Unified Dimensional Theories and Electromagnetism

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.

Unified Dimensional Theories and Electromagnetism

Postby unicole » Wed Sep 10, 2014 6:21 pm

Hello,
I understand that there are a few theories for other dimensions - higher spatial dimensions, higher energetic dimensions (i.e. the electromagnetic spectrum), and the multiverse which are other dimensions of possibilities. My question is, can all of these theories be simultaneously true? Or can the multiverse/ infinite possibilities be considered another dimension but like how color is a dimension of an object as well as shape - like connected but separate completely and requiring a different name? Or can only one of these theories be true?
For instance, could the universe be made up of just energy (electromagnetic radiation) which is manifesting as physical dimensions, but manifests differently as those dimensions rise? Or would there always have to be some sort of physical aspect associated, just as there is always an energetic aspect?
Also, how is electromagnetic radiation represented in the 1st, 2nd, and 4th dimensions? Do we know anything about that? Does it theoretically exist in higher dimensions than that?
I'm sorry this isn't worded better, I'm just a non-physics-educated person who likes to think deeply and read a lot. Thanks in advance for your help.
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Re: Unified Dimensional Theories and Electromagnetism

Postby PWrong » Thu Sep 11, 2014 8:43 am

Hi unicole

I understand that there are a few theories for other dimensions - higher spatial dimensions, higher energetic dimensions (i.e. the electromagnetic spectrum), and the multiverse which are other dimensions of possibilities.

These aren't really "theories" about other dimensions, so much as different meanings of the word "dimension". Just as "bark" can mean a sound a dog makes or the stuff on a tree, "dimension" can mean several different things.

Most of them derive from the mathematical meaning of the dimension of a vector space. The dimension of a set is how many real numbers you need to describe a point in the set. For example suppose you have a robot with six arms that can only move up or down. To describe the robot at any given time you need 6 numbers, one for each arm.

Spatial dimensions is about the dimension of space. In our universe we describe points in space with three coordinates, like x, y and z.

There's another sense of dimension that means the lengths, widths e.t.c. of an object. So a rectangular prism might have dimensions 1, 3 and 5. Or a table in an Excel spreadsheet might have dimensions 5 by 100.

I don't know what you're talking about with "higher energetic dimensions". Electric fields and magnetic fields are both vector fields.

Finally, the universes in a multiverse are sometimes called "other dimensions", but this is totally different from the other senses.

For instance, could the universe be made up of just energy (electromagnetic radiation) which is manifesting as physical dimensions, but manifests differently as those dimensions rise? Or would there always have to be some sort of physical aspect associated, just as there is always an energetic aspect?

Nope. You may have got this idea from the fact that matter can be converted into energy (E = mc^2). Electromagnetic radiation (light) is not the only form of energy either, there are several other kinds. Both matter and energy distort spacetime, but spacetime is consistently four dimensional. The dimension is just a simple number, it doesn't "manifest" or "rise" or anything like that.
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Re: Unified Dimensional Theories and Electromagnetism

Postby unicole » Fri Sep 12, 2014 9:25 pm

Thank you for your thoughtful response. I wish I understood more. I have never learned any of this formally so I appreciate your patience. I've read "too many" books on a variety of topics and I'm trying to integrate my understanding (esoteric, spiritual, ufo, philosophic, psychological, bioenergetic) with the more practical scientific known truths (of which my understanding ends at reading Scientific American monthly and watching Great Courses), which is probably why my questions are weird. I just have a lot of questions.

Here are a few more if you don't mind entertaining me:

How do we know that spacetime is consistently 4 dimensions? Is that just the definition of spacetime? In this 4 dimensional spacetime, is the 4th dimension time? Is it possible time is just a part of the 4th dimension? Like the flatland example of a sphere passing through 2D space experienced much differently than in 3D reality?

Could dark matter/dark energy be the multiverse?

In a very basic sense, where do the theories of spacial dimensions higher than 4 come from?

In the book Warped Passages by Lisa Randall, she describes some dimensions as being "very tiny" but what the hell does that mean? How can a spacial dimension be tiny? Aren't they all built up on each other?

Theorizing that there are 10 or more spacial dimensions, we would soon stop being able to comprehend them. So at these higher dimensional levels, would you still experience the first dimension?

Ultimately, my question regarding this is, assuming many dimensions exist within the universe, i.e. one system, there has to be a constant that ties them together - right?
I asked this question of a friend and he just kept repeating "Lorentz covariance" but the wikipedia just has a bunch of equations I don't yet understand.


