10th Dimension Explained?

[Khamsin]

It sounds like you're just calling dimensions higher than our own temporal, and dimensions less than our own spatial.

However, like in the video, if you pass a balloon through a 2D plane, it'll appear (from an "outside" point of view perpendicular to the plane) to be a dot expanding to a full balloon cross section, and then get smaller again until it vanishes. Or from the point of view of something within the 2D plane, it'd start as a dot, expand to a line, then back to a dot. Either way, the progression from dot to full section to dot appears temporal when passing through a 2D plane, but doesn't appear that way to us because the whole balloon exists at once for us.

Of course, the other way of looking at it is that in 2D only a slice of it appears at a time, but there is still the temporal aspect, even from our point of view, in that it is moving through the plane and is in different places at different times in 3D and in 2D as it passes through the plane.

Not only does the balloon appear to be changing with time in the 2D plane, it also appears to be changing with time in 3D space in a different way.

So, in the 10th dimension, is everything just... there... unmoving, unchanging, and every dimension below 10th is merely a cross-section moving through 10-space (or a cross-section moving through a cross-section moving through 10-space)? If the 10th dimension is simply everything that can and will ever be, all at once, how can anything vibrate? For something to vibrate, wouldn't that imply there's an 11th dimension where the vibrating strings are static, in every possible configuration it could be in while vibrating?

[Neosutra]

It sounds like you're just calling dimensions higher than our own temporal, and dimensions less than our own spatial.

However, like in the video, if you pass a balloon through a 2D plane, it'll appear (from an "outside" point of view perpendicular to the plane) to be a dot expanding to a full balloon cross section, and then get smaller again until it vanishes. Or from the point of view of something within the 2D plane, it'd start as a dot, expand to a line, then back to a dot. Either way, the progression from dot to full section to dot appears temporal when passing through a 2D plane, but doesn't appear that way to us because the whole balloon exists at once for us.

Of course, the other way of looking at it is that in 2D only a slice of it appears at a time, but there is still the temporal aspect, even from our point of view, in that it is moving through the plane and is in different places at different times in 3D and in 2D as it passes through the plane.

Not only does the balloon appear to be changing with time in the 2D plane, it also appears to be changing with time in 3D space in a different way.

So, in the 10th dimension, is everything just... there... unmoving, unchanging, and every dimension below 10th is merely a cross-section moving through 10-space (or a cross-section moving through a cross-section moving through 10-space)? If the 10th dimension is simply everything that can and will ever be, all at once, how can anything vibrate? For something to vibrate, wouldn't that imply there's an 11th dimension where the vibrating strings are static, in every possible configuration it could be in while vibrating?

No, dimensions dont get "higher order" as in: Being on the 5th dimension looking down at the 3rd dimensional spaces as less sophisticated, its not as simple as "an array of an array" for example, where movement through a lower order cell catergorizes a specific vector (time for example) in higher number dimensions.

There are instead 3 spatial dimensions, 1 temporal dimension, and 6 tiny dimensions curled up very tightly, that effect the forces of our spatial universe but not in a "direct" spatial way, thus we may never be aware of their existence, other then examining the specific forces on subatomic molecules (what restricts molecular movement, paths, gravity, etc). Having these so-called compact dimensions is very beneficial if String Theory is to describe a Theory of Everything. The idea is that degrees of freedom like the electric charge of an electron will then arise simply as motion in the extra compact directions. The principle that compact dimensions may lead to unifying theories is not new, but dates from the 1920's, since the theory of Kaluza and Klein. In a sense, String Theory is the ultimate Kaluza-Klein theory.

For simplicity, it is usually assumed that the extra dimensions are wrapped up on six circles. For realistic results they are treated as being wrapped up on mathematical elaborations known as Calabi-Yau Manifolds and Orbifolds.


