Do we really need to unify GR and QM?

[Gerinski]

Decades of work are being put in trying to find a unified theory which can accommodate both General Relativity and the Standard Model. I guess that the attractive of a unified theory is more than justified, but does it really need to be the case?
Is it possible that the universe works really with separate elements like

a) GR describing spacetime which is continuous
b) QM describing energy-matter which is quantized
c) a theory describing how do both interact with each other

Something like in the game of chess where you have a description of the chessboard, a description of the pieces, and the rules of the game?

It may look like 'c' is the same as the unified theory of the first paragraph, but in this case there is no need to search for a quantization of spacetime, spacetime would still be continuous, and 'c' would just be a theory describing how continuous spacetime and discrete energy interact with each other.

Is this possibility also being researched?

 

[friend]

So what you are basically asking is what justifies quantizing the gravitational field. So let's examine the reasons given for quantum gravity.

Some say that spacetime at small scales has no meaning because we would have to put a lot of energy into probing those small scales, so much so that it would create mini black holes at those scales, and we would never be able to probe spacetime at that scale. I have a problem with that. No one is saying that spacetime ends in large black holes just because we can't probe inside the event horizon. So just because we can't probe inside small black hole at the Planck level doesn't mean that spacetime has no meaning there, right?

 

[friend]

So what you are basically asking is what justifies quantizing the gravitational field. So let's examine the reasons given for quantum gravity.

Some say that spacetime at small scales has no meaning because we would have to put a lot of energy into probing those small scales, so much so that it would create mini black holes at those scales, and we would never be able to probe spacetime at that scale. I have a problem with that. No one is saying that spacetime ends in large black holes just because we can't probe inside the event horizon. So just because we can't probe inside small black hole at the Planck level doesn't mean that spacetime has no meaning there, right?

Another thing they say is that all the matter of a black hole gets crushed to a singularity, a single point so that we must consider both gravity and quantum mechanics. Perhaps they are right. But as I understand it, the matter never really reaches a singularity; it's always in the process of falling into, but never reaching the singularity. It would take an eternity to actually reach the singularity, right?

 

[Fredrik]

Is it possible that the universe works really with separate elements like

a) GR describing spacetime which is continuous
b) QM describing energy-matter which is quantized
c) a theory describing how do both interact with each other

GR doesn't just describe spacetime. It describes the relationship between spacetime and the matter in it. And it uses a classical description of matter, which we know is inadequate in certain situations. So in that sense, GR has already been falsified.

We can probably define quantum theories of matter on a spacetime obtained by solving Einstein's equation of GR, but then we would lose a key part of GR, the part about how matter and interactions influence the geometry.

 

[Harry Wilson]

For the same reason that one needed to have a quantised theory of electromagnetic radiation, Einstein suggested that we need a quantised theory of gravitation - otherwise, atoms would radiate away all of their energy gravitationally!

 

[marcus]

EDIT: Ooops, I had to be away from computer for a few minutes and in the meanwhile, the question was quite thoroughly answered making this post unnecessary, but I'll leave it anyway.

...
Is it possible that the universe works really with separate elements like

a) GR describing spacetime which is continuous
...

The conventional wisdom is GR does not work at extreme density. It has a limited domain of applicability beyond which it is not trusted: it blows up.
In the past, other man-made theories have had "singularities" or catastrophes of one sort or another that were CURED by improving or replacing the theory. Sometimes fixing the singularities involved quantizing e.g. what Planck did around 1900.

Also QM has its own problems. Quantum Field Theory gives a ridiculous value for vacuum energy, and does not tell us about the 80% of matter that is "dark". It is built on rigid background geometry (typically that of SR), while we know geometry is not rigid. Indeed, geometry and matter interact intimately, so QFT as it stands is merely an "effective" theory. It cannot be right and eventually will have to be thrown out.

 

[Gerinski]

Thanks

 

[friend]

- otherwise, atoms would radiate away all of their energy gravitationally!

Interesting! Has anyone ever done that calculation to see how long that would take? Yes, there is some angular momentum associated with orbiting electrons, but wouldn't there be problems with the electrons mass being distributed around the nucleus as opposed to a point particle?

 

[julian]

I think there was a similar thread "Maybe there is no grand unified theory?"

 

[DimReg]

For the same reason that one needed to have a quantised theory of electromagnetic radiation, Einstein suggested that we need a quantised theory of gravitation - otherwise, atoms would radiate away all of their energy gravitationally!

This doesn't make sense me. When you solve the hydrogen atom in qm, it has quantized energy levels. But the electric field has not been quantized yet. Quantization of the field doesn't seem to be a requirement for the stability of atoms.

 

[tom.stoer]

We have to be very careful and distinguish unifying GR with QM and quantizing GR.

[GR] uses a classical description of matter, which we know is inadequate in certain situations. So in that sense, GR has already been falsified.

means that we need to quantize GR.

