Likelihood of M-theory: 1-10 Scale

[marcus]

No, Marcus, I never said that. But I believe that NCG easily consumes CDT, and I'm hoping one of us will eventually convince you of this. What I have been trying to tell you is about some of the features that a decent approach to QG ought to have, and that CDT is clearly lacking.

that sounds very interesting if you can give it substance!
BTW I am not interested in primitive arguments like UGH DIS GOOD!
MINE IS BIGGER THAN YOURS! UGH DIS BETTER THAN DAT!
So I hope that you mean some logical connection when you say
NCG "consumes" CDT.

I never heard "consumes" in a mathematical discussion. It sounds more like poetry. what I hope you mean, and can show, is that CDT can be LOGICALLY DERIVED FROM NonComGeom.

I am still waiting for some logical connection to be established. It would, as I've said several times here, delight me. Unfortunately I cannot simply take your word for there being any connection at all. I need hard online evidence.

As to what you think you have been telling me, your memory of what you have said is doubtless different from mine.

You claim to have told me features which a theory of quantum gravity should have.
I have no idea what you are tallking about. Would you list them please?

cheers, Kea , list them and please do not be vague or use esoteric terminology. Say clearly and simply what features a satisfactory QG should have.
I want it in simple terms so that as many PF posters as possible will understand.
Go for it kiwibird!

 

[Kea]

You claim to have told me features which a theory of quantum gravity should have. I have no idea what you are tallking about. Would you list them please?

Hi Marcus

All right. Let's begin with the short list below. I have left out all technical jargon, but that means it might appear a bit vague, for which I apologise.

Features that a theory of QG should have
----------------------------------------

1. Unprejudiced geometry All path integral type approaches that I am aware of, including CDT, make a selection of contributing geometries with no backup physical arguments. Without going into fancy maths, there is a way to generalise the notion of a space such that there is more than one option for the real numbers. Any restriction to more ordinary spaces should be backed up with good physical grounds.

2. Geometric observables A rigorous notion of observable needs to be defined whilst respecting point 1.

3. Quantum general covariance Discussed a little in the "Third Road", QGC is a sort of Machian equivalence principle. GR began with a consideration of processes between separated matter domains. Separation between observers is not to be mistaken for basic discreteness of an objective reality at small scales. The only objective reality (in the sense that there is a universal observer) is a classical one. QGC must define the interaction of basic observables.

4. Solve the measurement problem

5. Recover Einstein's equations This means more than a concrete recovery of the equations in the limit of universal observation. Newton's equations describe the orbit of Mercury perfectly well, but the answer happens to be wrong to the limit of early 20th century observation. GR provides the correct answer, but more to the point: GR shows us when Newtonian mechanics breaks down. QG must be very clear about when GR breaks down. For example, it might say that we will not directly observe gravitational waves.

6. Calculation of Standard Model parameters QG should eventually be able to calculate numbers such as the fine structure constant and (rest) mass ratios. Masses are like quantum numbers. QG isn't QG if it can't tell us something about them.

7. Make new quantitative predictions Obviously.

8. Explain the 4 dimensionality of local classical spacetime Some people think CDT does this, but the physics is far from clear. Some people think quantum computation explains this. This really comes under point 5.

Cheers
Kea

 

[marcus]

Now we seem to be making rapid progress. I am glad to see your list of QG desiderata. I have no reason to quarrel with any because it is your list. Maybe i will try to formulate my own list, or borrow a definition of QG from Renate Loll lecture notes hep-th/0212340

...

Features that a theory of QG should have
----------------------------------------

1. Unprejudiced geometry
2. Geometric observables
3. Quantum general covariance
4. Solve the measurement problem
5. Recover Einstein's equations
6. Calculation of Standard Model parameters
7. Make new quantitative predictions
8. Explain the 4 dimensionality of local classical spacetime

this is actually a pretty good list. it may be helpful in this or other threads.
congratulations on boiling it down like this.
oh, please be specific about number 4. the measurement problem

 

[Kea]

please be specific about number 4: the measurement problem

Hi Marcus

The measurement problem is about the 'logic of measurement' and the context of an observer in the universe at large. Since logical issues are already raised by the generalised geometries that I referred to, and certainly in the question of what causality means, a proper definition of QG observables should also solve the so-called measurement problem.

Must go again.
Cheers
Kea

 

[marcus]

The measurement problem is about the 'logic of measurement' and the context of an observer in the universe at large. Since logical issues are already raised by the generalised geometries that I referred to, and certainly in the question of what causality means, a proper definition of QG observables should also solve the so-called measurement problem.

I think maybe I can put it in more concrete terms than that...in usual quantum mechanics the observer who measures is distinct from the experiment---but with the universe we can't stand outside it and measure.

