Is String Theory A Waste Of Time?

[marcus]

Marcus
On Strings I feel it’s future may well becoming a waste land. But I believe it has been very valuable in identifying the 11 dimensions issue. Lack of progress indicates that this idea is likely just wrong. But ANY future theory that proves 11 D as wrong, should also be able to explain why the 11 D issue appeared to be viable at all. Just this additional ‘test’ of future theories, I think that can be worth quite a bit.

Also, You mentioned something else I could use a little help on “how I think”

Among tested, well-established theories, General Relativity is the most background independent model we have.

Having never really put it into words before, but I’d though of GM as background dependent. That is with the “warping” of space time was still a manipulation of a background dependent interpretation of space and time.

Your comment tells me I need to Fine Tune my thinking a bit...

this is a sign we need a link to basic Differential Geometry primer where the idea of a "differentiable manifold" (often a "smooth manifold") is defined

does anyone have an Intro to D.G. or Intro to Manifolds link?

Randall there are two abstr. math. ideas you need that are actually very simple and easy to get-----Manifold and Metric-on-the-manifold.

For 150 years the fundamental paradigm for a continuum that everyone uses is a Manifold (defined by Riemann around 1850).

the most common meaning of B.I. is you start with a Manifold without a metric.

in a B.D. theory you start with a manifold and give yourself a metric on it to start with as well

have to go back later

 

[marcus]

Randall it is soooooo simple. I wish you would take a moment and think it over and come back and say honestly that you understand perfectly clear as day.

the reason we accumulate math concepts over the decades is ultimately MENTAL ECONOMY. they make thinking more efficient. and this is a case

the fundamental object in D.G. is the manifold which corresponds to the idea of a continuum without geometry. it is a blob that has coordinate functions defined on it
(local charts that are smooth and compat where they overlap)
but does not have any dingus or appliance that can tell you the distance between two points

because it has coordinates, at any point on the manifold you can explore all the possible directions in which you can take the derivative!
All the possible DEE-EXES, and when you think calmly and patiently about this for a while you realize that this collection of all possible dee-exes IS the tangent space. it captures the essence of what we want the tangentspace at any give point to do for us. and it is intrinsic (defined without reference to anything surrounding the manifold)

this is a fundamental Idea of Western Civilization, like the freedom of the individual and the rule of law etc. this is the Idea of the Continuum which has been standard for 150 years

It is INTRINSIC. it doesn't have to be embedded in any larger space for you to know its tangent space at each point and be able to do calculus etc, and it STILL HAS NO IDEA OF GEOMETRY built in.

to do geometry you introduce a "metric" gizmo which is a bi-linear dingus defined on the tangent space at every point blah blah
and once you have a metric g(m) defined at every point m of the manifold then you can compute distances, angles, areas, volumes etc.

The most common meaning of B.I. is that you start with a manifold without a metric.

In Gen Rel you start with a 4D spacetime manifold and some matter and you set up this equation and Presto! you PULL THE METRIC OUT OF THE HAT! (EDIT: selfAdjoint objects to the wording. I mean that you solve for the gravitational field, which is the metric. more discussion of details of this in later posts...)

the metric, or geometry, can be totally freeform and it is determined dynamically by interaction with matter through the equation of the model.

This is VERY DIFFERENT FROM perturbative STRING THEORY where they start with a manifold that already has a prior-chosen metric defined on it.
Having a prior chosen metric let's you define the twangy equation by which the little thangs be vibratin'. Without that prior metric you got nothing to start with, stringywise.

 

[selfAdjoint]

In Gen Rel you start with a 4D spacetime manifold and some matter and you set up this equation and Presto! you PULL THE METRIC OUT OF THE HAT!

That's not quite right. You don't need the matter, it's strictly geometry. You don't pull the metric out of a hat, you introduce it as a general symmetric quadratic form, the coefficients of which turn out to form form a symmetric rank two tensor. This is just a generalization of Pythagoras's (or Lorentz's) rule. You can then express the very special connection (Levi-Civita) in terms of derivatives of the metric tensor, and from the connection coefficients you define the curvature tensor (Riemann-Christoffel tensor). In Riemannian geometry the metric comes before everything else.

 

[marcus]

the fundamental string stumbling block is that in over 20 years nobody has succeeded in doing string without prior-choosing a metric

but to truly do Gen Rel you cannot choose the metric because geometry is a dynamic thing that comes out of the model----the geometry of the manifold is gravity and you do not stipulate it in advance

in standard vintage Gen Rel the gravitational field IS the metric g(m)
and it is what you solve for
it is the unknown distance function that the Einstein equation is about.

this is the basic obstacle that string research has always been up against

----------------------------

an amusing behavior of string theorists, which you can see recently over at the Coffee Table blog, is that whenever anybody reminds them of this major roadblock they immediately start talking defensively.

they don't stop, take a breath, and say "Yes that is right, we really need to put some effort into a nonperturbative, background independent formulation!"

Instead, they start making excuses and talking about the INADEQUACIES OF LOOP which is really irrelevant. They get into this complicated distracting discussion about how String "really" doesn't need to be B.I. and how it "really" is B.I. (if you define B.I. right) and how Loop is not "really" B.I. (if you define B.I. a certain way), and sometimes they start complaining that it isn't NICE of anyone to point out this defect because it might give non-experts the idea there was something wrong.

We just had an example of this at a couple of stringy blogs this month when folks were reacting to Smolin's paper "The Case for Background Independence". That paper was friendly advice, and the reaction was defensive, as if it were an attack. Check this out:

http://golem.ph.utexas.edu/string/archives/000621.html

I am waiting for someone like Andy Stromiger (who I suspect has guts) to come out with a clear statement on this and say "yes we need a B.I. formulation that we can really calculate with, and we ought to give his high priority and work on it, and we can do it"

 

[marcus]

... In Riemannian geometry the metric comes before everything else.

I agree totally. what I mean by pulling the metric out of a hat is that you SOLVE for the metric.

all the terms in the equation are defined based on the metric, so the metric comes before all that other stuff---curvature tensor like you say.

the idea I am trying to get across is somewhat simpler and more basic:

the gravitational field IS the metric
you don't start off knowing the metric
you SOLVE for it


exactly as you say, part of solving for the metric is going through stuff like the Riemann-Christophel tensor whose definition is based on the metric

thanks for adding some clarification, selfAdjoint.
would be great to have some standard links to basic D.G.
and a standard exposition of what B.I. is about
I appreciate your help

 

[marcus]

my idea of a really background independent nonperturbative approach to QG is Loll triangulations path integral. I will get some links

http://arxiv.org/hep-th/0404156

Emergence of a 4D World from Causal Quantum Gravity

http://arxiv.org/hep-th/0505154

Reconstructing the Universe

http://arxiv.org/hep-th/0505113

Spectral Dimension of the Universe

http://arxiv.org/hep-th/0411152

Semiclassical Universe from First Principles

more here
http://arxiv.org/find/grp_physics/1/au:+Loll/0/1/0/all/0/1

Eventually I hope to see some string theorists implement a version of string theory on the Loll CDT spacetime as a foundation. (rather than on their usual kind of manifold)

The original work in Dynamical Triangulations in early 1990s (which led to Loll CDT path integral in 1998) was actually an attempt by Ambjorn to find a NONPERTURBATIVE FORMULATION OF STRING---he thought he was doing matrix theory and he ended up with the CDT path integral.

One of Smolin's points is that a head-on effort to make string non-perturbative, or background independent, is likely to be fruitful (as it has been in the past) whether or not one finds a passage to the original goal

Another is that by throwing out assumptions one makes a theory more predictive---the less you assume the harder it is to build and the more restrictive it is---so the more falsifiable. So he proposes making the theory less dependent on comfortable background assumptions as a way out of the landscape confusion.

