Exploring the Incompatibility of QM & GR

[Marin]

Hello!

I know nowadays physicists try to make the grate unification - all 4 forces in a single theory that would govern all of their interactions :)

However many people say QM and GR are incompatible. Can anyone of you please explain to me why this is so?

I know that QM is a probability theory, whereas GR is a deterministic one, but after all - both of them include our reality as a separate 'boundary' case, don't they?

Then what splits them up and makes them so different to be even incompatible (at least for now)?

 

[Gianni2k]

The basics of the incompatibilty lie in the extremely small (Planck length) scenario. Basically GR predicts a "smooth" (C-infinite manifold) underlying space-time at the very small scale whilst QM, due to its intrinsic probabilistic nature, predicts this to be "rough" with pairs of particles and antiparticles continously being produced in the vacuum. This inconsistency leads to infinities popping out everywhere in the maths when you just try and cram things together. The calculations become pretty involved, this is just the main reason.

 

[Marin]

Thanks :)

But what happens then, if you apply QM to the biggest and heaviest objects (perhaps also the fastest), I mean there, where GR is supposed to govern the laws?

And what's the hindrance making GR probabilistic? (such as towards the masses/energies of the biggest objects probability disappears (tends to 1) or becomes insignificant in another way?)

 

[Gianni2k]

Hum ok, firstly applying QM to the "heaviest objects" such as planets is amost pointless as the QM effects are negligible. Secondly there is an intrinsic incompatibilty regarding particle number conservation, this is solved by the most basic Quantum field theory. For particle motion in SR there are causal problems when quantizing the theory. By making this a quantum field theory we solve these problems by allowing antiparticles to cancel the off light cone events which determine the causal issues. QM itself however cannot solve the problem. Of course SR is just the easiest special case of GR, so you can see how this would work in GR as well (particle paths determined by geodesics, curvature etc).

 

[Marin]

So you mean, what physicists now need is a quantised theory that governs the 'word of the biggest' to replace GR and in this matter be compatible with QM?

Do you know such types of approaches - another way of trying to understand the space and time?

Or a quantum gravity theory? - but such a theory would not be compatible with GR either, would it?

 

[Gianni2k]

What physicists need is a high-energy quantum gravity theory which reduces to GR at low energies (i.e. planets). This is basically what the whole of string theory is trying to do (in fact pretty successfully atm). Other approaches have been tried involving twistor theory, quantum loop gravity and foam approaches but I don't know of any which work as wekk as string theory.

 

[Marin]

ok, but isn't a high-energy quantum theory too far from human current technological abilities? I mean, there can be developed even several pretty good theories which all describe gravity very well in the next century but how are they going to prove them?

Mathematics is very beautiful (I could confirm it on my small experience with it till now) but we also know that there are plenty of examples where mathematics describe solutions which nature does not tolerate.

 

[Gianni2k]

One method is via extra dimensions. These quantum gravity theory work in extra compactified dimensionalities. Some of the high energy experiments can probe the results of the extra compactified dimensions and hint at a possible Qgravity theory.

 

[friend]

Hum ok, firstly applying QM to the "heaviest objects" such as planets is amost pointless as the QM effects are negligible. Secondly there is an intrinsic incompatibilty regarding particle number conservation, this is solved by the most basic Quantum field theory. For particle motion in SR there are causal problems when quantizing the theory. By making this a quantum field theory we solve these problems by allowing antiparticles to cancel the off light cone events which determine the causal issues. QM itself however cannot solve the problem. Of course SR is just the easiest special case of GR, so you can see how this would work in GR as well (particle paths determined by geodesics, curvature etc).

The invariance of the Hilbert-Einstein action produces Einstein's field equations. So do they just put the Hilbert-Einstein action in the path integral in order to produce quantum gravity?

 

[marcus]

...I know that QM is a probability theory, whereas GR is a deterministic one, but after all - both of them include our reality as a separate 'boundary' case, don't they?

Then what splits them up and makes them so different to be even incompatible (at least for now)?

Hi Marin,
I see you are new here---welcome to PhysicsForums!

I have a different point of view from Gianni's which I will lay out briefly for you.

GR is our current theory of geometry. It does not presuppose any fixed geometrical background. The metric (the distance function describing geometrical relationships) is the dynamical variable. The theory determines geometry. On the other hand, much of the rest of physics is developed by assuming at the start a fixed geometrical background, thus fixing the metric. It assumes the geometry is already determined!

I do not consider this an incompatibility. I consider it a problem, and one should appreciate the scale of the problem. In sum, while the rest of physics is based on provisional fixed-geometry spacetimes, GR is about the nature of spacetime itself: geometry and how matter interacts with it.

