Is String Theory A Waste Of Time?

[marcus]

Juan, I do not think it is a waste of time to show that something is false.

Interesting book, though!

I see the book Juan mentioned (that amazon says is due out in October) is by the same physicist/cosmologist/popular author who wrote "The Physics of Star Trek" and "Fear of Phyics: a Guide to the Perplexed".

Telos, you are definitely on to something about time spent drawing testable conclusions from a theory so that it may be shown false.

 

[marcus]

You can be sceptic of my evaluation of the theory (that is not a problem for me). But my evaluation is, exactly, that string theory is a waste of time (and money). I could search other words for you but the message would be the same.
...

I am skeptical of the broad way the evaluation is stated. There are several things to say. One is that your opinion is shared (in a qualified way) by a growing number of physicists, for reasons that were mentioned in this earlier PF thread:
https://www.physicsforums.com/showthread.php?t=80760

In this thread, which Ratzinger started in June 2005, some knowledgeable PF people like Haelfix, selfAdjoint, Ohwilleke, concisely reported some reasons why there has been a decline, over the past 3 years or so, in interest and popularity of string research.

Increasing worry and pessimism among string researchers was reflected in the Toronto discussion video.
https://www.physicsforums.com/showthread.php?t=84585
One encounters expressions of disillusion among graduate students---some of whom are changing fields---and symptomatic efforts being made by string-loyal bloggers (such as Motl and Distler) to shore up morale among the graduate students.

We also see some statistical indications of the decline in string interest, popularity, optimism. One can always argue about how to interpret the various statistical measures, however.

I must say that observing this string "downsizing" going on has increased my respect for the honesty and courage of certain researchers such as Andy Strominger. He made an excellent two minute statement in the Toronto discussion at time 1:28:20
It put me in mind of a story in the Bible where a general tells his soldiers that anyone who wants to can go home, and about half of them leave (this is called "downsizing"), then the remaining ones go on to win the battle.

Anyway Juan, I will try to say what I think about your message that string theory is a waste of time.

 

[marcus]

...Anyway Juan, I will try to say what I think about your message that string theory is a waste of time.

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.

 

[Telos]

Telos, you are definitely on to something about time spent drawing testable conclusions from a theory so that it may be shown false.

Wish I could say I thought of it myself!

 

[marcus]

Wish I could say I thought of it myself!

the important ideas are like that. you only pass them along, instead of originating them

 

[Juan R.]

As said, I do not think that the decline of string research program is just temporary one. In the past, there were difficulties but now people is seeing that each year original objectives of string theory are far, and far, and farther. String theory history looks like a divergent asymptotic series.

I must say that observing this string "downsizing" going on has increased my respect for the honesty and courage of certain researchers such as Andy Strominger.

Said I the contrary? I am against half-true that many string physicists popularized as the new standard in scientific communication. I am also against arrogance typical of many string theorists (of course not all).

Now, let me reply your very interesting comments.

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

I disagree; I provided abundant data in all aspects of the theory (geometry, hidden dimensions pointlike behavior, spectral decomposition, relativity, arrow of time, reductionism, etc.) and already explained that I was talking of string theory like a TOE on post #5.

As said by Nobel laureate P. Anderson this year, string theory is a futile exercise as physics. I substituted “futile exercise” by “waste of time” but my evaluation of string theory continues being correct.

I would state that string theorists provide none serious argument why we would believe on string theory, only bold statements like "it is the most promising way" or wrong claims like "is the only was to quantum gravity". I see an injustice here with people that are not string believers.

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.)

I am sorry to say this Marcus but this kind of argument is childish. A theory (or hypothesis) is not a “futile exercise as physics” on function of the number of papers or researchers working in it. Or would I remember to you the number of papers in early investigation of perturbative quantum gravity until was shown that QGR was nonrenormalizable on independence of parameter of expansion taken. All previous work in dozens of attempts to quantize GR directly were a waste of time.

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.

The premise is obvious when one know why was formulated string theory. String theory is a “theory” of physics. Its main objectives are unification of forces quantizing gravity, systematization of the standard model, and possibly the explanation of some cosmological mysterious.