 

[Hurkyl]

because it has coordinates, at any point on the manifold you can explore all the possible directions in which you can take the derivative! ...

I feel the need to make a slight correction: you need a differentiable manifold to do this extra stuff!


Some manifolds are just so miserable that there is no way to equip them with a differentiable structure. Thus, no derivatives for you!

Some other manifolds are too accomodating: there are many fundamentally different ways to equip them with a differentiable structure! So you have to select which one you like before using derivatives!

 

[marcus]

I feel the need to make a slight correction: you need a differentiable manifold to do this extra stuff!


Some manifolds are just so miserable that there is no way to equip them with a differentiable structure. Thus, no derivatives for you!

Some other manifolds are too accomodating: there are many fundamentally different ways to equip them with a differentiable structure! So you have to select which one you like before using derivatives!

You are absolutely right. I mean a differentiable manifold every time I say manifold. It just gets tiresome to type it after I have said it once.

Personally I like C-infinity, but at least C-one!

 

[Mike2]

The most common meaning of B.I. is that you start with a manifold without a metric.
...
the metric, or geometry, can be totally freeform and it is determined dynamically by interaction with matter through the equation of the model.

Interesting! If there are no particles, then it becomes impossible to say how far apart things are; there are no reference points to say how far apart things are with respect to. It becomes completely meaningless to say how far apart things are if there are no things between which to measure. So it seems, no particles, no metric. The laws of physics before particles seems to be totally invariant with whatever metric one might impose or imagine. Particles seem to arise with the emergence of a metric. The particle characteristics derive from various kinds of symmetry which are only describable with a metric. So... no metric, no particles.

So the question becomes, how did particle and/or the metric come into existence to begin with? How was the initial total symmetry broken? Did the metric have to start out with zero distance between particles? I'm sure without a metric to start with, we have to rely on topological characteristics to answer how a metric came to be.

 

[Hurkyl]

At least once you have a C1 manifold, there's a unique way to turn it into a C∞ manifold.

 

[Hurkyl]

Interesting! If there are no particles, then it becomes impossible to say how how far apart things are; there are no reference points to say how far apart things are with respect to.

The presence or lack of particles has no bearing upon whether the metric exists.

What you're touching upon is the problem of measurement.

The laws of physics before particles seems to be totally invariant with whatever metric one might impose or imagine.

Yes and no... the equations themselves are invariant, but they often take the metric as a parameter.


In fact, the metric isn't even fundamental -- General Relativity can be reformulated without any reference to a metric. (At least if I understand correctly)

 

[Mike2]

The presence or lack of particles has no bearing upon whether the metric exists.

I'm not sure what epoc of cosmology you are referring to when there was curved spacetime before particles existed.

As I recall, it requires matter to produce curved space in Einstein's eq.

Perhaps you are referring to massive particles only?

I'm trying to imagine what measure one would use when there are no objects to measure with respect to, or no center, or no edge. It would seem one measure would be just as effective an any other.

 

[marcus]

-- General Relativity can be reformulated without any reference to a metric. (At least if I understand correctly)

you understand correctly. I would just say that I've never heard anyone say that the metric formulation is any less fundamental than some other formulation (e.g. Sen-Ashtekar variables)

I think one can argue that neither is more fundamental they are just different ways. Maybe other people have differing views on this.

Thiemann's postdoc Bianca Dittrich (one of the strongest LQG researchers now) just posted a paper in which she chose to work with the metric instead of the connection formulation (Ashtekar style). Several others have made this choice also in some if not all of their recent papers (Reuter, Husain, Winkler, Modesto). So the metric continues in use in quantum gravity and there seems no clear choice for the moment.

Dittrich's paper was
http://www.arxiv.org/abs/gr-qc/0507106
Partial and Complete Observables for Canonical General Relativity
B. Dittrich
33 pages
"In this work we will consider the concepts of partial and complete observables for canonical general relativity. These concepts provide a method to calculate Dirac observables. The central result of this work is that one can compute Dirac observables for general relativity by dealing with just one constraint. For this we have to introduce spatial diffeomorphism invariant Hamiltonian constraints. It will turn out that these can be made to be Abelian. Furthermore the methods outlined here provide a connection between observables in the space--time picture, i.e. quantities invariant under space--time diffeomorphisms, and Dirac observables in the canonical picture."

 

[CarlB]

All the possible DEE-EXES, and when you think calmly and patiently about this for a while you realize that this collection of all possible dee-exes IS the tangent space. it captures the essence of what we want the tangentspace at any give point to do for us. and it is intrinsic (defined without reference to anything surrounding the manifold)

this is a fundamental Idea of Western Civilization, like the freedom of the individual and the rule of law etc. this is the Idea of the Continuum which has been standard for 150 years.
...
This is VERY DIFFERENT FROM perturbative STRING THEORY where they start with a manifold that already has a prior-chosen metric defined on it.

Having a prior chosen metric let's you define the twangy equation by which the little thangs be vibratin'. Without that prior metric you got nothing to start with, stringywise.

I think that the problem with defining geometry through the tangent vectors of the underlying manifold is the unusual symmetry breaking observed in the standard model. The conventional solution to this problem is to retain the assumption that space-time possesses, for example, left / right symmetry, but that the vacuum does not.

However, if you build up geometry from the tangent spaces of the points of the manifold, then you can arrange for the symmetry breaking to occur in space-time itself. This is a modification of the ideas of David Hestenes with the Geometric Algebra.

The GA takes the tangent vectors of the manifold and uses them as the generators of a Clifford algebra. The signature of the Clifford algebra is typically taken to be (-+++) or (+---); this is a feature that doesn't show up in the manifold but has to be added.

Anyway, if you begin with the GA, you end up with same symmetry that the usual version of space-time possesses, but it is possible to generalize the relationship between the tangent vectors and the Clifford algebra in a manner that reproduces the symmetry breaking that distinguishes between the symmetry of space-time and the symmetry of the observed vacuum.

Carl

 

[marcus]

... GA takes the tangent vectors of the manifold and uses them as the generators of a Clifford algebra. The signature of the Clifford algebra is typically taken to be (-+++) or (+---); this is a feature that doesn't show up in the manifold but has to be added.
...

Hi Carl, the original question that Randall asked was about background independence

what I want to focus attention on here is WHAT CAN YOU DO WITH NO PRIOR METRIC?

so there is no bilinear form on the tangent space at a point.

(when you talk about "signature" you are assuming some bilinear form on the tangent space, I want to stop well before that point and look around)

the B.I. viewpoint is all you have is the manifold----a continuum without prior assumed geometry----and then the gravitational field arises dynamically AS the geometry.

So we are going in opposite directions here: you are looking for more prior structure (which could be mathematically very nifty, like Clifford algebras) and I want to illustrate (in case anyone is interested in Background Independence) what it looks like with LESS prior structure.

The various non-string QG approaches tend to be built on a manifold WITHOUT metric, or to have even less structure.

For example in Loll CDT Triangulations YOU DON'T EVEN ASSUME THAT THE CONTINUUM IS A MANIFOLD. You just approximate it, in a certain sense, by manifolds. And of course there is no prior metric and no Clifford algebra or any of that stuff.

Background Independent means "no frills"
you try to assume as little as possible to get started with
and the surprise is when something we associate with familiar macroscopic space EMERGES.

Like 4D dimensionality, as reported here:
http://arxiv.org/hep-th/0404156

this is one of the articles I gave links to some 8 or 9 posts back. Maybe I should bring up that list of links.

