Do String Theory Dualities Challenge Traditional Ontology?

[Curious6]

In a recent post in his blog, Woit comments on a philosophy of science article by a philosopher who claims that the dualities in string theory imply the "dissolution of the ontological object". His claim is that because the dualities in string theory can describe two different sorts of behaviours of strings in spacetime which are indistinguishable from each other empirically, there is no more basis for a traditional ontological object. However, he keeps on referring to the "string", isn't the string itself a fundamental entity and the traditional ontological object. Also, could anybody provide any insight in the light of the string landscape, where the extremely large number of separate vacua can be interrelated by dualities?

Also, what is the "ontological object" in loop quantum gravity?

Any comments or insights would be appreciated!

 

[Kea]

hi

This sounds interesting. I am currently studying topos theory
with some philosophers who are keen on the idea of
"dissolution of the ontological object". To me this is essential
to QG.

Cheers
Kea

 

[Curious6]

OK, it would be interesting to know some philosophers' ideas or viewpoints here.

 

[Curious6]

The basic message I think the author is trying to convey here is that because of the dualities in string theory, there can be different descriptions for the same underlying phenomena (how a string moves in spacetime for example), but however I don't understand how this implies the dissolution of the ontological object. The string is unaffected, there are however various way to describe it mathematically in spacetime. What would be a philosopher's take on LQG? Are there also these dualities? Do people here believe that dualities do imply this dissoultion of the ontological object (i.e. is it a direct consequence or more of an interpretation)?

 

[RingoKid]

could you post a link to the original blog/site/comment ?

thanx

 

[Curious6]

Yes, the blog can be found on http://www.math.columbia.edu/~woit/blog and it should be the third or fourth entry (where he discusses philosophy and string theory). He provides a link to the page where you can read the article. Anymore comments?

 

[NanoTech]

There could be a correlation between the duality of light(being particle or wave) and the duality of strings(different vibrations create matter directly or indirectly)?

 

[marcus]

...

Also, what is the "ontological object" in loop quantum gravity?

Any comments or insights would be appreciated!

This is a great question, Curious! Thanks.

As far as I can see the two approaches to quantum gravity making the most rapid progress right at the moment are LQG and CDT (causal dynamical triangulations)

they have two different ontologies and also different pictures of the start-up of the expanding universe----both replace the big bang singularity with a physical picture without infinities, but the Loop picture has a prior contracting phase which the CDT picture, at least so far, does not.

I will try to respond to your question of what the underlying object or objects is (are) in Loop Quantum Gravity. I may have to duck, punt, waffle, and otherwise dodge difficult issues. I don't know if I can say anything. It will be interesting to see---and also to see if anyone else who knows something about LQG will help out.

 

[marcus]

I guess the fundamental ontology of LQG is the same as 1915 Gen Rel, which says there is nothing more basic than the gravitational field.

It says something that is a big item to assimilate: that the gravitational field can be defined without any spacetime to define it in.

Other fields, and physically real events, are located in or with respect to the gravitational field.

Philosophically this is a very big step. Einstein was savy, philosophically, and understood how radical it was and talked about it some. A lot of people still don't take the 1915 step seriously, but some do----perhaps a growing number now.

Philosophically I don't think LQG introduces anything new to to the ontology. It mainly just takes Einstein's 1915 insight seriously.
So LQG does not have any absolute enveloping spacetime. The most basic thing in it is the gravitational field.
All LQG does is introduce a way of writing QUANTUM STATES of the gravitational field.

So now i should try to say what the gravitational field is. I should take a break first and start a separate post about it.

 

[marcus]

What is the gravitational field. i will try to get started on this and then have a break.
It is tricky because it has the notion of "equivalence class"
In mathematics you can define a bunch of things and then clump together all of them that are MORPHABLE one into another--and are therefore essentially the same

there is an idea of "factoring out" meaningless differences

Now a gravitational field is really just a GEOMETRY, it is often called a metric and it basically a machine which tells you any areas and volumes and angles and distances that you want to know.

If you live in a screwed up funhousemirror world then you know it because the distances all come out wrong and the angles and volumes are funny.
Triangles don't have 180 degrees and all that. We all have those days.