Has string theory been interesting on mathematical topics? Of course, but that does not justify the hype around it and its study on physics dept. Moreover, let me say that the impact of string theory in the whole of mathematics is not so huge, at least, it is not more important (by orders of magnitude) that impact of some field theoretical techniques. For example, contrary to popular belief, Fields Medal awarded to Witten was not by the application of pure string theory methods to math, most of mathematical work of Witten was from field theory. Atiyah, who is many times more smart and versed that i in these topics, affirms that string theory has had an impact on mathematics which has been really quite extraordinary. Well, he said that in a popular interview. However, far from popular claims, I see not radical advances on mathematics as provided by the own Atiyah on "index theorems" (theory of quantum operators in quantum field theory).

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.

Already replied. That young mathematician, if interested in string “theory”, would focus on the mathematical branches below string physical theory, including non-commutative geometry, G2 manifolds, K theory, topology, and news branches of analyses and algebra, etc. Of course, with an eye in the “physical” stuff.

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.

This is a very, very astonishing simplification of the problem. Background independence is not the magical cure to all problems of string theory. Even if one day a background independent version of string theory is achieved (I doubt), string theory will continue to be a waste of time like a TOE. Moreover, it will continue to be as non-predictive like is now.

Do not forget that LQG is claimed background independent whereas continue to be an “inefficient” approach to quantum gravity. In fact, there is no possibility for obtaining a consistent classical limit converging to GR after of 40 years from Hamiltonina gravity: geometrodynamics, Astherkar QGR, LQG, etc.

Smolin, as others loop theoreticians, assumes that relationism is correct, but it is not as already said. The idea of that causality becomes a fuzzy notion because of fluctuation of light cones is completely wrong.

 

[lightcone]

i am sure strings are going to disappear and first sign of this is the idea os landscape of vacuua. it is such a comic trash that during seminar you feel like quiting physics because such are the things promoted as future directions.

but stringers cannot fool th world much long and more so because some of them are serious researchers with a conscience still alive.

plase read freeman Dyson: disturbing the universe and you will know hy string theory qualifies as a failure.

The problem of delay in this being branded a failure is obvious, INERTIA. there are too many researchers persuing it who are trained as stringers unlike the masters who were all high energy physicists. S now we have this young generation of ignorant people who doesn't even know where to find mistake to stop doing it since they simply do not know physics. It is just poor quality mathematics.

 

[marcus]

i am sure strings are going to disappear and first sign of this is the idea os landscape of vacuua. it is such a comic trash that during seminar you feel like quiting physics because such are the things promoted as future directions.

but stringers cannot fool th world much long and more so because some of them are serious researchers with a conscience still alive.
...

I agree with the respect you show for serious and principled researchers
"...serious researchers with a conscience..."

Public support for physics ultimately depends on the trust that nonspecialists have in the self-critical, "self-policing" ability of theorists to remain engaged with empirical reality. So your perception that there are some who are not indulging in a mathematical escapade is very important.

 

[marcus]

"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.

 

[RandallB]

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. Does the following make sense:

SR Special Relativity - background dependent
Works on a ‘dependant’ background of space and time in a classical manner. Just the Newton formulas were inadequate and the measures of space or distance over time need to be understood by the better formulas provided by relativity.

GR General Relativity - background independent
The use of a warping of time and space into “space/time’ to understand gravity, releases us from a background dependent measure. That is the physics we see, relativity included, is not dependent on any background traceable measure in either distance. But rather only dependent on the “relationships” between physics events that cannot be tied down to a measurable background reference of space and time.

A fine point but seems an important one I’d not fully recognized.

In a similar fashion :

Quantum Theory - background dependent
Quantized the minimum amount of energy to be found in light “packets” now photons. And set minimum size of change in measure we could expect to ever make in both time and distance (space). Natural limitations associated with this made near impossible to make significant progress until.

Quantum Mechanics - background independent
Instead of “warping” the relationship of time and space, used the uncertainty principal to allow measure and predictions at the quantum level to become understandable.
Thus one way to explain the inability of combining the physics of QM and GR even though they are both “background independent” is that they arrived at their independence in dramatically different forms (warping vs., probabilities) that we so far have been unable to interrelate.
(I'd previously considered not being able to combine the two as a dependent vs. independent issue)

Is this a reasonable tune up to my thinking?
Let me know if I’ve gone off track on the “background” issue as it is a bit new to me.

Also are there any other “well-established theories” that arrive at their background independence though some other manner than GR or QM? I’m assuming that most all, like M-Strings, have their foundation in QM.

Thanks
RB

 

[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