 

[marcus]

It is really remarkable, Carl. They don't even put in that space is supposed to be 4D and it COMES OUT THAT WAY at macroscopic scale, although at very short range the spectral dimension measured by diffusion processes comes out less. Carl I think you have read some CDT--weren't we discussing that in the "Introduction" thread? But in case anyone else is reading along with us I will bring up that list of CDT links from a few posts back

my idea of a really background independent nonperturbative approach to QG is Loll triangulations path integral. I will get some links

http://arxiv.org/hep-th/0404156

Emergence of a 4D World from Causal Quantum Gravity

http://arxiv.org/hep-th/0505154

Reconstructing the Universe

http://arxiv.org/hep-th/0505113

Spectral Dimension of the Universe

http://arxiv.org/hep-th/0411152

Semiclassical Universe from First Principles

more here
http://arxiv.org/find/grp_physics/1/au:+Loll/0/1/0/all/0/1

Eventually I hope to see some string theorists implement a version of string theory on the Loll CDT spacetime as a foundation. (rather than on their usual kind of manifold)

.

 

[Chronos]

Ouch. I am amazed that background independence is somehow irrelevant. It seems a difficult and awkward position from which to propose a 'theory of everything'.

 

[CarlB]

Hi Carl, the original question that Randall asked was about background independence

what I want to focus attention on here is WHAT CAN YOU DO WITH NO PRIOR METRIC?

so there is no bilinear form on the tangent space at a point.

(when you talk about "signature" you are assuming some bilinear form on the tangent space, I want to stop well before that point and look around).

When you require a mixed signature, I agree with you, that is, I agree that one must have something in addition to the manifold itself.

However, it is also possible to treat time as an independent variable. That is, one can treat time as separate from the geometry of space. If you do this, then the signature becomes (++++), and you don't need to specify a bilinear form. Instead, one defines the tangent vectors as velocity vectors. In other words, the metric is a result of the continua having a characteristic velocity. This is a classical way of treating space and time, that is separately.

Having read the links you've provided, I must say that I am singularly unimpressed with their lack of assumptions about the physical world. I saw no "emergence of a 4D World". Instead they begin with 4D simplices and end up with a 4D world. This is no more surprising to me than starting with little cubes and ending up with big cubes. Please correct me here. I see this as just a gravity from QM paper, not something that separates metric from manifold.

Carl

 

[marcus]

. I saw no "emergence of a 4D World". Instead they begin with 4D simplices and end up with a 4D world. This is no more surprising to me than starting with little cubes and ending up with big cubes. Please correct me here.
...

One way to understand it is to read the paper carefully and follow their references to the literature.

It may be that you have not read the first page of the article, Carl. this is page 2 (the abstract occupies page 1). Here is a quote from page 2:

----quote from "Emergence of a 4D world---
Note that the dynamical nature of “dimensionality” implies that the Hausdorff dimension of the quantum geometry is not a priori determined by the dimensionality at the cut-off scale a, which is simply the fixed dimensionality d of the building blocks of the regularized version of the theory. An example in point are the attempts to define theories of quantum geometry via “Euclidean Dynamical Triangulations”, much-studied during the 1980s and ‘90s. In these models, if the dimension d is larger than 2, and if all geometries contribute to the path integral with equal weight, a geometry with no linear extension and d_Hausdorff= infinity is created with probability one. If instead – as is natural for a gravityinspired theory – the Boltzmann weight of each geometry is taken to be the exponential of (minus) the Euclidean Einstein-Hilbert action, one finds for small values of the bare gravitational coupling constant a first-order phase transition to a phase of the opposite extreme, namely, one in which the quantum geometry satisfies d_Hausdorff= 2. This is indicative of a different type of degeneracy, where typical
(i.e. probability one) configurations are so-called branched polymers or trees (see [11, 12, 13, 14, 15, 16, 17] for details of the phase structure and geometric properties of the four-dimensional Euclidean theory).
----end quote----

The Dynamical Triangulations literature all through the 1990s is a history of frustration where they would put together, say, 4-simplices
and the result would be something of small dimensionality like 2
or the dimensionality would go off to infinity.

the 2004 result reported in "Emergence..." was highly nontrivial, as they say, and as they explain by reference to the earlier work.

this behavior has been discussed in quite a few papers---not just in 4D case but also in 3D

For instance look around page 7 of Loll's introductory paper "A discrete history..."
hep-th/0212340
which was written for grad students entering the field. She describes the 3D case, which is easier to picture.


in the 3D case, one randomly assembles 3-simplices (tetrahedrons), but for a decade or so the result was always something highly branched out or highly compacted---- either 2 dimensional or very high, essentially infinite, dimensional.

Loll provides some pictures, which I can't.

 

[CarlB]

But it's not starting from a point of "NO PRIOR METRIC". Instead they're talking about starting without a coordinate system. For example, from your very useful link:

A nice feature of such simplicial manifolds is that their geometric properties are completely described by the discrete set {l^2_i } of the squared lengths of their edges. Note that this amounts to a description of geometry without the use of coordinates.

http://www.arxiv.org/PS_cache/hep-th/pdf/0212/0212340.pdf

In fact, each of the simplices that these guys are adding up does possesses a metric structure. That's what gives the squared lengths of their edges. For that matter, if one knows the squared lengths of the edges, it's easy enough to define a coordinate system and metric for the simplice (which is assumed to be flat in the above link).

This concept of getting space back from just the edge lengths of simplices smells to me of pure mathematics. It's just not amazing to me except that so many people would work so hard on it. It's like a chapter from Bourbaki. What's more, it appears to provide no explanation for any physical phenomena such as masses or coupling constants or anything else not already covered by the standard model.

Carl

Also see:

The simplicial building blocks of the models are taken to be pieces of Minkowski space, and their edges have squared lengths +a^2 or -a^2. For example, the two types of four-simplices that are used in Lorentzian dynamical triangulations in dimension four are shown in Fig.5. The first of them has four time-like and six space-like links (and therefore contains 4 time-like and 1 space-like tetrahedron), whereas the second one has six time-like and four space-like links (and contains 5 time-like tetrahedra). Since both are subspaces of flat space with signature (− + ++), they possesses well-defined light-cone structures everywhere.

In general, gluings between pairs of d-simplices are only possible when the metric properties of their (d−1)-faces match. ...

So the metric nature of the simplices is quite explicit.

It seems to me that the whole difficulty in this endeavor comes from the requirement that the result be Lorentz symmetric. But there is also an apparent assumption of the existence of a global time:

Creating closed time-like curves will be avoided by requiring that all space-times contributing to the path sum possesses a global “time” function t.

The underlying problem here is not with QM or gravity, it is in the unification. The above seems to me to suggest that the real problem is the assumption of Lorentz symmetry.

By the way, Hestenes believes that there is a method of putting gravitation onto a flat copy of his space time algebra (STA). Thus the underlying manifold would be flat. The method was found by Lasenby, Doran and Gull. If this is the case, wouldn't it make the whole problem of having to sum over bizarre geometries trivial? Here's a link to his article, please comment (as I know little about gravitation):
http://modelingnts.la.asu.edu/pdf/NEW_GRAVITY.pdf

Carl

 

[RandallB]

Randall it is soooooo simple.

Amazing how something so simple can generate so many comments. – But rather helpful ones, as I took your advise and thought this one over a bit.

The tune up in my thinking was where I’d though of Special and General Relativity both as being Classical 4D ideas. My problem was thinking Classical as 4 D. But as said here:

However, it is also possible to treat time as an independent variable. That is, one can treat time as separate from the geometry of space. --- a classical way of treating space and time. .

