Why is theory of Gravity and QM incompatible?

[Imafungi]

I am wondering why if quantum mechanics is self consistent, equal to itself, and thought to be equal to reality, and the same can be said of the theory of Gravity, why the separate theories and equations can not be plugged through a process of guess and check/trial and error by supercomputers even, to arrive at the compatible solution?

Also this may be a separate question, but I am curious to know what the most agreed upon view is of what the manifold or field that is responsible for the existence of gravity is/is like and how it exists?

Also, is that field coupled to the EM field, as I know EM radiation follows the shape of that field? Would this make them two sides of the same coin so to speak?

Also, is it agreed upon that the Gravity field and EM field take up every infinitesimal point within the universe at all times, or within the universe are there, if even the smallest quantities, areas of pure, absolute nothingness?

This is my first post, I hope this is in the correct forum, and I hope these questions can be discussed, thanks.

 

[Matterwave]

1) Quantum mechanics and General Relativity work very well in their respective regimes. Quantum mechanics (more properly, for a Lorentz covariant version, quantum field theory) works very well describing every force of nature other than gravity. General Relativity works very well explaining gravity on the large scale. It is unknown how to explain gravity on the microscopic scale (scales ~Planck length).

2) The most accepted view of gravity is that it is a curvature of space-time itself. Space-time in general relativity is a 4 dimensional Lorentzian manifold made up of points called events.

3) The EM field moves in space-time just as everything else does, so it must also follow the curvature of space time. The EM field is a physical field of electric and magnetic fields on top of the background of space time. It affects space time through its stress-energy, and space-time affects it through its curvature. I don't know what you mean by "two sides of the same coin".

4) I have no idea what you're asking here.

 

[Imafungi]

1) Quantum mechanics and General Relativity work very well in their respective regimes. Quantum mechanics (more properly, for a Lorentz covariant version, quantum field theory) works very well describing every force of nature other than gravity. General Relativity works very well explaining gravity on the large scale. It is unknown how to explain gravity on the microscopic scale (scales ~Planck length).

What is the most accepted reason why they are incompatible? There must be an error somewhere in the thinking of quantum mechanics as it is now then, if it is a perfect self consistent description of reality, but missing a large chunk. Doesnt that mean something about the quantum mechanics equations must be altered to include gravity for it to truly check out?

Is it thought it cannot be explainable at Planck length because the 'smallest denominator' of gravity field quanta is much larger than potentially most subatomic particles?

Is it possible that by removing some of the probabilities in QM and by giving those probabilities and wave function values steady rates, or increasedly smaller probabilities, steadier and steadier rates with attempts to include gravity into QM, some values for gravity can be snuck in QM equations?

To attempt to be more clear; is it possible that by having such wide margins for potential energy levels in QM equations that that doesn't leave any room for gravity? Is it possible to eliminate or minimize the probabilities could find out that that is why gravity could not be included?

2) The most accepted view of gravity is that it is a curvature of space-time itself. Space-time in general relativity is a 4 dimensional Lorentzian manifold made up of points called events.

Are the points physical/material/energetic and do they obey conservation laws? Can they transform into other quantas of matter/energy? Is there a binding force that holds the points together?

3) The EM field moves in space-time just as everything else does, so it must also follow the curvature of space time. The EM field is a physical field of electric and magnetic fields on top of the background of space time. It affects space time through its stress-energy, and space-time affects it through its curvature. I don't know what you mean by "two sides of the same coin".

Is there space that is 'pure absolute nothingness' in between the points/events of space-time? Or are all the points of space-time dense in the sense of touching?

Im asking, is the fundamental essence/substance of all space throughout the universe this grid of space-time which is a somethingness not a nothingness? And if then space-time does take up every point of space-time which is everywhere within the universe, where is the room for EM field, is it snuck/squeezed in between, on top of? What I suggested with two sides of the same coin is could it be that EM field is an inherent aspect of space-time (gravity field) as perhaps magnetism and electricity are two sides of the same coin of a charged particle?

4) I have no idea what you're asking here.

I think I touched upon this in an above reply already, and I was mainly wondering if it is thought that within the universe there is any area, even one Planck length, that is true pure nothingness, or if every single Planck length of the universe contains real matter or energy.

 

[romsofia]

General relativity is background independent, AKA no fixed spacetime background, while quantum mechanics/field theory is not.
Loop quantum gravity, however, is a theory trying to be background independent (AKA the best theory for QG :P)!

 

[bcrowell]

See http://arxiv.org/abs/gr-qc/0108040 , Quantum Gravity: a Progress Report, S. Carlip, 2001, which gives a good, relatively nontechnical discussion of why it's difficult to reconcile quantum mechanics with gravity.

