Extra Dimensions: Exploring Beyond 3D

[richerrich]

I just want to clear this up: why can't 5th till 11th dimension be represented in 3 dimensions no matter how small this extra dimensions are? One analogy for an extra dimension is a long rope that represents one dimension but this rope is composed of thinner twisting ropes which now represent the extra dimensions. But even with this picture the twisting ropes can still be described in 3 dimensions. The only way i can think extra dimensions make sense is if mathematically we can prove that a point in normal 3D space has the same location as a point irregarldess where that point is in the extra dimensions.

Thank you

 

[MCPO John-117]

i don't think these extra dimensions are necessarily spacial. think of how different time is compared to spatial dimension. the unseen dimensions are beyond 3D comprehension. you can see them just the same as you can't "see" time. we can survive seeing only 3D so have no need to see more dimensions.

hope that helped
-John

 

[richerrich]

John, it is spatial as far as the physicists interviewed said. It's just incredibly tiny that in computations of practical applications it is considered 'insignificant'. The problem with math is that it can be so abstract that its physical interpretation can be exaggerated.

 

[jal]

... a point in normal 3D space has the same location as a point irregarldess where that point is in the extra dimensions.

From wiki

http://en.wikipedia.org/wiki/Point_(geometry )

In geometry, topology and related branches of mathematics a spatial point is a primitive notion upon which other concepts may be defined. In geometry, points have neither volume, area, length, nor any other higher dimensional analogue. Thus, a point is a 0-dimensional object. In branches of mathematics dealing with set theory, an element is often referred to as a point. A point could also be defined as a sphere which has a diameter of zero.
---
Therefore, you now need a definition of dimension.

from wiki
http://en.wikipedia.org/wiki/Dimension
In mathematics and physics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify each point within it.[1][2] Thus a line has a dimension of one because only one coordinate is needed to specify a point on it. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it (for example, to locate a point on the surface of a sphere you need both its latitude and its longitude). The inside of a cube, a cylinder or a sphere is three-dimensional because three co-ordinates are needed to locate a point within these spaces.
---
Now YOU need to do more reading.

jal

 

[JoaoPais]

Well, for extra space dimensions, i would advise you to read the "Flatland", by Edwin Abbott (or watch the movie, although it isn’t the same thing). It's a 19th century book, but it really expresses the difficulty of perception on more than the dimensions we're used to.
The dimensions could be spatial and it's mathematical possible. It's simply a really hard exercise to imagine a 4D spatial world to our "3D mind".

 

[richerrich]

... The inside of a cube, a cylinder or a sphere is three-dimensional because three co-ordinates are needed to locate a point within these spaces.
---
Now YOU need to do more reading.

jal

Jal, what i was trying to say was that a point in the extra dimension is a point located in a different set of x,y,z in our typical x,y,z location. This can be visualized although it would look convoluted the more dimensions there are. Now if you try to visualize this convoluted shape, a point in it can still be represented in 3D regardless of how extremely small the value of the coordinates.

 

[jal]

If a point has volume, it is 3d in 3 dimension. It also exists in all 3 dimensions at the same time.

If you have a 4th spatial dimension then do you want to assume that it requires four co-ordinates to locate a point within 3d spaces. Do you also need to assume that it exist in the 4th dimension?

Problem
How do you prove something that you cannot see or detect?
jal

 

[JoaoPais]

Problem
How do you prove something that you cannot see or detect?
jal

Well, there are a lot of physics based in mathematical predictions or simply theoretical conjectures, without a possibility of proof, so that shouldn't be a "problem"...

There is one possibility.
Imagine that there is half of the 4D space. Then the border will be 3D space and can be considered as our 3D world we see. Other part is our Universe. It is round at all and flat only in rather small regions.

I think that what you've done is think in our 3 dimensions as 2 dimensional space "flat", so that you could imagine a 4th dimension.
A more realistic view of a 4th dimension is to consider that, if you could look from it, you would see behind the walls, the inside of a box, or even the human body. Everything we see is in a 3D referential, that's why we have to go around a wall to see what's behind. In a 4D world you wouldn’t need to, because the wall is only an obstacle the first 3 dimensions, so in a 4th dimension, "light" from behind the wall could reach your eyes.
I think this other dimensions are inaccessible to us, because our material limitations. because we are made of baryonic atoms. The theory that space is composed of virtual particles, well i think that they exist in other dimensions, and if we provide them with enough energy, they "jump" to our 3D. This is a topic were I’ve come up with a lot of peculiar ideas =)

 

[JoaoPais]

If it accepted there are no fantastic actions you've been mentioned like penitration through the walls. We and all the bodies are enomous gathering of the strings with the outings on the 3D border. We can't disappear diving into the 4D medium because the border ties us.

I haven’t talked about any wall penetration or whatever, I was saying that from a 4d spatial world we could SEE behind a wall, not walk throw it. If you prefer, we could “jump” it, using a 4th dimension.
I’m aware of string theory, and I can understand what you meant by the borders, but that’s no different of what I’ve said, because those borders are what we perceive as material limitations, I think.