I.E. Classical is not 4 Dimensional but 3 D with time being separate from Euclidian space.

This classical way was fine for SR with the SR equations being more precise solutions to the ones Newton provided.

But the classical was unable to depict how gravity worked. So we have the first really significant application of Riemannian geometry (from mid 1800’s I think) in order to build General Relativity. As 4D thinking to create “Warped space-time” was needed. Thus I shouldn’t think of Time by itself as being a dimension independent of three spatial ones where all four would have a metric. But instead :

In Gen Rel you start with a 4D space-time manifold (without a metric) and some matter …. where you solve for the gravitational field, which is becomes the metric.

So on the main point - understanding GR as being non-classical, is because of the need for Riemannian, I think I’m very clear on that and how that works.

In the QM arena :
On the issue of “perturbative” (String & M Theory) and “non- perturbative” (CDT, Triangulations) Background Independence are both of these significantly different that the BI of Gen Rel?
Is QM by definition Background Independent? with perturbative just one way of recognizing that aspect of QM.
Or is there even such a thing a Background Dependent QM theory?

Thanks for the links, and comments from all.
RB

 

[Juan R.]

"inefficient"

CDT path integral has not given any signs of being an inefficient approach to quantum gravity, and to the extent that one can compare the two rather different approaches I would say that it is MORE background independent than canonical LQG.

Among tested, well-established theories, General Relativity is the most background independent model we have. When quantizing Gen Rel, it is obvious to try to preserve the B.I. feature if one can. The comparative success or failure of various attempts to do this is not relevant to the validity of the effort.

With both String and canonical Loop experiencing difficulties, one sees that it is actually the most background independent approach that is currently making the most progress.

I would remark that in post #99 i said (readers could think that i said other thing since you cited to me out of context)

Do not forget that LQG is claimed background independent whereas continue to be an “inefficient” approach to quantum gravity.

 

[marcus]

Juan, you are doing the right thing to re-focus the discussion on the main question. I will try to prevent any misunderstanding by also giving CONTEXT of quotation. It is a very good idea. Here is my post #96

1. it doesn't mean anything unless you say FOR WHOM it is a waste of time.

2. increasing numbers of people seem to be deciding that FOR THEM it is a waste of time, and so they are getting out of the field, or they are not writing so many research papers as they did. (However on arxiv I see a growing number of string papers by people at Beijing Normal and other large Chinese universities. These people do not think string is a waste of time for them and they are responsible for an increasing fraction of the research postings.)

3. your statement does not have a clear meaning unless you specify a waste of time AS WHAT. I think a lot of people would agree that string theory can lead to ideas and results that are interesting AS MATHEMATICS.

4. your statement would not apply to a mathematically gifted young person who goes into string and discovers something interesting and valuable AS MATHEMATICS. You cannot say that such a person is wasting their time!
What gives mathematics intrinsic WORTH is the interest it evokes from other mathematicians. It does not need to be a fundamental testable model of nature.

5. however your message, suitably qualified and restricted, is a very helpful one to have expressed---and voicing it actually DOES STRING THEORISTS A FAVOR by increasing the pressure on them to arrive at a nonperturbative background independent formulation that makes falsifiable predictions. This is the only way to be sure that string theorizing is not a waste of time AS PHYSICS.

You responded in a forceful and substantive way to ALL my points in your post #99, but right now I want to focus on your reply to point 5. You argued that it would NOT BE A MAGIC CURE for the troubles of string theory for researchers to concentrate their effort on finding a nonperturbative and background independent formulation, and you gave an example where background independence has, by itself, not led to complete success (as I would freely admit.)

Do not forget that LQG is claimed background independent whereas continue to be an “inefficient” approach to quantum gravity

And I will agree with you that there are no magic cures (this was your phrase in post #99) in other words no certain method to rescue string from the landscape quagmire and make it a predictive testable theory. But nevertheless, have a look at this chart that shows my perspective and will help you understand why I think that working on a nonperturbative version of string COULD help the field advance. the percentage change is output is over the 3 years 2002-2004:

[u]QG approach        % change in output            progress      [/u]
strings (least indep)      decline                bogged down in landscape
loops (indep)             increase    cosmology, Freidel TFT, uniqueness theorem
triangles (most indep)    rapid increase          dramatic advance

strings is the least indep, assuming a manifold WITH prior metric, and it has experienced a substantial decline in research output: number of papers per year. except in China, people seem to be leaving the field.

loops is more indep, assuming a manifold WITHOUT prior metric, and has had something like 50% increase in research output, people entering the field

CDT triangles is a small field, but it is the MOST indep, and its spacetime is not even a differentiable manifold (although piecewise flat manifs are used in an approximation method). So this is radical, taking independence to a new level, and this approach has made the most pronounced progress, with percentagewise more people entering the field

Juan, you can challenge any of this because this is largely my personal perspective. Progress is hard to measure objectively and one must use individual judgement. But I am giving you this comparison chart so you will better understand my point of view.

You have argued that it would NOT help string become more predictive (that is: falsifiable) to develop a version that DOES NOT ASSUME A PRIOR METRIC. This would be the first kind of independence to ask for---a version that you can CALCULATE from without depending on a prior metric on the manifold.

My guess is that, on the contrary, it WOULD help theorists arrive at a falsifiable theory, if they would focus effort on making it nonperturbative.
Nonperturbative theories are harder to construct, and the difficulty narrows down the range of options. By denying themselves the convenience of a prior-chosen metric, the researchers might very well arrive at a theory that could be falsified through inconsistency or by experiment. This is how scientific theories are supposed to be and would constitute a kind of long-delayed success. And so i see it as a hopeful possibility---but I certainly confess that it is not a certainty!

 

[Juan R.]

Juan, you are doing the right thing to re-focus the discussion on the main question. I will try to prevent any misunderstanding by also giving CONTEXT of quotation. It is a very good idea. Here is my post #96



You responded in a forceful and substantive way to ALL my points in your post #99, but right now I want to focus on your reply to point 5. You argued that it would NOT BE A MAGIC CURE for the troubles of string theory for researchers to concentrate their effort on finding a nonperturbative and background independent formulation, and you gave an example where background independence has, by itself, not led to complete success (as I would freely admit.)



And I will agree with you that there are no magic cures (this was your phrase in post #99) in other words no certain method to rescue string from the landscape quagmire and make it a predictive testable theory. But nevertheless, have a look at this chart that shows my perspective and will help you understand why I think that working on a nonperturbative version of string COULD help the field advance. the percentage change is output is over the 3 years 2002-2004:

[u]QG approach        % change in output            progress      [/u]
strings (least indep)      decline                bogged down in landscape
loops (indep)             increase    cosmology, Freidel TFT, uniqueness theorem
triangles (most indep)    rapid increase          dramatic advance

strings is the least indep, assuming a manifold WITH prior metric, and it has experienced a substantial decline in research output: number of papers per year. except in China, people seem to be leaving the field.

loops is more indep, assuming a manifold WITHOUT prior metric, and has had something like 50% increase in research output, people entering the field

CDT triangles is a small field, but it is the MOST indep, and its spacetime is not even a differentiable manifold (although piecewise flat manifs are used in an approximation method). So this is radical, taking independence to a new level, and this approach has made the most pronounced progress, with percentagewise more people entering the field

Juan, you can challenge any of this because this is largely my personal perspective. Progress is hard to measure objectively and one must use individual judgement. But I am giving you this comparison chart so you will better understand my point of view.

You have argued that it would NOT help string become more predictive (that is: falsifiable) to develop a version that DOES NOT ASSUME A PRIOR METRIC. This would be the first kind of independence to ask for---a version that you can CALCULATE from without depending on a prior metric on the manifold.

