Q: Are shadows 2-dimensional? Are there any real examples of 2-dimensional things in the universe?

Physicist: If you think of a shadow as the lack of light created by an object blocking a light source, then shadows are 3-D.  After all, it’s dark everywhere behind an object, not just on the surface of another object.

Is a shadow the dark volume behind stuff, or the dark surface on other things?

If, on the other hand, you define a shadow to be what we see and intuitively think of (the dark, parroting person on the wall, with whom you can shadow box) and not the volume in between, then shadows are 2-D.

However, that second definition is a little abstract, because there’s no real physical significance.  You could say that the border between countries is a one dimensional line along the ground, but there are no physical laws that have anything to do with national borders, so it doesn’t matter.

Defining exactly where the surface of an object is (what with all of their atoms) is like trying to define exactly where the surface of a ball pit is.

It’s impossible to get something that’s genuinely 2-D in our universe for several reasons, the simplest of which is that atoms themselves are 3-D.  So even the flattest flat thing will still have some 3-D-ness (at least a quarter of a nanometer or more).  That said, there are innumerable examples of things that behave as though they were 2-D.  In situations where one direction is restricted compared to the others you’ll often find that the physics follows suit.

Hurricanes and other very-large-scale weather phenomena roughly obey 2-dimensional physics.

For example, ripples on the surface of water are an example of 2-D waves that behave very differently from ordinary 3-D waves.  Weather systems that are substantially bigger across than they are tall, like hurricanes (e.g., Sandy was about 800 miles across, and only about 5-10 miles high), roughly obey 2-D fluid dynamics.  Normally the energy in a fluid (or gas) starts out with big eddies and moves into smaller and smaller eddies (you can see this if you pour cream into some coffee and then stare at it).  However, very weirdly, in a 2-D fluid you find that the opposite tends to be true: energy starts out in small eddies and moves to larger.

If it weren’t for the flatness of the atmosphere (and some obscure math involving “entropy flow” in 2-D fluids) we wouldn’t get hurricanes!

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15 Responses to Q: Are shadows 2-dimensional? Are there any real examples of 2-dimensional things in the universe?

  1. David Sher says:

    Orbits of planets and moons seem to be 2d. I’m no astrophysicist though.

  2. Amir says:

    I believe this “However, very weirdly, in a 2-D fluid you find that the opposite tends to be true: energy starts out in small eddies and moves to larger” part needs an answer gravy.

  3. The Physicist The Physicist says:

    It really does need some gravy. Unfortunately I can’t remember where I read that particular derivation. It’s in a book or paper or some notes or “other” on “non-equilibrium statistical mechanics” (which is like thermodynamics, but totally off the hook). It was something like; start with the Fokker-Planck and Navier-Stokes equations, and conservation of mass, then re-write all of it in terms of their the Fourier transforms.
    Then, after a day or two, ask for help (because that mess is pretty tricky). You find that in two dimensions the Fourier spectrum tends to “drift down” over time, which means that the size of the “structures” in the fluid get bigger.

  4. The Wonderer says:

    Could you post what the final Forrier transformation looks like?

  5. Buck Field says:

    Again, from a risk management point of view, it is a terrible idea to assert that the existence of hurricanes (physical reality) is dependent on concepts in people’s heads, i.e.: “obscure math involving “entropy flow” in 2-D fluids”.

    This violates a basic foundation of science, that reality exists independent of our perception, and given the profound impact of language on cognition, the “just an expression” justification does not stand in light of persistent, fundamental mysteries.

  6. David Blakey says:

    Wouldn’t rainbows or the the resultant prismatic effects of refraction two-D?

  7. Firepac says:

    If you have a projector and you project an image onto a screen, that image is 2D.

  8. Anthony ratay says:

    I think rainbows and the projector would fall in the same category as the shadow. There is depth to both the rainbow and the projector if you consider the space between the source ( the projector lense) and your eyes or camera iris.

    Are there any examples of anything other than 3 dimensional structures or systems in the universe?

  9. Paul Czerner says:

    A shadow is not a thing, it is the lack of a thing. And in the universe, an object is also the lack of every other object in the same space. That does not make the lack of everything else a 2-dimensional object.

  10. Adventureless_Hero says:

    The image on the projector screen would still have to form to the contours of the screen itself, which if looked at closely would have an uneven surface due to the rise and fall of the atoms that compose it.

    The same for a rainbow, only the canvas would be rain droplets in the sky instead of a projector screen.

    For examples of extra dimensional objects in our 3 dimensional world I figure black holes might come up. *I am so not ready for that can of wormholes…er uh worms*
    I imagine a 2d object escaping it’s constraints by bending the space it occupies; dot on a paper can’t move up or down unless you bend the page. So if a black hole rips through the 3d space we occupy, does it punch through to the 4th dimension? Are atoms compressed so tightly within a blackhole’s center they are smooshed into a 2d or 1d universe? I don’t figgin know! But it’s fun to think about. lol

  11. Mike Knight says:

    I’ve always imagined that at some point within the sub-atomic level as matter gradually transitions into energy strings there are real 2-D particles with energy strings being 1-D. The pure thought or pure information level that programs our reality could be considered 0-D.

  12. Richard courtright says:

    Mike you are absolutely correct about 0-D ,I have been thinking about similar stuff myself.

  13. Paul Moore says:

    Discounting the surface an image is projected onto as having dimension simply because the image clings to that dimension, but is not part of that structure, and discounting the “space between” a light source and it’s shadow as an entirely different structure than the image, I don’t see why both a shadow, a projected image, or the image on the shroud of Turin would not be considered 2D.

  14. ... says:

    I think it would be hard to conclude that it would be 2-d. Since we are aware of 2-d models I think we are biased in a way to be able to imagine 2d information out of patterns like the dark spot made by an object blocking light. The space in the shadow is exactly the same space sans photons traveling through it in reality. We may ultimately see that process as a darken triangle given the proper perspective. Also since an object like the shroud of Turin is made up of atoms which themselves are 3 dimensional structures it would be impossible for the combination of 3d structures to yield 2dimensional outcomes.

  15. Anthony says:

    Just to keep this going, the shadow and rainbows are also technically illusions that our brains construct to give a useful sense of depth and place in space.

    The shadow is just a tonal shift in the base color of the object cast in shadow. The tonal shifts are obviously due the the amount of light reflecting off its surface. The rainbow as stated above is a collection or system of droplets being struck with light which gives the rainbow effect. It only seems 2d because of our perspective from the ground. It has other notable qualities which are all visual effects and dependent on water droplets. It seems infinte but…… :)

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