Calabi-Yau Manifolds
http://upload.wikimedia.org/wikipedi...Calabi-Yau.png

From wiki:

Calabi-Yau manifolds are a special class of manifolds used in some branches of mathematics (such as algebraic geometry) as well as in theoretical physics. For instance, in superstring theory the extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi-Yau manifold. The precise definition of a Calabi-Yau manifold, given below, builds on a considerable mathematical background. The designation "Calabi-Yau space" for a member of this class was coined by physicists in the 1980s,[1] but mathematicians have been studying such manifolds since at least the 1950s. Physical insights about Calabi-Yau manifolds, especially mirror symmetry, led to tremendous progress in pure mathematics.

[divisortheory]

[quote=Max™]

A Spatial Dimension is a different manner in which things can unfold, a Temporal Dimension is a different Order in which they can unfold.

Mathematically there is a dimension, that's it. Mathematics doesn't know the concepts of space and time, those were created to support physics.

A different order in which they can unfold is no different than a different manner in which they can unfold.

Consider 3 sequences of actions:

A -> B -> C
B -> A -> C
A -> B -> D

All of those sequences just fit into the same 2-dimensional space.

In a truly 2 Dimensional space, there is no order, since it would be a static unchanging thing.
[/quote:e94d4]

Let me be more precise then.

Let t be the time that an action was performed, and let f(t) be the action that was performed. A 2 dimensional universe is the set

{(t, f(t)) | t >= 0}

The above list of 3 sequences of accents can be defined as follows:

S1 = {(1, A), (2, B), (3, C)}
S2 = {(1, B), (2, A), (3, C)}
S3 = {(1, A), (2, B), (3, D)}

Note that since S1, S2, and S3 are mutually exclusive, they must all come from a different universe.

3 Dimensional space with 2 Space+1 Time Dimension is a slice of a 4 Dimensional Space, where it gets weird is when you postulate added Time Dimensions instead of the extra Spatial Dimension we know and love.

I'm not postulating adding any "fdajlkfds" dimensions. I'm only talking about adding dimensions, because that's the only thing that makes sense. Furthermore, it's not weird, it's just like any other n-dimensional space in mathematics. There is no such thing as a "time" dimension or a "space" dimension, it's all relative to what dimension you're "sitting" in.

[Max™]

Math isn't Reality.

It is a method to describe reality, it has it's benefits, and it has flaws.

The way (some, not all) Mathematical models describe dimensions invariably is a flaw.

You aren't sitting in one dimension or another, you're sitting in them all.

A dimension is a freedom of movement, if you will.

A temporal Dimension varies from a spatial dimension if only because this Universe has an arrow of time (past future) so if you're looking from an outside perspective, you see the sum of all the 4-Dimensional World lines, where we can only see slices of them.

If the Balloon started as a point, and grew into a circle, then ended as a point while passing through a 2-D Universe, that would imply an order of events and change, thus a new freedom of movement, making it a 3-D Universe.

Unless the 2-D Universe was moving through ours, we would see the Balloon moving here, either description is relatively correct, so I'll drop that.

Technically you could think of our Universe as a collection of 2-D Sentences, the sum of the 2-D Sentences makes a 3-D Page, and flipping the pages produces the 4-D Universe we find ourselves within.

I never went in for the math side of describing reality, I'm the philosopher type, always was as a kid when I first started pondering these ideas, am now. The difference between us would be that to me, there is clearly a difference between a Temporal and Spatial freedom of movement, and to you, they are just values to be slotted into an equation.

Either way may be as correct as the other, I just find it easier to explain to other people using poetry and metaphor than talk of n-Dimensional substrates in n+X Dimensional Manifolds.


As for the "If so, wouldn't the 10th Dimension just be everything frozen and unchanging, except from the point of view of the 11th Dimension" that's really close to the postulations of M-Theory, and brings up a theory called Configuration space, in which every event we perceive, every sequence of worldlines could be viewed as single objects, mathematically particles even, and wouldn't make sense unless looked at from an outside dimension.

[divisortheory]

Math isn't Reality.

It is a method to describe reality

I beg to differ. Math is the only reality there is, physics (and by extension time) is a method to describe reality.

it has it's benefits, and it has flaws.

Name one flaw.

[Kaylia]

Math isn't Reality.

It is a method to describe reality

I beg to differ. Math is the only reality there is, physics (and by extension time) is a method to describe reality.

It's the correct answer.

