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For a point particle we have light cone: enter image description here

String Theory- with it's extended body concepts- however will not admit a light cone such as this. In particular the most problematic causal issue would be the following illustration:enter image description here

From the illustration the past light cone from the endpoint of the string leading in it's direction of motion is seen as overlapping the future light cone from the opposite end.

It is the rhomboid region that I wonder about- here it seems the past and future of the string would continually interfere with one and another.

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Why is the string pointing from the past to the future. – centralcharge Jul 4 '13 at 15:48

Two comments, which I think add up to an answer:

0) String theory has no off-shell formalism. (Indeed, it's not even clear that string theory has equations of motion in the traditional sense.) There are no observables measuring quantities strictly localized in the spacetime. Diagrams like the one you have above only appear inside the sum over virtual histories which defines string theory's S-matrix elements. So you can't necessarily make any physical conclusions by thinking about the position of strings in spacetime.

1) Inside the sum over histories, yes, the past and future continually interfere with each other. This always happens in Feynman integrals, even in ordinary quantum field theory. It's why antiparticles play such a crucial role in field theory; the sum over histories isn't necessarily causal, but it is when you have antiparticles and the right statistics. (In popular science, people talk about antiparticles being regular particles going backwards in time.)

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This appears to fall back to Quantum Field Theory and does not give an answer within the context of String Theory. That being said: in QFT the problem of closed loops in the Feynman Diagram (which the rhomboid region would clearly signify) is as of yet still unsolved and quite problematic. I believe that motivates my question (within the context of String Theory) even further.. – user1567 Jun 24 '12 at 20:17
"in QFT the problem of closed loops in the Feynman Diagram (which the rhomboid region would clearly signify) is as of yet still unsolved and quite problematic." Most physicists would disagree on that point. Even mathematicians acknowledge these days that the hard part is dealing with infrared problems like dressing photons, mass gaps, and the formation of bound states. – user1504 Jun 24 '12 at 20:48
the loop problem in Feynman Diagrams is not indicative of the "infrared problems"? – user1567 Jun 24 '12 at 20:56
The loop problem isn't a problem anymore. When it was a problem, it was a problem because of ultraviolet divergences in naive perturbation theory. But renormalization solves this problem, and we've had a physical understanding of renormalization since the 1970s; Ken Wilson got a Nobel Prize for it. Infrared problem aren't conceptual problems in the same way: UV problems mean you don't know what the right equations are; IR problems mean you don't know enough about the solution to these equations. – user1504 Jun 24 '12 at 21:10
On a different topic: My answer doesn't fall back on QFT. I used QFT examples to illustrate the main points: Strings embedded in spacetime only appear as intermediate virtual states in string theory. This could lead to causality problems, if the string-anti-string balance weren't right. But in the perturbative string theories which people actually study, the balance is right. – user1504 Jun 24 '12 at 21:15

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