I desire that somebody in-the-know here, explain to me in layman's terms (I'm not mathematically educated, but have a good conceptual grasp of physics) the exact nature of the problem of reconciling GR with QM.

Some of you know me and hence know that I have a philosophical/metaphysical agenda, but I promise not to impose any of that stuff upon you here in the physics forum. If it came to the crunch and I wanted to do woo then I'd start a new thread in the philosophy forum. So I'd be very grateful if someone would assist me in understanding this.

Thanks in advance.

Several reasons I can think of that make the two theories difficult to reconcile are:

[1] GR is a theory that treats space-time as a continuum, whilst QM is increasingly treating it as a fine lattice of discrete voxels;

[2] GR involves transformations of time that don't appear in many formulations of QM (though there are relativistic formulations of QM in existence, but these tend to be limited in application beyond subatomic particles)

[3] GR involves numerous quantities represented as higher-rank tensors than 2, which as far as I'm aware never appear in QM;

[4] The two theories involve describing phenomena at vast opposites of the size scale. QM tends to concentrate upon what happens at scales of 10-12 m or smaller, whilst GR deals with phenomena on a scale up to 30 orders of magnitude larger than this.

These are just some of the reasons I can think of at the moment, though there are doubtless more.

However, one of the more interesting connection between GR and QM centres upon the fact that in the world of bosons, the spin angular momentum pseudovector of a boson is equal to the rank of the tensor describing the force that boson is responsible for. The Higgs boson, responsible for mass, has spin 0, and mass is represented by tensors of rank 0 (i.e., ordinary scalars). Electomagnetism is mediated by photons, which have spin 1, and therefore is a force represented by a tensor of rank 1 (a vector). Gravity is the oddity, and in GM, is represented by a tensor of rank 2 (one of the reasons GM is mathematically intimidating), and consequently, physicists expect any candidate for the graviton to have spin 2. Indeed, thanks to some interesting work by particle physicists, the Standard Model only has room for one species of spin-2 boson, so the moment a spin-2 boson turns up in a particle accelerator, it'll count as discovery of the graviton.

I can unambigously state that, with the exception of [1], I understood exactly none of that.

There are four fundamental forces - gravity, electromagnetic, strong nuclear and weak nuclear. GR is essentially the theory of gravity and QM the theory of the other three. In GR mass causes space to curve, and the fact that objects are moving through a curved space accounts for the action of gravity upon them. In QM forces work through an exchange of messenger particles between the objects being attracted/repelled. As Cali says, there is hope that a messenger particle for gravity might be discovered in the future, but the theories are difficult to reconcile because they talk about forces in such different ways.

Another difficulty is singularities such as black holes. As Cali said, GR is a theory of large distances and QM one of small distances. GR predicts, however, that black holes should be of vanishingly small size. That transports the objects of GR into a quantum scale. This causes a problem with the uncertainty principle. It's impossible to know at the same time exactly where something is and how much momentum (mass times velocity) it has. Our combined uncertainty about position and momentum must always be greater than a certain minimum limit. When a star collapses to a black hole singularity, the uncertainty principle makes it difficult to say that its mass now lies within a very tiny region of space as GR requires. The trade off for that would be a problematic margin of error in its momentum and hence velocity - crudely put it wouldn't stay within the required tiny region.

Isn't the main stumbling block something about QM is built on a more or less fixed space and time background, but in GR these become part of the solutions? I'm probably bollixing up how that's phrased, but I think that can get across what I'm trying to say.

Actually, QM has its own version of curved spacetime, in the form of "quantum foam". In brief, it's the application of the uncertainty principle to the space-time metric. Which results in points in space at distances smaller than the Planck Length being effectively indeterminate in position. One can think of this as treating space-time as an extremely fine lattice of tiny voxels, but the content of the voxels themselves at distances below the voxel size is effectively unknowable.

logical bob wrote:There are four fundamental forces - gravity, electromagnetic, strong nuclear and weak nuclear. GR is essentially the theory of gravity and QM the theory of the other three.