Thank you!
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Re: Unified Dimensional Theories and Electromagnetism

Postby ICN5D » Sat Sep 13, 2014 3:22 am

unicole wrote:In a very basic sense, where do the theories of spacial dimensions higher than 4 come from?


This is a case of plain ole' geometry. By defining a dimension as an axis of freedom to move back and forth in, you can build these axes together into an n-dimensional universe. No matter how many dimensions you have, they all intersect at 90 degrees of each other. Moving left/right is 90 degrees to forward/backward. And, both of these directions are 90 degrees to up/down. Combining all three into one makes right/left, for/back, and up/down as a 3D space. If you attached future/past, you get a 4D space-time.

But, if keeping to space dimensions only, you end up with more and more 90 degree axes to move around in. So, for a real 4D space, we will find ana/kata to be perpendicular to all up/down, right/left, and for/back at the same time. A 5D space will have an additional axis 90 degrees to all four, and so on.


In the book Warped Passages by Lisa Randall, she describes some dimensions as being "very tiny" but what the hell does that mean? How can a spacial dimension be tiny? Aren't they all built up on each other?


I guess there could be two ways to be tiny. One type is just a small amount of thickness in that higher dimension. Like a sheet of paper, it's mostly 2D, with a very tiny amount of 3D thickness. In the same way as this, it's possible to have a mostly 3D object, with a tiny 4D thickness. Another way is the curled up, compactified dimension. This is the kind String Theory is based on. In this scenario, we have something more like a garden hose universe.

Imagine a person tightrope walking across a garden hose, suspended off the ground. The only sizable part of the hose is the length, which has only one dimension, only capable of forwards and backwards movement. Now consider what an ant would perceive. This critter is so small, it has two dimensions of freedom. Not only can an ant move lengthwise, but also around the hose, in the second dimension. Note how the second direction of left/right is self-repeating. Moving in a straight line leads back to the start. A person would not experience this hidden extra dimension because of size. Last time I heard, our universe had somewhere around 26 dimensions, as 4 extended large, and 22 tiny curled up directions, all 90 degrees to each other. Theoretically.


Theorizing that there are 10 or more spacial dimensions, we would soon stop being able to comprehend them. So at these higher dimensional levels, would you still experience the first dimension?


Well, if there's anything I've learned about wild high-D stuff, is that it's not all that incomprehensible. There are various tools at one's disposal that can potentially make high-D stuff easier to see. Well, you don't actually "see" them, but you have a very good model of it in your mind. It also depends on which shapes you're working with. Polytopes are highly complex, but toratopes (hyperdonuts) are very simple, and can be understood in very high-D. Of course, these are just geometric objects, when it comes to even more abstract spaces, then it's more difficult.

If you were 10D, you could see, perceive, feel and understand all 10 axes, even if it's the x-axis of the 1st dimension. Where, any axis could be x, it depends on orientation. Take a 10D cube for example. Holding it in your hands, you could still feel every sharp pointy 0D corner, joined by every 90 degree sharp 1D edge branching off the corners, joined by every flat 2D square panel, etc, all the way up to the 9D surface panels that your 10D hands are touching.
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Re: Unified Dimensional Theories and Electromagnetism

Postby wendy » Sun Sep 14, 2014 12:25 pm

The main reason that people have not given much thought to electromagnetism in higher dimensions, is that the notion of vector-products and curls have not been figured out for that space. It's quite complex to imagine how it might work, although i spent a good part of today doing just that.

The rotation-space in three dimensions is three dimensions itself, one can suppose the vector representing rotation is the north pole (right-hand-rule). Curl works quite well.

The rotation-space in four dimensions is a ectix (6d space), which does not map easily onto 4D. However, one can suppose that a wheel-rotation in 2d, is given by a 2-vector orthogonal to it. You could then do various products with a one-vector or a second two-vector, to produce some desired results. Just as in 3d, the motion creates an eddy around it, one might in 4D, require motion to make a circle to create the eddy: in other words, it is a kind of centrapedial swirl.

So i got out a number of rotations, and see if one can make sense of this activity.

You can do a 'dot product' over the vector and 2-vector to get a second vector. Likewise, a cross-product of a vector and a 2-vector would be a vector. The dot product of two 2-vectors would be a scalar, and there is at this time, no cross-product of two 2-vectors. I then tried to imagine how such a thing might happen, and after a few stabs, decided one might need to ink the stuff first.