To get a clearer idea of what a quantum geometry (QG) or quantum general relativity (QGR) should look like, please have a look at the July Scientific American article by Ambjorn and Loll. This article gives an idea of what the main goals of QG are.
http://www.scribd.com/doc/3366486/SelfOrganizing-Quantum-Universe-SCIAM-June-08
(I also have a link to this article in my signature.)

The goal is to produce a quantum continuum, where there are fluctuations and uncertainty in the local geometry especially at small scale, but where overall, on average, we see a nice smooth classical geometry emerge, like the macroscopic real world.

As you can see, Ambjorn Loll and their co-workers have made remarkable progress towards this goal recently. They generate random quantum universes in the computer and when they average them up, they get a classical spacetime. The individual quantum universes can be captured and explored--they show interesting non-classical properties at small scale. In work like this a new idea of the continuum is emerging.

This is what one should expect from QG as it matures. Their model also requires a positive cosmological constant in order to work---so it begins to suggest what the meaning of the cosmological constant is, where it comes from so to speak. No clear conclusions, but this is another thing that a mature QG should do: explain the acceleration in expansion.

A singularity is a place where a theory breaks down, in the past singularities have been eliminated by improving the theory. This indicates another thing that QG should do. It should say what is really going on at the center of a black hole and describe conditions around the time of the big bang. A number of recent QG papers pursue these two goals.

A good way to sample the current literature on this is to do a keyword search at slac.stanford spires database using the keyword "quantum cosmology". Here is a search of recent papers ranked by citation count. The most highly cited ones use the Loop approach and are largely based on computer models of the big bang. I set the date so as to select highly cited papers published since 2005.
http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=DK+quantum+cosmology+and+date+%3E+2005&FORMAT=WWW&SEQUENCE=citecount%28d%29
If you do the same spires search but change the date to be before, say, 2003, it will turn up a lot of highly cited string-based papers.
The shift in researcher's interest seems to follow from the fact that loop QG models resolve the big bang singularity and allow one to go back earlier in time beyond the singularity in the classical theory. There have recently been a number of papers using the same methodology to resolve the black hole singularity. I just saw one by Boehmer and Vandersloot that you could find on arxiv if you want a sample of how that is going.

So resolving classical singularities is another obvious goal and progress is currently being made on that.

So my perspective is I don't see an incompatibility. That is just how some people talk. Instead of an incompatibility, I see it in terms of goals.

The most important goal is to get a quantum geometry----which means a new mathematical model of the continuum. To see what I mean, look at the SciAm article. They aren't there yet but that's the direction. The quantum spacetime continuum should reproduce GR dynamical geometry at large scale and should eliminate the classic GR singularities so we can go back in time before the big bang and also get an idea of what happens in black holes. It should also clarify the way that matter and geometry interact, perhaps leading to a new understanding of what matter is. These are major challenges, not incompatibilities.

 

[Marin]

Hi, marcus!

Thanks for the indispensable explanation. I especially liked the article about QG - it's really exciting how their approaches go more and more nearer, and how they correct the mistakes by setting new computer parameters and ideas.

But if the calculations are so complex, how are they going to set the equations after that - or they're just trying to figure out the 'ingredients' by these simulations and then do all the hard mathematical work, knowing what has to come out?

After all, there are several candidates for the 'highly sought' QG. What do you think, which one has to be given the odds (for now)?

best regards, Marin

 

[marcus]

After all, there are several candidates for the 'highly sought' QG. What do you think, which one has to be given the odds (for now)?

best regards, Marin

Marin, it is really too early for us to be picking winners to put our bets on, but I will tell you what I think.
I think that all the approaches which are trying to find a quantum continuum, a new mathematical model of spacetime that embodies quantum geometry, are the same

in the sense that they will converge. Here is an example of this:
http://arxiv.org/abs/0806.4640
it has some non-technical parts that one can read to get an idea of what it is about. I will try to explain about 0806.4640:

Three years ago it used to be that spinfoam and canonical LQG were different. Then over the past year a new spinfoam model has been developed which agrees with LQG, or seems to at any rate.
We are talking about comparatively slight changes, not changes in the overall formalism but in how some particular thing is calculated. So now you can begin to think of spinfoam and LQG as a single combined approach.

Now in this 0806.4640 paper Freidel is arguing for a modification of the spinfoam model. Probably if this were adopted it would force a change in LQG. It might also make the path integral calculation more tractable. It might also bring that combined spinfoam/LQG approach closer to demonstrating the correct classical limit.

At the same time there have recently been papers----as I recall one by Dittrich and Ryan stands out----which work to bring the whole spinfoam business closer to the Ambjorn Loll approach, or to triangulation approaches in general.

I can't take the time to get this all clearly laid out now. But my overall feeling is that these approaches are converging and that they will all end up being the same approach.