My guess is that, on the contrary, it WOULD help theorists arrive at a falsifiable theory, if they would focus effort on making it nonperturbative.
Nonperturbative theories are harder to construct, and the difficulty narrows down the range of options. By denying themselves the convenience of a prior-chosen metric, the researchers might very well arrive at a theory that could be falsified through inconsistency or by experiment. This is how scientific theories are supposed to be and would constitute a kind of long-delayed success. And so i see it as a hopeful possibility---but I certainly confess that it is not a certainty!

In short, string theory fails because is NOT a theory about our universe. This validation of the theory is rather broad and is not based in specific issues like BI.

Our universe is TODAY 4D and non supersymmetric, therefore we may develop a quantum theory for 4D and nonsupersimmetriy. Perhaps tomorrow new experiments discover hidden dimensions or super partners of currently known particles, but FIRST one may develop a theory for the universe that we know TODAY.

The problem of 40 year of impressive failure of ST is in the violation of scientific method. String theorists followed an initial "beatiful" idea and develop a theory for 26, 10 or 11D with supersimmetry and other stuff according to mathematical incosistency of the beatiful initial idea. How there is no posibility for developing a consistent theory for 4D without supersymmetry, there is possibility for computing nothing of this world from ST. Precisely this is the history of the field on last 30 years. Nothing computed or when computed with wrong behavior (nuclear force), wrong models (spliting of metric violating GR) or discrepancies of 50 orders of magnitude between theory and data.

And all of that even ignoring recent advanced stuff that is developed in other fields of theoretical science and ignored by super masterminds string theorists (of course some are respectful and hones but others are not). Stuff known in chemistry during 30 years (see Nobel lecture by Prigogine) is being introduced these days by string theorists in a new revolution.

That is, that was known 20 or 30 years ago in other fields is the last fad for ignorant (but very arrogant) people like Witten, Vafa, Greene, Schwartz, Motl, etc.

already explained that even with 2 or 3 new revolutions, string theory continue to be a joke (irrelevant) for people working in serious stuff.

Finalize saying that the idea of nondifferentiable spacetimes is also one of my ideas, but string and M theorists (yes those that claim for the Final theory the theory most sophisticated of the world, etc, etc.) continue working with "old" differentiable manifolds (e.g. famous CY of string theory or the new G2 of M-theory).

The arrogance of many string theorists permit to me writte this hard words (that i newer wrote for other honest researchers, including trinagulation ones)

I would say that there is posibility for reduction of dimensionality on my work and contacted with the author of paper you cite time ago. We discussed the rumour that a decrease on Newton force has been measured. If finally true this is another hard knock for ST which always has claimed that Newton force may be stronger on small distances.

F = (1/r^(2+D))

with D additional dimensions. Curiously doing D = -2, that is, reduction of dimensionality, one obtains less force (if confirmed experimentally) and absence of divergences for r = 0.

This argument is not riguroius but offer an idea of the surprising things that one can learn from alternative points of view.

 

[Juan R.]

According to

https://www.physicsforums.com/showthread.php?t=85971

there is not violations of Newtonian force known.

 

[marcus]

According to

https://www.physicsforums.com/showthread.php?t=85971

there is not violations of Newtonian force known.

Hello Juan, I liked your most recent long post. We still should provide some documentation---I should supply some data for the percentage changes in research output over the 3 years 2002-2004 and so forth.
But I couldn't think of anything more to say right now.

Yes, about the short range Newton law measurments. I know. Ohwilleke noted this in a thread in this section also. If you want to post on Ohwilleke's thread you might get some discussion. I don't connect this immediately to string theory because I don't find string theory very interesting and in the long run it might not be all that important. but verifying Newton law of gravity at short range does seem interesting. maybe Ohwilleke or somebody will expand on this subject

GRAVITY NORMAL AT SMALL SCALES
https://www.physicsforums.com/showthread.php?t=85989

check it out. Haelfix and Chronos have already replied on that thread.

--------------------------

by the way, something different. Do you know the story (arivero told me) of the two men discussing whether a white-ish block of material soap or cheese
one says it is soap, the other says it is cheese, and to prove it he cuts a sample and starts chewing it up----he will show it is cheese by eating some.
After a while he begins to foam and bubble at the mouth, and he stops chewing and says:

"Sabe a jabon, pero es queso."

We might translate this as
IT TASTES LIKE EPICYCLES, BUT IT'S REALLY A THEORY OF EVERYTHING.

 

[CarlB]

But the classical was unable to depict how gravity worked. So we have the first really significant application of Riemannian geometry (from mid 1800’s I think) in order to build General Relativity. As 4D thinking to create “Warped space-time” was needed.

This is outside my area, but there are a few physicists who are convinced that gravity can be done on a Euclidean basis. I think the best explanation is that of David Hestenes:

Lasenby, Doran and Gull have recently created a powerful coordinate-free reformulation, re¯nement, and extension of general relativity [1,2]. It is a gauge theory on °at spacetime, but it retains the attractive geometric structure of Einstein's theory.
...
Indeed, the method amounts to a new approach to differential geometry which could fairly be called gauge geometry.
...
Part II develops gauge covariant Riemannian geometry on flat spacetime. The main objective is to clarify the fundamental ideas and provide a systematic account of the definitions, theorems, proofs, and computational techniques needed to apply the spacetime calculus efficiently to any physical problem. Specific physical applications are not addressedhere; excellent examples, which amply demonstrate the computational power of the calculus, have been worked out in [1,2] and [9-13].
...

http://modelingnts.la.asu.edu/pdf/NEW_GRAVITY.pdf

Unfortunately, understanding the above paper requires a certain amount of understanding of "geometric algebra", which is a type of Clifford algebra where the basis vectors are associated with the tangent vectors at a given point of the manifold of space-time.

Carl

 

[Juan R.]

This is outside my area, but there are a few physicists who are convinced that gravity can be done on a Euclidean basis.

Carl

Well, the popular understanding of GR is that gravity is spacetime curvature, but this is rather difficult to believe by several motives.

1) Nobody has measured spacetime curvature directly.

2) Spacetime curvature does not imply curved space. Usual popular image of curved space around Sun is pictorial only.

3) The curved spacetime view is not exclusive. E.g. torsion formulations, Cartan-Ehelers reformulation, etc.

4) The curved spacetime view is problematic on the Newtonian limit. Far from common understanding, nobody has derived the Newtonian limit from GR. This is easy to understand. In the limit c -> infinite the curvature of spacetime may be zero like correspond to the Newtonian approach but then, if gravity is curvature, gravity may be zero. Textbook’s derivation of Newton second law is a derivation valid only when c is finite and the approximation is non linear. c finite contradicts Newtonian theory. Ehlers reformulation of GR does not obtain the Newtonian limit (even if Ehlers claims the contrary). His formulation on flat spacetime has problems: I) the splitting of curved derivatives is not unique and additional equations does not contained in GR are needed, ii) the compatibility with Newtonian limit is done invoking “asymptotic flatness”, which is experimentally unsustainable.

5) The geometric approach breaks the unification with rest of forces.

6) Far from standard claims the geometric approach of GR does not explain the misterium of gravity. This is easy to understand. In Newtonian theory, one has an equation for computing the force, but none explaining of underlying mechanism of it. In Einstein (really Hilbert-Einstein-Grossmann) theory, one has equations for computing spacetime curvature, but none explaining of underlying mechanism of it. GR substitutes the question "How does Earth know that force that Sun does" by "How does Earth know the curvature that Sun does". Far from common statements in GR literature, GR does not explain gravity.

