# Is there any thing composed of elementary particles in this world that is not 3 dimensional? [closed]

Is there any thing composed of elementary particles in this world that is not 3 dimensional? I know that there is graphite which is singular atom thick. Is there anything in this world that has no depth? So I guess what I am asking is there an object that does not have volume

## closed as unclear what you're asking by Jon Custer, user108787, Wolpertinger, Qmechanic♦Nov 8 '16 at 13:10

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• Welcome on Physics SE :) What do you mean by 3-dimensional and what by objects? – Sanya Nov 7 '16 at 21:48
• For 3 dimensional I mean it has depth – user135530 Nov 10 '16 at 16:30
• @annav - nope. That's not an appropriate suggestion at all. – ChrisF Nov 13 '16 at 19:52

If by object you mean something composed of elementary particles then there are no two dimensional objects due to the uncertainty principle.

If we take the direction normal to the surface to be the $z$ axis then the uncertainty principle tells us that:

$$\sigma_z \sigma_{p_z} \ge \frac{\hbar}{2}$$

for an object to become two dimension would require $\sigma_z \rightarrow 0$ and that implies $\sigma_{p_z} \rightarrow \infty$ and therefore requires infinite energy.

However there are many examples of systems that are approximately two dimensional. Graphene would be a good example.

Even if you're willing to relax the requirement for the object to be something physical then I'm still not sure anything can be truly two dimensional. The example that springs to mind is an event horizon, but this is a classical concept and quantum gravity effects may well blur it into a region of finite volume. I suspect quantum mechanics will forbid anything from being truly two dimensional.

• Yes by object I mean somehting composed of elementary particles. Sorry! Should have been more specific. – user135530 Nov 8 '16 at 16:35

Coastlines, for example. Coastline of Great Britain has fractal dimension of 1.25. Source: https://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension

• Any real coastline gets blurry at some level, either because of the water going back and forth, or, if you really want to get deep, because at the atom level there is no well defined coastline. This looks like an illustration of a mathematical concept, not an actual physical fractal. – Javier Nov 8 '16 at 3:01
• I'm unconvinced that a coastline is an object ... – John Rennie Nov 8 '16 at 7:59