Shadows

[Elliott]

I was in the car today thinking if the second dimension was just a shadow of ours but not a shadow formed from light . When we see shadows they are always in two dimensions. This woud then make the first dimension a shadow of the second and we would be a shadoe from the fourth and so on. What do you think of this?

[Phi for All]

I was in the car today thinking if the second dimension was just a shadow of ours but not a shadow formed from light .

What do you mean, a shadow of "ours"? The first three dimensions are length, width and height. They are interdependent on each other. There are no one or two dimensional objects in our world. Do you mean something like a parallel universe?

[Elliott]

Yes something like a parallel universe but connected to ours more. It would be the same thing is happening in all the but in diffrent dimensions. Me typing this is happening in all dimensions but just being typed with diffrent dimensions. Meaning whatever the highest dimension is you there is controlling you which would be you so you don't notice since the same events are happening. Sorry I don't know much about physics. Just an idea I got today.

[Phi for All]

I am moving this to Modern/Theoretical Physics.

 

I would also recommend that you watch this excellent PBS series made from Brian Greene's book, The Elegant Universe. This explains much about modern string theory, higher dimensions, parallel universes and the like. The physics are top-notch.

 

Here's the link:

http://www.pbs.org/wgbh/nova/elegant/program.html

 

3 hours of great science.

[Elliott]

Thanks. I saw that a few months ago I will watch it tommarow when I have time to watch it the entire thing.

[DQW]

I was in the car today thinking if the second dimension

There is no such thing as a "second dimension".

 

... was just a shadow of ours

And by "ours", I assume you mean 3-dimensional space.

 

... but not a shadow formed from light . When we see shadows they are always in two dimensions. This woud then make the first dimension a shadow of the second

But in general, the shadow of a sheet of paper (2D object) is also 2 dimensional (unless you make the paper exactly coplanar with a point- or line-source of light). Notice that the dimensions of the shadow is simply equal to the dimensions of the space that the shadow forms on. So, if the shadow forms on a 2D surface, it will have no more than 2 dimensions. However, it is possible, as described just above, to pick the projection surface and arrange the light source such that there is a reduction of exactly one dimension.

 

and we would be a shadoe from the fourth and so on. What do you think of this?

In other words, you are asking if n-dimensional space can be treated as a projection (or as you call it, a "shadow") of n+1 dimensional space. The short answer to that is yes, one can easily pick a continuous map [imath]F~:~ \mathbf{R}^{n+1} \rightarrow \mathbf{R}^{n} [/imath] that does this.

[Elliott]

That helps!

And by "ours", I assume you mean 3-dimensional space

Yes

a sheet of paper (2D object)

I always heard paper is 2D but I always thought it was 3D since it has heigth if I am wrong tell me.

 

Anyone who posts something here use projection instead of shadow.

[YT2095]

yeah, I was thinking of Projection when I got a few posts in too

 

it`s an interesting idea, so the projection using Photons, would be the 2d and the Side view of this would be the 1D aspect when taking into acount the edge only?

 

I`ve no idea, it certainly sounds better than a sheet of paper that has a thicknes making 3d by default, maybe a photon is small enough to qualify? could a single Photon be in the Zero`th dimension, hence it lack of mass and incredible speed?

 

I don`t know enough to comment with any expertise, but I prefer that illustration to others

[DQW]

could a single Photon be in the Zero`th dimension,

As I've tried to say several times before, there is no ordinality to dimensions. Hence, no zero'th dimension. Things are not in some particular dimension; all things are in 3 dimensional space (or 4 dimensional spacetime, neglecting other dimensions for now). Things (actually, mathematical objects) can have different dimensions, which are only related to the dimension of the space they live in through the requirement that the former be smaller than or equal to the latter.

 

we hence it lack of mass and incredible speed?

This has nothing to do with the dimensions of the photon. Quarks and leptons are also considered pointlike particles - they are zero dimensional.

[YT2095]

hey cool, and I`m not arguing or challenging anything here, my point being that his idea of light hitting a wall would about as "Thin" as I can imagine something being thin as a really thin thing that was flatter than a really flat thing, and so much better than a sheet of paper. I mean if we`re going to Pixelate the universe, lets use something Tiny!

 

that`s all

[Daecon]

What would be "casting" this shadow, though?

[Severian]

Irrespective of the mechanism, it is still a projection. This is nothing different from the usual view of extra dimensions. If M-theory is correct, we are just a 4d projection in an 11d space. The shadow is still not perfectly thin though - like all physical manifestations it has a very small width - too small to see but there nevertheless.

[jdurg]

But isn't a shadow just an abscence of light due to the blockage of light by another object?

[Severian]

Yes, but that is true not just of the surface but all the bits between the surface and the object casting the shadow. The shadow has to fall on something to be seen, and the interface on which it falls has non-zero dimensions.