The solution is not a geometric approach to quantum gravity. The solution is a force-like approach to GR that can be quantized more a demonstration of that GR is, strictly speaking, wrong.

Regarding your link, not only the choosing of Minkoskian spacetime metric is not correct (related to imposibility for obtaining correct Newtonian limit, that was the source for the search of alternatives like NCG and similar), moreover, i see fundamental difficulties with the "gauge" line element (7.7) that appears to be the basis of all the "gauge" approach.

 

[Mike2]

At best String Theory can only be an effective theory, not a TOE. This is because there seems to be nothing in String/M-theory itself that explains where the strings or membranes came from to begin with. What process creates these membranes/strings from the background? I suppose that there was a background without strings when the universe was very, very small, and then at some later time some process gave rise to strings and/or other membranes. How did that happen?

I suspect that if we knew the process by which strings/membranes come into existence, then this might give us constraints on which strings/branes can exist and allow a choice from the landscape.

 

[RandallB]

there are a few physicists who are convinced that gravity can be done on a Euclidean basis. I think the best explanation is that of David Hestenes:
http://modelingnts.la.asu.edu/pdf/NEW_GRAVITY.pdf

If you know of one, I’d love to see where someone makes a serious attempt at a Euclidean explanation, I’ve never seen one.

I have to disagree on David Hestenes. He cannot be talking about a Euclidean basis while using GR and Riemannian geometry. That is 4D and Euclidean is 3D where time is just a variable. GR/Riemannian is also “Background Independent” as I understand it, and Euclidean would be Background Dependent.
While the successful current theories GR and QM are not.
At least I think QM is background independent.

The ideas that wish to replace or correct GR and/or QM, all seem to get more complex in both their concept and mathematics. Maybe that’s because reality is complex.

I still feel that String theory has been successful in showing that 11 dimensions “appear” to be required. Therefore, in my opinion any proposed new theory needs to explain why that appeared to be true. That includes variations on Strings, canonical science, and even Euclidean explanations.

RB

 

[Juan R.]

At best String Theory can only be an effective theory, not a TOE. This is because there seems to be nothing in String/M-theory itself that explains where the strings or membranes came from to begin with. What process creates these membranes/strings from the background? I suppose that there was a background without strings when the universe was very, very small, and then at some later time some process gave rise to strings and/or other membranes. How did that happen?

I suspect that if we knew the process by which strings/membranes come into existence, then this might give us constraints on which strings/branes can exist and allow a choice from the landscape.

An effective theory for that? From ST one can compute absolutely nothing and nothing can be explained on a sound basis. ST is mathematical gulash with no link with nothing of this world.

The strings of string M theory -really one would talk of the p-branes- are really inmortal on the formulation proposed. In fact some brane inspired cosmology models claim that the big bang was (of course is just a especulation) the outcome of a collision of two 5D branes.

 

[Juan R.]

If you know of one, I’d love to see where someone makes a serious attempt at a Euclidean explanation, I’ve never seen one.

I have to disagree on David Hestenes. He cannot be talking about a Euclidean basis while using GR and Riemannian geometry. That is 4D and Euclidean is 3D where time is just a variable. GR/Riemannian is also “Background Independent” as I understand it, and Euclidean would be Background Dependent.
While the successful current theories GR and QM are not.
At least I think QM is background independent.

RB

I will say nothing on your claim that QM is BI.

Regarding above link you would read it first before disagree . Already in the abstract you can see that are talking of a flat spacetime not a flat space. See also my post #131.

The ideas that wish to replace or correct GR and/or QM, all seem to get more complex in both their concept and mathematics. Maybe that’s because reality is complex.
RB

One may simply explain world. Often this is done by the use of more complex formulations and novel mathematical tools. All attempt to quantize gravity rely on new math and concepts do not included on GR + QM.

But whereas many of others approaches focus on physical insight, ST is just a mathematical goulash around an initially "beatiful" idea that was discarded in accelerator experiments many decades ago.

I still feel that String theory has been successful in showing that 11 dimensions “appear” to be required. Therefore, in my opinion any proposed new theory needs to explain why that appeared to be true. That includes variations on Strings, canonical science, and even Euclidean explanations.

RB

Required for what? for fulfilling ArXiv with dozens of ineffective preprints? After of more than 30 years, string theory is even poor that when began.

Things are much more simple: any proposed new theory needs to explain the world like it appears to us. Today we know that the world is 4D and non supersymmetric, therefore the first quantum theory of gravity may be a formulation for 4D and without supersimmetry. Precisely this is the point of LQG and other approaches.

If at 2007, supersimmetry is experimentally observed. No problem! your theory will continue to be correct (as Newtonian mechanics is in Formula 1), simply you will need generalize to supersimmetry.

The problem of ST and M theory is that 11D and supersymmetry, and the rest of mathematical gulash, are just a mathematical gulash added to the theory because was internally inconsistent or violated experimental data. For example supersymmetry was added ad hoc in the 80s because string theory without it predicted tachions which were newer observed

The aim of physics is to explain universe as it is, is not to develop a theory of "like world would be for me".

All on string theory is about things that are not about our universe. Nothing of standard model or of GR is obtained from ST. At the best, one obtains certain models (after of tricks and ad hoc asumptions) that look like but are not equivalent.

Almost any young student knows the myth that ST predicts gravity or that GR is recovered in the low energy limit but both of those claims are not true.

In fact, causality in ST is defined in a flat metric whereas causality in GR is not. Then what? In the past they say like ST is not 100% compatible with GR and ST is mathematically "beatiful" then the problem may be with GR.

In fact, you appears to ignore that only some years ago string theorists claimed that one would do not take GR "too seriously" . Even today some guys claim that one would ignore experimental data of GR in favor of string theory!

All of this is a nonsense, ST is outside of physics.

Those "details" are do that ST was a waste of time or in the words of P.W. Anderson

a futile exercise like physics

 

[marcus]

...

I still feel that String theory has been successful in showing that 11 dimensions “appear” to be required. Therefore, in my opinion any proposed new theory needs to explain why that appeared to be true. That includes variations on Strings, canonical science, and even Euclidean explanations.

strange thought, Randall

to the ancient alchemists, it appeared that all matter could be explained by combining 4 elements

shall we require of all future theories of matter that they explain why that appeared true to the alchemists?

 

[Juan R.]

strange thought, Randall

to the ancient alchemists, it appeared that all matter could be explained by combiniing 4 elements

shall we require of all future theories of matter that they explain why that appeared true to the alchemists?

Nice reply!

You explained better and shorter (= two time better) than my

 

[marcus]

Nice reply!

You explained better and shorter (= two time better) than my

I owe this entirely to your inspiring example, Juan
thank you kindly


however on another matter, I feel a deep attachment to the geometric explanation of gravity and, although I am disinclined to argue with you, I wish you would not so often castigate it with your disapproval

but if you must, by your very nature as Juan, then I guess you must

 

[CarlB]

If you know of one, I’d love to see where someone makes a serious attempt at a Euclidean explanation, I’ve never seen one. I have to disagree on David Hestenes. He cannot be talking about a Euclidean basis while using GR and Riemannian geometry. That is 4D and Euclidean is 3D where time is just a variable.

Look at chapter IV of this link, which is from Foundations of Physics, 35: 1-67 (2005):
http://modelingnts.la.asu.edu/pdf/GTG.w.GC.FP.pdf
http://modelingnts.la.asu.edu/html/GCgravity.html

I think the above link is a better article in its explanation of the theory than the one I originally posted.

GR/Riemannian is also “Background Independent” as I understand it, and Euclidean would be Background Dependent. While the successful current theories GR and QM are not. At least I think QM is background independent.

