Unifying Gravity and Quantum Mechanics: The Role of Spin-2 Fields

[faen]

Let's say if general relativity is wrong. What is then the problem of unifying gravity with quantum mechanics? Is there any problem at all then?

 

[jedishrfu]

The theory to replace GR and to bind gravity to QM will have to predict the same observables to the same or better accuracy. That's what it means for a theory to be successful. GR did that when it replaced Newtonian gravitation.

 

[faen]

The theory to replace GR and to bind gravity to QM will have to predict the same observables to the same or better accuracy. That's what it means for a theory to be successful. GR did that when it replaced Newtonian gravitation.

What is it that we can observe that GR predicts and that Newtonian gravitation can't?

 

[raymo39]

What is it that we can observe that GR predicts and that Newtonian gravitation can't?

Possibly the most famous example originally was the orbit of Mercury around the Sun. Newtonian gravitation (NG) can't fully describe the orbit, General relativity can. Other than that, we have gravitational lensing, which is really cool to see, not at all predicted by NG, black holes aren't in NG. And one thing that you may have used before is the GPS system. The amount that clocks change their rates isn't at all a factor in NG, but using GR allows us to have a satellite positioning system all over the globe using synchronised clocks.

 

[faen]

Possibly the most famous example originally was the orbit of Mercury around the Sun. Newtonian gravitation (NG) can't fully describe the orbit, General relativity can. Other than that, we have gravitational lensing, which is really cool to see, not at all predicted by NG, black holes aren't in NG. And one thing that you may have used before is the GPS system. The amount that clocks change their rates isn't at all a factor in NG, but using GR allows us to have a satellite positioning system all over the globe using synchronised clocks.

But I'd say that only explains that special relativity is true, that time is slowed in the field. That light is bent in gravity, does that really by itself prove that time is a dimension and that space is curved relative to it? That is what I disbelieve..

Also I'm still curious whether it is possible to describe some sort of gravitons without general relativity..

 

[raymo39]

But I'd say that only explains that special relativity is true, ...

Also I'm still curious whether it is possible to describe some sort of gravitons without general relativity..

Special relativity only describes motion with constant velocity. As soon as things start to curve or accelerate it falls apart. Which is what happens for most of the experimental evidence provided.

Now, brb. I've got to (ironically) go to my GR lecture.

 

[raymo39]

As for the graviton thing. They are required only by quantum field theory, not by general relativity

 

[Fredrik]

Let's say if general relativity is wrong. What is then the problem of unifying gravity with quantum mechanics? Is there any problem at all then?

We already know that GR is wrong. That's why we need a quantum theory of gravity. Maybe you meant something like "very very wrong". In that case, we would have even less of a clue about what a quantum theory of gravity would look like. So it would be much harder.

Maybe you meant that in that case, we might be able to unify QM with Newtonian gravity instead of with GR. I don't know QFT well enough to answer that, but I would guess that it's doable. It would however resurrect the already solved problem of how to unify special relativity and Newtonian gravity. (The solution is GR).

I guess now you want to know what happens if SR is very very wrong too. Since we already know that SR is much better than the alternative (which is classical mechanics in Galilean spacetime), we would pretty much have to start over with everything. Of course this is about as likely as discovering that the mouth is the wrong orifice into which to insert food, so that we would have to start over with eating.

 

[Fredrik]

As for the graviton thing. They are required only by quantum field theory, not by general relativity

But a QFT with gravitons will have GR as a low energy limit, or something. (I'm not entirely clear on the details).

 

[faen]

Special relativity only describes motion with constant velocity. As soon as things start to curve or accelerate it falls apart. Which is what happens for most of the experimental evidence provided.

Now, brb. I've got to (ironically) go to my GR lecture.

How does it fall apart only because things start to accelerate? It already predicts the same for acceleration as with motion, that you just need more and more force or that the mass get's bigger and bigger the more you want to accelerate it close to the speed of light.

Haha, I hope you had an interesting lecture. It is after all an interesting subject.

 

[faen]

We already know that GR is wrong. That's why we need a quantum theory of gravity. Maybe you meant something like "very very wrong". In that case, we would have even less of a clue about what a quantum theory of gravity would look like. So it would be much harder.

Maybe you meant that in that case, we might be able to unify QM with Newtonian gravity instead of with GR. I don't know QFT well enough to answer that, but I would guess that it's doable. It would however resurrect the already solved problem of how to unify special relativity and Newtonian gravity. (The solution is GR).

I guess now you want to know what happens if SR is very very wrong too. Since we already know that SR is much better than the alternative (which is classical mechanics in Galilean spacetime), we would pretty much have to start over with everything. Of course this is about as likely as discovering that the mouth is the wrong orifice into which to insert food, so that we would have to start over with eating.

How do we know that GR is wrong?

When I mean gravity I don't necessarily mean either Newtonian or general relativity gravity. I guess they may both not be sufficient explanations. However, is it impossible to say that gravity is just massless particles flowing through space causing matter and even light to accelerate in the direction of the source of the gravitational field?

 

[raymo39]

How does it fall apart only because things start to accelerate? It already predicts the same for acceleration as with motion, that you just need more and more force or that the mass get's bigger and bigger the more you want to accelerate it close to the speed of light.