But it does not mean that we need to unify GR with other forces. In approaches like LQG, CDT, AS etc. GR is quantized, but all other forces are "added by hand"; only string theory and SUGRA go even further and try to unify them, i.e. derive them from one single action.

Fredrik's claim is correct in the sense that we know that a) non-quantized matter and b) quantized matter on classical spacetime becomes a) physically incorrect or b) mathematically inconsistent. The claim from string theory is not based on such hard facts.

 

[Gerinski]

We have to be very careful and distinguish unifying GR with QM and quantizing GR.


means that we need to quantize GR.

But it does not mean that we need to unify GR with other forces. In approaches like LQG, CDT, AS etc. GR is quantized, but all other forces are "added by hand"; only string theory and SUGRA go even further and try to unify them, i.e. derive them from one single action.

Fredrik's claim is correct in the sense that we know that a) non-quantized matter and b) quantized matter on classical spacetime becomes a) physically incorrect or b) mathematically inconsistent. The claim from string theory is not based on such hard facts.

Thanks, this seems to answer also the neighbor thread 'Is space-time discrete or continuous?'

 

[tom.stoer]

No, it does not necessarily mean that spacetime is discrete; quantization does not always imply discreteness

 

[Demystifier]

For the same reason that one needed to have a quantised theory of electromagnetic radiation, Einstein suggested that we need a quantised theory of gravitation - otherwise, atoms would radiate away all of their energy gravitationally!

I don't think it's a valid argument. Electromagnetic radiation does not need to be quantized in order to PREVENT atoms to radiate away their energy. Just the opposite, given that atoms (electrons) are already quantized, electromagnetic field needs to be quantized in order to ALLOW spontaneous radiation from atoms in excited states.

 

[bcrowell]

See Carlip, "Is Quantum Gravity Necessary?," http://arxiv.org/abs/0803.3456

There are very general reasons why it's not easy to make a reasonable theory in which a quantized field interacts with a classical field. This originally came up in the Bohr-Kramers-Slater (BKS) theory, in which energy and momentum were conjectured to be conserved only on a statistical basis. Experiments as early as Bothe's in 1925 falsified the BKS theory by showing that when x-rays were emitted in a spherical wave into two hemispherical detectors, the two detectors were completely anticorrelated.

 

[friend]

So can QM or QFT be formulated on a discontinuous background? Or do we lose quantum effects if we do? Wouldn't the spacing distance in a discrete background form a hidden variable in quantum mechanics that's been already ruled out?

 

[tom.stoer]

There is no reason to assume that the background must be discrete. There are approaches where it is (LQG, ...) and where it isn't (strings, asymptotic safety approches).

If you look at LQG it's a - after all quantization issues - a standard QM theory of interacting discrete spin-like objects including matter d.o.f.; w/o any new hidden variables etc.; distance is a derived concept; the fundamental idea is that two vertices connected by a link do interact; everything else like geometry, distance, ... should be emergent

 

[friend]

There is no reason to assume that the background must be discrete. There are approaches where it is (LQG, ...) and where it isn't (strings, asymptotic safety approches).

If you look at LQG it's a - after all quantization issues - a standard QM theory of interacting discrete spin-like objects including matter d.o.f.; w/o any new hidden variables etc.; distance is a derived concept; the fundamental idea is that two vertices connected by a link do interact; everything else like geometry, distance, ... should be emergent

The trouble with these approaches (all of them?) is that they do not tell us where the quantization procedure comes from to begin with. They just assume it's valid to use with gravity and use it to their advantage. So they cannot speak to fundamentals, like whether QM requires or not a continuous background.

 

[tom.stoer]

The trouble with these approaches (all of them?) is that they do not tell us where the quantization procedure comes from to begin with. They just assume it's valid to use with gravity and use it to their advantage. So they cannot speak to fundamentals, like whether QM requires or not a continuous background.

I think you should distinguish clearly between discreteness and quantization.

The quantization used in LQG is - except for some technical details of the approach - standard. They carry out the quantization program and try to a) show it's consistency and b) test it against experimental results. In that sense they do nothing else but quantize a classical field theory, like QED and QCD. They all have to assume that the quantization procedure is well-defined and applicable.

The fact that the resulting spin network structure is discrete, is neither a priori clear, nor is it an assumption. It is a result derived from the formalism. So if LQG can be shown to agree with nature in terms of experiments, then there is some evidence that quantum gravity requires a discrete structure.

Nevertheless discreteness and quantization are not the same thing.

The question is whether we can answer the question "what it means that geometry is fundamentally discrete".

Suppose CDT is the correct description; it's a rather simple model using (discrete) triangulations of spacetime. Of course we can change the scale and look at spacetime at different resolutions, we can probe the triangulations, gravity and other interactions at different scales; we can calculate physical observables at different scales.

