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What is 'hyperspace"?


Morgan07

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Hello. My name is Morgan and I'm new to the forum (and a complete novice when it comes to physics). I'm trying to understand M theory. I'm in Poland and I don't have ready access to the books written by Briane Greene or Michio Kaku. I have watched some of their videos, however, and I think I've understood everything in them incorrectly. Forgive me if there are a lot of questions here, but I'm completely lost. Much appreciation for any help :-)

 

What is the "hyperspace" that Kaku refers to? Is it the 11th dimension or is something else?

 

My understanding so far is this:

 

1) Vibrating strings form everything.

2) There are 10 spatial dimensions, plus 1 dimension of time.

3) Somehow, a string can expand to form a brane (How do they do this? Does a brane vibrate the way a string does? Why would a string expand like this?)

4) Universes can form on branes. Our universe may have formed through a brane collision (How is it, then, that we can be sure that our universe is expanding? What if its just the brane that's expanding, since we apparently know that strings expand so much?)

5) There may be an infinite number of branes (and universes) floating around (Where do they float? Are they in hyperspace? The 11th dimension? What is the 11th dimension?)

 

Again, I'm really lost and would be grateful for a lifeline :-) Thanks!

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I think it's important to keep (1) geometry and (2) electromagentic fields and waves separate in your mind, at least initially.

 

Hyperspace refers to any geometry above 3 dimensions. For example, Kaku explains how a 2 dimensional man would perceive a 3D object passing through his 2D space as a line. Simlarly, Kaku implies that light could be just our limited 4D perception of something that exists in 5D, and so on. There can be infinitely many dimensions in geomtery of universe.

 

Strings, on the other hand, have to do with fields and waves on quantum level. The problem of quantum physics is the increasing number of elementary particles as well as particles of force fields that bind matter particles and their anti, mirror images. Strings theory does away with all of the elementary particles except for the set number of strings which vibrate. This is not a matter of geometry or space or hyperspace, but quantum electromagentic theory.

 

Now you can combine as many strings as you please with as many dimensions as you see fit.

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Hello Morgan – Welcome to hypography! :)

Hello. My name is Morgan and I'm new to the forum (and a complete novice when it comes to physics). I'm trying to understand M theory. I'm in Poland and I don't have ready access to the books written by Briane Greene or Michio Kaku. I have watched some of their videos, however, and I think I've understood everything in them incorrectly.

Greene, Kaku, and others physics popularizer are good writers, and their books are fairly easy to read regardless of how much science you’ve studied in a traditional school setting. If you like Kaku’s fun approach to physics as seen in his TV shows and videos, and like to read, I expect you’ll like books like his Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension, or Kip Thorne’s Black Holes and Time Warps: Einstein's Outrageous Legacy. A neat thing about these books, especially Black Holes and Time Warps, is that they put some real human characters to the physics they explain – I really enjoyed Thorne’s accounts of helping Carl Sagan make sci-fi physics in his novel Contact sensible, and making wagers with Steven Hawking.

 

If you’re really a complete novice at physics, there’ll be some comprehension problems, since advanced physics like string and brane theory are built on a foundation of firm understanding of basic mathematical physics. You don’t mention you age or life circmstances, Morgan, but if you’re in a position to, I strongly recommend you take all the math and science classes in traditional classroom setting you can. While not the wild ride of a Kaku or Thorne book, it’s a good and reliable way to get the prerequisite to really understand the wild, fun stuff.

 

In 1994, some years after Hyperspace and Black Holes and Time Warps came out, Lawrence Krauss wrote a short gem of popular science book titled Fear of Physics: A Guide for the Perplexed. I like this book a lot, because in addition to the usual discussion of advanced physics, he explains the underlying skills that make all physics possible, especially the process of guessing and estimation.

 

Anyway, in addition to getting all the traditional science education you can, I strongly recommend you get you to a library or brick-and-mortar or online bookstore and get your hands on the above popular physics books and any others that catch your eye. Science videos are good, but books are usually much better!

 

I also recommend you do some serious exploring of these and other subjects on wikipedia. My post above has lots of links to it – hypography has a special element (the

What is the "hyperspace" that Kaku refers to? Is it the 11th dimension or is something else?

Hyperspace simply means a geometric space with more than 3 dimensions.

 

For example, I can describe a cube in 3 dimensions as 8 points in 3-dimensional space with the following coordinates:

(1,1,1)-(2,1,1)-(2,2,1)-(1,2,1)-(1,2,2)-(1,1,2)-(2,1,2)-(2,2,2)

 

I can sketch the shadow this 3-D object casts on a flat surface like a sheet of paper:

 

I can do the same thing in 4-D space just by adding a number to each coordinate and doubling the number of coordinates, as follows:

(1,1,1,1)-(2,1,1,1)-(2,2,1,1)-(1,2,1,1)-(1,2,2,1)-(1,1,2,1)-(2,1,2,1)-(2,2,2,1)-(2,2,2,2)-(2,1,2,2)-(1,1,2,2)-(1,2,2,2)-(1,2,1,2)-(2,2,1,2)-(2,1,1,2)-(1,1,1,2)

 

 

Just as in 2-D or 3-D space, a hyperspace follows geometric rules depending on the kind of space it is – Euclidean, hyperbolic, etc. Euclidean space is the simplest, and the first taught in school. It’s common to abbreviate “3-dimensional Euclidean space” with “E3”, “4-dimensional Euclidean space” with “E4”, “99-dimensional Euclidean space” with “E9” and so on.

