# Proofs for strings.

1. Mar 8, 2004

### Mentat

Ok, I know about the search for supersymmetric partner particles (sparticles) and the tests on gravity variance at small scales, but what other tests are there that can be used to add proof to superstring theory?

2. Mar 8, 2004

### notevenwrong

Neither of the two tests you mention are evidence for string theory. For this to be true string theory would have to predict some properties of sparticles or deviations from Newton's laws. You won't find any such predictions. And you won't find any others. String theory is not a theory, it is a hope that a theory exists. Unless this hope can be realized, you don't have a theory, and as for predictions, there are none, nada, zip.

3. Mar 8, 2004

### Nereid

Staff Emeritus
Hello Mentat, nice to have you back with us (or is this only a temporary visit?).

Data on sparticles, a better understanding of 'dark matter', evidence of short-range deviation from inverse square behaviour of gravity, something interesting in the incidence of cosmic gamma rays beyond GKZ, .... lots of things may help constrain the wild zoo of SMT possibilities.

However, AFAIK, notevenwrong is basically correct - no concrete predictions yet, even in principle. But, for something so rich, it may take a decade (century?) or two for the theorists to really get to grips with the concepts.

4. Mar 9, 2004

### Mentat

That's a pretty negative view of superstrings, but you must admit that they did have a couple of postdictions, right?

Well, I can't think of any now, except that one of them had to do with black holes and Hawking radiation...I'll get back to you on that.

5. Mar 9, 2004

### Nereid

Staff Emeritus
gravity

is S(M)T's astonishing postdiction.

6. Mar 9, 2004

Staff Emeritus
Sort of.

7. Mar 10, 2004

### notevenwrong

What you are thinking of are the string theory calculations that purport to reproduce the correct entropy of black holes. These calculations work for special limits of black holes, not the physical ones believed to exist. This is sometimes given as evidence for the consistency of string theory as a quantum theory of gravity, but is not a prediction. Any quantum theory that includes gravity should come up with the same result, so this is really a consistency check, not a prediction. If anyone ever does observe the Hawking radiation from a black hole and the entropy is right, this will not show that string theory is correct.

8. Mar 21, 2004

### marcus

Sazzles' question about "Proofs for strings"

Sazzles, a new poster at PF, asked a question about Higgs boson and support for string theory which fits into this thread. I will gather some "proofs for strings" posts, like hers, together. I have bolded sazzles' initial question and included some response to give context.

Higgs boson

Hi, I don't really know much about string theory, but I was wondering whether the discovery of the Higgs boson would back up string theory, or contradict it?
Thanks.

Chen: Isn't it the Standard Model that requires the existence of the Higgs boson? String theory has enough room in it for as many particles as you want.

sazzles: I'm not sure, I was under the impression that the mode of vibration of a string gave rise to its mass, so a particle like a Higgs Boson would not be necessary. But, like I said, I don't really know much about string theory.

-----end quotes-----

9. Mar 21, 2004

### marcus

Both Mentat and sazzles are asking similar questions,
essentially about the possibility of having experimental evidence
for some type of string theory.

Mentat's question:
Ok, I know about the search for supersymmetric partner particles (sparticles) and the tests on gravity variance at small scales, but what other tests are there that can be used to add proof to superstring theory?

Sazzles question:
Hi, I don't really know much about string theory, but I was wondering whether the discovery of the Higgs boson would back up string theory, or contradict it?
Thanks.

One interesting take on this is that since string theory makes no firm predictions it is impossible for any experimental evidence to either affirm or deny it. In other words the theory is so vague and multifarious that it cannot be either right or wrong. From this standpoint, it would be an improvement if the theory could be made definite enough to prove wrong but, so far, this has not been done. This perspective has been presented at PF by several posters most notably

Last edited: Mar 21, 2004
10. Mar 21, 2004

### Mike2

In the search for a TOE (theory of everything), we precisely search for principles that apply in every circumstance whatsoever. In one sense it is a tautology of nature, inherently true for every interpretation that nature can provide. And perhaps like a tautology, a TOE would be impossible to prove wrong. So what's the complaint?

11. Mar 21, 2004

### marcus

Hi Mike2 nice of you to drop in! It was a bit quiet this morning. I have no complaint about string theories---I just dont find string mathematically or scientifically interesting.
To answer your question "what's the complaint?" you need a response from those who criticize string theory because (they say) it is not a scientific theory.