That is, what are converging are the efforts to construct a quantum geometry with a new idea of what spacetime is----a continuum like the Ambjorn Loll thing, which has uncertainty and fluctuation at small scale but looks smooth and classical at large scale. These approaches are characterized by the fact that none of them assume a fixed geometry at the beginning. They are independent of a prior fixed geometric framework and they want a model of the spacetime to emerge by itself according to quantum laws.

To some extent both Ambjorn Loll at Utrecht and the Loop Quantum Cosmology people at Penn State are able to do that. I think the other approaches will converge in with them.

You asked about analytical models. At Penn State they do both computer simulations and completely solvable analytical models----the analytical models confirm the computer numerical work. This is a plus for them. At Utrecht they are learning things using their numerical simulations but so far I think they have not reduced it to analytical form. Personally this does not worry me but people have different expectations. I like their new quantum continuum too much to worry about their lack of a closed analytic expression for it

best regards to you, it was a good question!

 

[Marin]

Hi again!

Till now, we said the physicists are looking for the quantum geometry, to get one step closer to the grate unification. My question goes to a different direction this time.

GR says, gravity emerges from the curvature of spacetime - in other words it's the warps and contortions that make us 'fall' this and that way, an entirely geometrical way of explaining how the force works.

On the other hand the 3 quantum forces are described by messenger particles. Thus, a graviton is suggested to exist, but not yet found. Is the new QG theory going to represent gravity as a geometrical - on large scales - and by gravitons (at small scales) and how such a duality would be possible? It seems to me that after QG is found it will still be very hard to unify forces if they have a 'different' theoretical origin (different way of understanding them). So are there any speculations how this is going to work?

 

[Gianni2k]

The graviton is a geometrical entity in itself, being the metric.

 

[Marin]

do you mean metric as the mathematical metric (e.g. metric spaces, etc.)

hmmm but spacetime itself has its own metric, I think it's called the Minkowski-metric (or the metric of the Minkowski space) :?

Why not then consider it as the graviton?

 

[Fra]

Hello Marin, I think it's interesting how different people describe the problem of "quantum gravity" in different ways. There are angles ranging from almost purely philosophical to almost purely mathematical.

Here is my highly personal and nonstandard opinion.

GR says, gravity emerges from the curvature of spacetime - in other words it's the warps and contortions that make us 'fall' this and that way, an entirely geometrical way of explaining how the force works.

I think of it as a description, rather than an explanation. Gravity is the curvature of spacetime. But the interesting part IMO, is not that reformulation.

It's Einsteins Equation that postulates a relation between geometry and the matter and energy distribution - this IMO is the truly ingenious part.

On the other hand the 3 quantum forces are described by messenger particles. Thus, a graviton is suggested to exist, but not yet found. Is the new QG theory going to represent gravity as a geometrical - on large scales - and by gravitons (at small scales) and how such a duality would be possible? It seems to me that after QG is found it will still be very hard to unify forces if they have a 'different' theoretical origin (different way of understanding them). So are there any speculations how this is going to work?

Statistical manifolds are one way to explain emergent manifolds from discrete events.

The notions of manifolds, geometry, geodesics and Einsteins equations could maybe be seen emergent from information processing.

Geodesics can be seen as a kind of the most probably paths expected to be taken by a random walker, or the test particle can be seen to simply "diffuse into the future".

But then mysterical part is howto interpret Einsteins equations. How does the expected path's of a random walker change in response to new information? This is what Einsteins Equations says. So the matter and energy distribution somehow seemst o represent the information?

Another problem with this is if we are talking about statistics - who is doing this statistics? IMO, it's the observer. The is another problem, because each observer have different observations and thus will arrive at differing manifolds. But maybe this is exactly the drive for interactions?

Some questions I'm asking is the information theoretic basis for Einsteins equations itself.

/Fredrik

 

[Fra]

do you mean metric as the mathematical metric (e.g. metric spaces, etc.)

hmmm but spacetime itself has its own metric, I think it's called the Minkowski-metric (or the metric of the Minkowski space) :?

Why not then consider it as the graviton?

Usually a graviton is more like a quantized "perturbation" of the metric, rather than the metric itself. And a perturbation is always made with respect of a background, giving something like uniqueness issues.

One question is what is measurable in GR?

/Fredrik

 

[Marin]

I think I'm getting deeper in the field's of pros :) I guess I have to wait some years and get some real knowledge at the university :)

Quantum gravity is indeed a very interesting topic, I just might go this way for the master :D Anyway there's lots of time till then, first I want to see where my maths abilities get limited. Hopefully not so soon from now ;)

 

[exponent137]

If we look at only macroscopic measurements: Where there appear dissagreement betwen QM and GR? For instance, photon fly in line in big distances, but not in small distances. So at big distances this is not problem. But what is problem?

 

[Gianni2k]

One question is what is measurable in GR?

To name one, the degree of deflection of light rays around massive objects.