The 10 or 11 dimensions posited as a model of the universe, with many thin dimensions, works something like imagining that a 1D world is not an infinitely thin line, but a piece of string, with some thickness. The idea is that we are a terous (4D) piece of fabric in 11 dimensions, and that in seven of the dimensions, it is thin, but non-zero.
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Re: Unified Dimensional Theories and Electromagnetism

Postby unicole » Mon Sep 15, 2014 5:07 am

wendy wrote:
You can do a 'dot product' over the vector and 2-vector to get a second vector. Likewise, a cross-product of a vector and a 2-vector would be a vector. The dot product of two 2-vectors would be a scalar, and there is at this time, no cross-product of two 2-vectors. I then tried to imagine how such a thing might happen, and after a few stabs, decided one might need to ink the stuff first.

Thank you! This all sounds very interesting but I do not know what it all means. What does it all mean? How can I learn more about how electromagnetisim works in 3D so I can better understand your 4D+? Are there any good books?

wendy wrote:
The 10 or 11 dimensions posited as a model of the universe, with many thin dimensions, works something like imagining that a 1D world is not an infinitely thin line, but a piece of string, with some thickness. The idea is that we are a terous (4D) piece of fabric in 11 dimensions, and that in seven of the dimensions, it is thin, but non-zero.

0_0

*_*

D;
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Re: Unified Dimensional Theories and Electromagnetism

Postby unicole » Mon Sep 15, 2014 5:14 am

ICN5D wrote: Imagine a person tightrope walking across a garden hose, suspended off the ground. The only sizable part of the hose is the length, which has only one dimension, only capable of forwards and backwards movement. Now consider what an ant would perceive. This critter is so small, it has two dimensions of freedom. Not only can an ant move lengthwise, but also around the hose, in the second dimension. Note how the second direction of left/right is self-repeating. Moving in a straight line leads back to the start. A person would not experience this hidden extra dimension because of size. Last time I heard, our universe had somewhere around 26 dimensions, as 4 extended large, and 22 tiny curled up directions, all 90 degrees to each other. Theoretically.


So in the lower dimension you may experience a higher dimension as actually having more "depth" or more complexity due to your perspective? In this hose scenario, is the "around the hose" the "curled up dimension"? i.e. an extra dimension available only to lower dimensions?
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Re: Unified Dimensional Theories and Electromagnetism

Postby ICN5D » Mon Sep 15, 2014 9:56 pm

unicole wrote:So in the lower dimension you may experience a higher dimension as actually having more "depth" or more complexity due to your perspective?


Kinda like that. A higher dimension is just a new, extra 90 degree direction to branch off into. Just like having in 3D: for/back, left/right, up/down, there will always be two directions one could go, into that higher dimension. I see them as a new up/down direction, where the current perspective becomes squished into a flat sheet.

High-D objects are bigger in a ways, but not size related. They extend into more 90 degree directions than 3, which makes them infinitely larger, but there's only so much of it. A cube is not infinitely large, but one can make an infinite number of square-shaped slices to a cube. This is because a square has zero 3D height. The same is true for a tesseract (4D cube) : it has an infinite amount of 3D cubes stacked along 4-space.


In this hose scenario, is the "around the hose" the "curled up dimension"? i.e. an extra dimension available only to lower dimensions?


Yep, that's how it works. Not so much as "accessible in lower dimensions", but more like accessible to smaller sizes. The larger you are, the fewer dimensions you have. The smaller you are, the more you get. Shrinking in size makes the space more and more expansive, around and within you. By shrinking down, not only do the relative distances get larger, but the local dimensionality of space has also changed. Now, you've got all these extra 90 degree directions to move and build tiny things in. Expanding in size will make those extra spaces too small, and become unnoticeable and unusable.
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Re: Unified Dimensional Theories and Electromagnetism

Postby unicole » Tue Sep 16, 2014 6:02 pm

wendy wrote:The 10 or 11 dimensions posited as a model of the universe, with many thin dimensions, works something like imagining that a 1D world is not an infinitely thin line, but a piece of string, with some thickness. The idea is that we are a terous (4D) piece of fabric in 11 dimensions, and that in seven of the dimensions, it is thin, but non-zero.


Hey Wendy! How does your curl investigation relate to the post in the thread "One experiences the fourth dimension all the time."?
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