Is there a limit to which strings can break, and thus subdivide? Why couldn't a string at the Planck length break into smaller strings? Couldn't strings decay into smaller and smaller strings indefinitely?
So, why don't strings break into smaller strings less than the Planck length, and so on, indefinitely?
So, I take it that it's an axiom of string theory that fundamental strings can't break. However, you don't have an explanation for why that is true besides pointing out that it is assumed to be true. Nevertheless, as strings can break, it seems absurd to assume that only fundamental strings can't break without explaining what in nature prevents that breakage. Is it possible in your mind that in reality strings might break at less than the Planck length?
Of course, string theory assumes fundamental strings can't break. But, string theory does not explain why they can't break, but only assumes they can't break. It's an assumption that may be wrong. How do you know smaller strings don't exist - or can't exist?
Strings, like real physical steel strings that make a "sound", can be divided as much as you like, both in practice, these days (you could look at an attosecond's worth of string vibration, or a fractional magnetic potential's worth of electron spin, say) and abstract-wise, or with math - the real stuff. A string is 'like' the real number 1, which you can divide as often as you want. What you're asking is the equivalent of: "is there a number larger than the real number 1 that I can divide that number by?".
I believe that all BenTheMan is saying is that string theory does not permit fundamental strings to break without explanation. It seems very odd to me to have a theory that says strings can break, but they can't break less than the Planck length. It makes more sense to say that strings can break into smaller strings until such point as you can explain why there is a limit to their breakage.
That just shows how intuitive the answer is. So, why can't strings break into smaller strings at less than the Planck length?
I don't think any scientist, never mind a string theorist like Ben, to be able to answer why a string cannot snap into smaller componants, other than to say, only than to say, it would be analogous to trying to remove all the emnery of an atom, and hoping the mass would remain. At Planck Level, our calculations cease to have a description below \(1.616 x 10^{-35}\), in a time \(5.3 x 10^{-44}\)... It's because anything we know about fundamental objects, seems to be well-described in these ''supposidly'' infinitely small scales. Now, there may be smaller things, solitons, but we don't have the technology to even test this.
No, that isn't it at all. They are funda-****ing-mental. Can you cut an electron in half? No. Because they are, in QED, fundamental! You don't actually know what a soliton is, do you? Stop pretending you know any string theory or quantum mechanics. Got a ****ing clue!