The criticism goes like this IIRC: the hallmark of a scientific theory has always been falsifiability. If it wasnt possible for an observation to shoot down a theory then that theory had no content.
It would be more like a fantasy or mathematical fairyland than a working scientific theory. I guess as the last 20 years have gone by string has been looking more and more like a complicated dream "landscape" than like actual testable physics. That is probably the gist of what these critics say----there was a long discussion on SPR about it.

I didnt read the whole discussion on SPR because, as I say, string doesnt interest me much. But you probably followed it and know the viewpoints I mean.

I assume you are familiar with the basic axiom of empirical science that a model has physical meaning only to the extent that it makes predictions which can be tested by experiment----logically a theory must be disprovable in order to have content.

Unlike say Astrology and the Tarot Cards and Taoism which are complicated intellectual systems too but more like tautologies in that you cant effectively test them

So the question that seems to interest people is "Is string theory Science or Pseudoscience?" and you can find people on either side of the issue.

12. Mar 21, 2004

### marcus

Mike, what I find interesting is the issue of what is space.

I strongly suspect it isn't a subset of an Euclidean or Minkowski continuum.
I suspect that space is not a differentiable manifold.

I was just reading a paper where the quantum states of space
are things like
$$|K,c\rangle$$

K being a knot and c being a discrete quantum number.

that is, all of space---this dynamic bendy ripply not-quite-flat set of relationships where all the galaxies live----is a point in a certain countable-dimension hilbertspace and the countable orthogonal basis for that, the "pure" states of space, is an object like
$$|K,c\rangle$$

and all the electrons and photons and other fields can be defined on top of that knot K, by adding labels to the nodes and links.

Well, that paper intrigues me because I want to know what space is. I want to know why and how it bends
as the matter flows around in it
I want to know why and how the density of dark energy and other
energy densities cause the thing to curve

and I would like to know how space is different at a microscopic level---at "planck" scale.

so I need a theories that dont just use some minkowswki space or continuum or manifold (some vintage 1850s thing) which is the same at all scales no matter how close you look. a background dependent theory with a precommitment to some differentiable manifold is just not very intriguing.

As a "TOE" it intuitively has to be wrong because it doesnt deal directly with the basic issue (which has been hanging up physics for nearly a century) of what space is.
other people can critcize stringery because it aint predictive, but I just pay it no mind

13. Mar 21, 2004

### jeff

But of course you don't understand string theory (or LQG) so your opinion is meaningless. However, you seem interested in spacetime geometry, so allow me to enlighten you about what strings have to say about that, since unlike with LQG, it's quite remarkable. In string theory, spacetime geometry - or just geometry for short - and gauge theory are related in an extraordinary way in that they can provide equivalent descriptions of the same physical systems. For example, suppose we have a system whose spacetime geometry includes N chunks of space, each with infinite extension along the same set of noncompact spatial directions and separated from each other along the same set of compact directions. Such objects are called D-branes and in string theory their presence is equivalent to a string theory which at low energies is just a U(1)N gauge theory. We can enlarge this symmetry by taking some of these branes to be coincident. If we take all to be coincident, we get a U(N) yang mills theory. There are many amazing examples of this sort of thing in string theory. This connection between geometry and gauge theory is very deep and is not yet completely understood, but is nonetheless affecting our perspective on and promises to deepen our understanding of gauge theories in ordinary quantum field theory. Anyone who dismisses this as "uninteresting" is probably too warped to take seriously.

Last edited: Mar 21, 2004
14. Mar 21, 2004

### Mike2

It might help to think in terms of how the universe started to begin with. For examples if everything started from a singularity, did it grow continuously, or did it grow in quantum leaps, or were other points added adjacent to the first point? I can't think of any other options.

If it grew continuously, then of course space is a continuum. If it grew in quantum leaps, then there is usually some equation on continous variables that give rise to these quantum states. If other points were simply added to the first, then there needs to be some sort of continuum to communicate the state of one point to the next. Without some sort of elasticity through a required continuum, then no information can travel from one place to the next.

15. Mar 21, 2004

### marcus

This shows ingenuity, you are proving the necessity of a continuum.

In a quantum system with a discrete spectrum corresponding to separate pure states
the continuous medium could be the hilbert space of linear combinations of pure states
there can be a continuous transition in the amplitudes saying which of the two states will be observed

in Loop Gravity the quantum states of space form a hilbert space
with a countable (discrete) basis you can think of as the pure states
and one can take continuously variable linear combinations or mixtures of these by combining pure states with various amplitudes.