 

[tom.stoer]

Regarding (1) I wouldn't say that quantum theory and gravity are incompatible, but that certain methods well-known from quantum theory become invalid when applied to the quantization of gravity.

 

[ChrisVer]

In general, the easiest way to see that there is something problematic with gravity, is that $G$ giving the coupling strength of gravity, is not a dimensionless parameter, but it depends on length... So at high energies/small lengths, the things/calculations becomes divergent. This is the non-renormalizability of gravity - although it's a problem, it's not too bad for some people who believe in Loop Quantum Gravity I guess. In case someone is used to particle physics, he can make an analogy to what happened with weak interactions, or the 4-point fermi interaction to be more precise, which was leading to divergences. Adding an additional "degree of freedom" (the W-boson propagator) you could solve these divergences. What someone suspects he can do, is add additional degrees for freedom for a Gravity interaction - these appear as oscillating modes or topologies of string configurations (to visualize it, imagine instead of having lines interacting, you have surfaces- the line interaction is just a low-energy approximation then).

Another thing, maybe supplementary to the above.
In general one can indeed try to incorporate EM (or other interactions) with gravity, by assuming extra dimensions. Kaluza and Klein were the first I think who got this idea...Nevertheless the way those extra dimensions are compactified, gives you the gauge couplings. The details of the theory are pretty fascinating but for sure difficult and non-trivial , finding practice in Supergravity and String or M- Theory (and maybe F-Theory)... One problem, at least from what I am able to understand up to now, is that those theories give rise to several particles which we haven't observed (eg model-(in)dependent axions). And of course although we have several theories- which we can somehow connect- beyond them lies the M-Theory (having those theories as limits) that we know almost nothing about.

 

[tom.stoer]

So at high energies/small lengths, the things/calculations becomes divergent. This is the non-renormalizability of gravity - although it's a problem, ...

This is perturbative non-renormalizability of gravity. There are reasons to believe in non-perturbative renormalizability (asymptotic safety). This is what I mean by

... certain methods ... becoming invalid when applied to ... gravity.

Perhaps no need for LQG, strings and all that.

 

[ChrisVer]

your idea is the idea of LQG I think, and I said that it's not considered as a problem from people who believe in LQD...it's in that theory that perturbative NR is not necessary...However strings can solve the problem, so it has some credit for it.
But then you make an effective theory, and as a person I don't really like effective theories. Although they do give results, they cannot be considered fundamental...

 

[Imafungi]

Regarding (1) I wouldn't say that quantum theory and gravity are incompatible, but that certain methods well-known from quantum theory become invalid when applied to the quantization of gravity.

In what sense could 'that which is responsible (besides the particle mass causing the gravity) for the phenomenon of gravity' exist in reality, and not itself be quantized?

In this non quantized gravity view of the underlying field which allows the act of gravity to exist, would it be imagined as if the entire universe was one pure, seamless, 3d substance of singular gravity particle? Like a liquid that was not made of molecules, atoms, or parts, but just pure singular substance? Thats what non quantized means right?

 

[Imafungi]

In general, the easiest way to see that there is something problematic with gravity, is that $G$ giving the coupling strength of gravity, is not a dimensionless parameter, but it depends on length... So at high energies/small lengths, the things/calculations becomes divergent. This is the non-renormalizability of gravity - although it's a problem, it's not too bad for some people who believe in Loop Quantum Gravity I guess. In case someone is used to particle physics, he can make an analogy to what happened with weak interactions, or the 4-point fermi interaction to be more precise, which was leading to divergences. Adding an additional "degree of freedom" (the W-boson propagator) you could solve these divergences. What someone suspects he can do, is add additional degrees for freedom for a Gravity interaction - these appear as oscillating modes or topologies of string configurations (to visualize it, imagine instead of having lines interacting, you have surfaces- the line interaction is just a low-energy approximation then).

Another thing, maybe supplementary to the above.
In general one can indeed try to incorporate EM (or other interactions) with gravity, by assuming extra dimensions. Kaluza and Klein were the first I think who got this idea...Nevertheless the way those extra dimensions are compactified, gives you the gauge couplings. The details of the theory are pretty fascinating but for sure difficult and non-trivial , finding practice in Supergravity and String or M- Theory (and maybe F-Theory)... One problem, at least from what I am able to understand up to now, is that those theories give rise to several particles which we haven't observed (eg model-(in)dependent axions). And of course although we have several theories- which we can somehow connect- beyond them lies the M-Theory (having those theories as limits) that we know almost nothing about.

Thanks for the informative reply.


