# A number of questions about string theory

I’m currently reading Brian Greene’s book The Elegant Universe (~2000), attempting to get to grips with ST. I’m about 1/3 of the way through, and I think I need some stuff clarified before I proceed much further. I had a bit of an issue with what I knew about ST before starting this book, but I’m afraid his rather enthusiastic take on it is not exactly sweeping me along the belief pathway. However the first 3 chapters explaining relativity were very good indeed.
1/ he hasn’t explicitly said whether the strings are open or closed, but every diagram so far has shown them as closed. The Wikipedia article says they can be either in various circumstances. Is this something that’s only been clarified since the book was published?

2/ he says that various modes of vibration of the strings correspond to various fundamental particles (electron, quark, graviton etc). By vibration does he mean a literal physical vibration? If so I can’t grasp what that even means for an infinitely-thin string. Is it that the term “vibration” is merely a handy analogy, like the spin of an electron, or is it actually a physical vibration in some sense?

3/ and does that mean that if the string comprising an electron, say, can have its mode of vibration changed by some means, that it instantly transforms into a different type of particle?

4/ vibrations in real string have only wavelength, amplitude and frequency. This does not seem to be enough variables to cope with all the fundamental particles known about, let alone the second set needed for supersymmetry. But perhaps this is an artefact of the vibrations being just an analogy, there are more degrees of movement available for a 1-dimensional entity?

I’m sure there are more to come that I can’t think of right now, but thanks to anyone who can help me along a bit here.

From what I remember of Elegant Universe, Greene hasn’t even started explaining string theory by the one-third point. He’s building up to it with what he thinks is the proper foundation. I’m pretty sure he’ll give you the answers you’re looking for if you work with him. That might be better than by getting people making a variety of points that might actually conflict with the book.

1, I don’t know.
2, I fail to see the difficulty in an infinitely-thin string vibrating. Why would it be any more difficult for a thin string than for a thick string? Explain your confusion in more detail, please.
3, keep in mind that there are still various conservation laws which need to be obeyed, which will prevent most spontaneous conversions from one particle to another. You’d need an interaction with some other particle or particles to balance out all the conservation laws.
4, vibrations in real strings also have polarization. A guitar string could vibrate up-and-down, or it could vibrate side-to-side (or it could vibrate diagonally, but that’s really just a combination of those two). For a 1-d string in 3-d space, there are only two independent polarizations available, but in higher numbers of dimensions, there are more. It’s my understanding that this is why the String Model needs so many spatial dimensions.

No expert on string theory and some of this is a re-hash of what Chronos has already said:

1. It’s not something that’s occured since Greene wrote his book. My guess is that Greene just kept things simpler by discussing clsoed strings only. Closed strings appear in all varities of string theory, open strings do not.

2. Does the fact that mathematics of tiny infinitely thin strings vibrating describes the universe very well (not that string theory has got to the point where this can be said of it) mean that there are actually these tiny strings? That’s one for the philosophers, I think especially when things get this small and this far out of everyday experince, put ontology on the backburner.

3. Standing waves on strings have to obey the equations governign standing waves on strings, do idealized strings suddenly flip from one mode of vibration to another spontaneously?

4. As Chronos says, I understand this is one of the reasons that string theory needs so many dimensions.

Thanks a lot for the responses!

On review, I’m actually about half-way through. We’re just going through dimensions > 4 that are so tightly curled they are undetectable sigh

1/ the guy who lent me the book says he does address the open vs closed issue, so I’ll get to that it seems

2/ well really, how can something that’s infinitely thin vibrate? There’s nothing to actually shake. But neither of you seem to have addressed my question: is the vibration referred to an actual physical back-and-forth motion of something, or is it an analogy on par with electron spin?

4/ yes, as he’s started to introduce extra dimensions I have to accept that vibration along them is possible, if inconceivable

Well my point is that strings in the everday definition are made up of matter, whereas in the string theory matter is made up of vibrations on these strings, so it’s a bit of a moot point if string theory posits the existance of actual tiny strings.

The best way to look at is that the equations governing standing waves on idealized (i.e. infinitely thin) strings in whatever dimesnions on quantum level allow us to recover some aspects of larger scale physics.

Physics is about mathematical models that make empircial predictions (not that string theory has yet got to the stage where it makes solid empircial predictions). Arguably ontology is not completely irrelevant, but it’s often moot.

Oh really, I haven’t got that from the book at all; he’s mentioned strings vibrating ad nauseum but not that these strings are made of vibrations (whatever the hell that means …). This is the kind of thing that makes me profoundly unsatisfied with what I read of string theory. Oh well, I’ll keep ploughing though, we’re up to wound and unwound strings (no mention of open strings yet).

If matter is made up of strings, then you can’t ask for strings to be made up of matter. They have to be something more basic. It’s not little billiard balls at the bottom. In fact, it’s the theories that have little billiard balls making up bigger ones that fail the common sense test.

