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Jimmy Snyder
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In Zwiebach's book "A First Course in String Theory", I read that the endpoints of an open string move at light speed. Do any of the interior points of a string also travel at light speed?
selfAdjoint said:No. And the more recent thing about open strings is to fix those ends on branes with Dirichlet boundary conditions (i.e. end points don't move around, but string is free to wiggle anyhow apart from that). That's where D-branes came from.
jimmysnyder said:Thanks, SelfAdjoint. Actually, I have a bunch of questions I would like to ask. Since they all are motivated by Zwiebach's book, the first question is: Do you have a copy of the book?
Your comments about Dirichlet conditions on the endpoints are helpful. In fact, in my original post I should have written: FREE endpoints of an open string move at light speed.
nrqed said:The ends *do* move around, even if they are fixed to a D-brane. Their motion is simply constrained to the space enclosed by the D-brane (like if its a D3 brane, the string moves in 3 spatial dimensions). Am I not right?
jimmysnyder said:Hi nrqed,
I am just starting Chapter 12. I found Chapter 10 exceedingly difficult because my background in QM is rather weak.
I need help understanding one point from page 98. The question that started this thread was directed toward clearing the matter up.
On page 98, it says that at each point on the world-sheet there is a timelike vector tangent to the world sheet. I can't understand the proof given in the book and I wonder if someone can explain it to me.
I sent an e-mail to Professor Zwiebach pointing out that since free endpoints move at light speed, there would fail to be timelike tangent vectors there. What is more, Quick Calculation 6.3 on page 99 indicates that there may be points where there are no timelike tangent vectors. He agreed with me and on his web page related to the book, he publishes these points. However, I also pointed out to him that these facts may render the proof on page 98 flawed. He has not commented on this, so my current situation is that I don't understand the proof and I don't completely trust it either.
At the same time, I consider the matter to be of utmost importance because the existence of the timelike tangent vector is at the heart of the parameterizations used in the following chapters.
I would be ever so grateful to anyone who could provide me with a proof that I could understand.
jimmysnyder said:Hi Pat,
Thanks for your careful reading of my post. No, I have never studied QFT at all. I did read the first few pages of Professor Zee's "QFT in a Nutshell", so I have seen the simple calculation of the 'sum of histories'. I know it's a prerequisite for Professor Zwiebach's book, but I thought I could pick it up as I went.
I forgot to ask you how far you have gotten in the book.
I must thank you for an important insight. When you said that you could paint one of the points, you made me realize what he means when he says:
"the string is not made of constituents that whose position we can keep track of"
His statement is not one that you could prove, it is an assumption. It is equivalent to saying that the string has no underlying structure, it is the fundamental 'thing'.
I wonder if the statement that a timelike tangent vector exists at each point on the world-sheet is not itself an assumption, and his 'proof' is irrelevant (to add to its growing list of deficiencies).
jimmysnyder said:Hi Pat,
I don't know how to quote your post, so I just repeated it below.
nrqed said:it is still classical (in the sense of not "quantum fuzzy") and that each piece evolves at a speed below (or equal to) the speed of light. Accepting that, then it seems to me that the existence of a timelike tangent vector everywhere
jimmysnyder said:The way I think of it is that although we can visualize the world-sheet, and we can think about the plane tangent to the sheet at any point, we cannot trace a curve on the sheet and say that the curve is the world line of any physical point. For the same reason, I don't think we can identify any piece of the world-sheet and view it as the subsheet of a piece of the string.
If your approach were correct, then why would the endpoints be treated special? Indeed, I asked Professor Zwiebach that same question, but he didn't answer me.
selfAdjoint said:Perhaps he sees the open string as a "thing with endpoints" but not further decomposable?
selfAdjoint said:This whole discussion seems odd to me
selfAdjoint said:because when they start really working with the worldsheet they do distinguish points on it, for example the "vertices".
nrqed said:I don't seen how to rule out that the tangent vectors be null instead of timelike. That restriction is something I don't understand. And it maybe what you are really worried about.
nrqed said:I don't know if you mean special in the sense that we can follow the endpoints or special in the sense that it moves at c.
nrqed said:Why can't we say that we can always find vectors tangent to the worldsheet which are either null or timelike (instead of saying that there must be at least one timelike tangent vector)? I don't know. Maybe that's your whole point.
nrqed said:Why can't all the string move at c, without vibrating or spinning, for example?
jimmysnyder said:selfAdjoint, thanks for your input. You bring up a number of interesting issues.
Wow! This is great food for thought. I wonder if the endpoints of a string can be considered constituents of the string. If so, that would mean that the world is made of strings and endpoints. Zwiebach never speaks of an open string without it's endpoints, but I don't see why not. The worldsheet of such a string would have no edge.
The speed of open strings is important because it is one of the fundamental properties of strings in string theory. It determines the behavior of strings and their interactions with each other and other particles. Understanding the speed of open strings is crucial in developing a comprehensive understanding of string theory and its predictions.
In string theory, the speed of open strings is determined by the tension and mass of the string. The speed is calculated by dividing the tension by the mass, which results in a value that is close to the speed of light. This is consistent with the idea that strings are fundamental particles with no internal structure.
No, according to the principles of special relativity, the speed of light is the maximum speed at which any object can travel. Since open strings are fundamental particles, they are also subject to this speed limit. Therefore, the speed of open strings cannot exceed the speed of light.
In string theory, the number of dimensions is not fixed, and it can vary depending on the specific type of string theory being studied. However, the speed of open strings is always constant and independent of the number of dimensions. This is because the speed is determined by the tension and mass of the string, which are intrinsic properties and do not depend on the number of dimensions.
At this point, the speed of open strings cannot be directly measured or tested experimentally. However, string theory makes predictions that can be tested through experiments, such as the existence of supersymmetric particles. If these predictions are confirmed, it would provide evidence for the validity of string theory and indirectly support the concept of the speed of open strings.