Anyway a grav field, or a geometry, or a metric, is just a machine that gives you any basic geometric readings about your world. Like you draw a triangle and ask it if the lines are straight and it tells you if they are and you ask it what the sum of the angles and it tells you that, and the area if you want to know, and so on.

Now the universe consists of a gravitational field AND a whole lot of matter, and the matter helps to SHAPE the gravitational field----it influences the geometry.

So if you draw a big triangle and put a mass like the sun inside there will be a different answer for the 180 degrees.

And both matter and geometry are DYNAMIC, that is they flow around and change. The grav field, which is the geometry, can even ripple (people are pretty sure that gravitational waves, ripples in the geometry, happen)

Now comes the important step. If you stop here you don't get the ontology.
We have to factor out the physically meaningless differences and get EQUIVALENCE CLASSES of metrics.

The universe consists of a grav field and matter. OK. I said that.
But the only mathematical language we have for describing that situation is to first postulate a LIMP CONTINUUM, a kind of damp amorphous graph paper we can use for writing down the metric on and writing down the distribution of matter on.

But, dammit, that is only temporary provisional CONVENIENCE because otherwise how are we going to write it down.

After that we have to factor out physically meaningless differences and identity all the different worlds where we wrote down two that look different on paper but you can morph one into the other.

Because a point only matters if something happens there, a point is WHERE SOMETHING HAPPENS and all that ever matters is relationships between events. So you can write down the same universe on two different pieces of graph paper and make it look different. But they are ontologically the same. They describe the same fundamental reality and the same history of the world. So you find you can morph one picture into the other.

So you have to equate just those that are equivalent and you end up with a bunch of equivalence classes of worlds. Because there are a lot that are NOT equivalent.

 

[Mike2]

What is the gravitational field. i will try to get started on this and then have a break.
It is tricky because it has the notion of "equivalence class"
In mathematics you can define a bunch of things and then clump together all of them that are MORPHABLE one into another--and are therefore essentially the same

there is an idea of "factoring out" meaningless differences

Now a gravitational field is really just a GEOMETRY, it is often called a metric and it basically a machine which tells you any areas and volumes and angles and distances that you want to know.

If you live in a screwed up funhousemirror world then you know it because the distances all come out wrong and the angles and volumes are funny.
Triangles don't have 180 degrees and all that. We all have those days.

Anyway a grav field, or a geometry, or a metric, is just a machine that gives you any basic geometric readings about your world. Like you draw a triangle and ask it if the lines are straight and it tells you if they are and you ask it what the sum of the angles and it tells you that, and the area if you want to know, and so on.

Now the universe consists of a gravitational field AND a whole lot of matter, and the matter helps to SHAPE the gravitational field----it influences the geometry.

So if you draw a big triangle and put a mass like the sun inside there will be a different answer for the 180 degrees.

And both matter and geometry are DYNAMIC, that is they flow around and change. The grav field, which is the geometry, can even ripple (people are pretty sure that gravitational waves, ripples in the geometry, happen)

Now comes the important step. If you stop here you don't get the ontology.
We have to factor out the physically meaningless differences and get EQUIVALENCE CLASSES of metrics..

Because a point only matters if something happens there, a point is WHERE SOMETHING HAPPENS and all that ever matters is relationships between events. So you can write down the same universe on two different pieces of graph paper and make it look different. But they are ontologically the same. They describe the same fundamental reality and the same history of the world. So you find you can morph one picture into the other.

So you have to equate just those that are equivalent and you end up with a bunch of equivalence classes of worlds. Because there are a lot that are NOT equivalent.

Are equivalence classes memberse of which all morphe into one another... are equivalence classes another way of describing a symmetry transformation of some kind. Is there a different equivalence class for each symmetry?

 

[marcus]

Mike it sounds like you completely grasp the idea of an equivalence class.

It doesn't seem like a very hard or complicated idea does it? It comes from mathematicians, which may be the reason that although it is a very simple idea the name for it has 5 syllables and sounds a bit solemn (eq-ui-va-lence-class)

the idea is you have a huge number of things some of which are essentially the same as others and only different in meaningless details
so you simplify by clumping or identifying things that are essentially the same, and creating a bunch of new identities that really ARE different one from another

because the meaningless differences (which physicists call "gauge") have been squeezed out.

