Proofs for Superstring Theory: Tests & Variance

[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?

 

[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.

 

[Nereid]

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.

 

[Mentat]

Originally posted by 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.

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.

 

[Nereid]

gravity

is S(M)T's astonishing postdiction.

 

[selfAdjoint]

Sort of.

 

[notevenwrong]

Originally posted by Mentat

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. [/B]

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.

 

[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.

-------from Sazzles' Higgs question thread----

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.

Chen: Well, me neither. You should probably wait from an answer from someone who knows about this...

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

 

[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

https://www.physicsforums.com/showthread.php?s=&postid=159335#post159335

https://www.physicsforums.com/showthread.php?s=&postid=148450#post148450

https://www.physicsforums.com/showthread.php?s=&postid=128657#post128657

https://www.physicsforums.com/showthread.php?s=&postid=149255#post149255

 

[Mike2]

Originally posted by marcus

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.

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?

 

[marcus]

Originally posted by 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?

Hi Mike2 nice of you to drop in! It was a bit quiet this morning. I have no complaint about string theories---I just don't 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 doesn't 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 can't 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.

 

[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 don't 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.

so you see why I don't worry much about string/brane business.
As a "TOE" it intuitively has to be wrong because it doesn't 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

 

[jeff]

Originally posted by marcus
I just don't find string mathematically or scientifically interesting.

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.

 

[Mike2]

Originally posted by 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.

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 continuous 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.

 

[marcus]

Originally posted by Mike2
...

If it grew continuously, then of course space is a continuum. If it grew in quantum leaps, then there is usually some equation on continuous 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. ...

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

 

[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.

 

[Mike2]

Originally posted by marcus

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

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.

 

[marcus]

Originally posted by 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.

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)

 

[Mike2]

Originally posted by marcus
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.

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?

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

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.

[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)

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

 

[marcus]

Originally posted by Mike2
So does he simply start with the assumption of discrete time steps, etc so he can use difference equations instead of differential equation?

No

...does he justify the assumption of discrete time?

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 weren't 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.

 

[MathematicalPhysicist]

Originally posted by Mentat
but what other tests are there that can be used to add proof to superstring theory?

to add?!
i didnt know it had already proof that it needs another proofs.

 

[elas]

The following quotes are taken from 'The elegant universe' and an interview given by the author to Nova. They summarise the professional view of the current state of string theory.

Page 18
“In the final analysis, though, nothing is a substitute for definitive, testable predictions that can determine whether string theory has truly lifted the veil of mystery hiding the deepest truths of out universe. It may be sometime before our level of comprehension has reached sufficient depth to achieve this aim,”…………….. “it could be decades or even centuries before string theory is fully developed and understood”.

Page 19
“in fact, the mathematics of string theory is so complicated that to date, no one even knows the exact equations of the theory.”

Page 117
“Nevertheless, physicists by their nature will not be satisfied until they feel that the deepest and most fundamental understanding of the universe has been unveiled.”......“There is ample evidence that quantum mechanics and general relativity do not provide this deep level of understanding”.

Page 142
“The second answer is based on the simple fact that as yet we do not know if string theory is a correct or final theory”


“I’ve spent something like 17 years working on a theory for which there is essentially no direct experimental support.”

Page 12
“Why, for instance, are there four fundamental forces? Why not five or three or perhaps only one? Why do the forces have such different properties? Why are the strong and weak forces confined to operate on microscopic scales while gravity and the electromagnetic force have unlimited range of influence? And why is there such an enormous spread in the intrinsic strength of these forces?

This last quote has been include because it is these questions that I have answered on my webpage. My point has always been that the solution lies in making the effort to connect one theory to reality, instead of piling complicated theories on top of each other. There is nothing wrong with string theory that cannot be resolved by applying of the Law of Economy.

 

[TeV]

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.

jeff,I agree on this one.
Mathematicaly,string theory is very interesting and demanding.
From the aspects of SST's math ,math of Standard model is ,let say so, boring and simple.It is interesting how simple basic idea of a string concept evolves to such hights that development of special math methods are required .Never thought by some top class theoretical mathematicians their abstract work would be ever needed in physics.Ironically,String theory has more stimulated and given to math than math has given to it.
I think it is becouse it's so general.As concerns predictions/observations ,I vagually remember (I could be wrong here) reading in Scientific American about patterns of background relic cosmic radiation form some sort of pixel image and String theory had fine interpretation for it ?Someone knows more on this?

 

[elas]

From the aspects of SST's math ,math of Standard model is ,let say so, boring and simple

It is to the glory of all God's work that they be done with the greatest simplicity
Isaac Newton

When faced with a number of possible solutions I invariably found the simplest solution to be the correct solution
Einstein

Perhaps the truth is only boring in the minds of mathematicians?

 

[selfAdjoint]

Actually SST, with all its vacua and all its apparent complexity arises from the following simple prescription: Start with the simplest possible action on the string worldsheet and see where the math takes you from there.

All the branes and compacted manifolds and all the rest of it result from working through the results of that starting point.

 

[lethe]

All the branes and compacted manifolds and all the rest of it result from working through the results of that starting point.

compactification is put in by hand, 10 dimensional Minkowski space is stable.

 

[elas]

Actually SST, with all its vacua and all its apparent complexity arises from the following simple prescription: Start with the simplest possible action on the string worldsheet and see where the math takes you from there.

For reasons that must be dealt with in a different forum. my main interest lies in trying to understand what is meant by 'vacua' in SST, and in the phenomenology section, which I understand to be the part that deals specifically with links between SST and Particle Physics.

Am I correct in thinking that 'vacua' originates with Dirac's 'hole and heap' analogy and if so my question is 'how does a zero point (the hole) have dimensions? Does SST answer this question?

Secondly the only paper claiming to use SST to define particle mass, gives the rest masses of quarks in terms I do not understand (see 'Phenomenology' question on this forum) are there other explanations of SST/Particle physics links?

Another paper (also from the list of reccomended sites) states that some versions of SST give figures for gravity and/or graviton that are larger than those generally thought to be good approximations in Particle physics. This agrees with my own proposals and I would like to trace more details on this aspect of SST.