The way you see it and describe it;

Do gravity particles stay gravity particles, or can they transform into any other particle? (under certain conditions)

Is it thought there is always the exact same number of gravity particles in the universe at all times?

Is the average density of an average area of gravity particles, such that in between them there is 'real pure absolute nothing space containing no particles, energy, waves, fields, matter, anything'?

Or every Planck length of space throughout the entire universe there are gravity particles and they are all perfectly touching?

My understanding would then follow, that the relative displacement, or local increasing of density where ever a mass is in the universe, in this field of gravity particles, is what causes the macro classical phenomenas we are familiar with as gravity.

 

[HakimPhilo]

Quoting this wikipedia entry:

There are other points of tension between quantum mechanics and general relativity.

• First, classical general relativity breaks down at singularities, and quantum mechanics becomes inconsistent with general relativity in the neighborhood of singularities (however, no one is certain that classical general relativity applies near singularities in the first place).
  
• Second, it is not clear how to determine the gravitational field of a particle, since under the Heisenberg uncertainty principle of quantum mechanics its location and velocity cannot be known with certainty. The resolution of these points may come from a better understanding of general relativity.
  
• Third, there is the Problem of Time in quantum gravity. Time has a different meaning in quantum mechanics and general relativity and hence there are subtle issues to resolve when trying to formulate a theory which combines the two.

 

[tom.stoer]

your idea is the idea of LQG I think, ...

no, as I said,

there are reasons to believe in non-perturbative renormalizability (asymptotic safety).

http://www.scholarpedia.org/article/Asymptotic_Safety_in_quantum_gravity

I think it's much too early to decide which approach to quantum gravity is correct. All I wanted to indicate is that the failure of a method (perturbative quantization) may require nothing else but a new method.

 

[tom.stoer]

In what sense could 'that which is responsible (besides the particle mass causing the gravity) for the phenomenon of gravity' exist in reality, and not itself be quantized?

In this non quantized gravity view of the underlying field which allows the act of gravity to exist, would it be imagined as if the entire universe was one pure, seamless, 3d substance of singular gravity particle? Like a liquid that was not made of molecules, atoms, or parts, but just pure singular substance? Thats what non quantized means right?

I don't really understand. I am talking about quantization of the gravitational field in the sense of a mathematical procedure.

 

[Imafungi]

I don't really understand. I am talking about quantization of the gravitational field in the sense of a mathematical procedure.

So the math procedure and subsequent theory arent attempting to state anything about Truth/Reality?

 

[tom.stoer]

So the math procedure and subsequent theory arent attempting to state anything about Truth/Reality?

In the same sense as any other physical theory - truth must always be understood the sense of a consistent mathematical description providing predictions which can be tested by experiments.

So what the research programs try to construct are mathematically consistent theories. But the main guiding principle - the experiment - is lost for quantum gravity! There is not one single experiment telling us that GR must be quantized. All we know is that we are in trouble when applying perturbative methods to gravity. So we must change this. And as long as we do not have any experimental hints it's a matter of taste whether we focus on strings, loops or other approaches.

I think it's difficult for physics to make statements about truth and reality, even if we know that a certain theory seems to work pretty well. The story about truth and nature is not easier when talking about research programs which are neither complete nor experimentally testable ;-)

 

[jtbell]

So the math procedure and subsequent theory arent attempting to state anything about Truth/Reality?

How would we know Truth or Reality if we were to find it?

 

[tom.stoer]

Back to the headline

Why is theory of Gravity and QM incompatible?

All I wanted to indicate us that - even so we can find this statement quite often - gravity and quantum theory are not incompatible; all what happens is that some approaches fail and therefore have to be adjusted when applied to gravity.

Think about a function f(x) = 1/x. The Taylor exansion at x₀=1 fails when applied to f(x) for x=-1. But that does not mean that the function f(x) does not exist for x=-1.

 

[ChrisVer]

So one tries through the 2dimensional gravity to reach the 4 dimensional one?
Well at any case, you have to introduce an effective term in your Lagrangian, and so/or build up an effective theory. Where does these terms come from?
I am sorry if I misunderstood some of the topics in the link you sent (and I didn't finish it yet)...although this will get of the topic too...

 

[Imafungi]

How would we know Truth or Reality if we were to find it?

If it makes logical/equal sense when compared to our total knowledge.

If I can debunk theories that are claimed to be truth/reality with logic, than those theories do not equal truth/reality.

People seem to have a fear of philosophy, or a fear of words, those who are heavily involved with math. But try to disprove this statement; 'There is a severely intimate relationship between math and words. They are both tautological languages. They both would like to be used to grasp reality'.

