I've just introduced myself to the concept of the 4th dimension. While many believe that time is the 4th dimension, there are quite a few that there can be a 4th spatial dimension.
I'll be glad if someone can help me visualise the world of the 4th spatial dimension. Anyone who's been to that world and can give us a proof (though I already believe that it exists) of its existense.
Can anyone of the 3d world ever visit the 4d world?
Thanks,
| ankur.vatsa wrote: |
I've just introduced myself to the concept of the 4th dimension. While many believe that time is the 4th dimension, there are quite a few that there can be a 4th spatial dimension.
I'll be glad if someone can help me visualise the world of the 4th spatial dimension. Anyone who's been to that world and can give us a proof (though I already believe that it exists) of its existense.
Can anyone of the 3d world ever visit the 4d world?
Thanks, |
Modern physics accepts time as the 4th dimension as encompassed in Relativity but I see that you have correctly identified what you mean in the title which is a pleasant change 
so I'll have a crack for you...
A 4th spacial dimension is fairly easy to explain but a devil to visualise. There is, of course, no proof of a 4th dimension's physical existence other than mathematical hypotheses, but there are some interesting ways of attacking the problem which might be of interest.
First thing to remember is that spacial dimensions are distinct - they exist regardless of the other dimensions. You can therefore go back and forth without going sideways. The classic 3 dimensions are normally represented by x,y and z. x is traditionally the horizontal direction, y the vertical and z the breadth (in/out). In 4-D topology (surfaces) then the 4th dimension is normally given the letter t (which is confusing as it could mean time, I know, but bear with me).
Now, each spatial dimension is perpendicular to the last. This means 'at a right angle, or 90 degrees.
(If this is patronising I apologise but I'll try to aim this at a non-science reader and hope that the more maths/science-literate will pick out anything of interest and skip the obvious stuff - I have included a section of links for the science reader at the end).
To construct a 4th dimension, therefore, we need a new perpendicular to the existing 3. One way of representing this is using the idea of a simple square. A square is 2 dimensional. Extend it into the 3rd and you have a cube. You can represent a cube on a 2-D surface like this screen by connecting 2 squares with diagonal lines. In the same way we can represent a 4-D extension of the cube (called a hypercube) with a 3 dimensional object which does the same thing. It doesn't really work well in 2 dimensions but here is a diagram which illustrates the principle.
A more 3-D looking version of the hypercube would be : 
So a hypercube is 2 cubes with the corners joined on the diagonal, just like a 2-D cube is 2 squares with the corners joined on the diagonal.
Here is a link to a nice Java application which lets you manipulate a hypercube on the screen.
http://torina.fe.uni-lj.si/~zlobec/cube/Cube.html
Here's a story aimed at younger readers which aims to illustrate the 4th dimension
http://camres.frih.net/4d.html
(I have copied this from the original site because it was unreadable due to bad background colour choice - I left a message at the site explaining this and left details to contact me if they object. The original is at http://www.geocities.com/CapeCanaveral/7997/flatland.html)
More Advanced Stuff for the science reader
http://www.geocities.com/CapeCanaveral/7997/
http://tetraspace.alkaline.org/
http://en.wikipedia.org/wiki/Fourth_dimension... This may sound wierd that the physics people didnt see this, but there is a 'SPACE' that is crossed when you go across a wormhold, so you are moving in a 'demision' that is not normally travesalble, so if this demision was regually traversible, then you wouldnt have to use a wormhole.
| Panthrowzay wrote: |
| ... This may sound wierd that the physics people didnt see this, but there is a 'SPACE' that is crossed when you go across a wormhold, so you are moving in a 'demision' that is not normally travesalble, so if this demision was regually traversible, then you wouldnt have to use a wormhole. |
What you say is absolutely correct. The wormhole exists in a theoretical 4th spatial dimension.
The analogy which explains it best is the paper.
Imagine the 3-D of normal space is a flat piece of paper in 2-D. To travel from one edge to the other you cross the length of the paper (space).
