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Mike2
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Do different points along a string travel faster than others points along the same string?
Originally posted by koi
I don't think you can think of a string as made up of points since there is nothing smaller than a string. Rather a string would be in a particular vibration state at a point in time. In one of my threads (minimum time) I stated that there is no smaller unit of time than Planck time which defines one complete "vibration" in one complete string. To go to a smaller point would need a distance smaller than Planck distance and a period of time smaller than Planck time. Then again, I still don't know if my observations are valid.
Originally posted by selfAdjoint
the free ends of the string are constrained by other physics to move at the speed of light. The vibrational motion of the string, AFAIK, is not linked to its translational movement in anything I have seen, but then I haven't seen very much.
Originally posted by koi
I'm not familiar with the world sheet (sorry, I'm just an ignorant physician). I am assuming that what you mean by continuous is that points along a range are infinitely divisible. However, time has been always "assumed" to be continuous just as distance has always been "assumed" to be continuous. String theory has shown that distance cannot be continuous in terms of infinite indivisibility because sub-Planck distances cannot exist within the framework of the theory (a string wouldn't fit). Furthermore, continuity as defined was a problem with point particles (not strings) since they had a zero dimension. The string does not have zero dimension. In fact it has 11 dimensions and a length of a Planck length.
I don't think continuity (as defined above) is a problem in terms of integration. My understanding is that integration is a summation of quantities in a defined range. Time would still be continuous in the sense that you must define it in multiples of Planck time. In other words, an integration across any defined range of time would be expressed in multiples of Planck length. I hope this makes sense.
Originally posted by Mike2
If time and space are discrete, then there is absolutely nothing between different points in space and different points in time.
Originally posted by koi
Think of a ruler with, say, Planck length markings. From a point particle standpoint, then I agree, between the marks there is absolutely nothing. But what if that whole space between the marks is taken up by an indivisible entity (such as a string). Then if you try to divide the space into a smaller measurement, you also divide the string, which renders the whole point of fundamentality moot.
Continuity and discontinuity are concepts in a point particle theory. Because the string has length, it takes up the whole Planck space from start to finish and there is no "in between."B]
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