 

If you can do geometry in E2 (“plane geometry”) or E3 (“solid geometry”), you can do it in E4 or higher by just adding a number to each coordinate and extending the usual rules and formulae.

 

For example, the distance of the longest diagonal in a “cube” in E2 (a square) with sides 1 unit long is [imath]\sqrt{1+1} = \sqrt{2} \,\dot= 1.414[/imath]

 

In E3, it’s [imath]\sqrt{1+1+1} = \sqrt{3} \,\dot= 1.732[/imath]

 

In E4, [imath]\sqrt{1+1+1+1} = \sqrt{4} = 2[/imath]

 

In E99, [imath]\sqrt{1+1+1+ \dots +1} = \sqrt{99} \,\dot= 9.950[/imath]

 

So that’s what a hyperspace is. It’s pretty simple stuff, and useful for un-simple stuff like … string theory ;)

 

Moving on to your specific questions:

My understanding so far is this:

 

1) Vibrating strings form everything.

2) There are 10 spatial dimensions, plus 1 dimension of time.

...

Lawcat’s post #3 has a good summary of the fundamentals of string theory, which I’ll not try restating here. Rather, I’ll just point to this webpage, which I think give another good summary of string and brane theory, and add a few bits of info in response to each of your questions. I don’t understand string or brane theory as well as someone with a graduate physics degree in it, and even they often claim not to understand it well, so please don’t take anything I say as expert or authoritative :shrug:

3) Somehow, a string can expand to form a brane (How do they do this? Does a brane vibrate the way a string does? Why would a string expand like this?)

A brane is a generalization of string. A string is a 1-D object (a line) in some 1+D (“1 plus dimentional) space. A membrane is a 2-brane, a 2-D (plane) in 2+D space. There’s no limit to how large the value of p can be in a p-brane.

 

Just as a line can be draw on a 2-D (plane) space or in a 3-D (solid) space, a string can be embedded in any 2+brane. String theorists attempt to pick some number of dimensions for the space and brane that allow them to write equations that describe the fundimental particles – photons, electrons, quarks, guons, etc. – that experiments in the physical universe suggest exist. It gets terribly complicated.

4) Universes can form on branes. Our universe may have formed through a brane collision (How is it, then, that we can be sure that our universe is expanding? What if its just the brane that's expanding, since we apparently know that strings expand so much?)

According colliding brane theories, it’s possible to explain how the fundimental particles that existed at the instant of the big bang. 2 branes collide, creating the strings that are the fundamental particles of the universe.

5) There may be an infinite number of branes (and universes) floating around (Where do they float? Are they in hyperspace? The 11th dimension? What is the 11th dimension?)

They’re in a space with at least 1 more dimension than they have. The usual 2-brane, then must be in at least 3-D space – at least 4-D if branes can collide with any but there two closest neighbors.

 

String theories that work pretty well have been written using 10, 11 and 26 spatial dimensions.

Again, I'm really lost and would be grateful for a lifeline :-) Thanks!

I’ve been really lost thinking about string theory for a few decades, but can share a few things – questions, and tentative answers – to think about that gave a bit of direction to my thinking.

 

One key line of question is, are added dimensions – 7, 23, or whatever – physically real in the sense that the usual 3 spatial dimension are? Or are they just features of a possibly useful way of describing physical reality?

 

If the added dimensions are real, why can’t we see them?

 

No matter how I’ve tried approaching this question, the answer requires that the added dimensions be special – distinct in an absolute way from the usual 3.

 

I’ve seen two main kinds of answers to the above question.

 

The oldest appears in SF literature such as Flatland: A Romance of Many Dimensions (1884) or Spaceland (2002). These suggest that our sense organs and instruments are simply built wrong for detecting the extent of object in the added dimensions, and that our bodies and/or all of the physical objects we encounter are “flat” – have nearly zero extent – in the extra dimensions

 

The usual answer that appears in physics literature is that the added dimensions aren’t Euclidean – in particular, have a spherical or similar geometry such that tiny distances along them result in them wrapping back to their starting place, as happens when one circumnavigates a globe. This is called compactification, and such dimensions, “compact” or “compactified” dimensions. It’s described memorably, I think, in a limerick written ca. the early 1980s by physicist Howard Georgi:

Steve Weinberg, returning from Texas,

brings dimensions galore to perplex us.

But the extra ones all

are rolled up in a ball

so tiny it never affects us.

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Wow! I can't thank you all enough for taking the time to answer the questions in my post. I'm actually in Poland and it's very difficult to get good books on the subject here. I think I have a better understanding now though (and more questions), so I will try to purchase some more books from the US and have them shipped. My background is not scientific at all. I actually run a fantasy-based tour company for romance writers, so I don't think any of you will be seeing me in the lab any time soon, but I have a tremendous amount of curiosity, so I'm glad that there is a forum like this, where I can ask questions. You guys are great!

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