object". There are mathematical objects of 1 (geometrical) dimension, like curves. Also, there are mathematical objects of 0D, like points, of 2D, like surfaces and also of higher-than-3D, which we cannot visualise, like hypercubes (an example is the 4D tesseract). And all these can realate to reality, e.g. a line representing the distance over which to measure a height, or a surface representing the surface area of a roof, and so on.

But if you by "object" mean a physical, real-life, tangible object or maybe particle, then there really is nothing that is not 3D.

Sometimes, certain categories of objects can be considered as lower-dimensional to all practical purposes in particular contexts. E.g. when working with human-scale sizes, an atom can effectively be considered as point-like, so 0D, when working with astronomical distance scales, a star or planet can effectively be treated as point-like, when rolling out a long wire, it can maybe effectively be considered line-like, so 1D, or when considering the interactions between charges in a capacitor, the capacitor plates themselves might be effectively considered a surface-like to an infinite extend, so 2D, and so on.

But there will of course always be an extend in all three dimension of any real-life object if your zoom-level is chosen fittingly.

Answer 7

Well, a simple example of a one-dimensional object is a string (consider it infinitely thin).

This string might be deformed and curved as much as you want. Interestingly enough, you can join together the two ends of the string, to create a (deformed) circle. In these cases the string would still be one dimensional, but it would be "embedded" in more dimensions. An example of a two-dimensional object embedded in three-dimensional would be a crumbled piece of paper.

Answer 8

‘1D’ is a mathematical abstraction. There are no ‘true’ physical embodiments of mathematical abstractions.