In usual QM there are two separate systems the cat-in-the-box or whatever, and the guy in the white coat standing outside. QM is about what the guy in the white coat can learn by preparing the experiment in a certain way and then making measurements. the observables are the measurements he is allowed to make.

the trouble with the universe is that the man in the white coat cannot stand outside it. so it breaks the sacred two-system model that is basic to QM.
now what can QM be a theory of?

maybe that is a concrete statement of the measurment problem

 

[Chronos]

The 'measurement problem' rubs me wrong. I'm not yet willing to concede it is physically meaningful. I try to keep an open mind, but the screen door remains shut - I'm trying to keep the flies out.

 

[marcus]

What is the absolute minimum list of requirements?

Oh, you re there Chronos, good. How would you pare kea list down to the bare bones?

 

[marcus]

Kea has a list of things that it would be NICE if a QG would eventually do for us. But we are just evolved fish on a small planet and we take what we can get.

...

Features that a theory of QG should have
----------------------------------------

1. Unprejudiced geometry
2. Geometric observables
3. Quantum general covariance
4. Solve the measurement problem
5. Recover Einstein's equations
6. Calculation of Standard Model parameters
7. Make new quantitative predictions
8. Explain the 4 dimensionality of local classical spacetime

Chronos let us chuck out #6. Once we get a QG, that is just a theory of spacetime and its geometry, then we can reconstruct the Std Mddle ON TOP OF IT and maybe things will improve, but that is a later chapter

the three I like very very much, of Kea list are these three, what about you?
5. Recover Einstein's equations
7. Make new quantitative predictions
8. Explain the 4 dimensionality of local classical spacetime

 

[Kea]

on Reconstructing...

The $\gamma = \frac{1}{3}$ from p39 of Reconstructing comes from AJL's reference [60]

http://arxiv.org/abs/hep-th/9401137
http://arxiv.org/abs/hep-th/9208030

on 2D gravity models and Ising spin systems. To quote the conclusion of the first paper: "The model is closely related to the matrix models studied in [-] and to the $c \rightarrow \infty$ limit of multiple Ising models studied in [-]. However, our approach has the virtue of being simple and avoids any use of matrix models..."

 

[marcus]

The $\gamma = \frac{1}{3}$ from Reconstructing comes from AJL's reference [60]
...

Kea thanks for helping with the detective work. it can be like herding cats
to try to track down all the notation in a major paper like this.

since Ambjorn is or has been a string theorist and sees lots of connections there
one can get concepts and notation crossing over from string theory

any other things to point out

 

[Kea]

The $\gamma = \frac{1}{3}$ from p39 of Reconstructing comes from AJL's reference [60]

http://arxiv.org/abs/hep-th/9401137
http://arxiv.org/abs/hep-th/9208030

The first paper's reference number [3] comes from the hey-day of String theory (sorry - no web version; library visits required)

Conformal field theory and 2D quantum gravity
J. Distler, H. Kawai; Nucl. Phys. B321 (1989) 509-527

On page 525 they have the formula for $\gamma$ for any genus $g$, not just $g = 0$ as considered by AJL and others. This is explained in more detail in the supertitled paper

Super-Liouville theory as a two-dimensional, superconformal supergravity theory
J. Distler, Z. Hlousek, H. Kawai; Intl. J. Mod. Phys. A5 (1990) 391-414

The formula for $g = 0$, on page 400, is

$$\gamma = 2 + \frac{1}{4} (D - 9 - \sqrt{(9 - D)(1 - D)})$$

in terms of a String theoretic dimension parameter. Below the formula the authors state: "Note here that the expression makes sense only for $D < 1$". Clearly this isn't true, but they are motivated by the connection between $D$ and a coefficient in their action, which they require to be real since they're afraid of ghosts. Since we don't care about String theory
we can happily ignore this statement and plug $\gamma = \frac{1}{3}$ into the formula, to find

$$D = \frac{544}{60} = 9.066666666$$

How cool is that! I'm not sure what it means yet. By the way, the partition function, on the same page 400, may be written

$$Z = \int_{0}^{\infty} \textrm{d}V S(V)$$

where

$$S(V) = \nu e^{- \frac{\lambda}{G} V} V^{-3 + \gamma}$$

roughly in the terminology of Reconstructing. Compare this to page 33 of Reconstructing where AJL discuss critical exponents in the Baby Universe papers. In summary, it appears that the cool things in Reconstructing have quite a lot to do with early Strings and superconformal theories, or, on the other hand, perhaps some of the later topological Strings stuff. We need to rope in Distler to look at CDT.

 

[selfAdjoint]

Chronos let us chuck out #6. Once we get a QG, that is just a theory of spacetime and its geometry, then we can reconstruct the Std Mddle ON TOP OF IT and maybe things will improve, but that is a later chapter

I don't see how you can say this. M-theory, for all its problems, proposes to do better than that, to get both background-free spacetime and the standard model (maybe supersized) out of the ONE theory. And that's the goal of Thiemann's Phoenix Program too. Why should we give up on this goal just because AJL have made a breakthrough with the Regge Calculus?