So there does not need to be any continuum in the sense of a manifold
(a la Riemann 1850)
but yes there is a linear space of mixtures of pure states
which kind of substitutes for that, takes on some of the functions
which a geometric continuum might have performed.

BTW the quantum evolution of the universe is followed by Bojowald
in several papers and it does, as you visualized, proceed in "jumps"
of the variables like volume, density, curvature, scalefactor
and as you might imagine these jumps are very tiny

after a few hundred jumps the model blurs into the semiclassical or classical model
so the quantization (of the evolution of space itself) is only evident near what was the classical singularity

after a few hundred steps (by the difference equation version of the einstein equation) the changes get so small that the new model converges to previous model

but LQG actually does away with the classical singularity, it does not exist in the history of the universe, so in that sense your description might need a slight modification

there are some links to Bojowald papers in the LQG "surrogate sticky", one of the recent posts there has them if you want

16. Mar 22, 2004

### modmans2ndcoming

if particles are really just vibrations of a string, then would that not explain why when you smash a particle into another, why you get all those other particles? the energy release changes the vibration of the strings that make up he particle and send them off shooting in all directions.

17. Mar 22, 2004

### Mike2

How are these quantum states determined if not by use of some diff eq on continuous variables. So there must exist some continuous variable somewhere. Perhaps you are suggesting that physical quantities are some sort of transformation of some other continuous space.

18. Mar 22, 2004

### marcus

Hi Mike, you sound interested and if you really are there's probably no substitute for reading the papers themselves

quantum theories are constructed from classical ones by a bag of "quantizing" techniques. I am not sure what you mean by determined but if I understand you mean "derived from" and I very much agree that quantum gravity is derived from classical GR gravity by
quantizing

A good recent paper is Bojowald's
"Recent Progress in Loop Quantum Cosmology"
the earlier differential equations are still there as limits of the quantized difference equation model.
He shows you the quantized Einstein or Friedmann equation and it is a difference equation (time goes in tiny discrete steps)
and what the difference equation predicts is the same
(in the limit) as the WheelerDeWitt and ultimately the Friedmann differential equation.

You say "there must be a continuous variable somewhere" and I you are right. down at a microscopic level things are discrete but in the limit (after hundreds of timesteps) things look continuous

so the continuity you want is in the large scale limit

and it is also back in the historical roots from which the quantized theory was derived---the classical theory that provided the inspiration and guidelines for constructing the quantum one

should I get some links for some Bojowald papers? he has some for more specialized audience and some for wider audience. If you want I will get 2 or 3 links and you can take your pick (or maybe you have the links already)

19. Mar 22, 2004

### Mike2

So does he simply start with the assumption of discrete time steps, etc so he can use difference equations instead of differential equation? Or does he justify the assumption of discrete time?

Traditional quantizing uses continuous variables (space and time) to quantized things that are not space and time, such as energy levels. Here you use space and time to quantize space and time. There seems to be a inconsistency in the definition of the variables.

I'd like to know the prerequisits of these papers you mention.

20. Mar 22, 2004

### marcus

No

its not an assumption, it is forced
he chooses a variable related to the expansion of space to serve as the clock and that variable like everything else turns out to be quantized (to advance in tiny steps)

back then near the big bang there werent any Rolexes
so you pick the steadiest natural process in sight
to serve as a time-reference for the other stuff going on
and all the processes in sight are quantized.

actually come to think of it I do not know of any physical clock that advances continuously

In any case, when you quantize GR (the Einstein equation governing
spacetime, geometry, energy density, volume, area etc) that
quantizes the whole shebang.

no continuous physical clock is available
discrete's the only time in town

You might look at Ashtekar
"Quantum Geometry in Action: Big Bang and Black Holes"

Or at Bojowald
"Quantum Gravity and the Big Bang"

Let me know if you have any trouble finding the arxiv preprints.

Mike, I think that continuity is just something that discrete systems exhibit in the limit
and that Bojowald is studying the universe within about 100 planck time units of the classical singularity and down at that level there just plain ISNT any continuity or continuous time.
So he just takes what nature offers.

LQG does not decide ahead of time to have things discrete---it is not a "lattice" type theory---one does not say well I think I will choose to have time go in little planck-size steps! The discreteness took the original researchers by surprise. Story of this in Rovelli's book, bottom page 193 top page 195. Kind of amusing. It was around 1995.

Whole story of humanity gradually discovering the fundamental discreteness of things is a kick.