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Sum-over-histories+Light cone=?!!
Is Feynman's sum-over-histories calculated within the light cone? That can't be so, because if all histories are to be "summed", we must include histories in which particles travel at speeds greater than c. This would also be necessary for the space-tearing Calabi-Yau transitions to work since then a string would always be available to shield the rest of the Universe by sweeping a world-sheet from the cataclysmic effects of a tear in spacetime since all strings would be completing all of their possible paths in spacetime. Ugh okay I'm even confusing myself at this point... Basically, why do we sum in histories of particles traveling at speeds greater than c if we know that (as of yet) that is physically impossible? I mean, I've heard of tachyons and all, but I'm sure even those cannot make an INSTANTANEOUS trip to another end of our Universe - which is one of the infinite number of paths that a given particle is supposed to be able to take.
Also, how is it "summed over", exactly? And how are the infinities cancelled out?
Thanks guys.
- Alisa
Is Feynman's sum-over-histories calculated within the light cone? That can't be so, because if all histories are to be "summed", we must include histories in which particles travel at speeds greater than c. This would also be necessary for the space-tearing Calabi-Yau transitions to work since then a string would always be available to shield the rest of the Universe by sweeping a world-sheet from the cataclysmic effects of a tear in spacetime since all strings would be completing all of their possible paths in spacetime. Ugh okay I'm even confusing myself at this point... Basically, why do we sum in histories of particles traveling at speeds greater than c if we know that (as of yet) that is physically impossible? I mean, I've heard of tachyons and all, but I'm sure even those cannot make an INSTANTANEOUS trip to another end of our Universe - which is one of the infinite number of paths that a given particle is supposed to be able to take.
Also, how is it "summed over", exactly? And how are the infinities cancelled out?
Thanks guys.
- Alisa