 

[marcus]

The first paper's reference number [3] comes from the hey-day of String theory (sorry - no web version; library visits required)

Conformal field theory and 2D quantum gravity
J. Distler, H. Kawai; Nucl. Phys. B321 (1989) 509-527
...

Back in the heyday of String theory, Jan Ambjorn was doing String research himself----I just checked his papers on arxiv.org (which only goes back to 1991) and he has over a 100 papers going back to when arxiv opened, and quite a lot of them are String.

I'd guess we can expect to continue seeing stringy references and notation in CDT, if for no other reason because of Ambjorn's earlier research activities.

 

[Kea]

Super-Liouville theory as a two-dimensional, superconformal supergravity theory
J. Distler, Z. Hlousek, H. Kawai; Intl. J. Mod. Phys. A5 (1990) 391-414

The formula for $g = 0$, on page 400, is

$$\gamma = 2 + \frac{1}{4} (D - 9 - \sqrt{(9 - D)(1 - D)})$$

From page 406: "From the point of view of the random surface theories, the particularly interesting quantity is the susceptibility exponent because of its relation to the Hausdorff dimension. Actually we only need $\gamma$
[for genus zero] since $d_{H}$ is proportional to $\gamma^{-1}$."

Of course this agrees with the $d_{H} = 3$ of section 6 of the Reconstructing paper.

 

[Mwyn]

how does m-theory explain quarks?

 

[marcus]

... to get both background-free spacetime and the standard model (maybe supersized) out of the ONE theory...

I see that as a longterm goal. (It seems obvious. I can't imagine anyone not looking forward to theorists putting quantum spacetime and matter into ONE theory.)

I prefer a minimalist definition of the "quantum theory of gravity" goal which can be inclusive of incremental efforts modestly aimed quantizing relativity, and I think overreaching efforts may prove a colossal waste of time.

I do not see the all-encompassing "ONE theory" criterion as a helpful way of deciding which models of quantum spacetime are interesting.

I object to defining "quantum theory of gravity" in a way that EXCLUDES those efforts which make no attempt at explaining the various particles and forces at this time.

I think that is rhetorically stacking the deck against the modest, one-step-at-a-time, approaches and in favor of the grandly ambitious (possibly premature) ones.

Getting a new quantum spacetime continuum is a hard problem. Indeed quantizing Gen Rel has been an historical roadblock. The CDT authors are focussing on that (not on incorporating the Std Mddle of Matter at the same time in one grand fell swoop) and I suspect that will prove the more efficient path for making progress towards the ultimate goal.

 

[Chronos]

Pardon me for being a little slow catching up with this thread [my regular computer commited suicide]. I would settle for the odd numbers on Kea's list. I think if you can accomplish that much, the rest should fall into place rather naturally. Of course I would also expect it to closely match all known observations supporting predictions of both GR and QFT. I also think it should be renormalizable at some scale. I'm not sure you could otherwise legitimately call it a quantum theory.

 

[marcus]

I would settle for the odd numbers on Kea's list...

Hi Chronos, you might wish to use a little caution, or get some clarification about the implications, before you buy #1. Here is it in full:

1. Unprejudiced geometry All path integral type approaches that I am aware of, including CDT, make a selection of contributing geometries with no backup physical arguments. Without going into fancy maths, there is a way to generalise the notion of a space such that there is more than one option for the real numbers. Any restriction to more ordinary spaces should be backed up with good physical grounds...

So, Chronos, certainly "unprejudiced" SOUNDS great and even PC and all, but am I "prejudiced" if i decide to use real and complex numbers, instead of fancier stuff like, say, quaternions, octonians, some noncommutative matrix algebra? what's the rhetorical slant here? shall physicists be saddled with the obligation to give solid physical reasons for using the real numbers? should they be called "prejudiced" if they don't justify NOT using quaternions? How much esoteric math will the thought police force me to eat, if I refuse to give them "physical grounds" for just using ordinary math.

my feeling is that IT IS UP TO THOSE PEOPLE USING ESOTERIC GEOMETRIES AND NUMBER SYSTEMS, to physically justify their choices if they want to. But those math tools which physicists usually suppose don't require justification, and which are traditional with physicists, they should keep on using without having to justify it. Especially, as recently with CDT, they work brilliantly in practice and lead to breakthroughs!

my thought is that working physicist like Renate Loll is too busy getting new results---using familiar, and rather modest, means like little chunks of Minkowski txyz space, and the real numbers. She does not have time to
justify, to some philosopher, her NOT using more esoteric math. She should not have to give "good physical reasons" for using the simple traditional mathematical materials that she find work.

 

[Kea]

I would settle for the odd numbers on Kea's list.

Hi Chronos

I always appreciate your point of view. I'm curious: what is your objection to point 2 (geometric observables)?

Cheers
Kea

 

[Chronos]

Hi Kea! No objection. I just think an unprejudiced geometry, which I interpreted as being diffeomorphism invariant and background independent, would naturally produce the correct geometric observables.