Surely an apple that is slightly green and slightly red sitting under a cloudy blue sky on a field of grass with cows and chickens and a crazy guy speeding through with a car; can be described in math. And so too can the terms 'energy' and 'matter' and 'gravity' and 'space' and 'time'. But if I can use words, language, logic, to defeat a mathematical concept which exclaims that it is the essence of truth or reality, I am forced to think that theory illogical, untrue, and not the actual essence of reality.

By using logic and physics I believe progress can be made as to 'what reality definitely cannot be like' and 'what reality can possibly be like', then over time, and energy and effort, can we know more and more about the definitely nots, and more and more about the probables.

 

[Imafungi]

Back to the headline


All I wanted to indicate us that - even so we can find this statement quite often - gravity and quantum theory are not incompatible; all what happens is that some approaches fail and therefore have to be adjusted when applied to gravity.

Think about a function f(x) = 1/x. The Taylor exansion at x₀=1 fails when applied to f(x) for x=-1. But that does not mean that the function f(x) does not exist for x=-1.

So what are the theories as to what and why the failure occurs at certain areas?

Even generalities, or maybe purely general ideas of what may be the case and cause, I would be most interested in hearing.

 

[Imafungi]

So one tries through the 2dimensional gravity to reach the 4 dimensional one?
Well at any case, you have to introduce an effective term in your Lagrangian, and so/or build up an effective theory. Where does these terms come from?
I am sorry if I misunderstood some of the topics in the link you sent (and I didn't finish it yet)...although this will get of the topic too...

I don't know the specific rules, but its fine by me if you get off topic, its my thread. The way I see it is all topics and physics are relevant to one another.

 

[tom.stoer]

So what are the theories as to what and why the failure occurs at certain areas?

Perturbative quantum gravity (i.e. quantization of gravitons as fluctuations of flat spacetime - like photons) failes due to divergencies which create an infinite tower of counter-terms due to the dimensionfull gravitational coupling constant G. So G=0, flat spacetime and gravitons is an invalid starting point.

This is what many approaches to quantum gravity (LQG, asymptotic safety, Regge, CDT) have in common: use-nonperturbative methods!

 

[Imafungi]

Perturbative quantum gravity (i.e. quantization of gravitons as fluctuations of flat spacetime - like photons) failes due to divergencies which create an infinite tower of counter-terms due to the dimensionfull gravitational coupling constant G. So G=0, flat spacetime and gravitons is an invalid starting point.

This is what many approaches to quantum gravity (LQG, asymptotic safety, Regge, CDT) have in common: use-nonperturbative methods!

Regardless, the leading concept is that the field of gravity (that which, along with a mass causes the phenomenon of gravity) is a medium of sorts? Like water is a medium or Earth is a medium or atmosphere is a medium; It is generally thought that gravity is a medium, composed of particles like the others?

Once this is known, I really don't see the big deal with trial and erroring down to the most likely candidates of mass of the gravity particles, any potential binding energy values between them and maybe how it is coupled with the EM field. (because EM field and Gravity field are thought to exist at all points in space right? And even more so, EM field has an intimate relationship with Gravity field as it follows its paths of least resistance.)

 

[Dale]

Regardless, the leading concept is that the field of gravity (that which, along with a mass causes the phenomenon of gravity) is a medium of sorts? Like water is a medium or Earth is a medium or atmosphere is a medium; It is generally thought that gravity is a medium, composed of particles like the others?

Please provide references for these claims, as well as for any other speculative topics you would like to discuss.

 

[tom.stoer]

Regardless, the leading concept is that the field of gravity (that which, along with a mass causes the phenomenon of gravity) is a medium of sorts? Like water is a medium or Earth is a medium or atmosphere is a medium; It is generally thought that gravity is a medium, composed of particles like the others?

Once this is known, I really don't see the big deal with trial and erroring down to the most likely candidates of mass of the gravity particles, any potential binding energy values between them and maybe how it is coupled with the EM field. (because EM field and Gravity field are thought to exist at all points in space right? And even more so, EM field has an intimate relationship with Gravity field as it follows its paths of least resistance.)

Neither is gravity described as a "medium" in general, nor is quantum gravity described using "classical particles" forming this medium. There are no "gravity particles" used in the mathematical models (there are no particles used in quantum field theory, either). It's about quantized fields, where "quantized" refers to a rather technical procedure not to be confused with "discrete".

The problem answering your question

why ... gravity and QM [are] incompatible

is that this requires rather deep knowledge of the mathematical models used to (successfully) describe gravity and QM in order to understand the obstacles when trying to combine them.

 

[Dale]

The thread is closed due to persistent personal speculation.