I was under the impression that gravity was the main problem? That, for some reason, GR doesn't apply (or, not accurately so) to quanta? If so, this is what I want to focus upon.

Rumraket wrote:I can unambigously state that, with the exception of [1], I understood exactly none of that.

I can help with that.

10-12 meters is what we would call very, very small.

The_Metatron wrote:

Rumraket wrote:I can unambigously state that, with the exception of [1], I understood exactly none of that.

I can help with that.

10-12 meters is what we would call very, very small.

Herald a plethora of dick jokes.

Gravity cannot be quantised and until it can it cannot be reconciled with the other three fundamental
forces. In order for this to happen it is necessary to know what happens inside a black hole. And this is
a problem given that nothing can be observed beyond the event horizon for light cannot escape from it

hackenslash does not think this is a problem and he has suggested on multiple occasions that gravity should not necessarily be regarded as a force. Obvious Leo thinks space does not exist and is no more than a mathematical model which does not accurately reflect physical reality. And Julian Barbour thinks time does not exist. So good to see plenty of thinking outside
of the box with regard to the exact nature of observable phenomena. Though how true any of it is another matter entirely

jamest wrote:

The_Metatron wrote:

Rumraket wrote:I can unambigously state that, with the exception of [1], I understood exactly none of that.

I can help with that.

10-12 meters is what we would call very, very small.

Herald a plethora of dick jokes.

Dick jokes eh?....

http://www.realclearscience.com/lists/b ... ynman.html

On topic -

GM is analogue
QM is digital

campermon wrote:

jamest wrote:

The_Metatron wrote:

Rumraket wrote:I can unambigously state that, with the exception of [1], I understood exactly none of that.

I can help with that.

10-12 meters is what we would call very, very small.

Herald a plethora of dick jokes.

Dick jokes eh?....

http://www.realclearscience.com/lists/b ... ynman.html

On topic -

GM is analogue
QM is digital

But why shouldn't valid discrete and continuous models of the same thing reconcile with each other?

One certainly expects analog signal analysis to reconcile with digital signal analysis, something would be seriously wrong with one and/or the other if they didn't.

They approximate - the way Newtonian physics does a decent job but Einstein more correct.

A unified theory would resolve this....in the meantime both theories are useful - QM in particular.

When thinking discrete vs continuous, analog/digital, it's usually the discrete is an approximation, or sampled, the underlying reality being continuous. What are the implications of the reverse?

crank wrote:When thinking discrete vs continuous, analog/digital, it's usually the discrete is an approximation, or sampled, the underlying reality being continuous. What are the implications of the reverse?

This might shed some light on that - or at least make good alternative reading to this this season.

I'm afraid in reading that, most of the shedding was done by my brain as it tried to glean something I could grasp. One error, calling someone 'barely 5 ft' tall 'very short', at least for his time, average height was around 5' 5", not that short. Same with Napoleon, he wasn't short at all. Bah, humbug.

the underlying reality being continuous

and you know this how ??

crank wrote:I'm afraid in reading that, most of the shedding was done by my brain as it tried to glean something I could grasp. One error, calling someone 'barely 5 ft' tall 'very short', at least for his time, average height was around 5' 5", not that short. Same with Napoleon, he wasn't short at all. Bah, humbug.

hmmmm. Well perhaps this will shed some light on the implications of reality being discrete rather than analog.

John Platko wrote:

crank wrote:I'm afraid in reading that, most of the shedding was done by my brain as it tried to glean something I could grasp. One error, calling someone 'barely 5 ft' tall 'very short', at least for his time, average height was around 5' 5", not that short. Same with Napoleon, he wasn't short at all. Bah, humbug.

hmmmm. Well perhaps this will shed some light on the implications of reality being discrete rather than analog.

Edit: Mindful of Goldilocks, perhaps this will give you something more suitable to chew on.

Macdoc wrote:

the underlying reality being continuous

and you know this how ??

I'm saying that's what has been assumed, and then asking what are the implications if it's discrete.