## 'Thickness'

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

### 'Thickness'

Hello! I have a question. As we, in 3D have only 3 extensions, and in 2D they have only 2, it is unable for us, to make any interaction with 2D, or any other dimensions. We imagine a 2D world without any thickness (any 3rd extension). But, if we add just a certain amount of 3D extension, we have a plane, with this minimal thickness, and the analogy still works, as we can locate a point in this plane with only 2 coordinates. Of course, if we say, that there is x dimensions, every dimensional world have all of the higher dimensional thicknesses. So we have 4-5-6-7... dimensional thicknesses too. If this is true, all of the other dimensional worlds can interact with each other. What do you think about this?
CollIB
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### Re: 'Thickness'

I've thought of that before but so far no one have detected the higher dimensional thickness

Either there are no large extra spatial dimension out there
Or our sense is adapted to 3D but not to other dimensions...yet
Secret
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### Re: 'Thickness'

Either there are no large extra spatial dimension out there

But if we think about gravity, the direction of the bending of our space time is a fourth direction. http://randomthoughts.ws/files/Gravitation_space_source.png
So interestingly, if you point your finger to the earth, you indicate a line, which goes out from our space time, seeing from a 4D perspective.
CollIB
Mononian

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### Re: 'Thickness'

Thickness in how many directions? A piece of string is a model of a 1d world, but has a 2d thickness perpendicular to the linear dimension. I suppose we could be all mr gumby?
The dream you dream alone is only a dream
the dream we dream together is reality.

wendy
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### Re: 'Thickness'

Nice work! You just independently invented the concept of the "curled-up" dimension!
Halfbaker
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### Re: 'Thickness'

If we want a "real" 2d world, we can imagine shadows in our 3d world. Shadows are true 2D objects with no thickness. If we regard the physical laws of our 3d world, and project them on to shadows, they will be percived by "shadow beings" to follow particular laws of 2d physics and they will have their own "real world" very different from ours. For instance they may even have a concept of 2d "mass density" , depending on how two equal area shadows have have different "shadow inertias"

However, we control our shadows, so in that sense, it is possible to interact with 2d beings. Apart from that, we probably won't have a meaningful interaction between them.

Also, I think we need some 4th spatial dimension for our world to explain the existence of mass, since 3d by itself only implies volume (lifting the 2d anology) and not mass.
Last edited by AmitX123 on Mon Sep 19, 2011 4:40 pm, edited 2 times in total.
AmitX123
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### Re: 'Thickness'

CollIB wrote:
Either there are no large extra spatial dimension out there

But if we think about gravity, the direction of the bending of our space time is a fourth direction. http://randomthoughts.ws/files/Gravitation_space_source.png
So interestingly, if you point your finger to the earth, you indicate a line, which goes out from our space time, seeing from a 4D perspective.

This effect need not involve a fourth dimension. For the famous rubber sheet example, we can also imagine the rubber sheet stretching/compressing in a 2d plane by projecting the original sheet on to 2d.
AmitX123
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### Re: 'Thickness'

AmitX123 wrote:Also, I think we need some 4th spatial dimension for our world to explain the existence of mass, since 3d by itself only implies volume (lifting the 2d anology) and not mass.

But if we accept, that we can have a little thickness in 4D, it means we have all the other higher dimension thicknesses too. I think the source of the gravity, and mass is the highest avaiable dimension object (10D if we thinking in the string theory), which effects all the lower dimensions.
CollIB
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### Re: 'Thickness'

Secret wrote:I've thought of that before but so far no one have detected the higher dimensional thickness [...]

But the point is that we can't detect that thickness, because we have no access to it.

Imagine a 2D world formed by plastic polygonal shapes trapped between two sheets of glass. Each polygonal shape is a perfect prism, so it has no evidence of any 3D features as far as its sides are concerned. The shapes can only interact with each other by their boundaries, because they are trapped between the glass sheets. Even though the shapes themselves may have quite a large thickness, say 1cm, but because they are confined by the glass, and because their sides have no 3D features, it is impossible for them to detect any 3D features at all. As far as they're concerned, the universe only exists in 2D, even though in reality they have quite a lot of 3D thickness.

Of course, this illusion of 2D remains as long as the radius of the prisms are relatively large compared to their thickness. If you have a very thin cylinder, for example, say its thickness is 1cm like everything else, but its radius is 0.001mm. Then there's a small chance that when it collides with something else, it may fall over sideways so that now it's no longer standing vertically between the two sheets of glass, but is rolling around. It's still confined, but now it starts to show some "odd features" because now its radius becomes its "thickness" and its thickness becomes its length. If two such cylinder collide, they may still bounce off each other like before, but they can also roll over each other or one can lie on top of the other. This will cause "strange effects" from the shapes' 2D point of view. They still have no way of measuring the "strange thickness" of the fallen cylinders, but they will observe that they have strange properties that are different from other non-fallen objects.

This is interesting because as long as the radius is not too far below the 3D thickness of the object, then it behaves "normally", but once its radius becomes too small, it has the risk of "falling over" and acquiring strange properties. So there is a size scale at which things start to turn strange (i.e., 3D effects start to show up). Does this remind you of the real world? Macroscopic objects behave "normally", but once you get down past a certain size, things start to act strangely. Conceivably, this is because objects smaller than a certain size starts to exhibit extra-dimensional properties.

And indeed, this is the idea behind "curled up" dimensions and string theory. When the object is big enough, you don't see anything strange because only their 3D properties are manifested. They are too big to "fall over" in the extra, confined dimensions. But when things get small enough, then the effects of the additional dimensions start to show up. Now they can "fall over" in the extra dimensions, and when we try to interpret the effects from our 3D-centric point of view, we find them really strange. But if we interpret them as the effect of having extra dimensions to "fall" or "rotate" in, then a lot of these effects become quite mundane. That's one of the neat things about string theory.
quickfur
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### Re: 'Thickness'

That's certainly put a very interesting light on string theory, quickfur! A nice intuitive explanation for once.

Keiji

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### Re: 'Thickness'

I believe that possibly a quantum of space-time in 3-space is actually 11-dimensional, perhaps more. It would take about 160 million trillion trillion quanta to make a length of one millimeter. This means that a 2D universe would have a slight thickness in 3, 4, 5 etc. dimensions. It would be only one quantum thick in the dimensions greater than two. Our 3D universe would be only one quantum thick in dimensions greater than three.
Pentoon
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