I believe that the standard model of QM is background dependent. Or more precisely, that it can be cast in a background dependent interpretation. Here's an arxiv article on the subject that explains it pretty much the way I see it, except that I think that background dependence is a good thing, not something to be gotten rid of:
http://arxiv.org/PS_cache/hep-th/pdf/0409/0409048.pdf

A typical QFT textbook will deal with the background dependence of the theory by showing that while the calculations do assume a background (in the form of a particular metric), the results of the calculations are compatible with Lorentz / Poincare symmetry. That is, if you assume a different reference frame, your calculation will be different but the final result will be the same. The fact that they have to show this is an indication that the theory is not in itself inherently background independent. From my point of view, this is evidence that the universe does have a "background". It's just that since we're a part of the universe, we have great difficulty figuring out exactly what that background is.

The ideas that wish to replace or correct GR and/or QM, all seem to get more complex in both their concept and mathematics. Maybe that’s because reality is complex.

Even simple equations can have very complex solutions. If one were to look at the table of the elements, one might conclude that Schroedinger's wave equation, which pretty much explains the thing, must also be complex. My guess is that simplicity should be at the core.

I still feel that String theory has been successful in showing that 11 dimensions “appear” to be required. Therefore, in my opinion any proposed new theory needs to explain why that appeared to be true. That includes variations on Strings, canonical science, and even Euclidean explanations.

I only bought one string theory textbook. Different chapters in the book purport to prove why N dimensions are necessary for a consistent theory. The only problem is that N is not a constant but changes from chapter to chapter.

My guess is that quarks and leptons are the results of a two stage condensation. The second stage is the combination of left and right handed massless chiral particles to form fermions. This is almost a part of the standard model, the difference being that the standard model requires a Higgs particle to be absorbed (or emitted) at the vertices where left and right handed chiral fermions convert to each other. The first stage of the condensation is one that produces the massless chiral fermions and is beyond the scope of this discussion. But this sort of concept does get back to string theory, or at least to the concept of hidden dimensions, by the fact that if one ignores a condensation of subparticles, (that is, if one only looks at the interactions of the combined system), one will end up with unexplained degrees of freedom. These extra degrees of freedom can be naturally explained through the notion of hidden dimensions.

As an example, if two subparticles combine to form a tightly bound composite particle, we will use center of mass coordinates for the composite particle. But there will still be a set of relative coordinates for the two subparticles. Since it is a bound state, the relative coordinates will be compact and therefore will look (mathematically) like a space of compactified dimensions. This gives some hope of determining the topology of string theory from the mechanics of the subparticles.

Carl

 

[RandallB]

strange thought, Randall

to the ancient alchemists, it appeared that all matter could be explained by combiniing 4 elements

shall we require of all future theories of matter that they explain why that appeared true to the alchemists?

Excellent point and
YES WE SHOULD
BUT - “ancient alchemists” ideas have been explained as wrong, based on current science. And we do understand how their old view of reality; lead them to think they way they did.
So that job has been done.
I also understand need for a New Theory to show the old wrong theories to be wrong to make way for a new one.
However, loudly proclaiming that GR and QM are wrong is far short of showing them to be wrong.

True enough not every idea that falls off the truck should qualifies to set yet another standard that must be disproved of proved by any future new theory. That will always be an individual judgment call. But where rigorous scientific interpretation of observations and rigorous math has been applied to build a view of a theory - some explanation as to why the theory was constructed incorrectly should be proved by a replacing better theory. Just as has been done with Alchemists Theories. If it cannot do so what makes the new theory better?
In the worst case view of both GR and QM they have certainly met that standard.
But, for all those that have better answers than GR or QM, I've never seen a reasoned explanation as to why GR and QM work so well and are yet wrong.

Now I’m no String or M theory expert, in fact I don’t see how they could be correct. But based the quality of the people and the work they have done, I trust and I believe the ideas were rigorously formed. And for me the idea of 10 or 11 dimensions was reasonable reached in this case. So for me I feel they have met the standard. Even though I do not believe in extra dimensions myself I feel it’s only responsible to accept the higher standard. Therefore if I want to show strings to be wrong, and there is something better, I must understand how they made the mistake of assuming the extra dimensions. If I can’t take the responsibility to do that, then why should anyone take a new idea seriously?

I just find this a more reasoned and logic approach to the issue rather than just cobbling a bunch of ideas together with no proofs, and no explanations of how the others made the wrong conclusions.

Is that easy to do – of course not it's harder, nobody promised easy.

RB

 

[selfAdjoint]

I have to disagree on David Hestenes. He cannot be talking about a Euclidean basis while using GR and Riemannian geometry. That is 4D and Euclidean is 3D where time is just a variable. GR/Riemannian is also “Background Independent” as I understand it, and Euclidean would be Background Dependent.

"Euclidean" in this context refers to any geometry where the line element ds^2 = g_{ab}dx^adx^b is positive definite. So you can have Riemannian geometry that is Euclidean. The line element of GR is not positive definite, because the "time" term is a different sign from the "space" terms.

And "background independent" is a property of the physics together with the geometry, not the kind of geometry alone. If the physics acts on the geometry, and the geometry determines the physics, so there is self-interaction, then you have background indpendence.

 

[marcus]

...And "background independent" is a property of the physics together with the geometry, not the kind of geometry alone. If the physics acts on the geometry, and the geometry determines the physics, so there is self-interaction, then you have background independence.

nice way to put it. points up a positive quality instead of the negative quality of not being dependent on something like a prior fixed choice of background metric. different ways of saying the same thing but more intuitive/evocative to say it in this positive way

 

[Juan R.]

however on another matter, I feel a deep attachment to the geometric explanation of gravity and, although I am disinclined to argue with you, I wish you would not so often castigate it with your disapproval

At the best, i think that you would only find difficulty with point 4) of post #131, since rest is standard or almost standard. And, of course, with my own solution to the problem.

I think that once the paper was published you could study it carefully and write a public comment if you consider that GR is still a good approach after of reading my work.

If i am wrong you will help to me to understand correctly gravitation .

If i am not wrong then I will help to you to understand correctly gravitation.

 

[Juan R.]

I only bought one string theory textbook. Different chapters in the book purport to prove why N dimensions are necessary for a consistent theory. The only problem is that N is not a constant but changes from chapter to chapter.

Carl

Very good point!

In fact the history of dimensions is

4D, 5D, 26D, 10D, 11D, ...

According to B. Greene some string theorists are now working in the posibility of more than one time dimension whereas others claim that the fail of compactification may indicate that there are still unknown 4D-versions of "string" theory.

Also the size of strings changes from "chapter to chapter" from "infinitely" small (Planck) to mm range to again "infinitely" small to infinitely large. There is a version that says that compactified dimension are the usual 4D ones, etc.

The rest of "theory" is also chapter-dependant and even book-dependant or author-dependant!

 

[Juan R.]

Now I’m no String or M theory expert, in fact I don’t see how they could be correct. But based the quality of the people and the work they have done, I trust and I believe the ideas were rigorously formed. And for me the idea of 10 or 11 dimensions was reasonable reached in this case. So for me I feel they have met the standard. Even though I do not believe in extra dimensions myself I feel it’s only responsible to accept the higher standard. Therefore if I want to show strings to be wrong, and there is something better, I must understand how they made the mistake of assuming the extra dimensions. If I can’t take the responsibility to do that, then why should anyone take a new idea seriously?

I just find this a more reasoned and logic approach to the issue rather than just cobbling a bunch of ideas together with no proofs, and no explanations of how the others made the wrong conclusions.