[Neosutra]

Either way may be as correct as the other, I just find it easier to explain to other people using poetry and metaphor than talk of n-Dimensional substrates in n+X Dimensional Manifolds.

n+X Dimensional Manifolds isnt beautify poetry? Nothing is more beautiful then math.

Except my wife if she is reading this >.>

[Septimus]

Either way may be as correct as the other, I just find it easier to explain to other people using poetry and metaphor than talk of n-Dimensional substrates in n+X Dimensional Manifolds.

n+X Dimensional Manifolds isnt beautify poetry? Nothing is more beautiful then math.

Except my wife if she is reading this >.>

Good save. It will keep her from beating you into the next dimension.

[Max™]

The flaw in purely mathematical description: You can't explain it to anyone without a good mathematics background.

Yes, math is in a sense reality, but human math is not, it, like physics, is just a method to describe reality.

I was explaining Superstring Theory to my girlfriend earlier, higher dimensions, and all that.

She has no head for math, nothing more than a high school math background.

I said this:

"Imagine a book, full of pages, and words. The words are akin to 2 Dimensional slices of reality, visible, but lacking depth without context. Sort of like what we see every day, planes and surfaces, images of what is actually there.

Take those words, and assemble them together and you get a page. Take all the 2 Dimensional slices of reality we can see, assemble them together, and you get a 3 Dimensional snapshot of our Universe. A page.

Take that page, and turn it, a moment passes, you turn to the next, another instant in time.

Take those pages you're turning through, look at them as a whole, and you have a Book. Take the 3 Dimensional snapshots of our Universe, look at them all together, and you have a 4 Dimensional object.

Take that Book, put it in a Library, and you have a Manifold of Universes, all with their own stories and writing styles. Histories, and physics.

Now, go back to the page, the words, what are they written on? If there was nothing holding the words, they would just be empty and illegible. The paper they are written on can be thought of as the curled up Dimensions of String Theory. We cannot interact directly with them, but it can be assumed that they are there."

Then I went into the curled up dimensions, freedoms of movement, and the structure of strings themselves, and how the way they can/do move through the curled up dimensions determines the particles we perceive... letters if you will.

I could see that "a ha" moment in her head as it clicked. Had I gone into the math behind the theories, there would have been no "oh! I understand that", unless I went through and taught her all of the math to fully realise what was being spoken of. Even then, there is something visceral about language and metaphor that just triggers images so well in our brains, well, mine at least.

[Neosutra]

I dont know, that approach is good for making people think they understand 10 dimensional physics, but I think there gets a point in math/science/physics that you start losing the essense of the theory when you break it down to far. I would venture to say, that while your approach works well in making people expand their perspective, it loses so much function that your not even explaining the same theory. Unfortunately, I just dont think String theory is simple enough to be explained to people w/o the math background, and attempting to do so may seem nice but really doesnt represent what the theory is. Having a beautiful poetic simplistic picture of it may be nice for the discovery channel, or to your girlfriend, but once you get to a certain level of simplicity, you give up the most important part of the theory, which is the mathematical methods used to explain it.

String theory is one of the few theories I would say is too complex to be putting on the shoulders of the general public, for now.

[Max™]

String Theory itself is overly complex though, it almost exists for it's own sake, as thought people don't want to let go of the mathematics of it.

It's been moving to less unwieldy theories bit by bit, M-Theory, Brane, myself I'm expecting them to morph into some form of Quantum/Probabilistic Wave Theory formulated in the 11th Dimensional Framework set down by Superstring Theory.

When you step back from the math, which in my opinion, only exists to prove a theory, not to be the focal point of it, you are still left with an amazing look into reality, existence, and the beauty of it all.

The Math is definitely too complex for the General public, but so are Relativistic Calculations, but with a little time and some metaphors you can get the way Relativity works across to someone well enough that they get how that aspect of the Universe works.

I wouldn't say my girlfriend understands String Theory, but she certainly won't think of the Universe the same way as she did, and she at least grasps the concept of it all.

[Neosutra]

Fair enough.

But I do agree, I dont think the string theory of today will look anything like the string theory 50 years from now, in complexity or design. So many unanswered questions, so exciting.