 

[JoaoPais]

Yes, i understand what you're saying, and that is correct. Bu i think you are not getting the idea of observation throw a space with more than 3 spatial dimensions, sorry. In this subject, the book "Flatland" is truly enlightening =). I suggest you to try it, it's really small and interesting =)

 

[JoaoPais]

Yes, it takes a lot of imagination to see in 4D space, but the novel also has a small “dissertation” on this. it's quite interesting =)
And if someone can really do it, yes, it would be a blind man, once they’re really used to imagine the space around them, it should be easier.

 

[richerrich]

Thank you all :)

 

[LaurieAG]

The problem with math is that it can be so abstract that its physical interpretation can be exaggerated.

richerrich, you probably studied the direct integral/differential relationships between speed (m/sec), acceleration (m/sec squared) and distance traveled (meters) if you studied elementary calculus from first principles (with time = delta x) at uni.

Other units (i.e. m^2/sec^4) that result from different integral relationships will be difficult to reconcile with their elementary cousins.

 

[julianbury]

This is about quantum entanglement.
Einstein called it "Spooky action at a distance."

In the case of photons being entangled,
changing the state of one of them instantly changes the other
at a distances measured in kilometers.

And I mean instantly!
Faster than the speed of light.

This is an often repeated experiment as it's so hard to believe.
Like everone else, I wonder how such a thing could work.

I speculate that there may be some kind of burrowing shortcut between the photons.
I think of this as a dimensional shortcut.

Does anybody have other notions?

(-_-)

 

[DaveC426913]

This is about quantum entanglement.
Einstein called it "Spooky action at a distance."

In the case of photons being entangled,
changing the state of one of them instantly changes the other
at a distances measured in kilometers.

And I mean instantly!
Faster than the speed of light.

This is an often repeated experiment as it's so hard to believe.
Like everone else, I wonder how such a thing could work.

I speculate that there may be some kind of burrowing shortcut between the photons.
I think of this as a dimensional shortcut.

Does anybody have other notions?

(-_-)

Start a new thread please.

 

[PatrickPowers]

I just want to clear this up: why can't 5th till 11th dimension be represented in 3 dimensions no matter how small this extra dimensions are? One analogy for an extra dimension is a long rope that represents one dimension but this rope is composed of thinner twisting ropes which now represent the extra dimensions. But even with this picture the twisting ropes can still be described in 3 dimensions. The only way i can think extra dimensions make sense is if mathematically we can prove that a point in normal 3D space has the same location as a point irregarldess where that point is in the extra dimensions.

Thank you

The extra dimensions could have no effect on the 3D location, and apply to something else like quantum states.

On the other hand time and space are not independent, so who knows?

 

[eloheim]

A more realistic view of a 4th dimension is to consider that, if you could look from it, you would see behind the walls, the inside of a box, or even the human body. Everything we see is in a 3D referential, that's why we have to go around a wall to see what's behind. In a 4D world you wouldn’t need to, because the wall is only an obstacle the first 3 dimensions, so in a 4th dimension, "light" from behind the wall could reach your eyes.

Exactly that was my favorite mental revelation from reading Flatland! (It's a seriously thin, tiny book btw; Dover Thrift edition like $1.50! Great stuff!)


In it, the author illustrates how for the 1-D "Line Segment" people, their world is like burrowing through an underground tunnel. All you can do is move forward or backward until you run into an obstacle. If one Line-Seg ran into another, he would see the outermost surface facing in that direction: his "face." [And if he met him coming from the opposite direction...] So if the Line-Seg man is 10 segments long, others can see either of his two faces, but were they to wish to find out what (e.g.) color those middle 8 segments are, they would have no choice but to dissect him! Like chop off the face, note the color of the newly exposed segment in front of you; chop off that segment, note the next color visible, and so on, until the unfortunate specimen can (at least) be conceptually reconstructed, and analyzed inside and out.

You'll notice, however, that observers with the aid of additional dimensions have no such problem. We, or even 2-D Square-Men living on a flat sheet-of-paper-like world, can naturally and instantly see the "hidden" inside segments of the Line-Man. We don't have to chop them up, we can just take notes. It's the same way for us observing the aforementioned 2-D Square-Men. To one another, their outer-facing borders are their visible faces, their skin. They could walk around one another to see all the exposed sides, but once again, if they are wondering about the inner working of their various bodily systems, dissection will be in order. Of course as Men of 3-Dimensions we can just glance down at them from above and see exactly what's going on in there, as it functions, without disturbing a thing.



Of course the punchline is to try making use of those analogies to imagine how a 4-D being might view us. It's not just that they could see "behind walls" and "inside boxes," but that they could see every spec of your inner being splayed out as plain as day. To me that was the only analogy that ever made me feel anywhere near to doing what is so obviously "just inherently impossible": visualizing what it might be like to exist in a 4-Dimensional universe... And now that I'm thinking about this again, looking more closely at exactly how (e.g.) a Line-Seg man might be able to glimpse what the Square-Man sees by nature (and so on) might be interesting.


And, it should be noted that the "compact" extra dimensions referred to by the OP are different from the type discussed above.