Is that easy to do – of course not it's harder, nobody promised easy.

RB

This sounds like the main argument for studying string theory that some string theorists use: "Because Witten believes on it".

That is not a scientific argument.

The "quality" of people is a subjective concept and, moreover, is not guarantee of a good work. Look for example the history of QFT, almost all great guys Schrödinger, Dirac, etc. did the wrong work and a new generation of young people did QFT. In fact, this argument against string theory has been recently used by Dyson.

Regarding the "quality" of the work they have done, i could say that the quality is very low, with lot of wrong details that are corrected after of decades. Material known in other fields is introduced decades after in string theory. In concrete points, I can assure that the quality of Seiberg's work on NC geomstry is low, the quality of Schwartz's work on unitarity is low, the quality of Witten's work on QM foundations is low, the quality of Nanopoulos' work on the arrow of time problem is low, etc.

So for me I feel they have met the standard.

Curiosly the standard in quantum gravity research is not that.

Therefore if I want to show strings to be wrong, and there is something better, I must understand how they made the mistake of assuming the extra dimensions.

Curiously science does not work on that way. Are string theorists who may show that universe is 11D! Curiously string theorists have shown nothing and none of their initial promises has been done after of more than 30 years!

It is time for exploring other alternatives.

 

[RandallB]

It is time for exploring other alternatives.

Well at least that's one point we completely agree on.
I just hope and even expect that a good alternative will prove strings wrong by show how/why it appeared to them there should be multi D's. I'd even expect proving so can be helpful.
RB

 

[RandallB]

"Euclidean" in this context refers to any geometry where the line element ds^2 = g_{ab}dx^adx^b is positive definite. So you can have Riemannian geometry that is Euclidean. The line element of GR is not positive definite, because the "time" term is a different sign from the "space" terms.

And "background independent" is a property of the physics together with the geometry, not the kind of geometry alone. If the physics acts on the geometry, and the geometry determines the physics, so there is self-interaction, then you have background indpendence.

So is GR consided background indpendent ??
Does "The line element of GR is not positive definite" address this issue?

The Lee Smolin link (Thanks for finding Marcus)
http://arxiv.org/abs/hep-th/0507235
Provides a firm argument the GR is “relational” or background independent.
At least where “warping” is concerned.
Is this generally accepted as the case or is this a “debated point” ?

 

[CarlB]

In fact the history of dimensions is
4D, 5D, 26D, 10D, 11D,

If you attribute the hidden dimensions in string theory to internal degrees of freedom between constituents of the supposedly fundamental particles, then the varying number of hidden dimensions is an obvious indication that the number of constituents varies between the particles.

If spin-1 bosons have more internal constituents than spin-1/2 fermions, (as one might expect if all these particles were condensed from fermionic subparticles) it is quite natural that in string theory, the fundamental bosons would have a larger number of hidden dimensions than the fundamental fermions.

The quarks and leptons seem to require 10 or 11 dimensions in total, while the various gauge bosons require 26. (I'm reading Polchinski.) These numbers are about right for the spin-1/2 fermions to be composed of three fundamental subparticles, while the spin-1 bosons are composed of six. That is, three subparticle fermions would have a total of something around 12 degrees of freedom, while six subparticles would have about 24.

Various authors have proposed that the quarks and leptons are condensed states and the number of subparticles is frequently given as three. My own proposal is along this line, but is somewhat radical:
http://brannenworks.com/PHENO2005.pdf

Carl

 

[Juan R.]

If you attribute the hidden dimensions in string theory to internal degrees of freedom between constituents of the supposedly fundamental particles, then the varying number of hidden dimensions is an obvious indication that the number of constituents varies between the particles.

If spin-1 bosons have more internal constituents than spin-1/2 fermions, (as one might expect if all these particles were condensed from fermionic subparticles) it is quite natural that in string theory, the fundamental bosons would have a larger number of hidden dimensions than the fundamental fermions.

The quarks and leptons seem to require 10 or 11 dimensions in total, while the various gauge bosons require 26. (I'm reading Polchinski.) These numbers are about right for the spin-1/2 fermions to be composed of three fundamental subparticles, while the spin-1 bosons are composed of six. That is, three subparticle fermions would have a total of something around 12 degrees of freedom, while six subparticles would have about 24.

Various authors have proposed that the quarks and leptons are condensed states and the number of subparticles is frequently given as three. My own proposal is along this line, but is somewhat radical:
http://brannenworks.com/PHENO2005.pdf

Carl

However, in string theory, the hidden dimensions are not related to internal degrees of freedom on a 4D universe.

"then the varying number of hidden dimensions is an obvious indication that the number of constituents varies between the particles."

I do not understand to you here. The varying number of hidden dimensions is just historical one. In superstring theory, the number of dimensions is 10 and 11 in the new M theory, but is not 10D for some particles and 26D for others. Superstring theory is a priori valid for both bosons and fermions. Only the old bosonic string theory is for 26D.

I do not know if fermions are elementary or composed objects. Nobody know that, still let me highlight that in superstring, brane and M theory fermions are elementary objects, of course are vibrational states of the p-brane but are not composed of collection of branes. They are the brane itself.

 

[CarlB]

However, in string theory, the hidden dimensions are not related to internal degrees of freedom on a 4D universe. ... I do not understand you here. The varying number of hidden dimensions is just historical one. In superstring theory, the number of dimensions is 10 and 11 in the new M theory, but is not 10D for some particles and 26D for others. Superstring theory is a priori valid for both bosons and fermions. Only the old bosonic string theory is for 26D.

I don't mean to argue that string theory is correct, but instead to point out that the dimensional regularization that leads to various assumptions of dimensions in string theory is an argument that can also be applied to the hidden dimensions arising from multi particle bound states.

Since string theory, like Kaluza-Klein, only deals with the lowest modes, there will inevitably be many different physical arrangements that will give those same modes. In other words, by ignoring all but the lowest energy modes, the mathematics problem of defining the physical situation from the spectrum is severely under constrained. What I'm suggesting is that the modes that correspond to the standard model can be written as the lowest modes resulting from composite particles. I think that this can be done in a manner compelling in its simplicity. But when you're done with this, there may be a way to solve the string theory vacua problem, at least on a particle type by particle type basis.

Carl

 

[Juan R.]

I don't mean to argue that string theory is correct, but instead to point out that the dimensional regularization that leads to various assumptions of dimensions in string theory is an argument that can also be applied to the hidden dimensions arising from multi particle bound states.

Since string theory, like Kaluza-Klein, only deals with the lowest modes, there will inevitably be many different physical arrangements that will give those same modes. In other words, by ignoring all but the lowest energy modes, the mathematics problem of defining the physical situation from the spectrum is severely under constrained. What I'm suggesting is that the modes that correspond to the standard model can be written as the lowest modes resulting from composite particles. I think that this can be done in a manner compelling in its simplicity. But when you're done with this, there may be a way to solve the string theory vacua problem, at least on a particle type by particle type basis.

Carl

Aha!

Well, unfortunately i cannot help to you here. I am a bit confused on the question of unification and i do not know which could be the best (promising!) way.

- Perhaps composite particles.
- Perhaps pure geometric arguments on 4D on style of Connes program.
- Etc.

Unfortunately, i cannot valuate your proposal now. I am just focusing in quantization of pure gravity and spacetime.

 

[sssddd]

i would really like to know the background of the guy who says string theory is a waste of time.

 

[RandallB]

i would really like to know the background of the guy who says string theory is a waste of time.

He has promoted links to canonical science in earlier posts here that might help. I could never make heads or tails of it though. Maybe you’ll have more luck.