The 10th Dimension

[Slice of Life]

Quarkboy, this is not how one should talk about physics to any audience. You're calculating yourself into a deep hole at the moment. For the layman you're derivation means nothing and somebody who has a bit mathematical training and is fond of conspiracy theories might conclude that the whole of quantum field physics is based on black mathematics, where limits can be swapped around freely and divergent terms are thrown away until something PRL-worthy comes out (which will be accepted because the referees are of course part of the conspiracy). That conclusion is then transported back to the laymen and in the end the crowd who doesn't believe in global warming and evolution because it's not in the bible has grown.

Saying let the zeta-function be defined by \zeta(s) = \sum_{n=1}^\infty 1/n^s and then saying zeta(-1) = -1/12 is a simply wrong. Yes, I do know what an analytical continuation means. I do not know what this all has to do with renormalization or string theory but QFT is not my subject of choice.

[Quarkboy]

Originally Posted by Slice of Life

Quarkboy, this is not how one should talk about physics to any audience. You're calculating yourself into a deep hole at the moment. For the layman you're derivation means nothing and somebody who has a bit mathematical training and is fond of conspiracy theories might conclude that the whole of quantum field physics is based on black mathematics, where limits can be swapped around freely and divergent terms are thrown away until something PRL-worthy comes out (which will be accepted because the referees are of course part of the conspiracy). That conclusion is then transported back to the laymen and in the end the crowd who doesn't believe in global warming and evolution because it's not in the bible has grown.

My point was show a part of the REAL calculation that was used in determining that string theory requires 10 dimensions of space-time, and that there is tricky and interesting math involved. I'm not going to go around preaching the greatness of string theory since I have my own serious reservations about its practical application. To me it's a fascinating mathematical construct the majority of which is very little understood. People like you who are afraid to let the public see the true complexity of what's going on because you fear losing funding for the research.... But what's ended up happening is a backlash within the community and a semi-public war between stringy theorists protecting their grant turf and alternative plans whose primary selling point now is "at least it's not string theory".

There's a reason I ran away to Japan for my post-doc. LHC will probably be the last gasp for string theory until it's proponents bail on it a few years later and the remaining people finally get back to answering the basic questions about it.

Saying let the zeta-function be defined by \zeta(s) = \sum_{n=1}^\infty 1/n^s and then saying zeta(-1) = -1/12 is a simply wrong. Yes, I do know what an analytical continuation means. I do not know what this all has to do with renormalization or string theory but QFT is not my subject of choice.

Well, the technical point is the zeta function is defined in that way for positive integer s. Then you extend that definition to the entire Re s > 0 complex half-plane by solving the functional equation it satisfies. Then you have enough points to uniquely analytically continue the function to the entire complex plan minus a point.
What this has to do with string theory is related to conformal symmetry. The field theory on the world-sheet of a string is a 2-dimensional manifold, and it has conformal symmetry. Translated into mathematics language that means we have analytic functions of one complex variable defined on some Riemann surface. The only way to preserve the analyticity of the fields (and thus, the overall conformal symmetry of the theory) is to renormalize, i.e. subtract out the infinities in a way that preserves the analytic structure, and this method using the zeta function is the standard way it's done. It predates string theory by quite a bit,, actually, even in physics.

Maybe I hit a nerve with people, but when I was in high school and I read about this fact about that sum in a book on String Theory (Green Schwarz and Witten), I thought it was COOL. I was intrigued, I thought "wow, that's neat, I wonder why that is?" I thought it would peak people's curiosity, but it seems in this climate people are more likely to assume scientists are always lying to them.

[USB500]

Originally Posted by Deathkillz

So how many of you believe in this theory find this theory plausible ? ^^ I find it whacky but surprisingly logical - all that follows now is the time machine

Source: http://www.tenthdimension.com/medialinks.php

Very interesting, since this reminds me on the ideas of alternate universes. And yes, although it stops at the 10th dimension, I believe in the plausibility of this theory.

Originally Posted by Riktasi

So basically, 10th dimension=

Yes?

then we don't have to argue on that

[innominate]

Originally Posted by Quarkboy

Maybe I hit a nerve with people, but when I was in high school and I read about this fact about that sum in a book on String Theory (Green Schwarz and Witten), I thought it was COOL. I was intrigued, I thought "wow, that's neat, I wonder why that is?" I thought it would peak people's curiosity, but it seems in this climate people are more likely to assume scientists are always lying to them.

No no, I'm interested as well, I just can't understand the equations nor really figure out what's going on. I might say: "pro!" to quarkboy, for boggling us with explicit equations, but if I try to remotely link the results of the equations to my layman understanding of string theory, I can't do it.

I'm in highschool and I've read 'A brief history of time' (stephen hawking) and string theory was described in the last chapter. Here's a bit of what I collected, in a, yes, very layman manner:

• By combining general relativity and the uncertainty principle, infinities occur.
  
• The infinities are eliminated via renormalization, a process which I suppose was afore-described by those explicit equations.
  
• String theory is the theory that basic objects are not particles, but are strings with a length but no other dimension (no 'time').
  
• There are things known as open strings and closed strings but I don't really know what they're about.
  
• Interaction between particles are described by the shape of the strings. The strings vibrate in waves, or something like that.
  
• String theory is only compatible if the universe consists of multiple dimensions. Why we can only observe the universe in 3 physical dimensions, is due to the fact that any number of physical dimensions other than 3 can't support life. Yes, anthropic principle.
  
• (I also remember something about the other dimensions curving up but I can't really remember what about)

So I may sound like a complete noob to those proficient in the area, but I just want to know what it's essentially about in the layman-way.

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With an ending quote in mind:

"You do not really understand something unless you can explain it to your grandmother."

-Albert Einstein

[Quarkboy]

Originally Posted by innominate

So I may sound like a complete noob to those proficient in the area, but I just want to know what it's essentially about in the layman-way.

---

With an ending quote in mind:

"You do not really understand something unless you can explain it to your grandmother."

-Albert Einstein

You don't sound like a noob, you sound like my Dad, who also read A Brief History of Time and thought he learned something. Unfortunately that book is now pretty outdated when it comes to string theory (as is Prof. Hawking himself, I might add).

The book I read in high school is a super high-level post-graduate reference (the first ever published on string theory), and well, it blew my mind at the time, simply from the fact that I stopped comprehending around page 12. That spurned me onward all the way to a Ph.D, oddly enough.

[Ascaloth]

You know, I thought I've seen all there is to see in forum arguments. But this argument in the language of high mathematics in this thread...now that's a whole new level entirely.