Fold the paper so the two edges are close together. Now drill a hole through the two edges and join them with a straw. The straw represents the 4th (spatial) dimension and the holes are the 'rip' in normal 3-D space. You can now cross from one edge to the other by moving only in the 4th spatial dimension and not at all in the opther 3. You literally cross absolutely NO space at all in NO time.
There are problems with this, though. Relativity treats time as the 4th dimension and also states that movement in spatial dimensions influences the temporal dimension. Moreover, this has been shown experimentally to be the case - it's called time dilation. This leads to a possible time-travel solution to the equations of relativity and potential paradoxes. I'll try to illustrate why.
For the sake of argument, let's believe that we can create a wormhole. Now there are two points in space, X and Y, which are connected by a stable wormhole. No time is needed to cross from Y to X or X to Y.
Now imagine that point Y is being moved around very rapidly. (This could possibly be done by dumping magnetic material at point Y and using magnets to oscillate it.
According to Relativity, the moving end should go forward in time faster than the stationary end due to time dilation. This means Y is farther in the future than X. If we then move from Y to X through the wormhole we have moved back in time.
Of course this is all speculation, but there is nothing impossible about any of it according to current physical theory (unlike many other supposed time travel ideas which either exceed c or do some other impossible stunt). Basically, if wormholes do exist in a 4th spatial dimension then it should be possible to time travel.
This (personally speaking) is one big reason I doubt the existence of wormholes at all in spacetime. I think there are two possibilities :
1) Relativity is wrong and time is not the 4th dimension (perhaps it could be the 0th dimension) or
2) Wormholes can only work in 1 spatial dimension less that you exist in (for us that would be 3-1 = 2 hence the paper example works but a 3-d example would be impossible). If there is a 4th spatial dimension then only 5-D beings could cross a wormhole using such a dimension....and so on...It essentially means that wormholes could indeed exist, and extra dimensions too, but they would be compeletely inaccessible from our spacetime....
Personally I reckon solution 2 is most likely but that is a hunch and not at all based on evidence (I'll just run to the bathroom and scrub my hands for typing such pseudo-scientific nonsense....shame, deep shame!!).
Regards
ChrisWow, I have never heard of a 4th dimension before, this is really interesting, thanks for explaining it.
My way of visualizing the 4th spacial dimension is essentially squashing 3-D space into a 2-D plane and it runs parallel to infinite other planes of the sort. And this 4-D space can be "squashed" into another 2-D plane and the fifth dimension is now the 3-D space. Hard to explain, but hopefully someone understands. But I think this kind of physics is car-azy.
Ankur, as to your question about proving the existence of extra spatial dimensions.....
There is no experimental evidence to support theories with extra spatial dimensions. This would be the scientific discovery of the century and would not have escaped everyone's attention.
However, there is a small chance that evidence of extra dimensions may be found at CERN when the new LHC particle accelerator starts up. This is due to switch on next year. See e.g. http://arxiv.org/PS_cache/hep-ph/pdf/0211/0211205.pdf. Perhaps the most intuitively obvious form of evidence would come from 'missing energy'; energy that is lost and cannot be accounted for by any other means, leading to the conculsion that it may have be lost to particles propagating in extra dimensions (we cannot observe particles moving in these extra dimensions directly, of course).
As to your question about whether we can visit the 4D world....
If it is shown that extra dimensions do exist at collider experiments then we are to assume that they are all around us, and we are living in a world with extra spatial dimensions right now. We clearly live in a world that so-far appears to have 3 spatial dimensions so there must be some reason why it is difficult to observe any extra ones. There are a currently a few theories for this which are rather subtle, but you could invesigate yourself by googling 'large extra dimensions' or 'small extra dimensions'.
Flynn[/url] [quote="Flynn"]Ankur, as to your question about proving the existence of extra spatial dimensions.....
Nice article yourself there Flynn .. :D
You sound like a physicist yourself (I'm just a generalist/teacher type who reads a lot and talks to real scientists when they let me).
Chris