Now the following could happen: when changing scale and zooming to finer triangulations = to higher resolutions the physical answers we get become scale independent. That means that finer and finer triangulations do not have any effect on physical observables (below some "fundamental length").

So we make two observations
1) the theory allows for arbitrary small triangulations, i.e. it has a continuum limit
2) below some length scale physics doesn't change

1) means that the theory is not fundamentally discrete
2) means that it behaves as if it were fundamentally discrete

 

[friend]

I think you should distinguish clearly between discreteness and quantization.

The quantization used in LQG is - except for some technical details of the approach - standard. They carry out the quantization program and try to a) show it's consistency and b) test it against experimental results. In that sense they do nothing else but quantize a classical field theory, like QED and QCD. They all have to assume that the quantization procedure is well-defined and applicable.

The fact that the resulting spin network structure is discrete, is neither a priori clear, nor is it an assumption. It is a result derived from the formalism. So if LQG can be shown to agree with nature in terms of experiments, then there is some evidence that quantum gravity requires a discrete structure.

Nevertheless discreteness and quantization are not the same thing.

My concern is for mathematical consistency. In LQG we start out assuming both QM and GR are valid. But we may end up destroying both. If you quantize the metric and with it areas of neighborhoods, then we may be destroying the Hausdorff property of manifolds and with it GR. We may also be destroying QM if QM requries a continuous background.

 

[tom.stoer]

In LQG we start out assuming both QM and GR are valid. But we may end up destroying both.

We use the Einstein-Hilbert metric as a formal starting point. Then we are transforming it according to some QM rules into a totally different theory. This new theory must contain GR in a certain limit (it is not clear whether LQG passes this test). But that does not necessarily destroy anything. Look at ordinary QM: you start with continuous x and p (as variables in phase space) but you may end up with discrete p (as eigenvalues of a hermitean operator acting on Hilbert space). This does not destroy Newtonian mechanics, but it is still contained in QM in a certain limit.

If you quantize the metric and with it areas of neighborhoods, then we may be destroying the Hausdorff property of manifolds and with it GR.

Yes, we do that. There is no manifold in LQG.

We may also be destroying QM if QM requries a continuous background.

I don't think that QM requires any continuous structure. Variables may be discrete (spin), time has completety disappeared.

But I agree, it is possible that a quantization procedure IS ill-defined or inconsistent (up to now it is by no means clear whether LQG is well-defined and does not lead to quantization anomalies or inconsistencies)

 

[schema]

Another thing they say is that all the matter of a black hole gets crushed to a singularity, a single point so that we must consider both gravity and quantum mechanics. Perhaps they are right. But as I understand it, the matter never really reaches a singularity; it's always in the process of falling into, but never reaching the singularity. It would take an eternity to actually reach the singularity, right?

There in lies the paradox. When you run the tensors to simulate a massive object approaching the singularity, you eventually reach a point where mass is approaching infinty, therefore time slows. when you reach a point where infinite mass takes up zero space, time has stopped completely: r=o

So technically you could be right that it takes an eternity.

 

[schema]

What if there is another field to consider before trying to comprehend a GUT? Entanglment? Recent experiments haves all but confirmed the possiblity of matter teleportaion via Entanglement. If this isn't suggestive of a hidden governing force, it certainly is another road block to understanding a complete theory of QM. Without a complete working model, unification is nothing but philosophical postulate *cough String Theory cough*.

 

[alemsalem]

If you keep GR classical you have to explain what the gravitational field of a single particle is, it can't be just a normal gravitational field for a particle that doesn't have a well defined positions (?) I don't think you can use $|\psi|^2$, <x> to replace mass density and position for a single particle,, so if its classical somehow it emerges from some other theory (like fluid dynamics emerging from quantum mechanics of atoms) ..

Feynman gave another similar argument, basically if you believe quantum mechanics all the way (superposition of Earth being inside and outside the milky way) then you need to quantize gravity somehow..

 

[friend]

If you keep GR classical you have to explain what the gravitational field of a single particle is, it can't be just a normal gravitational field for a particle that doesn't have a well defined positions (?) I don't think you can use $|\psi|^2$, <x> to replace mass density and position for a single particle,, so if its classical somehow it emerges from some other theory (like fluid dynamics emerging from quantum mechanics of atoms) ..

Feynman gave another similar argument, basically if you believe quantum mechanics all the way (superposition of Earth being inside and outside the milky way) then you need to quantize gravity somehow..

As I recall, the quantizing procedure to get particles relies on differential equations of a field on a continuous spacetime background. I don't know what the quantization procedure would be for QFT in a quantized spacetime background.

 

[nitsuj]

Indeed, geometry and matter interact intimately, so QFT as it stands is merely an "effective" theory. It cannot be right and eventually will have to be thrown out.

What an uplifting comment