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beskeptical
2004-Dec-23, 08:57 PM
Since the other thread ended up being about a Kurt Russel movie, I thought I'd restart the thread.

I enjoyed the show. They are showing it in my son's physics class.

But it failed to answer a whole bunch of my questions.

I understand how gravitons might leak off into the 7 other dimensions. And I gather from a previous lecture I heard on gravity that we assume there are 7 other dimensions because that explains the ratio of gravity diminishing with distance.

1) Why does string theory itself require the extra dimensions?

2) Are there any ideas on the shape of these dimensions other than that they are very small? In other words do physicists think it is one space with 7 dimensions or 7 different spaces?

3) The program went on and on about the 'math' of string theory and how the one genius figured out that the 5 different string theories were really the same theory from different angles, but it never seemed to attempt to explain any of the math at all.

E=MC2 is at least understandable in that mass and energy are two states of the same thing.

Anyone care to give a bit more math in laypersons language other than to say certain string conditions give mass certain properties? How does string theory tie the equations of big and small together?

Astronomy
2004-Dec-23, 09:24 PM
1) Why does string theory itself require the extra dimensions?


The "extra dimensions" idea is just an extension of GR. It's the hallmark of superstrings that these extra dimensions are wrapped up, coiled around, and "string-like".



2) Are there any ideas on the shape of these dimensions other than that they are very small? In other words do physicists think it is one space with 7 dimensions or 7 different spaces?


They are all "space-like" dimensions: in other words they behave like spatial dimensions and not like time-like dimensions. Why there should be only two kinds of dimensions is a deeper question that I cannot answer.



3) The program went on and on about the 'math' of string theory and how the one genius figured out that the 5 different string theories were really the same theory from different angles, but it never seemed to attempt to explain any of the math at all.

E=MC2 is at least understandable in that mass and energy are two states of the same thing.

Anyone care to give a bit more math in laypersons language other than to say certain string conditions give mass certain properties? How does string theory tie the equations of big and small together?

The math gets tricky right quick. I don't pretend to follow it. What it says, though, is that certain phenomena must appear as you allow for more dimensions (call them w,v,u, etc. if you'd like). Each time you try to measure something, you deal with these extra dimensions in a big set of equations that is called tensor-arithmetic. This "tensor" in GR has a whopping 256 terms in it that allow you to describe how things affect the geometry of the spacetime around them and how they respond to such a change. Luckily, most of these terms in our normal universe are equal to other terms or can be ignored. In standard FRW cosmology, you can derive relationships between all but 2 of the terms and then use two differential equations to get at them in order to solve the evolution of the entire universe for all time (in theory).

If your model has n-dimensions, it causes the "curvature" and "stress-energy" tensor to have n^4 terms. That's dealt with by means of arcane tensor arithmetic, linear algebra, and mathematics of groups, rings, and so forth that's really out-of-my league, so you will forgive me if I duck out at this point.

Normandy6644
2004-Dec-23, 11:24 PM
1) Why does string theory itself require the extra dimensions?

Strings need room to move, basically. Most of this stuff comes out of the math from the theory, and as best I understand it as present time, strings have to move in more than just 3 spatial dimension to give rise to all the atomic phenomena.


2) Are there any ideas on the shape of these dimensions other than that they are very small? In other words do physicists think it is one space with 7 dimensions or 7 different spaces?

They are a mathematical construction called a Calabi-Yau shape. Here is the mathworld page (http://mathworld.wolfram.com/Calabi-YauSpace.html) about them, though it's pretty intense. The book explains them pretty well without the advanced topology.


3) The program went on and on about the 'math' of string theory and how the one genius figured out that the 5 different string theories were really the same theory from different angles, but it never seemed to attempt to explain any of the math at all.

Probably because it's so horribly complicated. :wink:

Here (http://www.superstringtheory.com/) is a great site that explains a lot of string theory and its workings, including what math you need in order to study it. There is plenty of interesting and useful information there.

Kesh
2004-Dec-24, 02:45 AM
One reasons your questions weren't answered is that (here, at least) the other two episodes didn't air yet. Should be on next week, with more info.

Normandy6644
2004-Dec-24, 06:22 AM
Also, there is a third episode that I haven't seen on TV, but you can watch it online at the nova website.

Brady Yoon
2004-Dec-24, 07:31 PM
I saw the show, and I think the confusion is because string theory is so counterintuitive, as the physicists on the show said. It's very hard to describe something so complicated to the layman, so there could be confusion as the intellectual level of the material is lowered. Quantum mechanics is complicated enough.... string theory is another level altogether.

gzhpcu
2004-Dec-24, 08:33 PM
Here is a pretty good site with some introductory information on SS and M-theory:
elegant universe (http://www.pbs.org/wgbh/nova/elegant/program.html)

beskeptical
2004-Dec-26, 11:02 AM
One reasons your questions weren't answered is that (here, at least) the other two episodes didn't air yet. Should be on next week, with more info.No. I've seen all 3 episodes. Though I did miss the spatial graphic of the extra dimensions the first time and saw them on the re-run.

Normandy's 2nd link is helpful. That mathworld page makes it clear why they didn't bother to go into it in the program. You have to learn a second language to even start on the math stuff. :roll:

Kesh
2004-Dec-26, 09:15 PM
yeah, the math is incredibly difficult. Considering I had a terrible time just learning basic calculus, I didn't even try that.

Wally
2004-Dec-27, 01:51 PM
Since the other thread ended up being about a Kurt Russel movie, I thought I'd restart the thread.



Pretty bad, huh! Hijacking my own thread from the get-go like that. . . :P

I wonder if that's considered bad web etiquette. . . :wink: