Why Are Quantum Theory and General Relativity Not Compatible?

[Chronos]

I thought some here might enjoy a more pedestrian discussion of issues involved in unifying quantum theory with general relativity. I know I do. I need an occassional refresher course to get a grip on the brain bending stuff I usually read:

The Problem of Time
http://kims.ms.u-tokyo.ac.jp/The-problem-of-time-E.html

If there are any CNS fans out there, this related paper may be of interest:

A Possible Solution For The Problem Of Time In Quantum Cosmology
http://www.edge.org/3rd_culture/smolin/smolin_p1.html

It's a bit dated, but not so easy to find. Possible insight into the thought processes underlying Smolin's CNS conjecture.

 

[marcus]

...
A Possible Solution For The Problem Of Time In Quantum Cosmology
http://www.edge.org/3rd_culture/smolin/smolin_p1.html
...

the article by Stu Kauffman and Lee Smolin you link to is given a brief preface by Julian Barbour. As several people at PF may have already pointed out, Barbour has had a lot to say about the problem of time over the years

by chance, a few days ago I happened to learn that Smolin and Barbour co-wrote papers in 1987 and 1992

J. B. Barbour and L. Smolin Can quantum mechanics be applied to the universe as a whole? Yale University preprint, (1987).

http://www.arxiv.org/abs/hep-th/9203041
Extremal variety as the foundation of a cosmological quantum theory
Julian Barbour, Lee Smolin

In "the case for", Smolin cites gr-qc/0104097, which has references to other work by Barbour, but not these.

BTW I see that Smolin has "in preparation" a paper called
Essay on the Methodology and Ethics of Science
this could have connections with last year's "Scientific Alternatives to the Anthropic Principle" which several of us (myself certainly, you too I think) read with considerable interest.

 

[Chronos]

I follow Smolin's work with great interest [call me a fan]. I'm currently hoping to get the scoop on his take of this paper [which appears to be a serious challenge to CNS]:

http://arxiv.org/abs/astro-ph/0508050
A 2.1 Solar Mass Pulsar Measured by Relativistic Orbital Decay

And yes, I do look for stuff like this on a near daily basis. Color me curious... or in need of a hobby...

 

[marcus]

http://arxiv.org/abs/astro-ph/0508050
A 2.1 Solar Mass Pulsar Measured by Relativistic Orbital Decay
...

I see that their estimated error is plus/minus ten percent.

if that is confirmed it seems adequate to falsify CNS

that is very exciting

I assume you will be learning Lee's reaction to this before long.

"..The measured rate of change in orbital period, corrected for acceleration biases, is dP/dt=(-6.4+-0.9)x10^-14. Interpreted in the context of general relativity, and combined with measurement of Shapiro delay, it implies a pulsar mass of 2.1+-0.2 solar masses, the most massive pulsar measured.."

I see the authors are from Princeton, Cornell, British Columbia, Jodrell Bank, and the Bonn MPI for Radioastronomy

 

[Chronos]

Thanks marcus, I hope to hear from Dr. Smolin on this. It is a very solid paper, IMO. But, I don't think it falsifies CNS. It does, however, force some equation of state adjustments. I don't have the mental acuity to do that, but have an abiding interest in seeing how the real pro's tackle the issue.

 

[hellfire]

I thought some here might enjoy a more pedestrian discussion of issues involved in unifying quantum theory with general relativity. I know I do. I need an occassional refresher course to get a grip on the brain bending stuff I usually read:

The Problem of Time
http://kims.ms.u-tokyo.ac.jp/The-problem-of-time-E.html

I read that link and I do not understand it. My main confusion arises from the fact that it is claimed that H f = 0 means no time at all. Classically, H f = 0 is a constraint due to reparametrization invariance of the theory. It expresses a non-dynamical symmetry and does not mean that there is no time evolution and Hamiltonian formulation, but it just means that the non-dynamical degrees of freedom must be eliminated before one goes on to get the dynamics of the system. This is e.g. the case of the geodesic motion of a free point particle. Now, with this background I am unable to understand what is explained there. Any help?

By the way, I find it is a very good idea to have some "pedestrian discussions".

 

[Chronos]

I share your confusion, hellfire. All models I have seen seem to assume something that resembles a background state.

 

[marcus]

... All models I have seen seem to assume something that resembles a background state.

one way to clear up some of the confusion is to recognize the many meanings of the word "background"

I believe that the phrase "background independence" originally referred to a prior chosen "BACKGROUND METRIC" on a differentiable manifold.

If we just focus on this meaning then the issues are pretty clear. Either your theory requires a differentiable manifold or it doesnt.

If it does require a manifold then, to get started, do you need to start by equipping the manifold with a metric? That is, do you need some specified geometry at the outset?

If so, then in the most conventional sense, you are background dependent because you DEPEND ON A BACKGROUND METRIC. And if not, then your theory is background independent (a formless manifold, without prior geometry, suffices to get you started.)

General relativity is background independent in this long-established conventional sense. you don't have to choose a metric to begin with. In fact the metric IS the gravitational field that you are intending to solve for.

Hellfire and Chronos, I think you know this well, so when you talk about all theories having some "background" you must be generalizing the concept. But then (when background does not simply mean background geometry, or background metric on a manifold) it gets a little vague. perhaps usefully vague, i don't know if usefully or not.

But when one generalizes like this there is a danger of losing sight of the clear recognition that, in a conventional technical sense, where one is just referring to the metric, General Relativity is a background independent theory.

(and so are certain attempted quantizations of it)

 

[hellfire]

I think I know the meaning of background independence at least in the classical sense. What is completely unclear to me is why it is claimed that a hamiltonian constraint means that there is no time evolution at all (refer to my previous post). It would be very nice if you or someone else could explain this.

 

[marcus]

I think I know the meaning of background independence at least in the classical sense. What is completely unclear to me is why it is claimed that a hamiltonian constraint means that there is no time evolution at all (refer to my previous post). It would be very nice if you or someone else could explain this.

I will not explain so much as comment. The trend in QG research is to get away from the timeless canonical formalism.
As you most likely are well aware a lot of LQG people have moved into Spin Foams, which is a sum-over-histories, or path integral, approach.

Gambini has developed the Consistent Discretizations version of LQG, which has a hamiltonian TIME EVOLUTION OPERATOR instead of a constraint

The triagulations CDT method, which has been making headway and getting a lot of notice is a path integral approach.

So strictly canonical LQG, with the hamiltonian constraint and "frozen-time" formalism, is seeming to be LESS TYPICAL and more of an isolated example. It is less representative of the nonperturbative QG field.

To an overwhelming extent, whenever string theorists (a numerous and media-dominant bunch) TALK about QG alternatives to string, they focus on string canonical LQG. This produces the illusion that it is representative of non-string QG but it has become less so.

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

That said, how does one treat time in canonical LQG? Well, the way I understand it is that you have to have REAL WORLD QUANTUM CLOCKS that are themselves observables and you study CORRELATIONS between what some clock-observable says and what some other measurement observable says.

In other words the hilbertspace you build (on the configuration space of connection geometries on the spatial manifold Sigma) is GOOD FOR ALL TIME. If you have a clock observable that says it is tuesday, then it will correlate with observables that tell you about the condition of spacetime on tuesday.

All the probabilities are conditional probabilities, given that some clock observable says suchandsuch.

so it is the same hilbertspace for all eternity, and if your clock observable says that it is one twinkling after the big bang then the other observables conditioned on that reading tell you about the conditions of spacetime one twinkle after the big bang.

the keyword, for looking up papers about this, is "partial observable"

A recent paper is
http://www.arxiv.org/abs/gr-qc/0507106
Partial and Complete Observables for Canonical General Relativity
by Bianca Dittrich, a capable Potsdam person.

 

[marcus]

There is a wealth of discussion in this thread
"Smolin letter..."
https://www.physicsforums.com/showthread.php?t=85306
about background independence (including different meanings that a string theorist like Jaques Distler could attribute to it).
Look around post #8
https://www.physicsforums.com/showthread.php?p=720463#post720463

 

[Chronos]

Agreed, marcus. Thanks for the course correction. Since, under GR, gravity is all about geometry, it is logical to define background independence as a coordinate system that is emergent from first principles. I was confusing the difference between background independence and first principles. That's why I'm here... I need slapped every once in awhile.

 

[hellfire]

As far as I know, in case of the geodesic motion of a point mass the unphysical degree of freedom that leads to the vanishing Hamiltonian is eliminated selecting one of the coordinates (from the background spacetime) as the time coordinate. Thus if I extrapolate this I can assume that the requirement of background independence leads to the problem of time as it does not allow to select any preferred foliation of spacetime, correct?

 

[marcus]

Agreed, marcus. Thanks for the course correction...

I was not aware that one of us had corrected the other. We were talking about confusion and I think there is very understandable and legitimate confusion in discussing b.indep. that comes from the praiseworthy attempt to extend the concept.

As we both realize, if you put a very restricted construction on the term, it isn't confusing. It just means "not-having-to-use-a-prior-chosen-metric-on-the-manifold", that is, to put it more concisely, "not-resorting-to-prior-metric" or "independence from prior-chosen geometry"

So there is nothing philosophically profound or at all subtle, in that restricted sense term-----you look at some method and ask does it use a prior chosen metric on the manifold----if it does not then it is a b.indep. method----if it does rely on a prior choice of metric then it is b.dependent.

This is a time-worn well established terminology. It can be somewhat confusing like any technical terminology, but it is not VERY confusing.

However there is nothing wrong with trying to extend the restricted idea, to make it more profound, apply more generally, be more thought-provoking. That is a legitimate, more philosophical, function. I seem to recall that John Baez has a short essay on background independence somewhere, that goes into these broader deeper meanings of the idea.

You pay a price, of course. there is always increased risk of confusion when one generalizes an idea. that's life.

Smolin's essay "the case for..." has a great potential for causing confusion because it extends the idea in a philosophical way to a notion of DEGREES of b. independence.

there are two main messages:

1. string theorists should try to just get the plain very limited kind of restricted-sense independence...keep doing things on manifolds, guys, just KICK THE PRIOR METRIC HABIT. he says that it is do-able, shows some promising paths to try, and argues that it has a chance of helping them get to a predictive theory (which would then of course have to be tested but that is another matter)

2. then he goes beyond that and philosophizes about how can we go BEYOND just kicking the prior metric habit. what is the meaning of this quest for fewer prior assumptions? what is the essential idea here that we can extend? what more excess baggage can we maybe get rid of (besides the simple one of a prior metric which already 1915 Gen Rel got rid of)?
why should we want to go beyond and get MORE "b. indep" (now talking in the extended sense) and what might that do for us?

The moment he gets into talking about message 2. then he opens the gates to a whole lot of confusion, but that is the price of innovative thinking.

HEY GUYS, CHECK THIS OUT!
https://www.physicsforums.com/showthread.php?p=720728#post720728
new Etera Livine paper, black holes, LQG, entropy, renormalization of area, looks like Livine has some new ideas
"Quantum Black Holes: Entropy and Entanglement on the Horizon"
with another paper in the works called
"Reconstructing Quantum Geometry from Quantum Information: Entanglement as a Measure of Distance"

 

[Chronos]

Marcus, I like to think we do this all the time... offer views and discuss them. Yours are very interesting. I mostly ask questions. Hopefully, they are intersting questions.

 

[Chronos]

Don't get me started on time, hellfire... hehe.

 

[hellfire]

In the first link you gave us, Chronos, it is also mentioned that a selection of a preferred time coordinate leads to different representations that are not unitary equivalent. As far as I know systems with infinite dimensional phase spaces are not scope of the Stone von-Neumann theorem (which guarantees the unitary equivalence of different representations of the commutation relations). However, this does not impede that different representations in quantum field theory (with infinite dimensional phase space) are usually related by unitary transformations (Bogolyubov transformations). Is my understanding correct? If yes, what is different in this case that leads to representations which are not unitary equivalent?