One of the key points is understanding that acceleration doesn't just mean an increase in total velocity of the system, but changing direction of velocity is also acceleration. Consider circular motion in a 2d plane, like a ball on a string rotating at some constant rate (constant rpm) although the ball has a constant speed, it does not have constant velocity, because velocity is a vector quantity, so it has direction also! changing this direction is acceleration.

Now the key point of relativity, is that physics should be essentially the same in all frames of reference. Traditionally, frames of reference that are the same in special relativity are called inertial frames. If I take my experiment from one inertial frame into another, I should be able to describe everything using the same physics. It turns out that in the framework of special relativity, I cannot take my experiment into a frame of reference that is accelerating (with respect to a stationary frame) and expect my physics to be the same.

 

[Fredrik]

How do we know that GR is wrong?

Its description of matter is classical.

When I mean gravity I don't necessarily mean either Newtonian or general relativity gravity. I guess they may both not be sufficient explanations. However, is it impossible to say that gravity is just massless particles flowing through space causing matter and even light to accelerate in the direction of the source of the gravitational field?

It's not possible to fully make sense of a question like this without definitions of terms like "particle", and such terms are defined by theories. Particles in quantum theories are very different from particles in classical theories. A classical theory obviously won't do, so I would have to interpret the question as referring to the kind of particles that appear in quantum theories. The answer to that question is that if the theory doesn't involve massless spin-2 particles, it's not going to be anything like gravity, and if it does involve massless spin-2 particles, it's going to be a lot like general relativity.

 

[faen]

One of the key points is understanding that acceleration doesn't just mean an increase in total velocity of the system, but changing direction of velocity is also acceleration. Consider circular motion in a 2d plane, like a ball on a string rotating at some constant rate (constant rpm) although the ball has a constant speed, it does not have constant velocity, because velocity is a vector quantity, so it has direction also! changing this direction is acceleration.

Now the key point of relativity, is that physics should be essentially the same in all frames of reference. Traditionally, frames of reference that are the same in special relativity are called inertial frames. If I take my experiment from one inertial frame into another, I should be able to describe everything using the same physics. It turns out that in the framework of special relativity, I cannot take my experiment into a frame of reference that is accelerating (with respect to a stationary frame) and expect my physics to be the same.

In reality, if you have two frames of references accelerating relative to each other, is the physics measured to be the same then? And that special relativity can't predict why this is the case?

Its description of matter is classical. It's not possible to fully make sense of a question like this without definitions of terms like "particle", and such terms are defined by theories. Particles in quantum theories are very different from particles in classical theories. A classical theory obviously won't do, so I would have to interpret the question as referring to the kind of particles that appear in quantum theories. The answer to that question is that if the theory doesn't involve massless spin-2 particles, it's not going to be anything like gravity, and if it does involve massless spin-2 particles, it's going to be a lot like general relativity.

So if it is a spin 2 mass less particle that turns out to be responsible for gravity it means that space-time has to exist and that it is curved? Also ur basically saying that even without general relativity, it is very problematic to explain gravity in terms of quantum mechanics?

 

[mfb]

QFT includes special relativity (SR), and Newtonian gravity is not compatible with SR. I would expect that GR is the "easiest" theory of gravity which satisfies SR and the equivalence principle.

So if it is a spin 2 mass less particle that turns out to be responsible for gravity it means that space-time has to exist and that it is curved?

No, it means that a classical description with curved spacetime gives a good approximation if QM effects are not relevant.

 

[haael]

The answer to that question is that if the theory doesn't involve massless spin-2 particles, it's not going to be anything like gravity, and if it does involve massless spin-2 particles, it's going to be a lot like general relativity.

I'm not sure, but it doesn't sound correct.

We can describe gravity without spin-2 particles by sacrificing special relativity. I.e. in non-relativistic quantum mechanics we could describe gravity without spin-2 fields.

In any special-relativistic theory the only way to have gravity is by spin-2 field. This part is corrent.

But is any spin-2 field theory the general relativity? I doubt. These theories only agree up to first order. In particular, spin-2 field alone doesn't give you Einstein equation. In fact, you can get different theories of gravity with different equations, depending on the properties of the field.

The spin-2 field also doesn't have to be massless.

So, general relativity has something to with spin-2 fields, but there's a lot of space for research.

 

[Fredrik]

I'm not sure, but it doesn't sound correct.

We can describe gravity without spin-2 particles by sacrificing special relativity. I.e. in non-relativistic quantum mechanics we could describe gravity without spin-2 fields.

In any special-relativistic theory the only way to have gravity is by spin-2 field. This part is corrent.

But is any spin-2 field theory the general relativity? I doubt. These theories only agree up to first order. In particular, spin-2 field alone doesn't give you Einstein equation. In fact, you can get different theories of gravity with different equations, depending on the properties of the field.

The spin-2 field also doesn't have to be massless.

So, general relativity has something to with spin-2 fields, but there's a lot of space for research.

You may be right. My understanding of this is rather poor. I think I read a comment by Steven Weinberg a long time ago that said roughly that he and Feynman had independently arrived at the conclusion that a theory with interactions mediated by massless spin-2 particles is going to look more or less like general relativity. But I'm sure that what he had in mind was a QFT in Minkowski spacetime, not in Galilean spacetime.