No youmidunderstand what I said, ordinary matter is standign waves on these strings (or if you prefer matter is made of strings and gets it’s properties from these waves,it’s really much of a muchness), what the strings are themselves is a moot point, even fairly fundamentalproerties such as mass come from their vibrations.

He mentions it briefly in Chapter 12 (possibly later in the book, but that’s how far I am right now). One of the five versions of string theory allows open and closed strings; apparently the rest only allow closed strings.

I really loved the first two sections describing relativity and quantum mechanics. The string theory stuff is way over my head, but I’m going reeeeally slow, reading the endnotes whenever they don’t start with “For the mathematically inclined reader” and re-reading passages over and over, so I can at least get the basic idea. My mind is blown, like, every other page

I agree, the pre-string theory stuff in the book is as good an explanation of relativity as I’ve seen anywhere.

Perhaps it helps to think of string theory as just taking what’s worked for point particles, 0-dimensional objects – relativity, quantization, etc. – and applying it to 1-dimensional objects, i.e. strings; conceptually, there’s little difference beyond that, though string theory results in a considerably richer structure (and of course, you can go further than that, to 2-dimensional surfaces – branes, from membranes, whence the M in M-theory (somewhat depending on who’s telling the story) --, and so on).

This is certainly an avenue one might want to explore, if, say, certain things didn’t work out too well with particles, such as the quantization of general relativity – and indeed, string theory does work to round that particular corner.

One thing strings – classical strings, as in bits of actual string (though idealized as one dimensional) – can do that point particles can’t is vibrate, just like a guitar string does. You can think of this as literally a line vibrating, as in being pulled at and snapping back and forth – a 1D object has certainly enough structure for that (actually, classical relativistic strings can do far wilder things, like spontaneously developing cusps etc.). One can then ‘quantize’ the theory of the classical string, in order to get what is commonly called ‘string theory’; quantization is a process, more like a heuristic in most cases, which allows you to deduce a quantum theory from a classical one, and it proceeds in the string case more or less analogously to the point-particle case.

It’s there that questions like ‘what actually vibrates, and how?’ become a bit dicey; but that’s not a feature of string theory in particular, but of quantum theories in general. The thing is, nobody really knows what ‘quantization’ actually is or what it ‘means’, ontologically speaking. It was found to be necessary in order to make theory agree with experiment, and quite a few sophisticated techniques have been invented to deal with it and surrounding concepts, but the mystery of what, actually, a quantum particle (or quantum string) is, or why we need it, has at best tentative answers still.

This may seem dissatisfying, but in one sense, it’s quite natural: the objects of our everyday experience, that make up our ‘classical’ world, that we are familiar with on an intuitive, effortless basis, don’t suffice to create a working universe – the whole thing would come apart for various reasons, infinities and instabilities all over the place. So, to make a universe that works, you’ll need to recourse to different sorts of things alltogether – but then, those won’t be ones we have a very clear grasp of, being entirely removed from our ‘sphere of familiarity’.

Besides, I think there’s a good argument to be made that this familiarity, this intuitive making-sense of the objects around us, is really just habituation, being used to the weirdness of the classical world and thinking of it as normal. We don’t so much understand these things as we simply have learned what they do, and when, and how they react in a great many situations. The quantum world is not necessarily weirder than the classical one; it may just be that we haven’t gotten used to its weirdnesses yet, which to us feels as if it makes no goddamn sense whatsoever. But a quantum intelligence, suddenly confronted with our classical world, would perhaps not react any differently.

This all just to say that just because something is nonsense, doesn’t mean it’s wrong.

Of course, one might just answer the question “What is a quantum particle, anyway?” with “It’s something which obeys this set of equations”.

Well, to be honest I don’t find it any harder (or easier) to conceive of a 0-dimensional point vibrating around a point than a 1-dimensional string vibrating along its length - in both cases there is nothing in the plane of the vibration. However I think what you are getting at is a difference in the character of the vibrations; there are more degrees of freedom to vibrate a string than a point?

And I think you are confirming my suspicion that the term “vibrate” here is a conceptual analogy akin to electron “spin”, rather than being anything literally shaking back and forth?

True, and operationally, that’s probably what most physicists do anyway. But this isn’t the same, intuitive kind of understanding we (think we) have about everyday objects, and I suppose one could argue that is constitutes more of a description than an explanation of the quantum particle’s nature…

Not back and forth, just up and down (though of course in the quantum theory, things don’t fit nicely in such categories, but in the classical theory things work out rather intuitively). And while one could draw an analogy to how the concept of spin changes from classical to quantum realm, one should note that quantum strings can spin, as well, and that this spin has nothing to do with its rotation. Indeed, one could call the superstring just as well ‘spinning string’, as the spin already leads to (world-sheet) supersymmetry (as it does in the case of the spinning particle, but people tend to forget about that).