==========

there is an example that could come in handy, that of knots

think of all the freeform ways you can map a circle into ordinary 3D space, making various curves like the smoketrails of a stuntflyer, which can be quite tangled and complicated but which always return to the starting point.

this makes a huge infinity of loopy images in the sky, all of them being unbroken curves, and some of them are knotted in various ways

and a lot are essentially the same, like they are differently stretched out ovals, fat ovals, skinny ovals, variously draped ovals
and you find you can morph anyone of that class into any other by a smooth deformation of ordinary 3D space!

so you DEFINE an equivalence relation by saying "I will regard any two of these loop paths as equivalent if I can map one into the other by a smoolth deformation of 3-space. If I can moosh the sky so that one smoketrail becomes identical to the other."

and then you collect all the loop paths that are equivalent into a pile
and you find that you now have a nice small collection of piles.

the piles are abstract knots.

well, can you think of a simpler way of rigorously defining what a knot is?

humans naturally form equivalence classes, it is called "generalizing", and they naturally occur in everyday language-----so often when you go thru the mathematical or logical steps of defining an equivalence class you discover that you have an idea that is already intuitive or familiar.

like two square knots are the same knot even if they occur in different parts of space and one is upside down from the other, or is made with bigger rope, because you could smoothly map one to match the other
so they are equivalent-----they are the same knot----they belong to the same equivalence class

it's all really clear I think

And Einstein's 1915 Gen Rel is actually about equivalence classes of metrics. the gravitational field is not simply a given metric which is a solution of a certain differential equation------because two metrics which are deformable into each other really describe the same universe---so
the gravitational field is an equivalence class of metrics.

you can write down a representative of the class---some particular metric. but then you should really say (under your breath) "and I don't mean just this particular one, I mean this and all the others that you can get from this one by morphing it."

 

[selfAdjoint]

The thing that brought equivalence classes home to me so long ago was "modulo arithmetic" in number theory. Take odds and evens; all the even numbers are equivalent in that they are multiples of two, and all the odd numbers are equivalent in that they aren't^*. So if you form the class of all evens, call it E and the class of all odds, call it O, those are equivalence classes. And you can add them and multiply them according to the familiar rules E+E = E, O+O = E, O+E = E+O=O, and ExE=E, ExO=OxE=E, OxO=O. Instead of E and O you can use 0 and 1 respectively^# and restate the same rules to define the field Z₂.


^* More precisely, the evens leave a remainder of 0 on division by 2 and the odds leave a remainder of 1.

^#That is, the remainders on division by 2.

 

[Mike2]

there is an example that could come in handy, that of knots

think of all the freeform ways you can map a circle into ordinary 3D space, making various curves like the smoketrails of a stuntflyer, which can be quite tangled and complicated but which always return to the starting point

It sounds like equivalence classes can be assigned somewhat arbitrarily, that there is some freedom in what kind of morphology maps share. It also sounds like it is possible to have sub-equivalence classed within larger equivalence classes.

Do you suppose the ultimate laws of physics are described in terms of symmetries?

 

[selfAdjoint]

It sounds like equivalence classes can be assigned somewhat arbitrarily, that there is some freedom in what kind of morphology maps share. It also sounds like it is possible to have sub-equivalence classed within larger equivalence classes.

Do you suppose the ultimate laws of physics are described in terms of symmetries?

An equivalence has to satisfy a equiv a, a equiv b implies b equiv a, and a equiv b and b equiv c implies a equiv c. If you can prove a relationship has those properties then it's an equivalence and you can define equivalence classes that won't overlap, and then pass to the quotient thingy consisting of the classes treated as objects with whatever structure they have inherited from the underlying set.


And yes, all of physics is thought to be based on symmetries, active and broken. That's what those groups and Lie algebras and representations are all about.

 

[Demystifier]

In a recent post in his blog, Woit comments on a philosophy of science article by a philosopher who claims that the dualities in string theory imply the "dissolution of the ontological object". His claim is that because the dualities in string theory can describe two different sorts of behaviours of strings in spacetime which are indistinguishable from each other empirically, there is no more basis for a traditional ontological object. However, he keeps on referring to the "string", isn't the string itself a fundamental entity and the traditional ontological object.

This is not necessarily true if you allow for a truly ontological interpretation of quantum theory, such as the Bohmian interpretation. For the case of duality in string theory, see
http://arxiv.org/abs/hep-th/0605250