I am not a scientist - very much a layman, but I’m very interested in string theory, and have been trying to teach myself about it.
Two questions (well, about 1001 questions, but I’ll start with two).
I believe strings have length, but no thickness: they’re one dimensional. Can anyone help me understand the concept of a single dimension? (I’ll come to the problems I’m having with eleven dimensions later ).
Vibrating strings: I understand the concept of this - but - where do strings get their energy to vibrate from? Do they have any mass, and if not, why do they vibrate? I understand that massless particles like photons have a barely moving string and that due to quantum uncertainty the string has negative energy to counterbalance the positive. Probably a silly question, but how do they start vibrating and can they stop vibrating?
I’m sure someone will come along and discuss your question but I’d like to state that I cannot imagine a one dimesion or even a four dimension universe. Let alone eleven or twelve!
They don’t really “start” and “stop” vibrating, they just vibrate. It’s part of what they are. You may as well as how an electron “starts” moving around a nucleus. Incidentally, both “vibrate” and “move around”, respectively, are oversimplifications that come from trying to think about quantum systems with classical terminology.
Anyhow, the vibrations aren’t really directly connected with mass. In fact pretty much every particle we’ve seen (if I read Green, Schwartz, and Witten correctly) falls into the lowest string energy state. A string that’s really vibrating immediately has a huge amount of energy compared with any particle we can currently observe.
Ah! Easy for you, maybe. Not for me: every line I can imagine has at least an infitesimal thickness. How can it have properties in only one dimension - going from left to right, but not up and down or in and out?
That, in a way, is my question: does ’ they just vibrate’ mean we don’t how they became to be in a vibrating state. And, yes, I do wonder why an electron ‘moves around’ a nucleus.
[Second paragragh] I thought that vibrations were a form of energy, so how are the vibrations not the same as energy? Electrons and up and down quarks have mass. and mass is equivalent to energy, and if that’s right, then where does the mass/energy come from if not from vibrations?
I apologise if my suppostions aren’t correct: for example, I may have the concept of vibrating all wrong, but I’m trying to struggle through a dark and entangled path here! Any help is very much appreciated!
Think of a primary school number-line for a moment; there is a progression of numbers 1 2 3 4 etc, then we’re told that it goes in either direction, so it’s actually …-3 -2 -1 0 1 2 3…
Then we learn that the spaces between those numbers are not empty; so 1.5 represents a point between 1 and 2.
But any number (integer or decimal) on that line occupies an infinitesimal point on the line; zero is zero if you move in either direction from the dimensionless point that is zero, you’re not at zero any more, you’re at 0.0000000000…001 or -0.0000000000…001 - there is only one point on the number line that represents any given number and that point does not spread out along the line in either direction - that point has no size.
That’s how wide a one-dimensional line is - it has no width - it is the edge of an idealised knife-blade that tapers not down to one atom thickness, but carries on and tapers all the way down to zero.
Bear in mind that strings are theoretical mathematical constructs, and being such, do not have to fit the reality that you are familiar with. It is, however, useful to use analogies, and Greene’s The Elegant Universe does a decent job. I’d also recommend Abbott’s Flatland, Burger’s Sphereland, and Stewart’s Flatterland if you’re interested in exploring the perspectives of inhabitants of different dimensions.
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